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Proofgold Signed Transaction

vin
Pr3fd../7e5d8..
PUaM9../9e6a6..
vout
Pr3fd../4d14e.. 2,549.88 bars
TMLRo../72de7.. ownership of 9fe18.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMUNZ../f2221.. ownership of 2f9b7.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMbU5../761b6.. ownership of 59f06.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
TMcu9../2d696.. ownership of 24314.. as prop with payaddr Pr4zB.. rights free controlledby Pr4zB.. upto 0
Pr4zB../15473.. 800.00 bars
PUeWV../21ee9.. doc published by Pr4zB..
Param ChurchNum_3ary_proj_p : (((ιι) → ιι) → ((ιι) → ιι) → CN (ιι)) → ο
Param ChurchNum_8ary_proj_p : (((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → CN (ιι)) → ο
Definition TwoRamseyGraph_4_5_24_ChurchNums_3x8 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x4 . x0 (x1 (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)))) (x1 (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) 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. x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)))) (x1 (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6))) (x2 (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5))) (x2 (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)) (x3 (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . λ x6 . x6) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5) (λ x5 : ι → ι . x5)))) (λ x5 . x4)
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Param ChurchNums_3x8_eq : (((ιι) → ιι) → ((ιι) → ιι) → CN (ιι)) → (((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → CN (ιι)) → (((ιι) → ιι) → ((ιι) → ιι) → CN (ιι)) → (((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → ((ιι) → ιι) → CN (ιι)) → ο
Definition ChurchNums_3x8_neq := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . not (ChurchNums_3x8_eq x0 x1 x2 x3)
Known fc1b4.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_8ary_proj_p x1(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x3 x4 x5 : (ι → ι)ι → ι . x3) (λ x3 x4 x5 x6 x7 x8 x9 x10 : (ι → ι)ι → ι . x3) x0 x1 = λ x3 x4 . x3)∀ x2 : ο . ((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x4)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x4)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x5)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x4)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x6)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x4)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x8)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x5)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x5)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x5)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x5)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x11)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x6)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x6)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x8)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x6)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x10)x2)((x0 = λ x4 x5 x6 : (ι → ι)ι → ι . x6)(x1 = λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x11)x2)x2
Known f6916.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . x0 = x1x2 = x3ChurchNums_3x8_eq x0 x2 x1 x3
Known fa458.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_8ary_proj_p x2ChurchNum_8ary_proj_p x3(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x0 x2 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x1 x3 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x6) x0 x2 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x6) x1 x3 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x2 x1 x3 = λ x5 x6 . x5)ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x0 x2ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x5) x0 x2ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x1 x3ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x5) x1 x3ChurchNums_3x8_neq x0 x2 x1 x3False
Known 639c7.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_8ary_proj_p x2ChurchNum_8ary_proj_p x3(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x0 x2 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x1 x3 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x7) x0 x2 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x7) x1 x3 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x2 x1 x3 = λ x5 x6 . x5)ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x0 x2ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x6) x0 x2ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x1 x3ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x6) x1 x3ChurchNums_3x8_neq x0 x2 x1 x3False
Known FalseEFalseE : False∀ x0 : ο . x0
Known 99ba2.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_8ary_proj_p x2ChurchNum_8ary_proj_p x3(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x0 x2 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x1 x3 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x6) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x0 x2 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x6) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x5) x1 x3 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x2 x1 x3 = λ x5 x6 . x5)ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x0 x2ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x5) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x0 x2ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x1 x3ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x5) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x4) x1 x3ChurchNums_3x8_neq x0 x2 x1 x3False
Definition ChurchNums_8_perm_0_7_6_5_4_3_2_1 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 x2 x3 x4 x5 x6 x7 x8 : (ι → ι)ι → ι . x0 x1 x8 x7 x6 x5 x4 x3 x2
Definition ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2 := λ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . λ x2 x3 x4 : (ι → ι)ι → ι . x0 (x1 x2 x4 x4 x4 x4 x4 x4 x4) (x1 x4 x3 x3 x3 x3 x3 x3 x3) (x1 x3 x2 x2 x2 x2 x2 x2 x2)
Known 424ab.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_8ary_proj_p x1ChurchNum_3ary_proj_p (ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2 x0 x1)
Known 6bdd9.. : ∀ x0 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x0ChurchNum_8ary_proj_p (ChurchNums_8_perm_0_7_6_5_4_3_2_1 x0)
Known 33bbb.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_8ary_proj_p x2ChurchNum_8ary_proj_p x3TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x2 x1 x3 = TwoRamseyGraph_4_5_24_ChurchNums_3x8 (ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2 x0 x2) (ChurchNums_8_perm_0_7_6_5_4_3_2_1 x2) (ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2 x1 x3) (ChurchNums_8_perm_0_7_6_5_4_3_2_1 x3)
Known cef55.. : ChurchNum_3ary_proj_p (λ x0 x1 x2 : (ι → ι)ι → ι . x0)
Known 208f3.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x0)
Known a5963.. : ChurchNum_3ary_proj_p (λ x0 x1 x2 : (ι → ι)ι → ι . x2)
Known 080b7.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_8ary_proj_p x2ChurchNum_8ary_proj_p x3ChurchNums_3x8_eq (ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2 x0 x2) (ChurchNums_8_perm_0_7_6_5_4_3_2_1 x2) (ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2 x1 x3) (ChurchNums_8_perm_0_7_6_5_4_3_2_1 x3)ChurchNums_3x8_eq x0 x2 x1 x3
Known 94187.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x6)
Known 7734d.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x7)
Theorem 59f06.. : ∀ x0 x1 x2 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x3 x4 x5 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p x2ChurchNum_8ary_proj_p x3ChurchNum_8ary_proj_p x4ChurchNum_8ary_proj_p x5(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x7 x8 x9 : (ι → ι)ι → ι . x7) (λ x7 x8 x9 x10 x11 x12 x13 x14 : (ι → ι)ι → ι . x7) x0 x3 = λ x7 x8 . x7)not (∀ x6 : ο . ((x0 = λ x8 x9 x10 : (ι → ι)ι → ι . x8)(x3 = λ x8 x9 x10 x11 x12 x13 x14 x15 : (ι → ι)ι → ι . x12)x6)((x0 = λ x8 x9 x10 : (ι → ι)ι → ι . x9)(x3 = λ x8 x9 x10 x11 x12 x13 x14 x15 : (ι → ι)ι → ι . x9)x6)((x0 = λ x8 x9 x10 : (ι → ι)ι → ι . x9)(x3 = λ x8 x9 x10 x11 x12 x13 x14 x15 : (ι → ι)ι → ι . x15)x6)((x0 = λ x8 x9 x10 : (ι → ι)ι → ι . x10)(x3 = λ x8 x9 x10 x11 x12 x13 x14 x15 : (ι → ι)ι → ι . x12)x6)x6)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x7 x8 x9 : (ι → ι)ι → ι . x7) (λ x7 x8 x9 x10 x11 x12 x13 x14 : (ι → ι)ι → ι . x7) x1 x4 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x7 x8 x9 : (ι → ι)ι → ι . x7) (λ x7 x8 x9 x10 x11 x12 x13 x14 : (ι → ι)ι → ι . x7) x2 x5 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x3 x1 x4 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x3 x2 x5 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x1 x4 x2 x5 = λ x7 x8 . x7)ChurchNums_3x8_neq (λ x6 x7 x8 : (ι → ι)ι → ι . x6) (λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x6) x0 x3ChurchNums_3x8_neq (λ x6 x7 x8 : (ι → ι)ι → ι . x6) (λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x6) x1 x4ChurchNums_3x8_neq (λ x6 x7 x8 : (ι → ι)ι → ι . x6) (λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x6) x2 x5ChurchNums_3x8_neq x0 x3 x1 x4ChurchNums_3x8_neq x0 x3 x2 x5ChurchNums_3x8_neq x1 x4 x2 x5False (proof)
Definition oror := λ x0 x1 : ο . ∀ x2 : ο . (x0x2)(x1x2)x2
Known xmxm : ∀ x0 : ο . or x0 (not x0)
Known a5d1b.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . (∀ x4 : ο . ((x0 = λ x6 x7 x8 : (ι → ι)ι → ι . x6)(x2 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x10)x4)((x0 = λ x6 x7 x8 : (ι → ι)ι → ι . x7)(x2 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x7)x4)((x0 = λ x6 x7 x8 : (ι → ι)ι → ι . x7)(x2 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x13)x4)((x0 = λ x6 x7 x8 : (ι → ι)ι → ι . x8)(x2 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x10)x4)x4)(∀ x4 : ο . ((x1 = λ x6 x7 x8 : (ι → ι)ι → ι . x6)(x3 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x10)x4)((x1 = λ x6 x7 x8 : (ι → ι)ι → ι . x7)(x3 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x7)x4)((x1 = λ x6 x7 x8 : (ι → ι)ι → ι . x7)(x3 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x13)x4)((x1 = λ x6 x7 x8 : (ι → ι)ι → ι . x8)(x3 = λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x10)x4)x4)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x9) x0 x2 = λ x5 x6 . x5)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x5 x6 x7 : (ι → ι)ι → ι . x5) (λ x5 x6 x7 x8 x9 x10 x11 x12 : (ι → ι)ι → ι . x9) x1 x3 = λ x5 x6 . x5)ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x8) x0 x2ChurchNums_3x8_neq (λ x4 x5 x6 : (ι → ι)ι → ι . x4) (λ x4 x5 x6 x7 x8 x9 x10 x11 : (ι → ι)ι → ι . x8) x1 x3ChurchNums_3x8_neq x0 x2 x1 x3False
Known bfc1e.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNums_3x8_neq x0 x2 x1 x3ChurchNums_3x8_neq x1 x3 x0 x2
Known f60cd.. : ∀ x0 x1 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x2 x3 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_8ary_proj_p x2ChurchNum_8ary_proj_p x3TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x2 x1 x3 = TwoRamseyGraph_4_5_24_ChurchNums_3x8 x1 x3 x0 x2
Known 3a83b.. : ChurchNum_8ary_proj_p (λ x0 x1 x2 x3 x4 x5 x6 x7 : (ι → ι)ι → ι . x4)
Known 768c1.. : ((λ x1 x2 . x2) = λ x1 x2 . x1)∀ x0 : ο . x0
Theorem 9fe18.. : ∀ x0 x1 x2 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ∀ x3 x4 x5 : ((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)((ι → ι)ι → ι)(ι → ι)ι → ι . ChurchNum_3ary_proj_p x0ChurchNum_3ary_proj_p x1ChurchNum_3ary_proj_p x2ChurchNum_8ary_proj_p x3ChurchNum_8ary_proj_p x4ChurchNum_8ary_proj_p x5(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x7 x8 x9 : (ι → ι)ι → ι . x7) (λ x7 x8 x9 x10 x11 x12 x13 x14 : (ι → ι)ι → ι . x7) x0 x3 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x7 x8 x9 : (ι → ι)ι → ι . x7) (λ x7 x8 x9 x10 x11 x12 x13 x14 : (ι → ι)ι → ι . x7) x1 x4 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 (λ x7 x8 x9 : (ι → ι)ι → ι . x7) (λ x7 x8 x9 x10 x11 x12 x13 x14 : (ι → ι)ι → ι . x7) x2 x5 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x3 x1 x4 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x0 x3 x2 x5 = λ x7 x8 . x7)(TwoRamseyGraph_4_5_24_ChurchNums_3x8 x1 x4 x2 x5 = λ x7 x8 . x7)ChurchNums_3x8_neq (λ x6 x7 x8 : (ι → ι)ι → ι . x6) (λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x6) x0 x3ChurchNums_3x8_neq (λ x6 x7 x8 : (ι → ι)ι → ι . x6) (λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x6) x1 x4ChurchNums_3x8_neq (λ x6 x7 x8 : (ι → ι)ι → ι . x6) (λ x6 x7 x8 x9 x10 x11 x12 x13 : (ι → ι)ι → ι . x6) x2 x5ChurchNums_3x8_neq x0 x3 x1 x4ChurchNums_3x8_neq x0 x3 x2 x5ChurchNums_3x8_neq x1 x4 x2 x5False (proof)