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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Let x12 of type ι be given.
Let x13 of type ι be given.
Let x14 of type ι be given.
Let x15 of type ι be given.
Let x16 of type ι be given.
Let x17 of type ι be given.
Let x18 of type ι be given.
Let x19 of type ι be given.
Let x20 of type ι be given.
Let x21 of type ι be given.
Let x22 of type ι be given.
Let x23 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Assume H4: SNo x4.
Assume H5: SNo x5.
Assume H6: SNo x6.
Assume H7: SNo x7.
Assume H8: SNo x8.
Assume H9: SNo x9.
Assume H10: SNo x10.
Assume H11: SNo x11.
Assume H12: SNo x12.
Assume H13: SNo x13.
Assume H14: SNo x14.
Assume H15: SNo x15.
Assume H16: SNo x16.
Assume H17: SNo x17.
Assume H18: SNo x18.
Assume H19: SNo x19.
Assume H20: SNo x20.
Assume H21: SNo x21.
Assume H22: SNo x22.
Assume H23: SNo x23.
Assume H24: SNoLt 0 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 x23))))))))))).
Assume H25: SNoLe x12 (add_SNo x0 (minus_SNo x1)).
Assume H26: SNoLe x13 (add_SNo x1 (minus_SNo x2)).
Assume H27: SNoLe x14 (add_SNo x2 (minus_SNo x3)).
Assume H28: SNoLe x15 (add_SNo x3 (minus_SNo x4)).
Assume H29: SNoLe x16 (add_SNo x4 (minus_SNo x5)).
Assume H30: SNoLe x17 (add_SNo x5 (minus_SNo x6)).
Assume H31: SNoLe x18 (add_SNo x6 (minus_SNo x7)).
Assume H32: SNoLe x19 (add_SNo x7 (minus_SNo x8)).
Assume H33: SNoLe x20 (add_SNo x8 (minus_SNo x9)).
Assume H34: SNoLe x21 (add_SNo x9 (minus_SNo x10)).
Assume H35: SNoLe x22 (add_SNo x10 (minus_SNo x11)).
Assume H36: SNoLe x23 (add_SNo x11 (minus_SNo x0)).
Claim L37: ...
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Claim L38: ...
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Claim L39: ...
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Claim L40: ...
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Claim L41: ...
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Claim L42: ...
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Claim L43: ...
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Claim L44: ...
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Claim L45: ...
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Claim L46: ...
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Claim L47: ...
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Claim L48: ...
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Apply idl_negcycle_12 with x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, minus_SNo x12, minus_SNo x13, minus_SNo x14, minus_SNo x15, minus_SNo x16, minus_SNo x17, minus_SNo x18, minus_SNo x19, minus_SNo x20, minus_SNo x21, minus_SNo x22, minus_SNo x23 leaving 37 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.
The subproof is completed by applying H11.
The subproof is completed by applying L37.
The subproof is completed by applying L38.
The subproof is completed by applying L39.
The subproof is completed by applying L40.
The subproof is completed by applying L41.
The subproof is completed by applying L42.
The subproof is completed by applying L43.
The subproof is completed by applying L44.
The subproof is completed by applying L45.
The subproof is completed by applying L46.
The subproof is completed by applying L47.
The subproof is completed by applying L48.
Apply minus_SNo_Lt_contra3 with 0, add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (minus_SNo x23))))))))))) leaving 3 subgoals.
The subproof is completed by applying SNo_0.
Apply SNo_add_SNo_12 with minus_SNo x12, ..., ..., ..., ..., ..., ..., ..., ..., ..., ..., ... leaving 12 subgoals.
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