TSTP Solution File: LCL134-1 by Toma---0.4
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% File : Toma---0.4
% Problem : LCL134-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:13:54 EDT 2023
% Result : Unsatisfiable 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL134-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 19:51:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.65 % SZS status Unsatisfiable
% 0.20/0.65 % SZS output start Proof
% 0.20/0.65 original problem:
% 0.20/0.65 axioms:
% 0.20/0.65 implies(truth(), X) = X
% 0.20/0.65 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth()
% 0.20/0.65 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.20/0.65 implies(implies(not(X), not(Y)), implies(Y, X)) = truth()
% 0.20/0.65 goal:
% 0.20/0.65 implies(x(), truth()) != truth()
% 0.20/0.65 To show the unsatisfiability of the original goal,
% 0.20/0.65 it suffices to show that implies(x(), truth()) = truth() (skolemized goal) is valid under the axioms.
% 0.20/0.65 Here is an equational proof:
% 0.20/0.65 0: implies(truth(), X0) = X0.
% 0.20/0.65 Proof: Axiom.
% 0.20/0.65
% 0.20/0.65 1: implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))) = truth().
% 0.20/0.65 Proof: Axiom.
% 0.20/0.65
% 0.20/0.65 2: implies(implies(X0, X1), X1) = implies(implies(X1, X0), X0).
% 0.20/0.65 Proof: Axiom.
% 0.20/0.65
% 0.20/0.65 4: implies(implies(X2, truth()), truth()) = implies(X2, X2).
% 0.20/0.65 Proof: A critical pair between equations 2 and 0.
% 0.20/0.65
% 0.20/0.65 8: truth() = implies(implies(X0, truth()), implies(X3, implies(X0, X3))).
% 0.20/0.65 Proof: A critical pair between equations 1 and 0.
% 0.20/0.65
% 0.20/0.65 9: truth() = implies(X3, implies(implies(X3, X2), implies(truth(), X2))).
% 0.20/0.65 Proof: A critical pair between equations 1 and 0.
% 0.20/0.65
% 0.20/0.65 10: truth() = implies(implies(implies(implies(X3, X5), X5), X3), truth()).
% 0.20/0.65 Proof: A critical pair between equations 1 and 1.
% 0.20/0.65
% 0.20/0.65 13: implies(implies(X3, implies(X2, X3)), implies(X2, X3)) = implies(implies(implies(X3, X2), X2), X3).
% 0.20/0.65 Proof: A critical pair between equations 2 and 2.
% 0.20/0.65
% 0.20/0.65 16: truth() = implies(implies(implies(X3, implies(X5, X3)), implies(X5, X3)), truth()).
% 0.20/0.65 Proof: Rewrite equation 10,
% 0.20/0.65 lhs with equations []
% 0.20/0.65 rhs with equations [13].
% 0.20/0.65
% 0.20/0.65 17: truth() = implies(X3, implies(implies(X3, X2), X2)).
% 0.20/0.65 Proof: Rewrite equation 9,
% 0.20/0.65 lhs with equations []
% 0.20/0.65 rhs with equations [0].
% 0.20/0.65
% 0.20/0.65 27: truth() = implies(implies(truth(), implies(implies(X7, X7), X7)), truth()).
% 0.20/0.65 Proof: A critical pair between equations 16 and 17.
% 0.20/0.65
% 0.20/0.65 28: truth() = implies(implies(truth(), implies(truth(), implies(X6, truth()))), truth()).
% 0.20/0.65 Proof: A critical pair between equations 16 and 8.
% 0.20/0.65
% 0.20/0.65 31: truth() = implies(X6, X6).
% 0.20/0.65 Proof: Rewrite equation 28,
% 0.20/0.65 lhs with equations []
% 0.20/0.65 rhs with equations [0,0,4].
% 0.20/0.65
% 0.20/0.65 32: truth() = implies(X7, truth()).
% 0.20/0.65 Proof: Rewrite equation 27,
% 0.20/0.65 lhs with equations []
% 0.20/0.65 rhs with equations [31,0,0].
% 0.20/0.65
% 0.20/0.65 35: implies(x(), truth()) = truth().
% 0.20/0.65 Proof: Rewrite lhs with equations [32]
% 0.20/0.65 rhs with equations [].
% 0.20/0.65
% 0.20/0.65 % SZS output end Proof
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