TSTP Solution File: LCL133-1 by Toma---0.4
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% File : Toma---0.4
% Problem : LCL133-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n009.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 0.22s 0.65s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LCL133-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.14 % Command : toma --casc %s
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 05:26:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.65 % SZS status Unsatisfiable
% 0.22/0.65 % SZS output start Proof
% 0.22/0.65 original problem:
% 0.22/0.65 axioms:
% 0.22/0.65 implies(truth(), X) = X
% 0.22/0.65 implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))) = truth()
% 0.22/0.65 implies(implies(X, Y), Y) = implies(implies(Y, X), X)
% 0.22/0.65 implies(implies(not(X), not(Y)), implies(Y, X)) = truth()
% 0.22/0.65 implies(X, Y) = implies(Y, X)
% 0.22/0.65 goal:
% 0.22/0.65 x() != y()
% 0.22/0.65 To show the unsatisfiability of the original goal,
% 0.22/0.65 it suffices to show that x() = y() (skolemized goal) is valid under the axioms.
% 0.22/0.65 Here is an equational proof:
% 0.22/0.65 0: implies(truth(), X0) = X0.
% 0.22/0.65 Proof: Axiom.
% 0.22/0.65
% 0.22/0.65 1: implies(implies(X0, X1), implies(implies(X1, X2), implies(X0, X2))) = truth().
% 0.22/0.65 Proof: Axiom.
% 0.22/0.65
% 0.22/0.65 2: implies(implies(X0, X1), X1) = implies(implies(X1, X0), X0).
% 0.22/0.65 Proof: Axiom.
% 0.22/0.65
% 0.22/0.65 4: implies(X0, X1) = implies(X1, X0).
% 0.22/0.65 Proof: Axiom.
% 0.22/0.65
% 0.22/0.65 5: implies(X1, implies(X0, X1)) = implies(X0, implies(X1, X0)).
% 0.22/0.65 Proof: Rewrite equation 2,
% 0.22/0.65 lhs with equations [4]
% 0.22/0.65 rhs with equations [4].
% 0.22/0.65
% 0.22/0.65 6: implies(X2, truth()) = X2.
% 0.22/0.65 Proof: A critical pair between equations 4 and 0.
% 0.22/0.65
% 0.22/0.65 8: implies(X1, implies(truth(), X1)) = implies(X1, truth()).
% 0.22/0.65 Proof: A critical pair between equations 5 and 0.
% 0.22/0.65
% 0.22/0.65 16: truth() = implies(implies(implies(implies(X3, X5), X5), X3), truth()).
% 0.22/0.65 Proof: A critical pair between equations 1 and 1.
% 0.22/0.65
% 0.22/0.65 19: truth() = implies(X3, implies(X5, implies(X3, X5))).
% 0.22/0.65 Proof: Rewrite equation 16,
% 0.22/0.65 lhs with equations []
% 0.22/0.65 rhs with equations [4,4,6].
% 0.22/0.65
% 0.22/0.65 22: implies(X1, X1) = X1.
% 0.22/0.65 Proof: Rewrite equation 8,
% 0.22/0.65 lhs with equations [0]
% 0.22/0.65 rhs with equations [6].
% 0.22/0.65
% 0.22/0.65 26: truth() = implies(X6, implies(X6, X6)).
% 0.22/0.65 Proof: A critical pair between equations 19 and 22.
% 0.22/0.65
% 0.22/0.65 41: truth() = X6.
% 0.22/0.65 Proof: Rewrite equation 26,
% 0.22/0.65 lhs with equations []
% 0.22/0.65 rhs with equations [22,22].
% 0.22/0.65
% 0.22/0.65 42: truth() = X0.
% 0.22/0.65 Proof: Rewrite equation 0,
% 0.22/0.65 lhs with equations [41]
% 0.22/0.65 rhs with equations [].
% 0.22/0.65
% 0.22/0.65 43: truth() = X2.
% 0.22/0.65 Proof: Rewrite equation 6,
% 0.22/0.65 lhs with equations [42]
% 0.22/0.65 rhs with equations [].
% 0.22/0.65
% 0.22/0.65 44: truth() = X1.
% 0.22/0.65 Proof: Rewrite equation 22,
% 0.22/0.65 lhs with equations [43]
% 0.22/0.65 rhs with equations [].
% 0.22/0.65
% 0.22/0.65 45: x() = y().
% 0.22/0.65 Proof: Rewrite lhs with equations [44]
% 0.22/0.65 rhs with equations [44].
% 0.22/0.65
% 0.22/0.65 % SZS output end Proof
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