TSTP Solution File: GRP656-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP656-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n003.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 01:19:29 EDT 2023
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP656-10 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Mon Aug 28 20:33:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.38 Command-line arguments: --no-flatten-goal
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
% 0.13/0.38 Axiom 2 (f04): rd(mult(X, Y), Y) = X.
% 0.13/0.38 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 0.13/0.38 Axiom 4 (f05): mult(mult(X, Y), mult(Z, X)) = mult(mult(X, mult(Y, Z)), X).
% 0.13/0.38
% 0.13/0.38 Lemma 5: mult(mult(X, Y), mult(ld(Y, Z), X)) = mult(mult(X, Z), X).
% 0.13/0.38 Proof:
% 0.13/0.38 mult(mult(X, Y), mult(ld(Y, Z), X))
% 0.13/0.38 = { by axiom 4 (f05) }
% 0.13/0.38 mult(mult(X, mult(Y, ld(Y, Z))), X)
% 0.13/0.38 = { by axiom 3 (f01) }
% 0.13/0.38 mult(mult(X, Z), X)
% 0.13/0.38
% 0.13/0.38 Lemma 6: mult(ld(X, X), Y) = Y.
% 0.13/0.38 Proof:
% 0.13/0.38 mult(ld(X, X), Y)
% 0.13/0.38 = { by axiom 1 (f02) R->L }
% 0.13/0.38 ld(mult(Y, X), mult(mult(Y, X), mult(ld(X, X), Y)))
% 0.13/0.38 = { by lemma 5 }
% 0.13/0.38 ld(mult(Y, X), mult(mult(Y, X), Y))
% 0.13/0.38 = { by axiom 1 (f02) }
% 0.13/0.38 Y
% 0.13/0.38
% 0.13/0.38 Goal 1 (goal): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 0.13/0.38 The goal is true when:
% 0.13/0.38 X = ld(X, X)
% 0.13/0.38
% 0.13/0.38 Proof:
% 0.13/0.38 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 0.13/0.38 = { by lemma 6 R->L }
% 0.13/0.38 tuple(mult(ld(X, X), x1(ld(X, X))), mult(mult(ld(X, X), x1_2(ld(X, X))), ld(X, X)))
% 0.13/0.38 = { by lemma 5 R->L }
% 0.13/0.38 tuple(mult(ld(X, X), x1(ld(X, X))), mult(mult(ld(X, X), Y), mult(ld(Y, x1_2(ld(X, X))), ld(X, X))))
% 0.13/0.38 = { by lemma 6 }
% 0.13/0.38 tuple(mult(ld(X, X), x1(ld(X, X))), mult(Y, mult(ld(Y, x1_2(ld(X, X))), ld(X, X))))
% 0.13/0.38 = { by axiom 2 (f04) R->L }
% 0.13/0.39 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(mult(Y, mult(ld(Y, x1_2(ld(X, X))), ld(X, X))), Y), Y))
% 0.13/0.39 = { by axiom 4 (f05) R->L }
% 0.13/0.39 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(mult(Y, ld(Y, x1_2(ld(X, X)))), mult(ld(X, X), Y)), Y))
% 0.13/0.39 = { by axiom 3 (f01) }
% 0.13/0.39 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(x1_2(ld(X, X)), mult(ld(X, X), Y)), Y))
% 0.13/0.39 = { by lemma 6 }
% 0.13/0.39 tuple(mult(ld(X, X), x1(ld(X, X))), rd(mult(x1_2(ld(X, X)), Y), Y))
% 0.13/0.39 = { by axiom 2 (f04) }
% 0.13/0.39 tuple(mult(ld(X, X), x1(ld(X, X))), x1_2(ld(X, X)))
% 0.13/0.39 = { by lemma 6 }
% 0.13/0.39 tuple(x1(ld(X, X)), x1_2(ld(X, X)))
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39
% 0.13/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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