TSTP Solution File: GRP682-10 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : GRP682-10 : 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 : n007.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 01:19:40 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP682-10 : TPTP v8.1.2. Released v8.1.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:29:58 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.39 Command-line arguments: --flatten
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Axiom 1 (f02): rd(mult(X, X), X) = X.
% 0.19/0.39 Axiom 2 (f01): ld(X, mult(X, X)) = X.
% 0.19/0.39 Axiom 3 (f03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.19/0.39 Axiom 4 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.19/0.39 Axiom 5 (f07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 0.19/0.39 Axiom 6 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
% 0.19/0.39
% 0.19/0.39 Lemma 7: mult(ld(X, mult(X, Y)), Z) = ld(X, mult(X, mult(Y, Z))).
% 0.19/0.39 Proof:
% 0.19/0.39 mult(ld(X, mult(X, Y)), Z)
% 0.19/0.39 = { by axiom 6 (f05) R->L }
% 0.19/0.39 ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), mult(Y, Z)))
% 0.19/0.39 = { by axiom 2 (f01) }
% 0.19/0.39 ld(X, mult(ld(X, mult(X, X)), mult(Y, Z)))
% 0.19/0.39 = { by axiom 2 (f01) }
% 0.19/0.39 ld(X, mult(X, mult(Y, Z)))
% 0.19/0.39
% 0.19/0.39 Lemma 8: mult(ld(X, mult(X, Y)), rd(Y, Y)) = ld(X, mult(X, Y)).
% 0.19/0.39 Proof:
% 0.19/0.39 mult(ld(X, mult(X, Y)), rd(Y, Y))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 ld(X, mult(X, mult(Y, rd(Y, Y))))
% 0.19/0.39 = { by axiom 1 (f02) R->L }
% 0.19/0.39 ld(X, mult(X, mult(Y, rd(rd(mult(Y, Y), Y), Y))))
% 0.19/0.39 = { by axiom 4 (f04) R->L }
% 0.19/0.39 ld(X, mult(X, mult(Y, rd(mult(rd(Y, Y), Y), Y))))
% 0.19/0.39 = { by axiom 5 (f07) R->L }
% 0.19/0.39 ld(X, mult(X, mult(Y, ld(Y, mult(Y, ld(Y, Y))))))
% 0.19/0.39 = { by axiom 3 (f03) }
% 0.19/0.39 ld(X, mult(X, mult(Y, ld(Y, ld(Y, mult(Y, Y))))))
% 0.19/0.39 = { by axiom 2 (f01) }
% 0.19/0.39 ld(X, mult(X, mult(Y, ld(Y, Y))))
% 0.19/0.39 = { by axiom 3 (f03) }
% 0.19/0.39 ld(X, mult(X, ld(Y, mult(Y, Y))))
% 0.19/0.39 = { by axiom 2 (f01) }
% 0.19/0.39 ld(X, mult(X, Y))
% 0.19/0.39
% 0.19/0.39 Goal 1 (goal): ld(ld(x0, x1), mult(ld(x0, x1), x2)) = ld(x0, mult(x0, x2)).
% 0.19/0.39 Proof:
% 0.19/0.39 ld(ld(x0, x1), mult(ld(x0, x1), x2))
% 0.19/0.39 = { by lemma 8 R->L }
% 0.19/0.39 mult(ld(ld(x0, x1), mult(ld(x0, x1), x2)), rd(x2, x2))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 ld(ld(x0, x1), mult(ld(x0, x1), mult(x2, rd(x2, x2))))
% 0.19/0.39 = { by axiom 6 (f05) }
% 0.19/0.39 mult(ld(x0, mult(x0, x2)), rd(x2, x2))
% 0.19/0.39 = { by lemma 8 }
% 0.19/0.39 ld(x0, mult(x0, x2))
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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