TSTP Solution File: GRP684-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP684-1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n032.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 01:19:42 EDT 2023
% Result : Unsatisfiable 0.10s 0.34s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GRP684-1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Aug 28 21:17:30 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.10/0.34 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.10/0.34
% 0.10/0.34 % SZS status Unsatisfiable
% 0.10/0.34
% 0.10/0.34 % SZS output start Proof
% 0.10/0.34 Axiom 1 (c01): ld(X, mult(X, X)) = X.
% 0.10/0.34 Axiom 2 (c02): rd(mult(X, X), X) = X.
% 0.10/0.34 Axiom 3 (c03): mult(X, ld(X, Y)) = ld(X, mult(X, Y)).
% 0.10/0.34 Axiom 4 (c04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
% 0.10/0.34 Axiom 5 (c07): ld(X, mult(X, ld(Y, Y))) = rd(mult(rd(X, X), Y), Y).
% 0.10/0.34 Axiom 6 (c06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
% 0.10/0.34
% 0.10/0.34 Lemma 7: mult(ld(X, X), X) = X.
% 0.10/0.34 Proof:
% 0.10/0.34 mult(ld(X, X), X)
% 0.10/0.34 = { by axiom 1 (c01) R->L }
% 0.10/0.34 mult(ld(X, ld(X, mult(X, X))), X)
% 0.10/0.34 = { by axiom 3 (c03) R->L }
% 0.10/0.34 mult(ld(X, mult(X, ld(X, X))), X)
% 0.10/0.34 = { by axiom 5 (c07) }
% 0.10/0.34 mult(rd(mult(rd(X, X), X), X), X)
% 0.10/0.34 = { by axiom 4 (c04) }
% 0.10/0.34 mult(rd(rd(mult(X, X), X), X), X)
% 0.10/0.34 = { by axiom 2 (c02) }
% 0.10/0.34 mult(rd(X, X), X)
% 0.10/0.34 = { by axiom 4 (c04) }
% 0.10/0.34 rd(mult(X, X), X)
% 0.10/0.34 = { by axiom 2 (c02) }
% 0.10/0.34 X
% 0.10/0.34
% 0.10/0.34 Lemma 8: mult(X, rd(mult(Y, Z), Z)) = rd(mult(mult(X, Y), Z), Z).
% 0.10/0.34 Proof:
% 0.10/0.34 mult(X, rd(mult(Y, Z), Z))
% 0.10/0.34 = { by axiom 6 (c06) R->L }
% 0.10/0.34 rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
% 0.10/0.34 = { by axiom 2 (c02) }
% 0.10/0.34 rd(mult(mult(X, Y), Z), rd(mult(Z, Z), Z))
% 0.10/0.34 = { by axiom 2 (c02) }
% 0.10/0.34 rd(mult(mult(X, Y), Z), Z)
% 0.10/0.34
% 0.10/0.34 Lemma 9: rd(mult(mult(X, Y), Y), Y) = mult(X, Y).
% 0.10/0.34 Proof:
% 0.10/0.34 rd(mult(mult(X, Y), Y), Y)
% 0.10/0.34 = { by lemma 8 R->L }
% 0.10/0.34 mult(X, rd(mult(Y, Y), Y))
% 0.10/0.34 = { by axiom 2 (c02) }
% 0.10/0.34 mult(X, Y)
% 0.10/0.34
% 0.10/0.34 Goal 1 (goals): rd(mult(a, mult(b, c)), mult(b, c)) = rd(mult(a, c), c).
% 0.10/0.34 Proof:
% 0.10/0.34 rd(mult(a, mult(b, c)), mult(b, c))
% 0.10/0.34 = { by lemma 7 R->L }
% 0.10/0.34 rd(mult(mult(ld(a, a), a), mult(b, c)), mult(b, c))
% 0.10/0.34 = { by lemma 9 R->L }
% 0.10/0.34 rd(mult(mult(ld(a, a), a), mult(b, c)), rd(mult(mult(b, c), c), c))
% 0.10/0.34 = { by lemma 9 R->L }
% 0.10/0.34 rd(mult(mult(ld(a, a), a), rd(mult(mult(b, c), c), c)), rd(mult(mult(b, c), c), c))
% 0.10/0.34 = { by axiom 6 (c06) }
% 0.10/0.34 mult(ld(a, a), rd(mult(a, c), c))
% 0.10/0.34 = { by lemma 8 }
% 0.10/0.34 rd(mult(mult(ld(a, a), a), c), c)
% 0.10/0.34 = { by lemma 7 }
% 0.10/0.34 rd(mult(a, c), c)
% 0.10/0.34 % SZS output end Proof
% 0.10/0.34
% 0.10/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
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