TSTP Solution File: ALG245-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG245-1 : 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 : n008.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 : Wed Aug 30 16:42:43 EDT 2023
% Result : Unsatisfiable 7.67s 1.35s
% Output : Proof 7.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG245-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % 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 : n008.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 03:48:17 EDT 2023
% 0.12/0.33 % CPUTime :
% 7.67/1.35 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 7.67/1.35
% 7.67/1.35 % SZS status Unsatisfiable
% 7.67/1.35
% 7.67/1.36 % SZS output start Proof
% 7.67/1.36 Axiom 1 (c05): mult(X, X) = X.
% 7.67/1.36 Axiom 2 (c01): mult(X, mult(Y, Z)) = mult(mult(X, Y), mult(X, Z)).
% 7.67/1.36 Axiom 3 (c02): mult(mult(X, Y), Z) = mult(mult(X, Z), mult(Y, Z)).
% 7.67/1.36 Axiom 4 (c03): mult(mult(mult(X, Y), mult(Z, W)), mult(mult(mult(X, Y), mult(Z, W)), mult(mult(X, Z), mult(Y, W)))) = mult(mult(X, Z), mult(Y, W)).
% 7.67/1.36 Axiom 5 (c04): mult(mult(mult(mult(X, Y), mult(Z, W)), mult(mult(X, Z), mult(Y, W))), mult(mult(X, Z), mult(Y, W))) = mult(mult(X, Y), mult(Z, W)).
% 7.67/1.36
% 7.67/1.36 Lemma 6: mult(mult(X, Y), X) = mult(X, mult(Y, X)).
% 7.67/1.36 Proof:
% 7.67/1.36 mult(mult(X, Y), X)
% 7.67/1.36 = { by axiom 1 (c05) R->L }
% 7.67/1.36 mult(mult(X, Y), mult(X, X))
% 7.67/1.36 = { by axiom 2 (c01) R->L }
% 7.67/1.36 mult(X, mult(Y, X))
% 7.67/1.36
% 7.67/1.36 Goal 1 (goals): mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))) = mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d))).
% 7.67/1.36 Proof:
% 7.67/1.36 mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))
% 7.67/1.36 = { by axiom 1 (c05) R->L }
% 7.67/1.36 mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))))
% 7.67/1.36 = { by axiom 2 (c01) }
% 7.67/1.36 mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, b), mult(c, d))), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d))))
% 7.67/1.36 = { by axiom 5 (c04) }
% 7.67/1.36 mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, b), mult(c, d))), mult(mult(a, b), mult(c, d)))
% 7.67/1.36 = { by lemma 6 }
% 7.67/1.36 mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.36 = { by axiom 1 (c05) R->L }
% 7.67/1.36 mult(mult(mult(mult(mult(a, b), mult(a, b)), mult(c, d)), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.36 = { by axiom 3 (c02) }
% 7.67/1.36 mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, b), mult(c, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.36 = { by axiom 5 (c04) R->L }
% 7.67/1.37 mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d))), mult(mult(a, c), mult(b, d)))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 = { by axiom 2 (c01) }
% 7.67/1.37 mult(mult(mult(mult(mult(mult(a, b), mult(c, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 = { by axiom 4 (c03) }
% 7.67/1.37 mult(mult(mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 = { by axiom 1 (c05) R->L }
% 7.67/1.37 mult(mult(mult(mult(mult(mult(a, c), mult(b, d)), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, b), mult(c, d)), mult(mult(a, c), mult(b, d)))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 = { by axiom 3 (c02) R->L }
% 7.67/1.37 mult(mult(mult(mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d))), mult(mult(a, c), mult(b, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 = { by lemma 6 }
% 7.67/1.37 mult(mult(mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d))), mult(mult(mult(a, c), mult(b, d)), mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d))))), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 = { by axiom 4 (c03) }
% 7.67/1.37 mult(mult(mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d))), mult(mult(a, b), mult(c, d))), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 = { by axiom 5 (c04) }
% 7.67/1.37 mult(mult(mult(a, c), mult(b, d)), mult(mult(a, b), mult(c, d)))
% 7.67/1.37 % SZS output end Proof
% 7.67/1.37
% 7.67/1.37 RESULT: Unsatisfiable (the axioms are contradictory).
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