TSTP Solution File: GRP756-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP756-1 : 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 : n005.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 01:20:00 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP756-1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 01:34:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
% 0.20/0.42 Axiom 2 (f04): rd(mult(X, Y), Y) = X.
% 0.20/0.42 Axiom 3 (f01): mult(X, ld(X, Y)) = Y.
% 0.20/0.42 Axiom 4 (f05): mult(X, mult(mult(Y, Y), Z)) = mult(mult(X, Y), mult(Y, Z)).
% 0.20/0.42
% 0.20/0.42 Lemma 5: ld(mult(X, Y), mult(X, mult(mult(Y, Y), Z))) = mult(Y, Z).
% 0.20/0.42 Proof:
% 0.20/0.42 ld(mult(X, Y), mult(X, mult(mult(Y, Y), Z)))
% 0.20/0.42 = { by axiom 4 (f05) }
% 0.20/0.42 ld(mult(X, Y), mult(mult(X, Y), mult(Y, Z)))
% 0.20/0.42 = { by axiom 1 (f02) }
% 0.20/0.42 mult(Y, Z)
% 0.20/0.42
% 0.20/0.42 Lemma 6: mult(X, ld(mult(X, X), Y)) = ld(mult(Z, X), mult(Z, Y)).
% 0.20/0.42 Proof:
% 0.20/0.42 mult(X, ld(mult(X, X), Y))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 ld(mult(Z, X), mult(Z, mult(mult(X, X), ld(mult(X, X), Y))))
% 0.20/0.42 = { by axiom 3 (f01) }
% 0.20/0.42 ld(mult(Z, X), mult(Z, Y))
% 0.20/0.42
% 0.20/0.42 Lemma 7: mult(mult(X, Y), ld(mult(Z, Y), mult(Z, W))) = mult(X, W).
% 0.20/0.42 Proof:
% 0.20/0.42 mult(mult(X, Y), ld(mult(Z, Y), mult(Z, W)))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 mult(mult(X, Y), mult(Y, ld(mult(Y, Y), W)))
% 0.20/0.42 = { by axiom 4 (f05) R->L }
% 0.20/0.42 mult(X, mult(mult(Y, Y), ld(mult(Y, Y), W)))
% 0.20/0.42 = { by axiom 3 (f01) }
% 0.20/0.42 mult(X, W)
% 0.20/0.42
% 0.20/0.42 Lemma 8: mult(mult(X, ld(Y, Z)), ld(Z, mult(Y, W))) = mult(X, W).
% 0.20/0.42 Proof:
% 0.20/0.42 mult(mult(X, ld(Y, Z)), ld(Z, mult(Y, W)))
% 0.20/0.42 = { by axiom 3 (f01) R->L }
% 0.20/0.42 mult(mult(X, ld(Y, Z)), ld(mult(Y, ld(Y, Z)), mult(Y, W)))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 mult(X, W)
% 0.20/0.42
% 0.20/0.42 Lemma 9: mult(X, ld(Y, Y)) = X.
% 0.20/0.42 Proof:
% 0.20/0.42 mult(X, ld(Y, Y))
% 0.20/0.42 = { by axiom 2 (f04) R->L }
% 0.20/0.42 rd(mult(mult(X, ld(Y, Y)), Z), Z)
% 0.20/0.42 = { by axiom 1 (f02) R->L }
% 0.20/0.42 rd(mult(mult(X, ld(Y, Y)), ld(Y, mult(Y, Z))), Z)
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 rd(mult(X, Z), Z)
% 0.20/0.42 = { by axiom 2 (f04) }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Lemma 10: mult(ld(X, X), Y) = Y.
% 0.20/0.42 Proof:
% 0.20/0.42 mult(ld(X, X), Y)
% 0.20/0.42 = { by axiom 1 (f02) R->L }
% 0.20/0.42 mult(ld(X, X), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by axiom 1 (f02) R->L }
% 0.20/0.42 mult(ld(mult(W, Y), mult(mult(W, Y), ld(X, X))), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 mult(ld(mult(W, Y), mult(W, Y)), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 mult(mult(Y, ld(mult(Y, Y), Y)), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by lemma 9 R->L }
% 0.20/0.42 mult(mult(Y, ld(mult(Y, Y), mult(Y, ld(V, V)))), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by axiom 3 (f01) R->L }
% 0.20/0.42 mult(mult(Y, ld(mult(Y, Y), mult(Y, mult(mult(Y, Y), ld(mult(Y, Y), ld(V, V)))))), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by lemma 5 }
% 0.20/0.42 mult(mult(Y, mult(Y, ld(mult(Y, Y), ld(V, V)))), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by lemma 5 R->L }
% 0.20/0.42 mult(mult(Y, ld(mult(Z, Y), mult(Z, mult(mult(Y, Y), ld(mult(Y, Y), ld(V, V)))))), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by axiom 3 (f01) }
% 0.20/0.42 mult(mult(Y, ld(mult(Z, Y), mult(Z, ld(V, V)))), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 mult(mult(Y, ld(mult(Z, Y), Z)), ld(Z, mult(Z, Y)))
% 0.20/0.42 = { by lemma 9 R->L }
% 0.20/0.42 mult(mult(Y, ld(mult(Z, Y), Z)), ld(Z, mult(mult(Z, Y), ld(U, U))))
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 mult(Y, ld(U, U))
% 0.20/0.42 = { by lemma 9 }
% 0.20/0.42 Y
% 0.20/0.42
% 0.20/0.42 Lemma 11: mult(X, ld(mult(Y, X), mult(Y, Z))) = Z.
% 0.20/0.42 Proof:
% 0.20/0.42 mult(X, ld(mult(Y, X), mult(Y, Z)))
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 mult(mult(ld(W, W), X), ld(mult(Y, X), mult(Y, Z)))
% 0.20/0.42 = { by lemma 7 }
% 0.20/0.42 mult(ld(W, W), Z)
% 0.20/0.42 = { by lemma 10 }
% 0.20/0.42 Z
% 0.20/0.42
% 0.20/0.42 Goal 1 (goals): mult(mult(a, b), c) = mult(a, mult(b, c)).
% 0.20/0.42 Proof:
% 0.20/0.42 mult(mult(a, b), c)
% 0.20/0.42 = { by lemma 11 R->L }
% 0.20/0.42 mult(mult(a, b), mult(b, ld(mult(X, b), mult(X, c))))
% 0.20/0.42 = { by axiom 4 (f05) R->L }
% 0.20/0.42 mult(a, mult(mult(b, b), ld(mult(X, b), mult(X, c))))
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 mult(a, mult(ld(Y, Y), mult(mult(b, b), ld(mult(X, b), mult(X, c)))))
% 0.20/0.42 = { by axiom 4 (f05) }
% 0.20/0.42 mult(a, mult(mult(ld(Y, Y), b), mult(b, ld(mult(X, b), mult(X, c)))))
% 0.20/0.42 = { by lemma 10 }
% 0.20/0.42 mult(a, mult(b, mult(b, ld(mult(X, b), mult(X, c)))))
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 mult(a, mult(b, c))
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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