TSTP Solution File: GRP435-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP435-1 : TPTP v8.1.2. Released v2.6.0.
% 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 01:18:25 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP435-1 : TPTP v8.1.2. Released v2.6.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 23:00:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 Axiom 1 (single_axiom): inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), Z)), X), Y), multiply(W, inverse(W)))) = Z.
% 0.19/0.43
% 0.19/0.43 Lemma 2: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(Y, inverse(Y))
% 0.19/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(Y, inverse(Y)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.43 inverse(multiply(multiply(multiply(V, multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.19/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(X, inverse(X)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.43 multiply(X, inverse(X))
% 0.19/0.43
% 0.19/0.43 Lemma 3: inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W)))) = inverse(multiply(Y, Z)).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W))))
% 0.19/0.43 = { by lemma 2 }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, Z), inverse(multiply(Y, Z)))), Y), Z), multiply(W, inverse(W))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.43 inverse(multiply(Y, Z))
% 0.19/0.43
% 0.19/0.43 Lemma 4: inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y)) = multiply(W, inverse(W)).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y))
% 0.19/0.43 = { by lemma 3 R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X)), Y), multiply(V, inverse(V))))
% 0.19/0.43 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y), multiply(W, inverse(W)))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X)), Y), multiply(V, inverse(V))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.43 multiply(W, inverse(W))
% 0.19/0.43
% 0.19/0.43 Lemma 5: inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y))) = multiply(Z, inverse(Z)).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y)))
% 0.19/0.43 = { by lemma 2 }
% 0.19/0.43 inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))), Y), inverse(Y)))
% 0.19/0.43 = { by lemma 4 }
% 0.19/0.43 multiply(Z, inverse(Z))
% 0.19/0.43
% 0.19/0.43 Lemma 6: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z)))) = inverse(Y).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z))))
% 0.19/0.43 = { by lemma 2 }
% 0.19/0.43 inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))), Y), multiply(Z, inverse(Z))))
% 0.19/0.43 = { by lemma 5 R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(W, inverse(W))), Y), inverse(Y))), inverse(multiply(W, inverse(W)))), Y), multiply(Z, inverse(Z))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.43 inverse(Y)
% 0.19/0.43
% 0.19/0.43 Lemma 7: inverse(multiply(multiply(X, inverse(X)), Y)) = inverse(Y).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(multiply(multiply(X, inverse(X)), Y))
% 0.19/0.43 = { by lemma 3 R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), multiply(X, inverse(X))), Y), multiply(W, inverse(W))))
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(Z, inverse(Z))), multiply(V, inverse(V))), inverse(multiply(V, inverse(V))))), inverse(multiply(Z, inverse(Z)))), multiply(V, inverse(V))))), Y), multiply(W, inverse(W))))
% 0.19/0.43 = { by lemma 5 }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(multiply(multiply(multiply(U, inverse(U)), inverse(multiply(Z, inverse(Z)))), multiply(V, inverse(V))))), Y), multiply(W, inverse(W))))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(multiply(Z, inverse(Z))))), Y), multiply(W, inverse(W))))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 inverse(Y)
% 0.19/0.43
% 0.19/0.43 Lemma 8: inverse(multiply(multiply(multiply(inverse(X), Y), inverse(Y)), multiply(Z, inverse(Z)))) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(X), Y), inverse(Y)), multiply(Z, inverse(Z))))
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), X)), Y), inverse(Y)), multiply(Z, inverse(Z))))
% 0.19/0.43 = { by axiom 1 (single_axiom) }
% 0.19/0.44 X
% 0.19/0.44
% 0.19/0.44 Lemma 9: inverse(multiply(X, multiply(Y, inverse(Y)))) = inverse(X).
% 0.19/0.44 Proof:
% 0.19/0.44 inverse(multiply(X, multiply(Y, inverse(Y))))
% 0.19/0.44 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.44 inverse(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), X)), Z), inverse(Z)), multiply(W, inverse(W)))), multiply(Y, inverse(Y))))
% 0.19/0.44 = { by lemma 8 }
% 0.19/0.44 inverse(multiply(multiply(multiply(Z, inverse(Z)), X), multiply(Y, inverse(Y))))
% 0.19/0.44 = { by lemma 6 }
% 0.19/0.44 inverse(X)
% 0.19/0.44
% 0.19/0.44 Lemma 10: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.44 = { by lemma 8 R->L }
% 0.19/0.44 inverse(multiply(multiply(multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), Z), inverse(Z)), multiply(W, inverse(W))))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 inverse(multiply(multiply(multiply(inverse(X), Z), inverse(Z)), multiply(W, inverse(W))))
% 0.19/0.44 = { by lemma 8 }
% 0.19/0.44 X
% 0.19/0.44
% 0.19/0.44 Lemma 11: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 inverse(multiply(inverse(multiply(X, Y)), X))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 inverse(multiply(multiply(inverse(multiply(X, Y)), X), multiply(Z, inverse(Z))))
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 inverse(multiply(multiply(inverse(multiply(multiply(X, multiply(W, inverse(W))), Y)), X), multiply(Z, inverse(Z))))
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, multiply(W, inverse(W))), Y)), X), multiply(W, inverse(W))), multiply(Z, inverse(Z))))
% 0.19/0.44 = { by axiom 1 (single_axiom) }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 12: inverse(multiply(X, inverse(multiply(Y, X)))) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 inverse(multiply(X, inverse(multiply(Y, X))))
% 0.19/0.44 = { by lemma 11 R->L }
% 0.19/0.44 inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), Y)), inverse(multiply(Y, X))))
% 0.19/0.44 = { by lemma 11 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(a3, b3), c3)
% 0.19/0.44 = { by lemma 11 R->L }
% 0.19/0.44 multiply(multiply(inverse(multiply(inverse(multiply(multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))), a3)), multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))))), b3), c3)
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))), a3), multiply(Y, inverse(Y)))), multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))))), b3), c3)
% 0.19/0.44 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.44 multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(a3, multiply(b3, c3)), X)), a3), multiply(b3, c3)), multiply(Z, inverse(Z)))), inverse(multiply(multiply(a3, multiply(b3, c3)), X))), a3), multiply(Y, inverse(Y)))), multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))))), b3), c3)
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(a3, multiply(b3, c3)), X)), a3), multiply(b3, c3))), inverse(multiply(multiply(a3, multiply(b3, c3)), X))), a3), multiply(Y, inverse(Y)))), multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))))), b3), c3)
% 0.19/0.44 = { by axiom 1 (single_axiom) }
% 0.19/0.44 multiply(multiply(inverse(multiply(multiply(b3, c3), multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))))), b3), c3)
% 0.19/0.44 = { by lemma 12 R->L }
% 0.19/0.44 inverse(multiply(multiply(W, inverse(W)), inverse(multiply(multiply(multiply(inverse(multiply(multiply(b3, c3), multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))))), b3), c3), multiply(W, inverse(W))))))
% 0.19/0.44 = { by axiom 1 (single_axiom) }
% 0.19/0.44 inverse(multiply(multiply(W, inverse(W)), multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 7 }
% 0.19/0.44 inverse(multiply(X, inverse(multiply(multiply(a3, multiply(b3, c3)), X))))
% 0.19/0.44 = { by lemma 12 }
% 0.19/0.44 multiply(a3, multiply(b3, c3))
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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