TSTP Solution File: GRP412-1 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP412-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n020.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 : Mon Jun 24 07:12:16 EDT 2024
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP412-1 : TPTP v8.2.0. Released v2.6.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n020.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 : Thu Jun 20 11:59:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.42 Command-line arguments: --no-flatten-goal
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(X, inverse(Y))), Z))), Y))) = Z.
% 0.20/0.48
% 0.20/0.48 Lemma 2: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X)) = multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z))).
% 0.20/0.48 Proof:
% 0.20/0.48 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))
% 0.20/0.48 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.48 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))))), Z)))
% 0.20/0.48 = { by axiom 1 (single_axiom) }
% 0.20/0.48 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z)))
% 0.20/0.48
% 0.20/0.48 Lemma 3: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X)) = W.
% 0.20/0.48 Proof:
% 0.20/0.48 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X))
% 0.20/0.48 = { by lemma 2 }
% 0.20/0.48 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), W))), Z)))
% 0.20/0.48 = { by axiom 1 (single_axiom) }
% 0.20/0.48 W
% 0.20/0.48
% 0.20/0.48 Lemma 4: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y)))) = Z.
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y))))
% 0.20/0.48 = { by lemma 2 R->L }
% 0.20/0.48 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), inverse(W))), Z))), W)))
% 0.20/0.48 = { by axiom 1 (single_axiom) }
% 0.20/0.48 Z
% 0.20/0.48
% 0.20/0.48 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z)) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z))
% 0.20/0.48 = { by lemma 3 R->L }
% 0.20/0.48 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z)))), Y))))
% 0.20/0.48 = { by lemma 4 }
% 0.20/0.48 multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z))
% 0.20/0.48 = { by lemma 4 R->L }
% 0.20/0.48 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z)))), Y))))
% 0.20/0.48 = { by lemma 3 }
% 0.20/0.48 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 0.20/0.48
% 0.20/0.48 Lemma 6: multiply(X, multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z))))) = multiply(inverse(multiply(W, V)), multiply(W, V)).
% 0.20/0.48 Proof:
% 0.20/0.48 multiply(X, multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 0.20/0.48 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.48 multiply(multiply(U, inverse(multiply(multiply(multiply(inverse(T), T), inverse(multiply(inverse(multiply(U, inverse(T))), X))), T))), multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 0.20/0.48 = { by lemma 2 R->L }
% 0.20/0.48 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 0.20/0.48 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.48 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(V))), multiply(multiply(inverse(Z), Z), X)))), V))), Z)))))
% 0.20/0.48 = { by lemma 4 }
% 0.20/0.48 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(V))), multiply(multiply(inverse(Z), Z), X)))), V))
% 0.20/0.49 = { by lemma 5 R->L }
% 0.20/0.49 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V))
% 0.20/0.49 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.49 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(S))), multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V))))), S)))
% 0.20/0.49 = { by lemma 5 }
% 0.20/0.49 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), inverse(S))), multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V))))), S)))
% 0.20/0.49 = { by lemma 5 }
% 0.20/0.49 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), inverse(S))), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), multiply(W, V))))), S)))
% 0.20/0.49 = { by lemma 3 }
% 0.20/0.49 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(S))), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), multiply(W, V))))), S)))
% 0.20/0.49 = { by lemma 3 }
% 0.20/0.49 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(S))), multiply(inverse(multiply(W, V)), multiply(W, V))))), S)))
% 0.20/0.49 = { by axiom 1 (single_axiom) }
% 0.20/0.49 multiply(inverse(multiply(W, V)), multiply(W, V))
% 0.20/0.49
% 0.20/0.49 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.49 Proof:
% 0.20/0.49 multiply(inverse(a1), a1)
% 0.20/0.49 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.49 multiply(inverse(a1), multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), inverse(Z))), a1))), Z))))
% 0.20/0.49 = { by lemma 2 }
% 0.20/0.49 multiply(inverse(a1), multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(a1)), Y)))))
% 0.20/0.49 = { by lemma 6 }
% 0.20/0.49 multiply(inverse(multiply(W, V)), multiply(W, V))
% 0.20/0.49 = { by lemma 6 R->L }
% 0.20/0.49 multiply(inverse(b1), multiply(inverse(multiply(U, inverse(T))), multiply(U, inverse(multiply(multiply(multiply(inverse(T), T), inverse(b1)), T)))))
% 0.20/0.49 = { by lemma 2 R->L }
% 0.20/0.49 multiply(inverse(b1), multiply(inverse(multiply(U, inverse(T))), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(S))), b1))), S))))
% 0.20/0.49 = { by axiom 1 (single_axiom) }
% 0.20/0.49 multiply(inverse(b1), b1)
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49
% 0.20/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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