TSTP Solution File: GRP411-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP411-1 : 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 : 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 : Thu Aug 31 01:18:19 EDT 2023
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP411-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % 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 : n020.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 23:39:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.45 Command-line arguments: --no-flatten-goal
% 0.20/0.45
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45
% 0.20/0.51 % SZS output start Proof
% 0.20/0.52 Axiom 1 (single_axiom): multiply(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))) = Y.
% 0.20/0.52
% 0.20/0.52 Lemma 2: multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))) = multiply(inverse(multiply(W, inverse(multiply(Y, Z)))), multiply(W, inverse(Z))).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.52 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.52 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(W, inverse(multiply(Y, Z)))), multiply(W, inverse(Z))), inverse(multiply(inverse(Z), Z)))))), multiply(X, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.52 = { by axiom 1 (single_axiom) }
% 0.20/0.52 multiply(inverse(multiply(W, inverse(multiply(Y, Z)))), multiply(W, inverse(Z)))
% 0.20/0.52
% 0.20/0.52 Lemma 3: multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))
% 0.20/0.52 = { by lemma 2 R->L }
% 0.20/0.52 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(inverse(Z), Z)))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.52 = { by axiom 1 (single_axiom) }
% 0.20/0.52 Y
% 0.20/0.52
% 0.20/0.52 Lemma 4: inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))) = Y.
% 0.20/0.52 Proof:
% 0.20/0.52 inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))
% 0.20/0.52 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.52 multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.20/0.52 = { by lemma 3 }
% 0.20/0.52 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.20/0.52 = { by axiom 1 (single_axiom) }
% 0.20/0.52 Y
% 0.20/0.52
% 0.20/0.52 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z)) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z))
% 0.20/0.52 = { by lemma 4 R->L }
% 0.20/0.52 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.52 = { by lemma 3 R->L }
% 0.20/0.52 multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.52 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.52 multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.20/0.52 = { by axiom 1 (single_axiom) }
% 0.20/0.52 multiply(multiply(inverse(multiply(T, inverse(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.20/0.52 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.52 multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.20/0.52 = { by axiom 1 (single_axiom) }
% 0.20/0.52 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.52 = { by lemma 3 }
% 0.20/0.52 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.52 = { by lemma 4 }
% 0.20/0.52 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 0.20/0.52
% 0.20/0.52 Lemma 6: multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W)) = multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W)).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.20/0.52 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.52 multiply(inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z)))), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.20/0.52 = { by lemma 5 R->L }
% 0.20/0.52 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W))
% 0.20/0.52
% 0.20/0.52 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(Y), Y)
% 0.20/0.52 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.52 multiply(inverse(Y), multiply(multiply(inverse(multiply(U, inverse(multiply(Y, W)))), multiply(U, inverse(W))), inverse(multiply(inverse(W), W))))
% 0.20/0.52 = { by lemma 6 }
% 0.20/0.52 multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(multiply(inverse(W), W))))
% 0.20/0.52 = { by lemma 6 R->L }
% 0.20/0.52 multiply(inverse(X), multiply(multiply(inverse(multiply(Z, inverse(multiply(X, W)))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W))))
% 0.20/0.52 = { by axiom 1 (single_axiom) }
% 0.20/0.52 multiply(inverse(X), X)
% 0.20/0.52
% 0.20/0.53 Lemma 8: multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(W), W))) = inverse(Z).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(W), W)))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Z), Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 0.20/0.53 = { by axiom 1 (single_axiom) }
% 0.20/0.53 inverse(Z)
% 0.20/0.53
% 0.20/0.53 Lemma 9: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(Z), Z)))), multiply(W, inverse(multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 8 }
% 0.20/0.53 inverse(multiply(inverse(Z), Z))
% 0.20/0.53
% 0.20/0.53 Lemma 10: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)) = multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z)).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(inverse(U), U))), inverse(multiply(inverse(U), U)))))), multiply(X, Z))
% 0.20/0.53 = { by lemma 6 R->L }
% 0.20/0.53 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(U), U)))))), multiply(T, inverse(inverse(multiply(inverse(U), U))))), Z))
% 0.20/0.53 = { by lemma 9 }
% 0.20/0.53 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(T, inverse(inverse(multiply(inverse(U), U))))), multiply(T, inverse(inverse(multiply(inverse(U), U))))), Z))
% 0.20/0.53 = { by lemma 7 R->L }
% 0.20/0.53 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z))
% 0.20/0.53
% 0.20/0.53 Lemma 11: multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)), inverse(multiply(inverse(W), W))) = Z.
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)), inverse(multiply(inverse(W), W)))
% 0.20/0.53 = { by lemma 4 R->L }
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(W), W)))
% 0.20/0.53 = { by lemma 8 }
% 0.20/0.53 inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))
% 0.20/0.53 = { by lemma 4 }
% 0.20/0.53 Z
% 0.20/0.53
% 0.20/0.53 Lemma 12: multiply(multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(Y), Y), Z)), inverse(multiply(inverse(W), W))) = Z.
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(Y), Y), Z)), inverse(multiply(inverse(W), W)))
% 0.20/0.53 = { by lemma 10 R->L }
% 0.20/0.53 multiply(multiply(inverse(multiply(V, inverse(multiply(inverse(U), U)))), multiply(V, Z)), inverse(multiply(inverse(W), W)))
% 0.20/0.53 = { by lemma 11 }
% 0.20/0.53 Z
% 0.20/0.53
% 0.20/0.53 Lemma 13: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 multiply(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(V), V)))), multiply(W, inverse(multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 10 }
% 0.20/0.53 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(multiply(inverse(U), U), inverse(multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 9 }
% 0.20/0.53 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(T), T)))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 10 }
% 0.20/0.53 multiply(multiply(inverse(multiply(inverse(S), S)), multiply(multiply(inverse(X2), X2), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.53 = { by lemma 12 }
% 0.20/0.53 multiply(inverse(Z), Z)
% 0.20/0.53
% 0.20/0.53 Lemma 14: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.20/0.53 Proof:
% 0.20/0.53 inverse(multiply(inverse(X), X))
% 0.20/0.53 = { by lemma 9 R->L }
% 0.20/0.53 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W)))
% 0.20/0.53 = { by lemma 13 }
% 0.20/0.53 multiply(inverse(Y), Y)
% 0.20/0.53
% 0.20/0.53 Lemma 15: multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W)))) = Z.
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W))))
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, inverse(multiply(inverse(V), V)))))
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 multiply(inverse(multiply(inverse(U), U)), multiply(multiply(inverse(Y), Y), multiply(Z, inverse(multiply(inverse(V), V)))))
% 0.20/0.53 = { by lemma 10 R->L }
% 0.20/0.53 multiply(inverse(multiply(T, inverse(multiply(inverse(S), S)))), multiply(T, multiply(Z, inverse(multiply(inverse(V), V)))))
% 0.20/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.53 multiply(multiply(inverse(multiply(X2, inverse(multiply(multiply(inverse(multiply(T, inverse(multiply(inverse(S), S)))), multiply(T, multiply(Z, inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(V), V)))))), multiply(X2, inverse(inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))
% 0.20/0.53 = { by lemma 11 }
% 0.20/0.53 multiply(multiply(inverse(multiply(X2, inverse(multiply(Z, inverse(multiply(inverse(V), V)))))), multiply(X2, inverse(inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))
% 0.20/0.53 = { by lemma 2 }
% 0.20/0.53 multiply(inverse(multiply(Y2, inverse(multiply(multiply(Z, inverse(multiply(inverse(V), V))), V)))), multiply(Y2, inverse(V)))
% 0.20/0.53 = { by lemma 3 }
% 0.20/0.53 Z
% 0.20/0.53
% 0.20/0.53 Lemma 16: inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W)))) = inverse(multiply(X, inverse(W))).
% 0.20/0.53 Proof:
% 0.20/0.53 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W))))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(W), W))), W))))
% 0.20/0.53 = { by lemma 7 }
% 0.20/0.53 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(W))), multiply(X, inverse(W))), inverse(multiply(inverse(W), W))), W))))
% 0.20/0.53 = { by lemma 4 }
% 0.20/0.53 inverse(multiply(X, inverse(W)))
% 0.20/0.53
% 0.20/0.53 Lemma 17: inverse(multiply(X, inverse(multiply(multiply(inverse(Y), Y), Z)))) = inverse(multiply(X, inverse(Z))).
% 0.20/0.53 Proof:
% 0.20/0.53 inverse(multiply(X, inverse(multiply(multiply(inverse(Y), Y), Z))))
% 0.20/0.53 = { by lemma 13 R->L }
% 0.20/0.53 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))))
% 0.20/0.53 = { by lemma 16 }
% 0.20/0.53 inverse(multiply(X, inverse(Z)))
% 0.20/0.53
% 0.20/0.53 Lemma 18: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.20/0.53 = { by lemma 4 R->L }
% 0.20/0.53 multiply(inverse(multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Y, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), multiply(W, Z))
% 0.20/0.53 = { by lemma 5 }
% 0.20/0.53 multiply(inverse(multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Y, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), multiply(X, Z))
% 0.20/0.53 = { by lemma 4 }
% 0.20/0.53 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.20/0.53
% 0.20/0.53 Lemma 19: multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), multiply(inverse(W), W)) = Y.
% 0.20/0.53 Proof:
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, multiply(inverse(U), U)))))
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, inverse(multiply(inverse(T), T))))))
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.53 = { by lemma 14 R->L }
% 0.20/0.53 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(X2), X2)))), multiply(V, inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.53 = { by lemma 10 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(Y2), Y2)), multiply(multiply(inverse(Z2), Z2), inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.54 = { by lemma 14 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(multiply(inverse(Z2), Z2), inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.54 = { by lemma 14 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(multiply(inverse(Z2), Z2), inverse(multiply(inverse(V2), V2))))))
% 0.20/0.54 = { by lemma 13 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 15 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(T2), T2), multiply(multiply(inverse(S2), S2), multiply(Y, multiply(inverse(U2), U2))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 17 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(S2), S2), multiply(Y, multiply(inverse(U2), U2)))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 17 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 14 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(X, inverse(multiply(inverse(X3), X3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 18 }
% 0.20/0.54 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(multiply(inverse(Y3), Y3), inverse(multiply(inverse(X3), X3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 9 }
% 0.20/0.54 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), inverse(multiply(inverse(Z3), Z3))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 14 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), inverse(multiply(inverse(Z3), Z3))), inverse(multiply(inverse(multiply(inverse(U2), U2)), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by lemma 9 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(multiply(inverse(Y3), Y3), inverse(multiply(inverse(U2), U2)))), inverse(multiply(inverse(multiply(inverse(U2), U2)), multiply(inverse(U2), U2))))
% 0.20/0.54 = { by axiom 1 (single_axiom) }
% 0.20/0.54 Y
% 0.20/0.54
% 0.20/0.54 Lemma 20: multiply(multiply(inverse(X), X), Y) = Y.
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(multiply(inverse(X), X), Y)
% 0.20/0.54 = { by lemma 13 R->L }
% 0.20/0.54 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W))), Y)
% 0.20/0.54 = { by lemma 19 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W))), Y)))), multiply(V, multiply(inverse(U), U))), multiply(inverse(T), T))
% 0.20/0.54 = { by lemma 16 }
% 0.20/0.54 multiply(multiply(inverse(multiply(V, inverse(Y))), multiply(V, multiply(inverse(U), U))), multiply(inverse(T), T))
% 0.20/0.54 = { by lemma 19 }
% 0.20/0.54 Y
% 0.20/0.54
% 0.20/0.54 Lemma 21: multiply(X, multiply(inverse(Y), Y)) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(X, multiply(inverse(Y), Y))
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 multiply(multiply(inverse(Z), Z), multiply(X, multiply(inverse(Y), Y)))
% 0.20/0.54 = { by lemma 12 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), multiply(multiply(inverse(Z), Z), multiply(X, multiply(inverse(Y), Y))))), inverse(multiply(inverse(U), U)))
% 0.20/0.54 = { by lemma 15 }
% 0.20/0.54 multiply(multiply(inverse(multiply(inverse(W), W)), X), inverse(multiply(inverse(U), U)))
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(T), T), X)), inverse(multiply(inverse(U), U)))
% 0.20/0.54 = { by lemma 12 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 22: multiply(inverse(X), multiply(X, Y)) = inverse(inverse(Y)).
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(inverse(X), multiply(X, Y))
% 0.20/0.54 = { by lemma 21 R->L }
% 0.20/0.54 multiply(inverse(multiply(X, multiply(inverse(Z), Z))), multiply(X, Y))
% 0.20/0.54 = { by lemma 18 }
% 0.20/0.54 multiply(inverse(multiply(inverse(Y), multiply(inverse(Z), Z))), multiply(inverse(Y), Y))
% 0.20/0.54 = { by lemma 7 R->L }
% 0.20/0.54 multiply(inverse(multiply(inverse(Y), multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 0.20/0.54 = { by lemma 21 }
% 0.20/0.54 multiply(inverse(inverse(Y)), multiply(inverse(W), W))
% 0.20/0.54 = { by lemma 21 }
% 0.20/0.54 inverse(inverse(Y))
% 0.20/0.54
% 0.20/0.54 Lemma 23: inverse(inverse(X)) = X.
% 0.20/0.54 Proof:
% 0.20/0.54 inverse(inverse(X))
% 0.20/0.54 = { by lemma 21 R->L }
% 0.20/0.54 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 0.20/0.54 = { by lemma 14 R->L }
% 0.20/0.54 multiply(inverse(inverse(X)), inverse(multiply(inverse(Z), Z)))
% 0.20/0.54 = { by lemma 22 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(W), W), X)), inverse(multiply(inverse(Z), Z)))
% 0.20/0.54 = { by lemma 12 }
% 0.20/0.54 X
% 0.20/0.54
% 0.20/0.54 Lemma 24: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 0.20/0.54 = { by lemma 7 }
% 0.20/0.54 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 0.20/0.54 = { by lemma 18 R->L }
% 0.20/0.54 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.20/0.54
% 0.20/0.54 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(multiply(a3, b3), c3)
% 0.20/0.54 = { by lemma 23 R->L }
% 0.20/0.54 multiply(inverse(inverse(multiply(a3, b3))), c3)
% 0.20/0.54 = { by lemma 19 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(a3, b3))), c3)))), multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.20/0.54 = { by lemma 16 R->L }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), multiply(inverse(inverse(multiply(a3, b3))), c3))))), multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.20/0.54 = { by lemma 9 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(inverse(multiply(a3, b3))), c3))))), multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.20/0.54 = { by lemma 24 }
% 0.20/0.54 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, c3))))), multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.20/0.54 = { by lemma 19 }
% 0.20/0.54 multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 20 R->L }
% 0.20/0.54 multiply(inverse(multiply(b3, multiply(multiply(inverse(T), T), inverse(multiply(a3, b3))))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 14 R->L }
% 0.20/0.54 multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(S), S)), inverse(multiply(a3, b3))))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 21 R->L }
% 0.20/0.54 multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(S), S)), multiply(inverse(multiply(a3, b3)), multiply(inverse(X2), X2))))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 24 }
% 0.20/0.54 multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(a3), multiply(a3, b3))), multiply(inverse(a3), multiply(inverse(X2), X2))))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 21 }
% 0.20/0.54 multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(a3), multiply(a3, b3))), inverse(a3)))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 22 }
% 0.20/0.54 multiply(inverse(multiply(b3, multiply(inverse(inverse(inverse(b3))), inverse(a3)))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 multiply(inverse(multiply(b3, multiply(inverse(b3), inverse(a3)))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 23 R->L }
% 0.20/0.54 multiply(inverse(multiply(inverse(inverse(b3)), multiply(inverse(b3), inverse(a3)))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 22 }
% 0.20/0.54 multiply(inverse(inverse(inverse(inverse(a3)))), multiply(b3, c3))
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 multiply(inverse(inverse(a3)), multiply(b3, c3))
% 0.20/0.54 = { by lemma 23 }
% 0.20/0.54 multiply(a3, multiply(b3, c3))
% 0.20/0.54 % SZS output end Proof
% 0.20/0.54
% 0.20/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------