TSTP Solution File: GRP423-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP423-1 : 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 : n013.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 01:18:22 EDT 2023
% Result : Unsatisfiable 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP423-1 : 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 : n013.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 21:25:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.49 Command-line arguments: --no-flatten-goal
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49
% 0.19/0.53 % SZS output start Proof
% 0.19/0.54 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))) = Y.
% 0.19/0.54
% 0.19/0.54 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z)) = inverse(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))), multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 inverse(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.19/0.54
% 0.19/0.54 Lemma 3: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(W, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.19/0.54
% 0.19/0.54 Lemma 4: multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z)))) = multiply(inverse(multiply(W, multiply(V, U))), multiply(W, multiply(V, U))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))
% 0.19/0.54 = { by lemma 2 R->L }
% 0.19/0.54 multiply(X, multiply(inverse(multiply(V, inverse(multiply(inverse(X), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(X), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U))), multiply(inverse(multiply(V, inverse(multiply(inverse(X), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.19/0.54 = { by lemma 3 R->L }
% 0.19/0.54 multiply(inverse(multiply(W, multiply(V, U))), multiply(W, multiply(V, U)))
% 0.19/0.54
% 0.19/0.54 Lemma 5: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(Y), Y)
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 multiply(inverse(Y), inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(Y), multiply(inverse(X2), inverse(multiply(inverse(X2), X2))))))), multiply(S, X2))))
% 0.19/0.54 = { by lemma 4 }
% 0.19/0.54 multiply(inverse(multiply(V, multiply(U, T))), multiply(V, multiply(U, T)))
% 0.19/0.54 = { by lemma 4 R->L }
% 0.19/0.54 multiply(inverse(X), inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), multiply(inverse(W), inverse(multiply(inverse(W), W))))))), multiply(Z, W))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 multiply(inverse(X), X)
% 0.19/0.54
% 0.19/0.54 Lemma 6: multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))) = inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, X))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))), multiply(inverse(X), inverse(multiply(inverse(X), X))))))), multiply(Z, X)))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, X)))
% 0.19/0.54
% 0.19/0.54 Lemma 7: inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))) = Y.
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.54 = { by lemma 6 R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 Y
% 0.19/0.54
% 0.19/0.54 Lemma 8: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Z), Z))))) = Y.
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.54 = { by lemma 5 }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))))
% 0.19/0.54 = { by lemma 5 }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Y)))), multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))))
% 0.19/0.54 = { by lemma 7 }
% 0.19/0.54 Y
% 0.19/0.54
% 0.19/0.54 Lemma 9: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y)))
% 0.19/0.54 = { by lemma 5 }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.54 = { by lemma 8 }
% 0.19/0.54 inverse(multiply(inverse(Z), Z))
% 0.19/0.54
% 0.19/0.54 Lemma 10: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(inverse(X), X))
% 0.19/0.54 = { by lemma 8 R->L }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))
% 0.19/0.54 = { by lemma 9 R->L }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))
% 0.19/0.54 = { by lemma 7 }
% 0.19/0.54 multiply(inverse(Y), Y)
% 0.19/0.54
% 0.19/0.54 Lemma 11: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 0.19/0.54 = { by lemma 5 }
% 0.19/0.54 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 0.19/0.54 = { by lemma 3 R->L }
% 0.19/0.54 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.19/0.54
% 0.19/0.54 Lemma 12: inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Z), Z)))) = Y.
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Z), Z))))
% 0.19/0.54 = { by lemma 10 R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(W), W)))))
% 0.19/0.54 = { by lemma 11 R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(Y), inverse(multiply(inverse(W), W)))))
% 0.19/0.54 = { by lemma 10 R->L }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(U), U))), multiply(inverse(Y), inverse(multiply(inverse(W), W)))))
% 0.19/0.54 = { by lemma 8 }
% 0.19/0.54 Y
% 0.19/0.54
% 0.19/0.54 Lemma 13: multiply(Z, multiply(inverse(Z), Y)) = multiply(X, multiply(inverse(X), Y)).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(Z, multiply(inverse(Z), Y))
% 0.19/0.54 = { by lemma 12 R->L }
% 0.19/0.54 multiply(Z, multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(V), V))))), Y))
% 0.19/0.54 = { by lemma 7 R->L }
% 0.19/0.54 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V)))))), multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(V), V))))), Y))
% 0.19/0.54 = { by lemma 3 R->L }
% 0.19/0.54 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, X)), multiply(W, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V)))))), multiply(inverse(inverse(multiply(inverse(multiply(W, X)), multiply(W, multiply(inverse(V), V))))), Y))
% 0.19/0.54 = { by lemma 7 }
% 0.19/0.54 multiply(X, multiply(inverse(inverse(multiply(inverse(multiply(W, X)), multiply(W, multiply(inverse(V), V))))), Y))
% 0.19/0.54 = { by lemma 12 }
% 0.19/0.54 multiply(X, multiply(inverse(X), Y))
% 0.19/0.54
% 0.19/0.54 Lemma 14: multiply(multiply(inverse(X), X), Y) = Y.
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(multiply(inverse(X), X), Y)
% 0.19/0.54 = { by lemma 10 R->L }
% 0.19/0.54 multiply(inverse(multiply(inverse(Z), Z)), Y)
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))))
% 0.19/0.54 = { by lemma 6 }
% 0.19/0.54 inverse(multiply(inverse(multiply(W, multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))))))))), multiply(W, multiply(inverse(Z), Z))))
% 0.19/0.54 = { by lemma 6 }
% 0.19/0.55 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))), multiply(W, multiply(inverse(Z), Z))))
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 inverse(multiply(inverse(multiply(V, Y)), multiply(V, multiply(inverse(U), U))))
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 Y
% 0.19/0.55
% 0.19/0.55 Lemma 15: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(X, multiply(inverse(X), Y))
% 0.19/0.55 = { by lemma 13 }
% 0.19/0.55 multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(inverse(Z), Z)), Y))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(W), W), Y))
% 0.19/0.55 = { by lemma 14 }
% 0.19/0.55 multiply(multiply(inverse(W), W), Y)
% 0.19/0.55 = { by lemma 14 }
% 0.19/0.55 Y
% 0.19/0.55
% 0.19/0.55 Lemma 16: multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z)) = multiply(W, multiply(inverse(W), Z)).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z))
% 0.19/0.55 = { by lemma 11 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(multiply(inverse(U), U), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.19/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(S), inverse(multiply(inverse(S), S))))))), multiply(T, S))), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.19/0.55 = { by lemma 9 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2))), multiply(inverse(S), inverse(multiply(inverse(S), S))))))), multiply(T, S))), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 multiply(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2)), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.19/0.55 = { by lemma 9 R->L }
% 0.19/0.55 multiply(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2)), multiply(inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2))), Z))
% 0.19/0.55 = { by lemma 13 R->L }
% 0.19/0.55 multiply(W, multiply(inverse(W), Z))
% 0.19/0.55
% 0.19/0.55 Lemma 17: inverse(inverse(X)) = X.
% 0.19/0.55 Proof:
% 0.19/0.55 inverse(inverse(X))
% 0.19/0.55 = { by lemma 15 R->L }
% 0.19/0.55 inverse(inverse(multiply(Y, multiply(inverse(Y), X))))
% 0.19/0.55 = { by lemma 16 R->L }
% 0.19/0.55 inverse(inverse(multiply(inverse(multiply(Z, multiply(inverse(W), W))), multiply(Z, X))))
% 0.19/0.55 = { by lemma 10 R->L }
% 0.19/0.55 inverse(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(V), V)))), multiply(Z, X))))
% 0.19/0.55 = { by lemma 10 R->L }
% 0.19/0.55 inverse(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(inverse(X), X))))), multiply(Z, X))))
% 0.19/0.55 = { by lemma 15 R->L }
% 0.19/0.55 inverse(inverse(multiply(inverse(multiply(Z, inverse(multiply(X, multiply(inverse(X), inverse(multiply(inverse(X), X))))))), multiply(Z, X))))
% 0.19/0.55 = { by lemma 2 R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 X
% 0.19/0.55
% 0.19/0.55 Lemma 18: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(X), X)
% 0.19/0.55 = { by lemma 5 }
% 0.19/0.55 multiply(inverse(multiply(Z, multiply(W, V))), multiply(Z, multiply(W, V)))
% 0.19/0.55 = { by lemma 4 R->L }
% 0.19/0.55 multiply(Y, inverse(multiply(inverse(multiply(U, inverse(multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Y), Y))))))), multiply(U, Y))))
% 0.19/0.55 = { by lemma 15 }
% 0.19/0.55 multiply(Y, inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(inverse(Y), Y))))), multiply(U, Y))))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(Y, inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(T), T)))), multiply(U, Y))))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(Y, inverse(multiply(inverse(multiply(U, multiply(inverse(S), S))), multiply(U, Y))))
% 0.19/0.55 = { by lemma 16 }
% 0.19/0.55 multiply(Y, inverse(multiply(X2, multiply(inverse(X2), Y))))
% 0.19/0.55 = { by lemma 15 }
% 0.19/0.55 multiply(Y, inverse(Y))
% 0.19/0.55
% 0.19/0.55 Lemma 19: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 0.19/0.55 Proof:
% 0.19/0.55 inverse(multiply(inverse(X), Y))
% 0.19/0.55 = { by lemma 15 R->L }
% 0.19/0.55 inverse(multiply(inverse(X), multiply(Y, multiply(inverse(Y), Y))))
% 0.19/0.55 = { by lemma 15 R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(Y, multiply(inverse(Y), X))), multiply(Y, multiply(inverse(Y), Y))))
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 multiply(inverse(Y), X)
% 0.19/0.55
% 0.19/0.55 Lemma 20: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.55 = { by lemma 18 R->L }
% 0.19/0.55 multiply(X, multiply(inverse(multiply(Z, multiply(W, V))), multiply(Z, multiply(W, V))))
% 0.19/0.55 = { by lemma 4 R->L }
% 0.19/0.55 multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))))
% 0.19/0.55 = { by lemma 13 R->L }
% 0.19/0.55 multiply(S, multiply(inverse(S), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))))
% 0.19/0.55 = { by lemma 15 }
% 0.19/0.55 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 X
% 0.19/0.55
% 0.19/0.55 Lemma 21: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 0.19/0.55 Proof:
% 0.19/0.55 inverse(multiply(inverse(multiply(X, Y)), X))
% 0.19/0.55 = { by lemma 19 }
% 0.19/0.55 multiply(inverse(X), multiply(X, Y))
% 0.19/0.55 = { by lemma 15 R->L }
% 0.19/0.55 multiply(inverse(multiply(X, multiply(inverse(X), X))), multiply(X, Y))
% 0.19/0.55 = { by lemma 16 }
% 0.19/0.55 multiply(Z, multiply(inverse(Z), Y))
% 0.19/0.55 = { by lemma 15 }
% 0.19/0.55 Y
% 0.19/0.55
% 0.19/0.55 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(multiply(a3, b3), c3)
% 0.19/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.55 multiply(multiply(a3, b3), inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))))
% 0.19/0.55 = { by lemma 21 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))), inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))))), inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))))
% 0.19/0.55 = { by lemma 8 R->L }
% 0.19/0.55 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))), inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))))), inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))))), inverse(multiply(inverse(Y), Y)))))
% 0.19/0.55 = { by lemma 21 }
% 0.19/0.55 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), inverse(multiply(inverse(Y), Y)))))
% 0.19/0.55 = { by lemma 19 }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), inverse(multiply(inverse(Y), Y)))), inverse(multiply(inverse(X), X)))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(inverse(Z), Z))), inverse(multiply(inverse(X), X)))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 0.19/0.55 = { by lemma 18 }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(V, inverse(V)))), multiply(inverse(W), W))
% 0.19/0.55 = { by lemma 18 }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(V, inverse(V)))), multiply(U, inverse(U)))
% 0.19/0.55 = { by lemma 20 }
% 0.19/0.55 inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(V, inverse(V))))
% 0.19/0.55 = { by lemma 20 }
% 0.19/0.55 inverse(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))))
% 0.19/0.55 = { by lemma 17 }
% 0.19/0.55 multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))
% 0.19/0.55 = { by lemma 19 }
% 0.19/0.55 multiply(a3, multiply(inverse(multiply(inverse(b3), inverse(multiply(inverse(b3), b3)))), c3))
% 0.19/0.55 = { by lemma 19 }
% 0.19/0.55 multiply(a3, multiply(multiply(inverse(inverse(multiply(inverse(b3), b3))), b3), c3))
% 0.19/0.55 = { by lemma 17 }
% 0.19/0.55 multiply(a3, multiply(multiply(multiply(inverse(b3), b3), b3), c3))
% 0.19/0.55 = { by lemma 14 }
% 0.19/0.55 multiply(a3, multiply(b3, c3))
% 0.19/0.55 % SZS output end Proof
% 0.19/0.55
% 0.19/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------