TSTP Solution File: GRP438-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP438-1 : 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 : n017.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 01:18:26 EDT 2023
% Result : Unsatisfiable 0.20s 0.65s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP438-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 22:30:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.65 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.65
% 0.20/0.65 % SZS status Unsatisfiable
% 0.20/0.65
% 0.20/0.71 % SZS output start Proof
% 0.20/0.71 Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), X))))) = W.
% 0.20/0.71
% 0.20/0.71 Lemma 2: multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X))))) = W.
% 0.20/0.71 Proof:
% 0.20/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X)))))
% 0.20/0.71 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(W, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V)))))), X)))))
% 0.20/0.71 = { by axiom 1 (single_axiom) }
% 0.20/0.71 W
% 0.20/0.71
% 0.20/0.71 Lemma 3: multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(W))), multiply(W, multiply(V, X))))) = multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y))).
% 0.20/0.71 Proof:
% 0.20/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(W))), multiply(W, multiply(V, X)))))
% 0.20/0.71 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y)))))), inverse(W))), multiply(W, multiply(V, X)))))
% 0.20/0.71 = { by lemma 2 }
% 0.20/0.71 multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y)))
% 0.20/0.71
% 0.20/0.71 Lemma 4: multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y))) = W.
% 0.20/0.71 Proof:
% 0.20/0.71 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y)))
% 0.20/0.71 = { by lemma 3 R->L }
% 0.20/0.71 multiply(V, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(U))), multiply(U, multiply(Z, V)))))
% 0.20/0.71 = { by lemma 2 }
% 0.20/0.71 W
% 0.20/0.71
% 0.20/0.71 Lemma 5: multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V))) = W.
% 0.20/0.71 Proof:
% 0.20/0.71 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V)))
% 0.20/0.71 = { by lemma 3 R->L }
% 0.20/0.71 multiply(U, inverse(multiply(multiply(V, multiply(Y, inverse(Z))), multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z)))))), U)))))
% 0.20/0.71 = { by axiom 1 (single_axiom) }
% 0.20/0.71 W
% 0.20/0.71
% 0.20/0.71 Lemma 6: multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), Z))) = W.
% 0.20/0.71 Proof:
% 0.20/0.71 multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), Z)))
% 0.20/0.71 = { by lemma 5 R->L }
% 0.20/0.71 multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(W, multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y))))))))), inverse(X))))))
% 0.20/0.71 = { by axiom 1 (single_axiom) }
% 0.20/0.71 W
% 0.20/0.71
% 0.20/0.71 Lemma 7: inverse(multiply(multiply(inverse(X), inverse(multiply(W, Z))), W)) = inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y)).
% 0.20/0.71 Proof:
% 0.20/0.71 inverse(multiply(multiply(inverse(X), inverse(multiply(W, Z))), W))
% 0.20/0.71 = { by lemma 2 R->L }
% 0.20/0.71 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(W, Z))), W))))), inverse(S))), multiply(S, multiply(inverse(T), V)))))
% 0.20/0.71 = { by lemma 4 R->L }
% 0.20/0.71 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(W, multiply(T, multiply(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X)))))), W))))), inverse(S))), multiply(S, multiply(inverse(T), V)))))
% 0.20/0.71 = { by lemma 6 }
% 0.20/0.71 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))))), inverse(S))), multiply(S, multiply(inverse(T), V)))))
% 0.20/0.71 = { by lemma 2 }
% 0.20/0.71 inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))
% 0.20/0.71
% 0.20/0.71 Lemma 8: inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), X))))), Y)) = W.
% 0.20/0.71 Proof:
% 0.20/0.71 inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), X))))), Y))
% 0.20/0.72 = { by lemma 2 R->L }
% 0.20/0.72 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(Z), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), X))))), Y))))), inverse(T))), multiply(T, multiply(inverse(Z), V)))))
% 0.20/0.72 = { by lemma 5 R->L }
% 0.20/0.72 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(Z), inverse(multiply(multiply(X, inverse(multiply(multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(inverse(Z), W), multiply(inverse(X2), inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(X2))))))))), inverse(Z))), multiply(Z, multiply(multiply(inverse(Z), W), X))))), Y))))), inverse(T))), multiply(T, multiply(inverse(Z), V)))))
% 0.20/0.72 = { by lemma 2 }
% 0.20/0.72 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(Z), inverse(multiply(multiply(inverse(X2), inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(X2)))))), Y))))), inverse(T))), multiply(T, multiply(inverse(Z), V)))))
% 0.20/0.72 = { by lemma 6 }
% 0.20/0.72 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(Z), W))), inverse(T))), multiply(T, multiply(inverse(Z), V)))))
% 0.20/0.72 = { by lemma 3 }
% 0.20/0.72 multiply(Y2, multiply(multiply(inverse(Y2), inverse(multiply(multiply(inverse(U), inverse(multiply(inverse(Z), W))), inverse(Z)))), inverse(U)))
% 0.20/0.72 = { by lemma 4 }
% 0.20/0.72 W
% 0.20/0.72
% 0.20/0.72 Lemma 9: multiply(W, multiply(multiply(inverse(W), Y), inverse(Z))) = multiply(X, multiply(multiply(inverse(X), Y), inverse(Z))).
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(W, multiply(multiply(inverse(W), Y), inverse(Z)))
% 0.20/0.72 = { by lemma 8 R->L }
% 0.20/0.72 multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(Z), inverse(multiply(U, multiply(X, multiply(multiply(inverse(X), Y), inverse(Z)))))), U))), inverse(Z)))
% 0.20/0.72 = { by lemma 3 R->L }
% 0.20/0.72 multiply(V, inverse(multiply(multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(U, multiply(X, multiply(multiply(inverse(X), Y), inverse(Z)))))), inverse(T))), multiply(T, multiply(U, V)))))
% 0.20/0.72 = { by lemma 2 }
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), Y), inverse(Z)))
% 0.20/0.72
% 0.20/0.72 Lemma 10: multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), inverse(multiply(W, Y))), W))), inverse(multiply(inverse(V), Z)))) = V.
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), inverse(multiply(W, Y))), W))), inverse(multiply(inverse(V), Z))))
% 0.20/0.72 = { by lemma 7 }
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), inverse(multiply(multiply(inverse(U), inverse(multiply(Y, multiply(multiply(inverse(Y), Z), multiply(T, inverse(U)))))), Y))), multiply(inverse(U), inverse(multiply(Y, multiply(multiply(inverse(Y), Z), multiply(T, inverse(U))))))))), inverse(multiply(inverse(V), Z))))
% 0.20/0.72 = { by lemma 6 }
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(U), inverse(multiply(Y, multiply(multiply(inverse(Y), Z), multiply(T, inverse(U))))))))), inverse(multiply(inverse(V), Z))))
% 0.20/0.72 = { by lemma 8 R->L }
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(U), inverse(multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(multiply(S, inverse(multiply(X2, multiply(Y2, multiply(multiply(inverse(Y2), multiply(T, inverse(U))), S))))), X2))))))))), inverse(multiply(inverse(V), Z))))
% 0.20/0.72 = { by lemma 9 }
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(U), inverse(multiply(V, multiply(multiply(inverse(V), Z), inverse(multiply(multiply(S, inverse(multiply(X2, multiply(Y2, multiply(multiply(inverse(Y2), multiply(T, inverse(U))), S))))), X2))))))))), inverse(multiply(inverse(V), Z))))
% 0.20/0.72 = { by lemma 8 }
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(U), inverse(multiply(V, multiply(multiply(inverse(V), Z), multiply(T, inverse(U))))))))), inverse(multiply(inverse(V), Z))))
% 0.20/0.72 = { by lemma 5 }
% 0.20/0.72 V
% 0.20/0.72
% 0.20/0.72 Lemma 11: multiply(multiply(X, inverse(multiply(W, Z))), W) = multiply(multiply(X, inverse(multiply(Y, Z))), Y).
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(multiply(X, inverse(multiply(W, Z))), W)
% 0.20/0.72 = { by lemma 10 R->L }
% 0.20/0.72 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(multiply(inverse(U), T)), inverse(multiply(S, U))), S))), inverse(multiply(inverse(multiply(multiply(X, inverse(multiply(W, Z))), W)), T))))
% 0.20/0.72 = { by lemma 8 R->L }
% 0.20/0.72 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(multiply(inverse(U), T)), inverse(multiply(S, U))), S))), inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(X2, inverse(multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), X), X2))))), Y2)), inverse(multiply(W, Z))), W)), T))))
% 0.20/0.72 = { by lemma 7 }
% 0.20/0.72 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(multiply(inverse(U), T)), inverse(multiply(S, U))), S))), inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(X2, inverse(multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), X), X2))))), Y2)), inverse(multiply(Y, Z))), Y)), T))))
% 0.20/0.72 = { by lemma 8 }
% 0.20/0.72 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(multiply(inverse(U), T)), inverse(multiply(S, U))), S))), inverse(multiply(inverse(multiply(multiply(X, inverse(multiply(Y, Z))), Y)), T))))
% 0.20/0.72 = { by lemma 10 }
% 0.20/0.72 multiply(multiply(X, inverse(multiply(Y, Z))), Y)
% 0.20/0.72
% 0.20/0.72 Lemma 12: multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), W))))) = X.
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), W)))))
% 0.20/0.72 = { by lemma 11 }
% 0.20/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(X, Y))), X)))))
% 0.20/0.72 = { by axiom 1 (single_axiom) }
% 0.20/0.72 X
% 0.20/0.72
% 0.20/0.72 Lemma 13: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(Y, inverse(Y))
% 0.20/0.72 = { by lemma 12 R->L }
% 0.20/0.72 multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))))
% 0.20/0.72 = { by lemma 12 R->L }
% 0.20/0.72 multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))), inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(S, U))), S))))))
% 0.20/0.72 = { by lemma 9 }
% 0.20/0.72 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))), inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(S, U))), S))))))
% 0.20/0.72 = { by lemma 12 }
% 0.20/0.72 multiply(X, multiply(inverse(X), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))))
% 0.20/0.72 = { by lemma 12 }
% 0.20/0.72 multiply(X, inverse(X))
% 0.20/0.72
% 0.20/0.72 Lemma 14: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.20/0.72 = { by lemma 2 R->L }
% 0.20/0.72 multiply(X, inverse(multiply(Y, multiply(Z, inverse(multiply(multiply(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V), multiply(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V)), inverse(multiply(Y, inverse(Y)))), inverse(T))), multiply(T, multiply(Y, Z))))))))
% 0.20/0.72 = { by lemma 8 }
% 0.20/0.72 multiply(X, inverse(multiply(Y, multiply(Z, inverse(multiply(multiply(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), inverse(T))), multiply(T, multiply(Y, Z))))))))
% 0.20/0.72 = { by lemma 3 }
% 0.20/0.72 multiply(X, inverse(multiply(Y, multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), Y))), inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V)))))))
% 0.20/0.72 = { by lemma 8 }
% 0.20/0.72 multiply(X, inverse(multiply(Y, multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), Y))), multiply(Y, inverse(Y)))))))
% 0.20/0.72 = { by lemma 13 R->L }
% 0.20/0.72 multiply(X, inverse(multiply(Y, multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(Y, inverse(Y)), Y))), multiply(Y, inverse(Y)))))))
% 0.20/0.72 = { by lemma 12 }
% 0.20/0.72 X
% 0.20/0.72
% 0.20/0.72 Lemma 15: multiply(multiply(X, inverse(Z)), Z) = multiply(multiply(X, inverse(Y)), Y).
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(multiply(X, inverse(Z)), Z)
% 0.20/0.72 = { by lemma 12 R->L }
% 0.20/0.72 multiply(multiply(X, inverse(multiply(Z, inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), inverse(multiply(U, W))), U))))))), Z)
% 0.20/0.72 = { by lemma 11 }
% 0.20/0.72 multiply(multiply(X, inverse(multiply(Y, inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), inverse(multiply(U, W))), U))))))), Y)
% 0.20/0.72 = { by lemma 12 }
% 0.20/0.72 multiply(multiply(X, inverse(Y)), Y)
% 0.20/0.72
% 0.20/0.72 Lemma 16: multiply(multiply(Z, inverse(Z)), X) = multiply(multiply(X, inverse(Y)), Y).
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(multiply(Z, inverse(Z)), X)
% 0.20/0.72 = { by lemma 13 }
% 0.20/0.72 multiply(multiply(X, inverse(X)), X)
% 0.20/0.72 = { by lemma 15 R->L }
% 0.20/0.72 multiply(multiply(X, inverse(Y)), Y)
% 0.20/0.72
% 0.20/0.72 Lemma 17: multiply(multiply(X, inverse(multiply(W, inverse(W)))), Z) = multiply(multiply(X, inverse(multiply(Y, inverse(Z)))), Y).
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(multiply(X, inverse(multiply(W, inverse(W)))), Z)
% 0.20/0.72 = { by lemma 13 }
% 0.20/0.72 multiply(multiply(X, inverse(multiply(Z, inverse(Z)))), Z)
% 0.20/0.72 = { by lemma 11 R->L }
% 0.20/0.72 multiply(multiply(X, inverse(multiply(Y, inverse(Z)))), Y)
% 0.20/0.72
% 0.20/0.72 Lemma 18: multiply(multiply(X, inverse(multiply(Y, multiply(Z, inverse(Z))))), Y) = X.
% 0.20/0.72 Proof:
% 0.20/0.72 multiply(multiply(X, inverse(multiply(Y, multiply(Z, inverse(Z))))), Y)
% 0.20/0.72 = { by lemma 14 R->L }
% 0.20/0.72 multiply(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(Z, inverse(Z)))), multiply(Z, inverse(Z))))), Y)
% 0.20/0.72 = { by lemma 16 R->L }
% 0.20/0.72 multiply(multiply(X, inverse(multiply(multiply(W, inverse(W)), Y))), Y)
% 0.20/0.72 = { by lemma 16 }
% 0.20/0.73 multiply(multiply(X, inverse(multiply(multiply(Y, inverse(inverse(multiply(V, inverse(V))))), inverse(multiply(V, inverse(V)))))), Y)
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 multiply(multiply(X, inverse(multiply(Y, inverse(inverse(multiply(V, inverse(V))))))), Y)
% 0.20/0.73 = { by lemma 17 R->L }
% 0.20/0.73 multiply(multiply(X, inverse(multiply(U, inverse(U)))), inverse(multiply(V, inverse(V))))
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 multiply(X, inverse(multiply(U, inverse(U))))
% 0.20/0.73 = { by lemma 14 }
% 0.20/0.73 X
% 0.20/0.73
% 0.20/0.73 Lemma 19: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(X, multiply(Y, inverse(Y)))
% 0.20/0.73 = { by lemma 10 R->L }
% 0.20/0.73 multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(multiply(inverse(W), V)), inverse(multiply(U, W))), U))), inverse(multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), V))))
% 0.20/0.73 = { by lemma 8 R->L }
% 0.20/0.73 multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(multiply(inverse(W), V)), inverse(multiply(U, W))), U))), inverse(multiply(inverse(multiply(multiply(X, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), T)), V))))
% 0.20/0.73 = { by lemma 10 }
% 0.20/0.73 multiply(multiply(X, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), T)
% 0.20/0.73 = { by lemma 18 }
% 0.20/0.73 multiply(multiply(X, inverse(multiply(T, multiply(S, inverse(S))))), T)
% 0.20/0.73 = { by lemma 18 }
% 0.20/0.73 X
% 0.20/0.73
% 0.20/0.73 Lemma 20: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(multiply(X, inverse(X)), Y)
% 0.20/0.73 = { by lemma 16 }
% 0.20/0.73 multiply(multiply(Y, inverse(Z)), Z)
% 0.20/0.73 = { by lemma 19 R->L }
% 0.20/0.73 multiply(multiply(Y, inverse(multiply(Z, multiply(W, inverse(W))))), Z)
% 0.20/0.73 = { by lemma 18 }
% 0.20/0.73 Y
% 0.20/0.73
% 0.20/0.73 Lemma 21: multiply(multiply(X, Y), inverse(Y)) = X.
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(multiply(X, Y), inverse(Y))
% 0.20/0.73 = { by lemma 20 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Y), Y))), inverse(Y)))
% 0.20/0.73 = { by lemma 11 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(X, Y))), X))
% 0.20/0.73 = { by lemma 20 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(Y)), Y), inverse(multiply(X, Y))), X))
% 0.20/0.73 = { by lemma 15 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), multiply(Z, inverse(Z))), inverse(multiply(X, Y))), X))
% 0.20/0.73 = { by lemma 20 }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(X, Y))), X))
% 0.20/0.73 = { by lemma 20 }
% 0.20/0.73 multiply(multiply(X, Y), multiply(inverse(multiply(X, Y)), X))
% 0.20/0.73 = { by lemma 14 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(inverse(multiply(X, Y)), inverse(multiply(X, inverse(X)))), X))
% 0.20/0.73 = { by lemma 19 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(X, inverse(X)), multiply(W, inverse(W))))), X))
% 0.20/0.73 = { by lemma 8 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(X, inverse(X)), multiply(W, inverse(W))))), inverse(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), X), V))))), U))))
% 0.20/0.73 = { by lemma 8 R->L }
% 0.20/0.73 multiply(multiply(X, Y), multiply(multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(inverse(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), X), V))))), U)), inverse(X)), multiply(W, inverse(W))))), inverse(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), X), V))))), U))))
% 0.20/0.73 = { by lemma 3 R->L }
% 0.20/0.73 multiply(S, inverse(multiply(multiply(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), X), V))))), U), multiply(multiply(inverse(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), X), V))))), U)), inverse(X)), inverse(X2))), multiply(X2, multiply(multiply(W, inverse(W)), S)))))
% 0.20/0.73 = { by lemma 20 R->L }
% 0.20/0.73 multiply(S, inverse(multiply(multiply(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), X), V))))), U), multiply(multiply(inverse(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), X), V))))), U)), inverse(multiply(multiply(W, inverse(W)), X))), inverse(X2))), multiply(X2, multiply(multiply(W, inverse(W)), S)))))
% 0.20/0.73 = { by lemma 2 }
% 0.20/0.73 X
% 0.20/0.73
% 0.20/0.73 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.73 Proof:
% 0.20/0.73 multiply(multiply(a3, b3), c3)
% 0.20/0.73 = { by lemma 14 R->L }
% 0.20/0.73 multiply(multiply(multiply(a3, b3), inverse(multiply(X, inverse(X)))), c3)
% 0.20/0.73 = { by lemma 17 }
% 0.20/0.73 multiply(multiply(multiply(a3, b3), inverse(multiply(multiply(b3, c3), inverse(c3)))), multiply(b3, c3))
% 0.20/0.73 = { by lemma 21 }
% 0.20/0.73 multiply(multiply(multiply(a3, b3), inverse(b3)), multiply(b3, c3))
% 0.20/0.73 = { by lemma 21 }
% 0.20/0.73 multiply(a3, multiply(b3, c3))
% 0.20/0.73 % SZS output end Proof
% 0.20/0.73
% 0.20/0.73 RESULT: Unsatisfiable (the axioms are contradictory).
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