TSTP Solution File: GRP428-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP428-1 : 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 : n002.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 01:18:23 EDT 2023
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP428-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % 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 : n002.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 : Tue Aug 29 02:27:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Command-line arguments: --no-flatten-goal
% 0.20/0.48
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48
% 0.20/0.54 % SZS output start Proof
% 0.20/0.54 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(inverse(X), Z))), W), inverse(multiply(Y, W))))) = Z.
% 0.20/0.54
% 0.20/0.54 Lemma 2: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W)))) = multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), Z)), U), inverse(multiply(V, U))))).
% 0.20/0.54 Proof:
% 0.20/0.54 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W))))
% 0.20/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.54 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(Y), inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W))))))), U), inverse(multiply(V, U)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), Z)), U), inverse(multiply(V, U)))))
% 0.20/0.55
% 0.20/0.55 Lemma 3: multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), W), inverse(multiply(Y, W)))))) = Z.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), W), inverse(multiply(Y, W))))))
% 0.20/0.55 = { by lemma 2 R->L }
% 0.20/0.55 multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 Z
% 0.20/0.55
% 0.20/0.55 Lemma 4: multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(W, Z)))))) = multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U))))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(W, Z))))))
% 0.20/0.55 = { by lemma 3 R->L }
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U))))))), Z), inverse(multiply(W, Z))))))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U)))))
% 0.20/0.55
% 0.20/0.55 Lemma 5: multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(X), Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V)))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(X), Z)))))
% 0.20/0.55 = { by lemma 3 R->L }
% 0.20/0.55 multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)), multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))))), Z), inverse(multiply(inverse(X), Z)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))
% 0.20/0.55
% 0.20/0.55 Lemma 6: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Z), W)), V), inverse(multiply(Z, V))))))) = multiply(inverse(inverse(Y)), W).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Z), W)), V), inverse(multiply(Z, V)))))))
% 0.20/0.55 = { by lemma 2 R->L }
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(U), multiply(inverse(inverse(Y)), W))), T), inverse(multiply(U, T))))))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), multiply(inverse(U), multiply(inverse(inverse(Y)), W)))), X2), inverse(multiply(S, X2)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(inverse(inverse(Y)), W)
% 0.20/0.55
% 0.20/0.55 Lemma 7: multiply(inverse(inverse(X)), multiply(inverse(X), Y)) = multiply(inverse(Z), multiply(Z, Y)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(inverse(X)), multiply(inverse(X), Y))
% 0.20/0.55 = { by lemma 6 R->L }
% 0.20/0.55 multiply(inverse(Z), multiply(Z, multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), Y))), V), inverse(multiply(W, V)))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(inverse(Z), multiply(Z, Y))
% 0.20/0.55
% 0.20/0.55 Lemma 8: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), multiply(Y, Z)))), W), inverse(multiply(X, W)))) = Z.
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), multiply(Y, Z)))), W), inverse(multiply(X, W))))
% 0.20/0.55 = { by lemma 5 R->L }
% 0.20/0.55 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(Y, Z))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.55 = { by lemma 7 R->L }
% 0.20/0.55 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(inverse(V)), multiply(inverse(V), Z))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 Z
% 0.20/0.55
% 0.20/0.55 Lemma 9: multiply(inverse(Z), multiply(Z, Y)) = multiply(inverse(X), multiply(X, Y)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(Z), multiply(Z, Y))
% 0.20/0.55 = { by lemma 3 R->L }
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(Z), multiply(Z, Y)))), V), inverse(multiply(W, V))))))
% 0.20/0.55 = { by lemma 8 }
% 0.20/0.55 multiply(inverse(X), multiply(X, Y))
% 0.20/0.55
% 0.20/0.55 Lemma 10: multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(Z), W), inverse(multiply(X, W))))))) = Z.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(Z), W), inverse(multiply(X, W)))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))), W), inverse(multiply(X, W)))))))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 Z
% 0.20/0.55
% 0.20/0.55 Lemma 11: multiply(multiply(inverse(X), W), inverse(multiply(Z, W))) = multiply(multiply(inverse(X), Y), inverse(multiply(Z, Y))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(multiply(inverse(X), W), inverse(multiply(Z, W)))
% 0.20/0.55 = { by lemma 3 R->L }
% 0.20/0.55 multiply(multiply(inverse(multiply(inverse(T2), multiply(T2, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), W), inverse(multiply(Z, W)))
% 0.20/0.55 = { by lemma 9 }
% 0.20/0.55 multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), W), inverse(multiply(Z, W)))
% 0.20/0.55 = { by lemma 10 R->L }
% 0.20/0.55 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), W), inverse(multiply(Z, W)))), X2), inverse(multiply(T, X2)))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(Y2)), inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(inverse(inverse(inverse(Y2))), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U)))))))), W2), inverse(multiply(Z2, W2))))))), W), inverse(multiply(Z, W)))), X2), inverse(multiply(T, X2)))))))
% 0.20/0.55 = { by lemma 2 }
% 0.20/0.55 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(V2), inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(inverse(inverse(inverse(Y2))), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U)))))))), W2), inverse(multiply(Z2, W2)))))), U2), inverse(multiply(V2, U2))))), X2), inverse(multiply(T, X2)))))))
% 0.20/0.55 = { by lemma 2 R->L }
% 0.20/0.55 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(Y2)), inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(inverse(inverse(inverse(Y2))), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U)))))))), W2), inverse(multiply(Z2, W2))))))), Y), inverse(multiply(Z, Y)))), X2), inverse(multiply(T, X2)))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), Y), inverse(multiply(Z, Y)))), X2), inverse(multiply(T, X2)))))))
% 0.20/0.55 = { by lemma 10 }
% 0.20/0.55 multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), Y), inverse(multiply(Z, Y)))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 multiply(multiply(inverse(X), Y), inverse(multiply(Z, Y)))
% 0.20/0.55
% 0.20/0.55 Lemma 12: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(Y, inverse(Y))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(multiply(S, inverse(multiply(multiply(inverse(multiply(inverse(Y2), multiply(inverse(S), Y))), Z2), inverse(multiply(Y2, Z2))))), inverse(Y))
% 0.20/0.55 = { by lemma 4 R->L }
% 0.20/0.55 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2)))))), inverse(Y))
% 0.20/0.55 = { by lemma 3 R->L }
% 0.20/0.55 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2)))))), inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2))))))))
% 0.20/0.55 = { by lemma 11 R->L }
% 0.20/0.55 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T)))))), inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T))))))))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T)))))), inverse(X))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(Z), X))), V), inverse(multiply(W, V))))), inverse(X))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(X, inverse(X))
% 0.20/0.55
% 0.20/0.55 Lemma 13: multiply(inverse(Z), multiply(Z, inverse(X))) = multiply(inverse(X), multiply(Y, inverse(Y))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(Z), multiply(Z, inverse(X)))
% 0.20/0.55 = { by lemma 9 }
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(X)))
% 0.20/0.55 = { by lemma 12 R->L }
% 0.20/0.55 multiply(inverse(X), multiply(Y, inverse(Y)))
% 0.20/0.55
% 0.20/0.55 Lemma 14: multiply(inverse(X), multiply(X, Y)) = multiply(Y, multiply(Z, inverse(Z))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, Y))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(W), multiply(inverse(X), multiply(X, Y))))), U), inverse(multiply(V, U)))))
% 0.20/0.55 = { by lemma 4 R->L }
% 0.20/0.55 multiply(inverse(T), multiply(T, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), S), inverse(multiply(W, S))))))
% 0.20/0.55 = { by lemma 13 }
% 0.20/0.55 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), S), inverse(multiply(W, S)))), multiply(Z, inverse(Z)))
% 0.20/0.55 = { by lemma 8 }
% 0.20/0.55 multiply(Y, multiply(Z, inverse(Z)))
% 0.20/0.55
% 0.20/0.55 Lemma 15: inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))) = multiply(Y, inverse(multiply(W, inverse(W)))).
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))))
% 0.20/0.55 = { by lemma 5 R->L }
% 0.20/0.55 multiply(Y, inverse(multiply(multiply(inverse(Y), V), inverse(multiply(inverse(Y), V)))))
% 0.20/0.55 = { by lemma 12 R->L }
% 0.20/0.55 multiply(Y, inverse(multiply(W, inverse(W))))
% 0.20/0.55
% 0.20/0.55 Lemma 16: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z)))))) = Y.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z))))))
% 0.20/0.55 = { by lemma 14 }
% 0.20/0.55 multiply(multiply(Y, inverse(multiply(Z, inverse(Z)))), multiply(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))), inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))))
% 0.20/0.55 = { by lemma 15 R->L }
% 0.20/0.55 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V)))), multiply(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))), inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(U), multiply(inverse(W), Y))), T), inverse(multiply(U, T)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 Y
% 0.20/0.55
% 0.20/0.55 Lemma 17: multiply(inverse(X), multiply(X, multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, multiply(Y, inverse(Y))))
% 0.20/0.55 = { by lemma 12 }
% 0.20/0.55 multiply(inverse(X), multiply(X, multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z))))))
% 0.20/0.55 = { by lemma 16 }
% 0.20/0.55 multiply(Z, inverse(Z))
% 0.20/0.55
% 0.20/0.55 Lemma 18: multiply(inverse(X), multiply(X, inverse(multiply(Y, inverse(Y))))) = multiply(Z, inverse(Z)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(multiply(Y, inverse(Y)))))
% 0.20/0.55 = { by lemma 13 }
% 0.20/0.55 multiply(inverse(multiply(Y, inverse(Y))), multiply(W, inverse(W)))
% 0.20/0.55 = { by lemma 17 R->L }
% 0.20/0.55 multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(V), multiply(V, multiply(Y, inverse(Y)))))
% 0.20/0.55 = { by lemma 14 }
% 0.20/0.55 multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(Y, inverse(Y)), multiply(U, inverse(U))))
% 0.20/0.55 = { by lemma 17 }
% 0.20/0.55 multiply(Z, inverse(Z))
% 0.20/0.55
% 0.20/0.55 Lemma 19: multiply(inverse(X), multiply(X, inverse(inverse(Y)))) = Y.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(X, inverse(inverse(Y))))
% 0.20/0.55 = { by lemma 13 }
% 0.20/0.55 multiply(inverse(inverse(Y)), multiply(Z, inverse(Z)))
% 0.20/0.55 = { by lemma 18 R->L }
% 0.20/0.55 multiply(inverse(inverse(Y)), multiply(inverse(W), multiply(W, inverse(multiply(V, inverse(V))))))
% 0.20/0.55 = { by lemma 6 R->L }
% 0.20/0.55 multiply(inverse(U), multiply(U, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(W), multiply(W, inverse(multiply(V, inverse(V))))))), S), inverse(multiply(T, S)))))))
% 0.20/0.55 = { by lemma 8 }
% 0.20/0.55 multiply(inverse(U), multiply(U, multiply(Y, inverse(multiply(V, inverse(V))))))
% 0.20/0.55 = { by lemma 16 }
% 0.20/0.55 Y
% 0.20/0.55
% 0.20/0.55 Lemma 20: inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))) = inverse(inverse(Y)).
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))))
% 0.20/0.55 = { by lemma 19 R->L }
% 0.20/0.55 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(W), multiply(W, inverse(inverse(Y)))))), Z), inverse(multiply(X, Z))))
% 0.20/0.55 = { by lemma 8 }
% 0.20/0.55 inverse(inverse(Y))
% 0.20/0.55
% 0.20/0.55 Lemma 21: multiply(inverse(inverse(inverse(X))), X) = multiply(Y, inverse(Y)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(inverse(inverse(X))), X)
% 0.20/0.55 = { by lemma 19 R->L }
% 0.20/0.55 multiply(inverse(inverse(inverse(X))), multiply(inverse(inverse(X)), multiply(inverse(X), inverse(inverse(X)))))
% 0.20/0.55 = { by lemma 17 }
% 0.20/0.55 multiply(Y, inverse(Y))
% 0.20/0.55
% 0.20/0.55 Lemma 22: inverse(inverse(inverse(inverse(X)))) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(inverse(inverse(inverse(X))))
% 0.20/0.55 = { by lemma 20 R->L }
% 0.20/0.55 inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))
% 0.20/0.55 = { by lemma 19 R->L }
% 0.20/0.55 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z)))))))), multiply(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))), inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))))))
% 0.20/0.55 = { by lemma 21 R->L }
% 0.20/0.55 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z)))))))), multiply(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))), inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 23: multiply(inverse(X), multiply(X, Y)) = inverse(inverse(Y)).
% 0.20/0.55 Proof:
% 0.20/0.56 multiply(inverse(X), multiply(X, Y))
% 0.20/0.56 = { by lemma 7 R->L }
% 0.20/0.56 multiply(inverse(inverse(inverse(inverse(Y)))), multiply(inverse(inverse(inverse(Y))), Y))
% 0.20/0.56 = { by lemma 21 }
% 0.20/0.56 multiply(inverse(inverse(inverse(inverse(Y)))), multiply(inverse(inverse(inverse(Y))), inverse(inverse(inverse(inverse(Y))))))
% 0.20/0.56 = { by lemma 19 }
% 0.20/0.56 inverse(inverse(Y))
% 0.20/0.56
% 0.20/0.56 Lemma 24: multiply(inverse(multiply(X, Y)), X) = inverse(inverse(inverse(Y))).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(inverse(multiply(X, Y)), X)
% 0.20/0.56 = { by lemma 22 R->L }
% 0.20/0.56 inverse(inverse(inverse(inverse(multiply(inverse(multiply(X, Y)), X)))))
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 inverse(multiply(multiply(inverse(multiply(inverse(Z), inverse(inverse(multiply(inverse(multiply(X, Y)), X))))), W), inverse(multiply(Z, W))))
% 0.20/0.56 = { by lemma 5 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(X, Y)), X)))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(multiply(X, Y)), X))), S), inverse(multiply(T, S))))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 22 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(inverse(inverse(inverse(inverse(multiply(X, Y)))))), X))), S), inverse(multiply(T, S))))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 2 }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(X, Y)))), inverse(multiply(multiply(inverse(multiply(inverse(X2), X)), Y2), inverse(multiply(X2, Y2)))))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(X, Y)))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 23 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), Y), inverse(multiply(X, Y)))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 8 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(W2), multiply(inverse(V2), multiply(V2, inverse(Z2))))), U2), inverse(multiply(W2, U2)))), Y), inverse(multiply(X, Y)))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 11 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(W2), multiply(inverse(V2), multiply(V2, inverse(Z2))))), U2), inverse(multiply(W2, U2)))), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 16 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(multiply(inverse(T2), multiply(T2, multiply(inverse(X), inverse(multiply(S2, inverse(S2))))))))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(multiply(inverse(T2), multiply(T2, inverse(multiply(multiply(inverse(multiply(inverse(Z2), inverse(X))), X3), inverse(multiply(Z2, X3))))))))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 4 }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(multiply(Z2, inverse(multiply(multiply(inverse(multiply(inverse(Y3), multiply(inverse(Z2), inverse(X)))), Z3), inverse(multiply(Y3, Z3)))))))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 15 }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(multiply(Z2, multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X)))))))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 multiply(V, inverse(multiply(multiply(inverse(inverse(Y)), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.56 = { by lemma 5 }
% 0.20/0.56 inverse(multiply(multiply(inverse(multiply(inverse(W3), inverse(Y))), V3), inverse(multiply(W3, V3))))
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 inverse(inverse(inverse(Y)))
% 0.20/0.56
% 0.20/0.56 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(inverse(b2), b2), a2)
% 0.20/0.56 = { by lemma 22 R->L }
% 0.20/0.56 multiply(multiply(inverse(b2), inverse(inverse(inverse(inverse(b2))))), a2)
% 0.20/0.56 = { by lemma 24 R->L }
% 0.20/0.56 multiply(multiply(inverse(b2), multiply(inverse(multiply(multiply(X, b2), inverse(b2))), multiply(X, b2))), a2)
% 0.20/0.56 = { by lemma 22 R->L }
% 0.20/0.56 multiply(multiply(inverse(b2), multiply(inverse(multiply(multiply(X, b2), inverse(inverse(inverse(inverse(inverse(b2))))))), multiply(X, b2))), a2)
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 multiply(multiply(inverse(b2), multiply(inverse(multiply(multiply(X, b2), inverse(multiply(multiply(inverse(multiply(inverse(Y), inverse(inverse(inverse(b2))))), Z), inverse(multiply(Y, Z)))))), multiply(X, b2))), a2)
% 0.20/0.56 = { by lemma 24 R->L }
% 0.20/0.56 multiply(multiply(inverse(b2), multiply(inverse(multiply(multiply(X, b2), inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(inverse(multiply(X, b2)), X))), Z), inverse(multiply(Y, Z)))))), multiply(X, b2))), a2)
% 0.20/0.56 = { by axiom 1 (single_axiom) }
% 0.20/0.56 multiply(multiply(inverse(b2), multiply(inverse(X), multiply(X, b2))), a2)
% 0.20/0.56 = { by lemma 23 }
% 0.20/0.56 multiply(multiply(inverse(b2), inverse(inverse(b2))), a2)
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 multiply(multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))), a2)
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(W, inverse(W)))), U), inverse(multiply(V, U)))), a2)
% 0.20/0.56 = { by lemma 18 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(T), multiply(T, inverse(multiply(a2, inverse(a2))))))), U), inverse(multiply(V, U)))), a2)
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 multiply(inverse(multiply(a2, inverse(a2))), a2)
% 0.20/0.56 = { by lemma 24 }
% 0.20/0.56 inverse(inverse(inverse(inverse(a2))))
% 0.20/0.56 = { by lemma 22 }
% 0.20/0.56 a2
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------