TSTP Solution File: GRP499-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP499-1 : 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 : n022.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 01:18:40 EDT 2023
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP499-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % 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 : n022.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 19:55:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.52 Command-line arguments: --no-flatten-goal
% 0.20/0.52
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52
% 0.20/0.57 % SZS output start Proof
% 0.20/0.57 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.57 Axiom 2 (single_axiom): double_divide(inverse(X), inverse(double_divide(inverse(double_divide(X, double_divide(Y, Z))), double_divide(W, double_divide(Y, W))))) = Z.
% 0.20/0.57
% 0.20/0.57 Lemma 3: double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), multiply(double_divide(Z, W), X))) = W.
% 0.20/0.57 Proof:
% 0.20/0.57 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), multiply(double_divide(Z, W), X)))
% 0.20/0.57 = { by axiom 1 (multiply) }
% 0.20/0.57 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), inverse(double_divide(X, double_divide(Z, W)))))
% 0.20/0.57 = { by axiom 1 (multiply) }
% 0.20/0.57 double_divide(inverse(X), inverse(double_divide(inverse(double_divide(X, double_divide(Z, W))), double_divide(Y, double_divide(Z, Y)))))
% 0.20/0.57 = { by axiom 2 (single_axiom) }
% 0.20/0.57 W
% 0.20/0.57
% 0.20/0.57 Lemma 4: double_divide(inverse(X), multiply(double_divide(Y, double_divide(inverse(Z), Y)), multiply(W, X))) = multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, W), Z)).
% 0.20/0.57 Proof:
% 0.20/0.57 double_divide(inverse(X), multiply(double_divide(Y, double_divide(inverse(Z), Y)), multiply(W, X)))
% 0.20/0.57 = { by lemma 3 R->L }
% 0.20/0.57 double_divide(inverse(X), multiply(double_divide(Y, double_divide(inverse(Z), Y)), multiply(double_divide(inverse(Z), multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, W), Z))), X)))
% 0.20/0.57 = { by lemma 3 }
% 0.20/0.57 multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, W), Z))
% 0.20/0.57
% 0.20/0.57 Lemma 5: multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(inverse(Z), W)), Z)) = W.
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(inverse(Z), W)), Z))
% 0.20/0.57 = { by lemma 4 R->L }
% 0.20/0.57 double_divide(inverse(V), multiply(double_divide(U, double_divide(inverse(Z), U)), multiply(double_divide(inverse(Z), W), V)))
% 0.20/0.57 = { by lemma 3 }
% 0.20/0.57 W
% 0.20/0.57
% 0.20/0.57 Lemma 6: multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(Z, double_divide(W, Z))), V)) = double_divide(W, inverse(V)).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(Z, double_divide(W, Z))), V))
% 0.20/0.57 = { by lemma 4 R->L }
% 0.20/0.57 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(Z, double_divide(W, Z)), U)))
% 0.20/0.57 = { by lemma 5 R->L }
% 0.20/0.58 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))))
% 0.20/0.58 = { by lemma 3 R->L }
% 0.20/0.58 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), double_divide(inverse(Y2), multiply(double_divide(Z2, double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), Z2)), multiply(double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))), Y2)))))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), double_divide(inverse(Y2), multiply(double_divide(Z2, double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), Z2)), multiply(double_divide(S, W), Y2)))))
% 0.20/0.58 = { by lemma 3 R->L }
% 0.20/0.58 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), double_divide(inverse(Y2), multiply(double_divide(Z2, double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), Z2)), multiply(double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), multiply(double_divide(inverse(V), double_divide(W, inverse(V))), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))), Y2)))))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(inverse(V), double_divide(W, inverse(V))), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))))
% 0.20/0.58 = { by lemma 5 }
% 0.20/0.58 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(inverse(V), double_divide(W, inverse(V))), U)))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 double_divide(W, inverse(V))
% 0.20/0.58
% 0.20/0.58 Lemma 7: multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, Z), Z)) = double_divide(W, multiply(double_divide(W, V), V)).
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, Z), Z))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(Z, double_divide(Y, Z))))
% 0.20/0.58 = { by lemma 5 R->L }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(Z, double_divide(Y, multiply(double_divide(U, double_divide(T, U)), multiply(double_divide(T, double_divide(inverse(S), Z)), S))))))
% 0.20/0.58 = { by lemma 5 R->L }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(multiply(double_divide(U, double_divide(T, U)), multiply(double_divide(T, double_divide(inverse(S), Z)), S)), double_divide(Y, multiply(double_divide(U, double_divide(T, U)), multiply(double_divide(T, double_divide(inverse(S), Z)), S))))))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(multiply(double_divide(U, double_divide(T, U)), multiply(double_divide(T, double_divide(inverse(S), Z)), S)), double_divide(Y, inverse(double_divide(multiply(double_divide(T, double_divide(inverse(S), Z)), S), double_divide(U, double_divide(T, U))))))))
% 0.20/0.58 = { by lemma 6 R->L }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(multiply(double_divide(U, double_divide(T, U)), multiply(double_divide(T, double_divide(inverse(S), Z)), S)), multiply(double_divide(X2, double_divide(Y2, X2)), multiply(double_divide(Y2, double_divide(multiply(double_divide(Z2, double_divide(W2, Z2)), multiply(double_divide(W2, double_divide(inverse(V2), double_divide(V, double_divide(W, V)))), V2)), double_divide(Y, multiply(double_divide(Z2, double_divide(W2, Z2)), multiply(double_divide(W2, double_divide(inverse(V2), double_divide(V, double_divide(W, V)))), V2))))), double_divide(multiply(double_divide(T, double_divide(inverse(S), Z)), S), double_divide(U, double_divide(T, U))))))))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(inverse(double_divide(multiply(double_divide(T, double_divide(inverse(S), Z)), S), double_divide(U, double_divide(T, U)))), multiply(double_divide(X2, double_divide(Y2, X2)), multiply(double_divide(Y2, double_divide(multiply(double_divide(Z2, double_divide(W2, Z2)), multiply(double_divide(W2, double_divide(inverse(V2), double_divide(V, double_divide(W, V)))), V2)), double_divide(Y, multiply(double_divide(Z2, double_divide(W2, Z2)), multiply(double_divide(W2, double_divide(inverse(V2), double_divide(V, double_divide(W, V)))), V2))))), double_divide(multiply(double_divide(T, double_divide(inverse(S), Z)), S), double_divide(U, double_divide(T, U))))))))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(multiply(double_divide(Z2, double_divide(W2, Z2)), multiply(double_divide(W2, double_divide(inverse(V2), double_divide(V, double_divide(W, V)))), V2)), double_divide(Y, multiply(double_divide(Z2, double_divide(W2, Z2)), multiply(double_divide(W2, double_divide(inverse(V2), double_divide(V, double_divide(W, V)))), V2))))))
% 0.20/0.58 = { by lemma 5 }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(double_divide(V, double_divide(W, V)), double_divide(Y, multiply(double_divide(Z2, double_divide(W2, Z2)), multiply(double_divide(W2, double_divide(inverse(V2), double_divide(V, double_divide(W, V)))), V2))))))
% 0.20/0.58 = { by lemma 5 }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), inverse(double_divide(double_divide(V, double_divide(W, V)), double_divide(Y, double_divide(V, double_divide(W, V))))))
% 0.20/0.58 = { by axiom 1 (multiply) R->L }
% 0.20/0.58 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(V, double_divide(W, V))), double_divide(V, double_divide(W, V))))
% 0.20/0.58 = { by lemma 6 }
% 0.20/0.58 double_divide(W, inverse(double_divide(V, double_divide(W, V))))
% 0.20/0.58 = { by axiom 1 (multiply) R->L }
% 0.20/0.58 double_divide(W, multiply(double_divide(W, V), V))
% 0.20/0.58
% 0.20/0.58 Lemma 8: double_divide(inverse(X), double_divide(Y, multiply(double_divide(Y, Z), Z))) = X.
% 0.20/0.58 Proof:
% 0.20/0.58 double_divide(inverse(X), double_divide(Y, multiply(double_divide(Y, Z), Z)))
% 0.20/0.58 = { by lemma 7 R->L }
% 0.20/0.58 double_divide(inverse(X), multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, X), X)))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 X
% 0.20/0.58
% 0.20/0.58 Lemma 9: multiply(double_divide(X, multiply(double_divide(X, Y), Y)), inverse(Z)) = inverse(Z).
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), inverse(Z))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 inverse(double_divide(inverse(Z), double_divide(X, multiply(double_divide(X, Y), Y))))
% 0.20/0.58 = { by lemma 8 }
% 0.20/0.58 inverse(Z)
% 0.20/0.58
% 0.20/0.58 Lemma 10: multiply(double_divide(X, multiply(double_divide(X, Y), Y)), Z) = Z.
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), Z)
% 0.20/0.58 = { by lemma 5 R->L }
% 0.20/0.58 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(inverse(U), Z)), U)))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), inverse(double_divide(multiply(double_divide(V, double_divide(inverse(U), Z)), U), double_divide(W, double_divide(V, W)))))
% 0.20/0.58 = { by lemma 9 }
% 0.20/0.58 inverse(double_divide(multiply(double_divide(V, double_divide(inverse(U), Z)), U), double_divide(W, double_divide(V, W))))
% 0.20/0.58 = { by axiom 1 (multiply) R->L }
% 0.20/0.58 multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(inverse(U), Z)), U))
% 0.20/0.58 = { by lemma 5 }
% 0.20/0.58 Z
% 0.20/0.58
% 0.20/0.58 Lemma 11: double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), X)) = multiply(double_divide(Z, W), W).
% 0.20/0.58 Proof:
% 0.20/0.58 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), X))
% 0.20/0.58 = { by lemma 10 R->L }
% 0.20/0.58 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), multiply(double_divide(Z, multiply(double_divide(Z, W), W)), X)))
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 multiply(double_divide(Z, W), W)
% 0.20/0.58
% 0.20/0.58 Lemma 12: double_divide(inverse(multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)), Z) = multiply(double_divide(X, W), W).
% 0.20/0.58 Proof:
% 0.20/0.58 double_divide(inverse(multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)), Z)
% 0.20/0.58 = { by lemma 5 R->L }
% 0.20/0.58 double_divide(inverse(multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)), multiply(double_divide(V, double_divide(X, V)), multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)))
% 0.20/0.58 = { by lemma 11 }
% 0.20/0.58 multiply(double_divide(X, W), W)
% 0.20/0.58
% 0.20/0.58 Lemma 13: multiply(multiply(double_divide(X, Y), Y), X) = double_divide(inverse(Z), Z).
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(multiply(double_divide(X, Y), Y), X)
% 0.20/0.58 = { by lemma 12 R->L }
% 0.20/0.58 multiply(double_divide(inverse(multiply(double_divide(X, double_divide(inverse(W), X)), W)), X), X)
% 0.20/0.58 = { by lemma 11 R->L }
% 0.20/0.58 double_divide(inverse(Z), multiply(double_divide(X, double_divide(inverse(multiply(double_divide(X, double_divide(inverse(W), X)), W)), X)), Z))
% 0.20/0.58 = { by lemma 12 }
% 0.20/0.58 double_divide(inverse(Z), multiply(double_divide(X, multiply(double_divide(X, V), V)), Z))
% 0.20/0.58 = { by lemma 10 }
% 0.20/0.58 double_divide(inverse(Z), Z)
% 0.20/0.58
% 0.20/0.58 Lemma 14: double_divide(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.20/0.58 Proof:
% 0.20/0.58 double_divide(inverse(X), X)
% 0.20/0.58 = { by lemma 13 R->L }
% 0.20/0.58 multiply(multiply(double_divide(Z, W), W), Z)
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 inverse(double_divide(Z, multiply(double_divide(Z, W), W)))
% 0.20/0.58 = { by lemma 9 R->L }
% 0.20/0.58 multiply(double_divide(Z, multiply(double_divide(Z, W), W)), inverse(double_divide(Z, multiply(double_divide(Z, W), W))))
% 0.20/0.58 = { by axiom 1 (multiply) }
% 0.20/0.58 inverse(double_divide(inverse(double_divide(Z, multiply(double_divide(Z, W), W))), double_divide(Z, multiply(double_divide(Z, W), W))))
% 0.20/0.58 = { by lemma 10 R->L }
% 0.20/0.58 inverse(double_divide(inverse(double_divide(Z, multiply(double_divide(Z, W), W))), multiply(double_divide(V, multiply(double_divide(V, U), U)), double_divide(Z, multiply(double_divide(Z, W), W)))))
% 0.20/0.58 = { by lemma 12 R->L }
% 0.20/0.58 inverse(double_divide(inverse(double_divide(Z, multiply(double_divide(Z, W), W))), multiply(double_divide(V, double_divide(inverse(multiply(double_divide(V, double_divide(inverse(T), V)), T)), V)), double_divide(Z, multiply(double_divide(Z, W), W)))))
% 0.20/0.58 = { by lemma 11 }
% 0.20/0.58 inverse(multiply(double_divide(inverse(multiply(double_divide(V, double_divide(inverse(T), V)), T)), S), S))
% 0.20/0.58 = { by lemma 11 R->L }
% 0.20/0.58 inverse(double_divide(inverse(Y), multiply(double_divide(V, double_divide(inverse(multiply(double_divide(V, double_divide(inverse(T), V)), T)), V)), Y)))
% 0.20/0.58 = { by lemma 12 }
% 0.20/0.58 inverse(double_divide(inverse(Y), multiply(double_divide(V, multiply(double_divide(V, X2), X2)), Y)))
% 0.20/0.58 = { by lemma 10 }
% 0.20/0.58 inverse(double_divide(inverse(Y), Y))
% 0.20/0.58 = { by axiom 1 (multiply) R->L }
% 0.20/0.58 multiply(Y, inverse(Y))
% 0.20/0.58
% 0.20/0.58 Lemma 15: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(inverse(X), X)
% 0.20/0.58 = { by lemma 10 R->L }
% 0.20/0.58 multiply(multiply(double_divide(Z, multiply(double_divide(Z, W), W)), inverse(X)), X)
% 0.20/0.58 = { by lemma 8 R->L }
% 0.20/0.58 multiply(multiply(double_divide(inverse(double_divide(Z, multiply(double_divide(Z, W), W))), double_divide(Z, multiply(double_divide(Z, W), W))), inverse(X)), X)
% 0.20/0.58 = { by lemma 14 }
% 0.20/0.58 multiply(multiply(multiply(V, inverse(V)), inverse(X)), X)
% 0.20/0.58 = { by lemma 14 R->L }
% 0.20/0.58 multiply(multiply(double_divide(inverse(inverse(X)), inverse(X)), inverse(X)), X)
% 0.20/0.58 = { by lemma 3 R->L }
% 0.20/0.58 multiply(double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(inverse(X)), T)), multiply(double_divide(inverse(inverse(X)), multiply(double_divide(inverse(inverse(X)), inverse(X)), inverse(X))), U))), X)
% 0.20/0.58 = { by lemma 4 }
% 0.20/0.58 multiply(multiply(double_divide(S, double_divide(X2, S)), multiply(double_divide(X2, double_divide(inverse(inverse(X)), multiply(double_divide(inverse(inverse(X)), inverse(X)), inverse(X)))), inverse(X))), X)
% 0.20/0.58 = { by lemma 7 R->L }
% 0.20/0.58 multiply(multiply(double_divide(S, double_divide(X2, S)), multiply(double_divide(X2, multiply(double_divide(Y2, double_divide(Z2, Y2)), multiply(double_divide(Z2, X), X))), inverse(X))), X)
% 0.20/0.58 = { by lemma 4 R->L }
% 0.20/0.58 multiply(double_divide(inverse(W2), multiply(double_divide(V2, double_divide(inverse(inverse(X)), V2)), multiply(multiply(double_divide(Y2, double_divide(Z2, Y2)), multiply(double_divide(Z2, X), X)), W2))), X)
% 0.20/0.58 = { by lemma 4 R->L }
% 0.20/0.58 multiply(double_divide(inverse(W2), multiply(double_divide(V2, double_divide(inverse(inverse(X)), V2)), multiply(double_divide(inverse(inverse(X)), multiply(double_divide(X, double_divide(inverse(X), X)), multiply(X, inverse(X)))), W2))), X)
% 0.20/0.58 = { by lemma 3 }
% 0.20/0.58 multiply(multiply(double_divide(X, double_divide(inverse(X), X)), multiply(X, inverse(X))), X)
% 0.20/0.58 = { by lemma 14 }
% 0.20/0.58 multiply(multiply(double_divide(X, multiply(X, inverse(X))), multiply(X, inverse(X))), X)
% 0.20/0.58 = { by lemma 13 }
% 0.20/0.58 double_divide(inverse(U2), U2)
% 0.20/0.58 = { by lemma 14 }
% 0.20/0.58 multiply(Y, inverse(Y))
% 0.20/0.58
% 0.20/0.58 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.58 Proof:
% 0.20/0.58 multiply(inverse(a1), a1)
% 0.20/0.58 = { by lemma 15 }
% 0.20/0.58 multiply(X, inverse(X))
% 0.20/0.58 = { by lemma 15 R->L }
% 0.20/0.58 multiply(inverse(b1), b1)
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58
% 0.20/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------