TSTP Solution File: GRP475-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP475-1 : 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 : n019.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 01:18:35 EDT 2023
% Result : Unsatisfiable 0.19s 0.58s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP475-1 : 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
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon Aug 28 23:30:57 EDT 2023
% 0.15/0.33 % CPUTime :
% 0.19/0.58 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.58
% 0.19/0.58 % SZS status Unsatisfiable
% 0.19/0.58
% 0.19/0.65 % SZS output start Proof
% 0.19/0.65 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.19/0.65 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, Y), Z), divide(W, Z))), divide(Y, X)) = W.
% 0.19/0.65
% 0.19/0.65 Lemma 3: divide(inverse(divide(multiply(divide(X, Y), Z), multiply(W, Z))), divide(Y, X)) = W.
% 0.19/0.65 Proof:
% 0.19/0.65 divide(inverse(divide(multiply(divide(X, Y), Z), multiply(W, Z))), divide(Y, X))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 divide(inverse(divide(multiply(divide(X, Y), Z), divide(W, inverse(Z)))), divide(Y, X))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 divide(inverse(divide(divide(divide(X, Y), inverse(Z)), divide(W, inverse(Z)))), divide(Y, X))
% 0.19/0.65 = { by axiom 2 (single_axiom) }
% 0.19/0.65 W
% 0.19/0.65
% 0.19/0.65 Lemma 4: inverse(divide(multiply(divide(X, Y), Z), multiply(divide(W, divide(Y, X)), Z))) = W.
% 0.19/0.65 Proof:
% 0.19/0.65 inverse(divide(multiply(divide(X, Y), Z), multiply(divide(W, divide(Y, X)), Z)))
% 0.19/0.65 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.65 divide(inverse(divide(divide(divide(V, U), divide(Y, X)), divide(inverse(divide(multiply(divide(X, Y), Z), multiply(divide(W, divide(Y, X)), Z))), divide(Y, X)))), divide(U, V))
% 0.19/0.65 = { by lemma 3 }
% 0.19/0.65 divide(inverse(divide(divide(divide(V, U), divide(Y, X)), divide(W, divide(Y, X)))), divide(U, V))
% 0.19/0.65 = { by axiom 2 (single_axiom) }
% 0.19/0.65 W
% 0.19/0.65
% 0.19/0.65 Lemma 5: divide(inverse(divide(divide(multiply(X, Y), Z), divide(W, Z))), divide(inverse(Y), X)) = W.
% 0.19/0.65 Proof:
% 0.19/0.65 divide(inverse(divide(divide(multiply(X, Y), Z), divide(W, Z))), divide(inverse(Y), X))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 divide(inverse(divide(divide(divide(X, inverse(Y)), Z), divide(W, Z))), divide(inverse(Y), X))
% 0.19/0.65 = { by axiom 2 (single_axiom) }
% 0.19/0.65 W
% 0.19/0.65
% 0.19/0.65 Lemma 6: divide(inverse(divide(divide(X, Y), divide(Z, Y))), multiply(divide(inverse(W), V), divide(divide(multiply(V, W), U), divide(X, U)))) = Z.
% 0.19/0.65 Proof:
% 0.19/0.65 divide(inverse(divide(divide(X, Y), divide(Z, Y))), multiply(divide(inverse(W), V), divide(divide(multiply(V, W), U), divide(X, U))))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 divide(inverse(divide(divide(X, Y), divide(Z, Y))), divide(divide(inverse(W), V), inverse(divide(divide(multiply(V, W), U), divide(X, U)))))
% 0.19/0.65 = { by lemma 5 R->L }
% 0.19/0.65 divide(inverse(divide(divide(divide(inverse(divide(divide(multiply(V, W), U), divide(X, U))), divide(inverse(W), V)), Y), divide(Z, Y))), divide(divide(inverse(W), V), inverse(divide(divide(multiply(V, W), U), divide(X, U)))))
% 0.19/0.65 = { by axiom 2 (single_axiom) }
% 0.19/0.65 Z
% 0.19/0.65
% 0.19/0.65 Lemma 7: inverse(divide(divide(X, Y), divide(Z, Y))) = inverse(divide(multiply(X, W), multiply(Z, W))).
% 0.19/0.65 Proof:
% 0.19/0.65 inverse(divide(divide(X, Y), divide(Z, Y)))
% 0.19/0.65 = { by lemma 4 R->L }
% 0.19/0.65 inverse(divide(multiply(divide(inverse(divide(divide(multiply(V, U), T), divide(X, T))), divide(inverse(U), V)), W), multiply(divide(inverse(divide(divide(X, Y), divide(Z, Y))), divide(divide(inverse(U), V), inverse(divide(divide(multiply(V, U), T), divide(X, T))))), W)))
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 inverse(divide(multiply(divide(inverse(divide(divide(multiply(V, U), T), divide(X, T))), divide(inverse(U), V)), W), multiply(divide(inverse(divide(divide(X, Y), divide(Z, Y))), multiply(divide(inverse(U), V), divide(divide(multiply(V, U), T), divide(X, T)))), W)))
% 0.19/0.65 = { by lemma 6 }
% 0.19/0.65 inverse(divide(multiply(divide(inverse(divide(divide(multiply(V, U), T), divide(X, T))), divide(inverse(U), V)), W), multiply(Z, W)))
% 0.19/0.65 = { by lemma 5 }
% 0.19/0.65 inverse(divide(multiply(X, W), multiply(Z, W)))
% 0.19/0.65
% 0.19/0.65 Lemma 8: divide(inverse(divide(divide(multiply(divide(X, Y), divide(divide(divide(Y, X), Z), divide(W, Z))), V), divide(U, V))), W) = U.
% 0.19/0.65 Proof:
% 0.19/0.65 divide(inverse(divide(divide(multiply(divide(X, Y), divide(divide(divide(Y, X), Z), divide(W, Z))), V), divide(U, V))), W)
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 divide(inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(W, Z)))), V), divide(U, V))), W)
% 0.19/0.65 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.65 divide(inverse(divide(divide(divide(divide(X, Y), inverse(divide(divide(divide(Y, X), Z), divide(W, Z)))), V), divide(U, V))), divide(inverse(divide(divide(divide(Y, X), Z), divide(W, Z))), divide(X, Y)))
% 0.19/0.65 = { by axiom 2 (single_axiom) }
% 0.19/0.65 U
% 0.19/0.65
% 0.19/0.65 Lemma 9: multiply(X, divide(multiply(divide(Y, Z), W), multiply(divide(V, divide(Z, Y)), W))) = divide(X, V).
% 0.19/0.65 Proof:
% 0.19/0.65 multiply(X, divide(multiply(divide(Y, Z), W), multiply(divide(V, divide(Z, Y)), W)))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 divide(X, inverse(divide(multiply(divide(Y, Z), W), multiply(divide(V, divide(Z, Y)), W))))
% 0.19/0.65 = { by lemma 4 }
% 0.19/0.65 divide(X, V)
% 0.19/0.65
% 0.19/0.65 Lemma 10: divide(divide(inverse(divide(divide(divide(X, Y), Z), W)), divide(Y, X)), Z) = W.
% 0.19/0.65 Proof:
% 0.19/0.65 divide(divide(inverse(divide(divide(divide(X, Y), Z), W)), divide(Y, X)), Z)
% 0.19/0.65 = { by lemma 3 R->L }
% 0.19/0.65 divide(divide(inverse(divide(divide(divide(X, Y), Z), W)), divide(Y, X)), divide(inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), divide(U, V)))
% 0.19/0.65 = { by lemma 8 R->L }
% 0.19/0.65 divide(divide(inverse(divide(divide(divide(X, Y), Z), divide(inverse(divide(divide(multiply(divide(U, V), divide(divide(divide(V, U), Y2), divide(Z, Y2))), Z2), divide(W, Z2))), Z))), divide(Y, X)), divide(inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), divide(U, V)))
% 0.19/0.65 = { by axiom 2 (single_axiom) }
% 0.19/0.66 divide(inverse(divide(divide(multiply(divide(U, V), divide(divide(divide(V, U), Y2), divide(Z, Y2))), Z2), divide(W, Z2))), divide(inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), divide(U, V)))
% 0.19/0.66 = { by lemma 7 }
% 0.19/0.66 divide(inverse(divide(multiply(multiply(divide(U, V), divide(divide(divide(V, U), Y2), divide(Z, Y2))), W2), multiply(W, W2))), divide(inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), divide(U, V)))
% 0.19/0.66 = { by lemma 9 R->L }
% 0.19/0.66 divide(inverse(divide(multiply(multiply(divide(U, V), divide(divide(divide(V, U), Y2), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), W2), multiply(W, W2))), divide(inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), divide(U, V)))
% 0.19/0.66 = { by lemma 9 R->L }
% 0.19/0.66 divide(inverse(divide(multiply(multiply(divide(U, V), divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), W2), multiply(W, W2))), divide(inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), divide(U, V)))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 divide(inverse(divide(multiply(divide(divide(U, V), inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2)))))), W2), multiply(W, W2))), divide(inverse(divide(multiply(divide(V, U), divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))), multiply(Z, divide(multiply(divide(T, S), X2), multiply(divide(Y2, divide(S, T)), X2))))), divide(U, V)))
% 0.19/0.66 = { by lemma 3 }
% 0.19/0.66 W
% 0.19/0.66
% 0.19/0.66 Lemma 11: divide(inverse(divide(multiply(X, Y), multiply(Z, Y))), multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(X, U)))) = Z.
% 0.19/0.66 Proof:
% 0.19/0.66 divide(inverse(divide(multiply(X, Y), multiply(Z, Y))), multiply(divide(W, V), divide(multiply(divide(V, W), U), multiply(X, U))))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 divide(inverse(divide(multiply(X, Y), multiply(Z, Y))), divide(divide(W, V), inverse(divide(multiply(divide(V, W), U), multiply(X, U)))))
% 0.19/0.66 = { by lemma 7 R->L }
% 0.19/0.66 divide(inverse(divide(divide(X, T), divide(Z, T))), divide(divide(W, V), inverse(divide(multiply(divide(V, W), U), multiply(X, U)))))
% 0.19/0.66 = { by lemma 3 R->L }
% 0.19/0.66 divide(inverse(divide(divide(divide(inverse(divide(multiply(divide(V, W), U), multiply(X, U))), divide(W, V)), T), divide(Z, T))), divide(divide(W, V), inverse(divide(multiply(divide(V, W), U), multiply(X, U)))))
% 0.19/0.66 = { by axiom 2 (single_axiom) }
% 0.19/0.66 Z
% 0.19/0.66
% 0.19/0.66 Lemma 12: inverse(divide(multiply(divide(X, divide(Y, Z)), W), multiply(divide(V, U), W))) = divide(divide(inverse(divide(U, V)), divide(Z, Y)), X).
% 0.19/0.66 Proof:
% 0.19/0.66 inverse(divide(multiply(divide(X, divide(Y, Z)), W), multiply(divide(V, U), W)))
% 0.19/0.66 = { by lemma 10 R->L }
% 0.19/0.66 divide(divide(inverse(divide(divide(divide(Y, Z), X), inverse(divide(multiply(divide(X, divide(Y, Z)), W), multiply(divide(V, U), W))))), divide(Z, Y)), X)
% 0.19/0.66 = { by axiom 1 (multiply) R->L }
% 0.19/0.66 divide(divide(inverse(multiply(divide(divide(Y, Z), X), divide(multiply(divide(X, divide(Y, Z)), W), multiply(divide(V, U), W)))), divide(Z, Y)), X)
% 0.19/0.66 = { by lemma 10 R->L }
% 0.19/0.66 divide(divide(inverse(divide(divide(inverse(divide(divide(divide(T, S), X2), multiply(divide(divide(Y, Z), X), divide(multiply(divide(X, divide(Y, Z)), W), multiply(divide(V, U), W))))), divide(S, T)), X2)), divide(Z, Y)), X)
% 0.19/0.66 = { by lemma 4 R->L }
% 0.19/0.66 divide(divide(inverse(divide(divide(inverse(divide(inverse(divide(multiply(divide(V, U), Y2), multiply(divide(divide(divide(T, S), X2), divide(U, V)), Y2))), multiply(divide(divide(Y, Z), X), divide(multiply(divide(X, divide(Y, Z)), W), multiply(divide(V, U), W))))), divide(S, T)), X2)), divide(Z, Y)), X)
% 0.19/0.66 = { by lemma 11 }
% 0.19/0.66 divide(divide(inverse(divide(divide(inverse(divide(divide(divide(T, S), X2), divide(U, V))), divide(S, T)), X2)), divide(Z, Y)), X)
% 0.19/0.66 = { by lemma 10 }
% 0.19/0.66 divide(divide(inverse(divide(U, V)), divide(Z, Y)), X)
% 0.19/0.66
% 0.19/0.66 Lemma 13: multiply(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Z, W)) = inverse(divide(W, Z)).
% 0.19/0.66 Proof:
% 0.19/0.66 multiply(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Z, W))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 divide(divide(inverse(divide(X, Y)), divide(Y, X)), inverse(divide(Z, W)))
% 0.19/0.66 = { by lemma 12 R->L }
% 0.19/0.66 inverse(divide(multiply(divide(inverse(divide(Z, W)), divide(X, Y)), V), multiply(divide(Y, X), V)))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 inverse(divide(divide(divide(inverse(divide(Z, W)), divide(X, Y)), inverse(V)), multiply(divide(Y, X), V)))
% 0.19/0.66 = { by lemma 12 R->L }
% 0.19/0.66 inverse(divide(inverse(divide(multiply(divide(inverse(V), divide(Y, X)), U), multiply(divide(W, Z), U))), multiply(divide(Y, X), V)))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 inverse(divide(inverse(divide(multiply(divide(inverse(V), divide(Y, X)), U), multiply(divide(W, Z), U))), divide(divide(Y, X), inverse(V))))
% 0.19/0.66 = { by lemma 3 }
% 0.19/0.66 inverse(divide(W, Z))
% 0.19/0.66
% 0.19/0.66 Lemma 14: divide(inverse(divide(inverse(divide(X, Y)), multiply(Z, divide(Y, X)))), multiply(divide(W, V), divide(V, W))) = Z.
% 0.19/0.66 Proof:
% 0.19/0.66 divide(inverse(divide(inverse(divide(X, Y)), multiply(Z, divide(Y, X)))), multiply(divide(W, V), divide(V, W)))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 divide(inverse(divide(inverse(divide(X, Y)), multiply(Z, divide(Y, X)))), divide(divide(W, V), inverse(divide(V, W))))
% 0.19/0.66 = { by lemma 13 R->L }
% 0.19/0.66 divide(inverse(divide(multiply(divide(inverse(divide(V, W)), divide(W, V)), divide(Y, X)), multiply(Z, divide(Y, X)))), divide(divide(W, V), inverse(divide(V, W))))
% 0.19/0.66 = { by lemma 3 }
% 0.19/0.66 Z
% 0.19/0.66
% 0.19/0.66 Lemma 15: multiply(inverse(divide(multiply(multiply(divide(X, Y), divide(divide(divide(Y, X), Z), divide(inverse(W), Z))), V), multiply(U, V))), W) = U.
% 0.19/0.66 Proof:
% 0.19/0.66 multiply(inverse(divide(multiply(multiply(divide(X, Y), divide(divide(divide(Y, X), Z), divide(inverse(W), Z))), V), multiply(U, V))), W)
% 0.19/0.66 = { by lemma 7 R->L }
% 0.19/0.66 multiply(inverse(divide(divide(multiply(divide(X, Y), divide(divide(divide(Y, X), Z), divide(inverse(W), Z))), T), divide(U, T))), W)
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 divide(inverse(divide(divide(multiply(divide(X, Y), divide(divide(divide(Y, X), Z), divide(inverse(W), Z))), T), divide(U, T))), inverse(W))
% 0.19/0.66 = { by lemma 8 }
% 0.19/0.66 U
% 0.19/0.66
% 0.19/0.66 Lemma 16: multiply(multiply(X, divide(Y, Z)), divide(Z, Y)) = X.
% 0.19/0.66 Proof:
% 0.19/0.66 multiply(multiply(X, divide(Y, Z)), divide(Z, Y))
% 0.19/0.66 = { by lemma 14 R->L }
% 0.19/0.66 divide(inverse(divide(inverse(divide(W, multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V))), multiply(multiply(multiply(X, divide(Y, Z)), divide(Z, Y)), divide(multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V), W)))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.66 = { by axiom 1 (multiply) }
% 0.19/0.66 divide(inverse(divide(inverse(divide(W, multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V))), multiply(divide(multiply(X, divide(Y, Z)), inverse(divide(Z, Y))), divide(multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V), W)))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.66 = { by lemma 15 R->L }
% 0.19/0.66 divide(inverse(divide(inverse(divide(W, multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V))), multiply(divide(multiply(X, divide(Y, Z)), inverse(divide(Z, Y))), divide(multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V), multiply(inverse(divide(multiply(multiply(divide(S, X2), divide(divide(divide(X2, S), Y2), divide(inverse(V), Y2))), Z2), multiply(W, Z2))), V))))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.66 = { by lemma 15 R->L }
% 0.19/0.66 divide(inverse(divide(inverse(divide(multiply(inverse(divide(multiply(multiply(divide(S, X2), divide(divide(divide(X2, S), Y2), divide(inverse(V), Y2))), Z2), multiply(W, Z2))), V), multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V))), multiply(divide(multiply(X, divide(Y, Z)), inverse(divide(Z, Y))), divide(multiply(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z))), V), multiply(inverse(divide(multiply(multiply(divide(S, X2), divide(divide(divide(X2, S), Y2), divide(inverse(V), Y2))), Z2), multiply(W, Z2))), V))))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.66 = { by lemma 11 }
% 0.19/0.66 divide(inverse(divide(inverse(divide(Z, Y)), multiply(X, divide(Y, Z)))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.66 = { by lemma 14 }
% 0.19/0.66 X
% 0.19/0.66
% 0.19/0.66 Lemma 17: divide(inverse(multiply(X, Y)), multiply(divide(Z, W), divide(W, Z))) = divide(inverse(Y), X).
% 0.19/0.66 Proof:
% 0.19/0.66 divide(inverse(multiply(X, Y)), multiply(divide(Z, W), divide(W, Z)))
% 0.19/0.66 = { by lemma 6 R->L }
% 0.19/0.66 divide(inverse(divide(inverse(divide(divide(V, U), divide(multiply(X, Y), U))), multiply(divide(inverse(Y), X), divide(divide(multiply(X, Y), U), divide(V, U))))), multiply(divide(Z, W), divide(W, Z)))
% 0.19/0.66 = { by lemma 14 }
% 0.19/0.66 divide(inverse(Y), X)
% 0.19/0.66
% 0.19/0.66 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.67 Proof:
% 0.19/0.67 multiply(inverse(a1), a1)
% 0.19/0.67 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.67 multiply(inverse(a1), divide(inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))), divide(Y, X)))
% 0.19/0.67 = { by axiom 2 (single_axiom) R->L }
% 0.19/0.67 multiply(inverse(divide(inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))), divide(Y, X))), divide(inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))), divide(Y, X)))
% 0.19/0.67 = { by axiom 1 (multiply) }
% 0.19/0.67 divide(inverse(divide(inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))), divide(Y, X))), inverse(divide(inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))), divide(Y, X))))
% 0.19/0.67 = { by lemma 13 R->L }
% 0.19/0.67 divide(inverse(divide(inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))), divide(Y, X))), multiply(divide(inverse(divide(W, V)), divide(V, W)), divide(divide(Y, X), inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))))))
% 0.19/0.67 = { by lemma 17 R->L }
% 0.19/0.67 divide(inverse(multiply(multiply(divide(inverse(divide(W, V)), divide(V, W)), divide(divide(Y, X), inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))))), divide(inverse(divide(divide(divide(X, Y), Z), divide(a1, Z))), divide(Y, X)))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.67 = { by lemma 16 }
% 0.19/0.67 divide(inverse(divide(inverse(divide(W, V)), divide(V, W))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.67 = { by lemma 16 R->L }
% 0.19/0.67 divide(inverse(multiply(multiply(divide(inverse(divide(W, V)), divide(V, W)), divide(divide(S, X2), inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))))), divide(inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))), divide(S, X2)))), multiply(divide(U, T), divide(T, U)))
% 0.19/0.67 = { by lemma 17 }
% 0.19/0.67 divide(inverse(divide(inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))), divide(S, X2))), multiply(divide(inverse(divide(W, V)), divide(V, W)), divide(divide(S, X2), inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))))))
% 0.19/0.67 = { by lemma 13 }
% 0.19/0.67 divide(inverse(divide(inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))), divide(S, X2))), inverse(divide(inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))), divide(S, X2))))
% 0.19/0.67 = { by axiom 1 (multiply) R->L }
% 0.19/0.67 multiply(inverse(divide(inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))), divide(S, X2))), divide(inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))), divide(S, X2)))
% 0.19/0.67 = { by axiom 2 (single_axiom) }
% 0.19/0.67 multiply(inverse(b1), divide(inverse(divide(divide(divide(X2, S), Y2), divide(b1, Y2))), divide(S, X2)))
% 0.19/0.67 = { by axiom 2 (single_axiom) }
% 0.19/0.67 multiply(inverse(b1), b1)
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67
% 0.19/0.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------