TSTP Solution File: GRP471-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP471-1 : 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 : n023.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 01:18:34 EDT 2023
% Result : Unsatisfiable 2.87s 0.76s
% Output : Proof 4.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP471-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 20:42:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 2.87/0.76 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.87/0.76
% 2.87/0.76 % SZS status Unsatisfiable
% 2.87/0.76
% 3.35/0.84 % SZS output start Proof
% 3.35/0.84 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 3.35/0.84 Axiom 2 (single_axiom): divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)) = Y.
% 3.35/0.84
% 3.35/0.84 Lemma 3: divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, divide(W, V))))) = divide(V, W).
% 3.35/0.84 Proof:
% 3.35/0.84 divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, divide(W, V)))))
% 3.35/0.84 = { by axiom 1 (multiply) }
% 3.35/0.84 divide(inverse(X), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, divide(W, V))))))
% 3.35/0.84 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.84 divide(inverse(divide(inverse(divide(divide(Z, Y), divide(X, divide(W, V)))), divide(divide(V, W), divide(Z, Y)))), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, divide(W, V))))))
% 3.35/0.84 = { by axiom 2 (single_axiom) }
% 3.35/0.84 divide(V, W)
% 3.35/0.84
% 3.35/0.84 Lemma 4: divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, W)))) = multiply(divide(divide(V, U), T), divide(T, divide(W, divide(U, V)))).
% 3.35/0.84 Proof:
% 3.35/0.84 divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, W))))
% 3.35/0.84 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.84 divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, divide(inverse(divide(T, divide(W, divide(U, V)))), divide(divide(V, U), T))))))
% 3.35/0.84 = { by lemma 3 }
% 3.35/0.84 divide(divide(divide(V, U), T), inverse(divide(T, divide(W, divide(U, V)))))
% 3.35/0.84 = { by axiom 1 (multiply) R->L }
% 3.35/0.84 multiply(divide(divide(V, U), T), divide(T, divide(W, divide(U, V))))
% 3.35/0.84
% 3.35/0.84 Lemma 5: multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X)))) = divide(V, W).
% 3.35/0.84 Proof:
% 3.35/0.84 multiply(divide(divide(X, Y), Z), divide(Z, divide(divide(W, V), divide(Y, X))))
% 3.35/0.84 = { by lemma 4 R->L }
% 3.35/0.84 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, divide(W, V)))))
% 3.35/0.84 = { by lemma 3 }
% 3.35/0.84 divide(V, W)
% 3.35/0.84
% 3.35/0.84 Lemma 6: multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), Z) = W.
% 3.35/0.84 Proof:
% 3.35/0.84 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), Z)
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))))), Z)
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 divide(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))))), inverse(Z))
% 3.35/0.85 = { by lemma 3 R->L }
% 3.35/0.85 divide(inverse(S), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(S, divide(inverse(Z), multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))))))))))
% 3.35/0.85 = { by lemma 3 }
% 3.35/0.85 divide(inverse(S), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(S, divide(divide(divide(T, U), V), inverse(divide(V, divide(W, divide(U, T)))))))))
% 3.35/0.85 = { by lemma 3 }
% 3.35/0.85 divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))
% 3.35/0.85 = { by axiom 2 (single_axiom) }
% 3.35/0.85 W
% 3.35/0.85
% 3.35/0.85 Lemma 7: multiply(divide(divide(V, U), T), divide(T, divide(W, divide(U, V)))) = multiply(divide(divide(X, Y), Z), divide(Z, divide(W, divide(Y, X)))).
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(divide(divide(V, U), T), divide(T, divide(W, divide(U, V))))
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 divide(divide(divide(V, U), T), inverse(divide(T, divide(W, divide(U, V)))))
% 3.35/0.85 = { by lemma 3 R->L }
% 3.35/0.85 divide(inverse(S), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(S, divide(inverse(divide(T, divide(W, divide(U, V)))), divide(divide(V, U), T))))))
% 3.35/0.85 = { by axiom 2 (single_axiom) }
% 3.35/0.85 divide(inverse(S), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(S, W))))
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 divide(inverse(S), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(S, divide(inverse(divide(Z, divide(W, divide(Y, X)))), divide(divide(X, Y), Z))))))
% 3.35/0.85 = { by lemma 3 }
% 3.35/0.85 divide(divide(divide(X, Y), Z), inverse(divide(Z, divide(W, divide(Y, X)))))
% 3.35/0.85 = { by axiom 1 (multiply) R->L }
% 3.35/0.85 multiply(divide(divide(X, Y), Z), divide(Z, divide(W, divide(Y, X))))
% 3.35/0.85
% 3.35/0.85 Lemma 8: divide(inverse(divide(X, divide(Y, Z))), divide(multiply(divide(divide(W, V), U), divide(U, divide(Z, divide(V, W)))), X)) = Y.
% 3.35/0.85 Proof:
% 3.35/0.85 divide(inverse(divide(X, divide(Y, Z))), divide(multiply(divide(divide(W, V), U), divide(U, divide(Z, divide(V, W)))), X))
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 divide(inverse(divide(X, divide(Y, Z))), divide(divide(divide(divide(W, V), U), inverse(divide(U, divide(Z, divide(V, W))))), X))
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 divide(inverse(divide(X, divide(Y, divide(inverse(divide(U, divide(Z, divide(V, W)))), divide(divide(W, V), U))))), divide(divide(divide(divide(W, V), U), inverse(divide(U, divide(Z, divide(V, W))))), X))
% 3.35/0.85 = { by axiom 2 (single_axiom) }
% 3.35/0.85 Y
% 3.35/0.85
% 3.35/0.85 Lemma 9: multiply(divide(multiply(divide(divide(X, divide(Y, Z)), W), divide(W, V)), U), divide(U, multiply(T, divide(X, divide(V, divide(Z, Y)))))) = multiply(divide(divide(S, X2), Y2), divide(Y2, divide(T, divide(X2, S)))).
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(divide(multiply(divide(divide(X, divide(Y, Z)), W), divide(W, V)), U), divide(U, multiply(T, divide(X, divide(V, divide(Z, Y))))))
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 divide(divide(multiply(divide(divide(X, divide(Y, Z)), W), divide(W, V)), U), inverse(divide(U, multiply(T, divide(X, divide(V, divide(Z, Y)))))))
% 3.35/0.85 = { by lemma 3 R->L }
% 3.35/0.85 divide(inverse(Z2), multiply(divide(W2, V2), divide(divide(V2, W2), divide(Z2, divide(inverse(divide(U, multiply(T, divide(X, divide(V, divide(Z, Y)))))), divide(multiply(divide(divide(X, divide(Y, Z)), W), divide(W, V)), U))))))
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 divide(inverse(Z2), multiply(divide(W2, V2), divide(divide(V2, W2), divide(Z2, divide(inverse(divide(U, divide(T, inverse(divide(X, divide(V, divide(Z, Y))))))), divide(multiply(divide(divide(X, divide(Y, Z)), W), divide(W, V)), U))))))
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 divide(inverse(Z2), multiply(divide(W2, V2), divide(divide(V2, W2), divide(Z2, divide(inverse(divide(U, divide(T, inverse(divide(X, divide(V, divide(Z, Y))))))), divide(multiply(divide(divide(X, divide(Y, Z)), W), divide(W, divide(inverse(divide(X, divide(V, divide(Z, Y)))), divide(divide(Y, Z), X)))), U))))))
% 3.35/0.85 = { by lemma 8 }
% 3.35/0.85 divide(inverse(Z2), multiply(divide(W2, V2), divide(divide(V2, W2), divide(Z2, T))))
% 3.35/0.85 = { by lemma 4 }
% 3.35/0.85 multiply(divide(divide(S, X2), Y2), divide(Y2, divide(T, divide(X2, S))))
% 3.35/0.85
% 3.35/0.85 Lemma 10: multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, multiply(divide(divide(V, U), T), divide(T, divide(Z, divide(U, V)))))) = X.
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, multiply(divide(divide(V, U), T), divide(T, divide(Z, divide(U, V))))))
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 multiply(divide(multiply(divide(divide(inverse(divide(S, divide(X, divide(X2, Y2)))), divide(divide(Y2, X2), S)), Y), divide(Y, Z)), W), divide(W, multiply(divide(divide(V, U), T), divide(T, divide(Z, divide(U, V))))))
% 3.35/0.85 = { by lemma 7 }
% 3.35/0.85 multiply(divide(multiply(divide(divide(inverse(divide(S, divide(X, divide(X2, Y2)))), divide(divide(Y2, X2), S)), Y), divide(Y, Z)), W), divide(W, multiply(divide(divide(divide(Y2, X2), S), inverse(divide(S, divide(X, divide(X2, Y2))))), divide(inverse(divide(S, divide(X, divide(X2, Y2)))), divide(Z, divide(S, divide(Y2, X2)))))))
% 3.35/0.85 = { by lemma 9 }
% 3.35/0.85 multiply(divide(divide(Z2, W2), V2), divide(V2, divide(divide(divide(divide(Y2, X2), S), inverse(divide(S, divide(X, divide(X2, Y2))))), divide(W2, Z2))))
% 3.35/0.85 = { by lemma 5 }
% 3.35/0.85 divide(inverse(divide(S, divide(X, divide(X2, Y2)))), divide(divide(Y2, X2), S))
% 3.35/0.85 = { by axiom 2 (single_axiom) }
% 3.35/0.85 X
% 3.35/0.85
% 3.35/0.85 Lemma 11: multiply(divide(X, W), multiply(W, Z)) = multiply(divide(X, Y), multiply(Y, Z)).
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(divide(X, W), multiply(W, Z))
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 multiply(divide(X, W), divide(W, inverse(Z)))
% 3.35/0.85 = { by lemma 10 R->L }
% 3.35/0.85 multiply(divide(multiply(divide(multiply(divide(X, W), divide(W, inverse(Z))), V2), divide(V2, multiply(divide(divide(U, T), S), divide(S, divide(inverse(Z), divide(T, U)))))), X2), divide(X2, multiply(divide(divide(Y2, Z2), W2), divide(W2, divide(multiply(divide(divide(U, T), S), divide(S, divide(inverse(Z), divide(T, U)))), divide(Z2, Y2))))))
% 3.35/0.85 = { by lemma 10 }
% 3.35/0.85 multiply(divide(X, X2), divide(X2, multiply(divide(divide(Y2, Z2), W2), divide(W2, divide(multiply(divide(divide(U, T), S), divide(S, divide(inverse(Z), divide(T, U)))), divide(Z2, Y2))))))
% 3.35/0.85 = { by lemma 10 R->L }
% 3.35/0.85 multiply(divide(multiply(divide(multiply(divide(X, Y), divide(Y, inverse(Z))), V), divide(V, multiply(divide(divide(U, T), S), divide(S, divide(inverse(Z), divide(T, U)))))), X2), divide(X2, multiply(divide(divide(Y2, Z2), W2), divide(W2, divide(multiply(divide(divide(U, T), S), divide(S, divide(inverse(Z), divide(T, U)))), divide(Z2, Y2))))))
% 3.35/0.85 = { by lemma 10 }
% 3.35/0.85 multiply(divide(X, Y), divide(Y, inverse(Z)))
% 3.35/0.85 = { by axiom 1 (multiply) R->L }
% 3.35/0.85 multiply(divide(X, Y), multiply(Y, Z))
% 3.35/0.85
% 3.35/0.85 Lemma 12: multiply(divide(X, multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, V)))), V) = multiply(divide(X, U), multiply(U, W)).
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(divide(X, multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, V)))), V)
% 3.35/0.85 = { by lemma 6 R->L }
% 3.35/0.85 multiply(divide(X, multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, V)))), multiply(multiply(divide(Y, Z), divide(divide(Z, Y), divide(W, V))), W))
% 3.35/0.85 = { by lemma 11 R->L }
% 3.35/0.85 multiply(divide(X, U), multiply(U, W))
% 3.35/0.85
% 3.35/0.85 Lemma 13: multiply(divide(Z, W), divide(W, Z)) = multiply(divide(X, Y), divide(Y, X)).
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(divide(Z, W), divide(W, Z))
% 3.35/0.85 = { by lemma 3 R->L }
% 3.35/0.85 multiply(divide(inverse(V), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(V, divide(W, Z))))), divide(W, Z))
% 3.35/0.85 = { by lemma 12 }
% 3.35/0.85 multiply(divide(inverse(V), S), multiply(S, V))
% 3.35/0.85 = { by lemma 12 R->L }
% 3.35/0.85 multiply(divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(Y, X))))), divide(Y, X))
% 3.35/0.85 = { by lemma 3 }
% 3.35/0.85 multiply(divide(X, Y), divide(Y, X))
% 3.35/0.85
% 3.35/0.85 Lemma 14: multiply(multiply(multiply(divide(divide(X, Y), Z), divide(Z, W)), W), Y) = X.
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(multiply(multiply(divide(divide(X, Y), Z), divide(Z, W)), W), Y)
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 multiply(multiply(multiply(divide(divide(X, Y), Z), divide(Z, W)), W), divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V)))
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 multiply(multiply(multiply(divide(divide(X, divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V))), Z), divide(Z, W)), W), divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V)))
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 multiply(divide(multiply(divide(divide(X, divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V))), Z), divide(Z, W)), inverse(W)), divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V)))
% 3.35/0.85 = { by lemma 3 R->L }
% 3.35/0.85 multiply(divide(multiply(divide(divide(X, divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V))), Z), divide(Z, W)), inverse(W)), divide(inverse(W), multiply(divide(divide(divide(S, X2), Y2), inverse(divide(Y2, divide(X, divide(X2, S))))), divide(divide(inverse(divide(Y2, divide(X, divide(X2, S)))), divide(divide(S, X2), Y2)), divide(W, divide(divide(divide(T, U), V), inverse(divide(V, divide(Y, divide(U, T))))))))))
% 3.35/0.85 = { by axiom 2 (single_axiom) }
% 3.35/0.85 multiply(divide(multiply(divide(divide(X, divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V))), Z), divide(Z, W)), inverse(W)), divide(inverse(W), multiply(divide(divide(divide(S, X2), Y2), inverse(divide(Y2, divide(X, divide(X2, S))))), divide(X, divide(W, divide(divide(divide(T, U), V), inverse(divide(V, divide(Y, divide(U, T))))))))))
% 3.35/0.85 = { by axiom 1 (multiply) R->L }
% 3.35/0.85 multiply(divide(multiply(divide(divide(X, divide(inverse(divide(V, divide(Y, divide(U, T)))), divide(divide(T, U), V))), Z), divide(Z, W)), inverse(W)), divide(inverse(W), multiply(multiply(divide(divide(S, X2), Y2), divide(Y2, divide(X, divide(X2, S)))), divide(X, divide(W, divide(divide(divide(T, U), V), inverse(divide(V, divide(Y, divide(U, T))))))))))
% 3.35/0.85 = { by lemma 9 }
% 3.35/0.85 multiply(divide(divide(Z2, W2), V2), divide(V2, divide(multiply(divide(divide(S, X2), Y2), divide(Y2, divide(X, divide(X2, S)))), divide(W2, Z2))))
% 3.35/0.85 = { by lemma 4 R->L }
% 3.35/0.85 divide(inverse(U2), multiply(divide(T2, S2), divide(divide(S2, T2), divide(U2, multiply(divide(divide(S, X2), Y2), divide(Y2, divide(X, divide(X2, S))))))))
% 3.35/0.85 = { by axiom 1 (multiply) }
% 3.35/0.85 divide(inverse(U2), divide(divide(T2, S2), inverse(divide(divide(S2, T2), divide(U2, multiply(divide(divide(S, X2), Y2), divide(Y2, divide(X, divide(X2, S)))))))))
% 3.35/0.85 = { by axiom 2 (single_axiom) R->L }
% 3.35/0.85 divide(inverse(divide(inverse(divide(divide(S2, T2), divide(U2, divide(divide(divide(S, X2), Y2), inverse(divide(Y2, divide(X, divide(X2, S)))))))), divide(divide(inverse(divide(Y2, divide(X, divide(X2, S)))), divide(divide(S, X2), Y2)), divide(S2, T2)))), divide(divide(T2, S2), inverse(divide(divide(S2, T2), divide(U2, multiply(divide(divide(S, X2), Y2), divide(Y2, divide(X, divide(X2, S)))))))))
% 3.35/0.85 = { by axiom 1 (multiply) R->L }
% 3.35/0.85 divide(inverse(divide(inverse(divide(divide(S2, T2), divide(U2, multiply(divide(divide(S, X2), Y2), divide(Y2, divide(X, divide(X2, S))))))), divide(divide(inverse(divide(Y2, divide(X, divide(X2, S)))), divide(divide(S, X2), Y2)), divide(S2, T2)))), divide(divide(T2, S2), inverse(divide(divide(S2, T2), divide(U2, multiply(divide(divide(S, X2), Y2), divide(Y2, divide(X, divide(X2, S)))))))))
% 3.35/0.85 = { by axiom 2 (single_axiom) }
% 3.35/0.85 divide(inverse(divide(Y2, divide(X, divide(X2, S)))), divide(divide(S, X2), Y2))
% 3.35/0.85 = { by axiom 2 (single_axiom) }
% 3.35/0.85 X
% 3.35/0.85
% 3.35/0.85 Lemma 15: multiply(multiply(multiply(divide(X, Y), divide(Y, X)), divide(Z, W)), W) = Z.
% 3.35/0.85 Proof:
% 3.35/0.85 multiply(multiply(multiply(divide(X, Y), divide(Y, X)), divide(Z, W)), W)
% 3.35/0.85 = { by lemma 13 }
% 3.35/0.86 multiply(multiply(multiply(divide(divide(Z, W), V), divide(V, divide(Z, W))), divide(Z, W)), W)
% 3.35/0.86 = { by lemma 14 }
% 3.35/0.86 Z
% 3.35/0.86
% 3.35/0.86 Lemma 16: multiply(X, multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y))))) = multiply(divide(V, U), divide(U, V)).
% 3.35/0.86 Proof:
% 3.35/0.86 multiply(X, multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))))
% 3.35/0.86 = { by lemma 6 R->L }
% 3.35/0.86 multiply(multiply(multiply(divide(T, S), divide(divide(S, T), divide(X2, X))), X2), multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))))
% 3.35/0.86 = { by axiom 1 (multiply) }
% 3.35/0.86 multiply(multiply(divide(divide(T, S), inverse(divide(divide(S, T), divide(X2, X)))), X2), multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))))
% 4.05/0.86 = { by lemma 8 R->L }
% 4.05/0.86 multiply(multiply(divide(divide(T, S), inverse(divide(divide(S, T), divide(X2, X)))), divide(inverse(divide(divide(S, T), divide(X2, X))), divide(multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))), divide(S, T)))), multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))))
% 4.05/0.86 = { by axiom 1 (multiply) }
% 4.05/0.86 multiply(divide(divide(divide(T, S), inverse(divide(divide(S, T), divide(X2, X)))), inverse(divide(inverse(divide(divide(S, T), divide(X2, X))), divide(multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))), divide(S, T))))), multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))))
% 4.05/0.86 = { by axiom 2 (single_axiom) R->L }
% 4.05/0.86 multiply(divide(divide(divide(T, S), inverse(divide(divide(S, T), divide(X2, X)))), inverse(divide(inverse(divide(divide(S, T), divide(X2, X))), divide(multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))), divide(S, T))))), divide(inverse(divide(inverse(divide(divide(S, T), divide(X2, X))), divide(multiply(divide(divide(Y, Z), W), divide(W, divide(X, divide(Z, Y)))), divide(S, T)))), divide(divide(T, S), inverse(divide(divide(S, T), divide(X2, X))))))
% 4.05/0.86 = { by lemma 13 R->L }
% 4.05/0.86 multiply(divide(V, U), divide(U, V))
% 4.05/0.86
% 4.05/0.86 Lemma 17: multiply(multiply(multiply(multiply(divide(X, Y), Z), divide(inverse(Z), W)), W), Y) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(multiply(multiply(multiply(divide(X, Y), Z), divide(inverse(Z), W)), W), Y)
% 4.05/0.86 = { by axiom 1 (multiply) }
% 4.05/0.86 multiply(multiply(multiply(divide(divide(X, Y), inverse(Z)), divide(inverse(Z), W)), W), Y)
% 4.05/0.86 = { by lemma 14 }
% 4.05/0.86 X
% 4.05/0.86
% 4.05/0.86 Lemma 18: multiply(inverse(divide(X, Y)), X) = Y.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(inverse(divide(X, Y)), X)
% 4.05/0.86 = { by lemma 5 R->L }
% 4.05/0.86 multiply(inverse(multiply(divide(divide(Z, W), V), divide(V, divide(divide(Y, X), divide(W, Z))))), X)
% 4.05/0.86 = { by lemma 15 R->L }
% 4.05/0.86 multiply(multiply(multiply(multiply(divide(U, T), divide(T, U)), divide(inverse(multiply(divide(divide(Z, W), V), divide(V, divide(divide(Y, X), divide(W, Z))))), S)), S), X)
% 4.05/0.86 = { by lemma 16 R->L }
% 4.05/0.86 multiply(multiply(multiply(multiply(divide(Y, X), multiply(divide(divide(Z, W), V), divide(V, divide(divide(Y, X), divide(W, Z))))), divide(inverse(multiply(divide(divide(Z, W), V), divide(V, divide(divide(Y, X), divide(W, Z))))), S)), S), X)
% 4.05/0.86 = { by lemma 17 }
% 4.05/0.86 Y
% 4.05/0.86
% 4.05/0.86 Lemma 19: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(inverse(multiply(X, Y)), X)
% 4.05/0.86 = { by axiom 1 (multiply) }
% 4.05/0.86 multiply(inverse(divide(X, inverse(Y))), X)
% 4.05/0.86 = { by lemma 18 }
% 4.05/0.86 inverse(Y)
% 4.05/0.86
% 4.05/0.86 Lemma 20: multiply(divide(multiply(divide(X, Y), divide(Y, divide(Z, W))), V), divide(V, divide(W, Z))) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(divide(multiply(divide(X, Y), divide(Y, divide(Z, W))), V), divide(V, divide(W, Z)))
% 4.05/0.86 = { by lemma 5 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(X, Y), divide(Y, divide(Z, W))), V), divide(V, multiply(divide(divide(U, T), S), divide(S, divide(divide(Z, W), divide(T, U))))))
% 4.05/0.86 = { by lemma 10 }
% 4.05/0.86 X
% 4.05/0.86
% 4.05/0.86 Lemma 21: multiply(multiply(X, divide(Y, Z)), Z) = multiply(divide(X, W), multiply(W, Y)).
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(multiply(X, divide(Y, Z)), Z)
% 4.05/0.86 = { by axiom 1 (multiply) }
% 4.05/0.86 multiply(divide(X, inverse(divide(Y, Z))), Z)
% 4.05/0.86 = { by lemma 18 R->L }
% 4.05/0.86 multiply(divide(X, inverse(divide(Y, Z))), multiply(inverse(divide(Y, Z)), Y))
% 4.05/0.86 = { by lemma 11 R->L }
% 4.05/0.86 multiply(divide(X, W), multiply(W, Y))
% 4.05/0.86
% 4.05/0.86 Lemma 22: multiply(multiply(divide(W, V), divide(V, W)), X) = multiply(divide(divide(X, Y), Z), multiply(Z, Y)).
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(multiply(divide(W, V), divide(V, W)), X)
% 4.05/0.86 = { by lemma 13 }
% 4.05/0.86 multiply(multiply(divide(X, Y), divide(Y, X)), X)
% 4.05/0.86 = { by lemma 21 }
% 4.05/0.86 multiply(divide(divide(X, Y), Z), multiply(Z, Y))
% 4.05/0.86
% 4.05/0.86 Lemma 23: multiply(multiply(divide(X, Y), divide(Y, X)), multiply(divide(Z, W), divide(W, divide(V, U)))) = multiply(Z, divide(U, V)).
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(multiply(divide(X, Y), divide(Y, X)), multiply(divide(Z, W), divide(W, divide(V, U))))
% 4.05/0.86 = { by lemma 22 }
% 4.05/0.86 multiply(divide(divide(multiply(divide(Z, W), divide(W, divide(V, U))), T), S), multiply(S, T))
% 4.05/0.86 = { by lemma 21 R->L }
% 4.05/0.86 multiply(multiply(divide(multiply(divide(Z, W), divide(W, divide(V, U))), T), divide(T, divide(U, V))), divide(U, V))
% 4.05/0.86 = { by lemma 20 }
% 4.05/0.86 multiply(Z, divide(U, V))
% 4.05/0.86
% 4.05/0.86 Lemma 24: inverse(divide(X, Y)) = divide(Y, X).
% 4.05/0.86 Proof:
% 4.05/0.86 inverse(divide(X, Y))
% 4.05/0.86 = { by lemma 19 R->L }
% 4.05/0.86 multiply(inverse(multiply(Z, divide(X, Y))), Z)
% 4.05/0.86 = { by lemma 15 R->L }
% 4.05/0.86 multiply(multiply(multiply(multiply(divide(W, V), divide(V, W)), divide(inverse(multiply(Z, divide(X, Y))), U)), U), Z)
% 4.05/0.86 = { by lemma 20 R->L }
% 4.05/0.86 multiply(multiply(multiply(multiply(multiply(divide(multiply(divide(divide(W, V), T), divide(T, divide(W, V))), S), divide(S, divide(V, W))), divide(V, W)), divide(inverse(multiply(Z, divide(X, Y))), U)), U), Z)
% 4.05/0.86 = { by lemma 21 }
% 4.05/0.86 multiply(multiply(multiply(multiply(divide(divide(multiply(divide(divide(W, V), T), divide(T, divide(W, V))), S), X2), multiply(X2, S)), divide(inverse(multiply(Z, divide(X, Y))), U)), U), Z)
% 4.05/0.86 = { by lemma 22 R->L }
% 4.05/0.86 multiply(multiply(multiply(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), multiply(divide(divide(W, V), T), divide(T, divide(W, V)))), divide(inverse(multiply(Z, divide(X, Y))), U)), U), Z)
% 4.05/0.86 = { by lemma 16 R->L }
% 4.05/0.86 multiply(multiply(multiply(multiply(multiply(multiply(divide(divide(W, V), T), divide(T, divide(W, V))), multiply(divide(divide(Y, X), W2), divide(W2, divide(multiply(divide(divide(W, V), T), divide(T, divide(W, V))), divide(X, Y))))), multiply(divide(divide(W, V), T), divide(T, divide(W, V)))), divide(inverse(multiply(Z, divide(X, Y))), U)), U), Z)
% 4.05/0.86 = { by lemma 23 }
% 4.05/0.86 multiply(multiply(multiply(multiply(multiply(divide(Y, X), divide(divide(X, Y), multiply(divide(divide(W, V), T), divide(T, divide(W, V))))), multiply(divide(divide(W, V), T), divide(T, divide(W, V)))), divide(inverse(multiply(Z, divide(X, Y))), U)), U), Z)
% 4.05/0.86 = { by lemma 21 }
% 4.05/0.86 multiply(multiply(multiply(multiply(divide(divide(Y, X), Z), multiply(Z, divide(X, Y))), divide(inverse(multiply(Z, divide(X, Y))), U)), U), Z)
% 4.05/0.86 = { by lemma 17 }
% 4.05/0.86 divide(Y, X)
% 4.05/0.86
% 4.05/0.86 Lemma 25: divide(X, divide(Y, Z)) = multiply(X, divide(Z, Y)).
% 4.05/0.86 Proof:
% 4.05/0.86 divide(X, divide(Y, Z))
% 4.05/0.86 = { by lemma 24 R->L }
% 4.05/0.86 divide(X, inverse(divide(Z, Y)))
% 4.05/0.86 = { by axiom 1 (multiply) R->L }
% 4.05/0.86 multiply(X, divide(Z, Y))
% 4.05/0.86
% 4.05/0.86 Lemma 26: multiply(divide(X, Y), Y) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(divide(X, Y), Y)
% 4.05/0.86 = { by lemma 24 R->L }
% 4.05/0.86 multiply(inverse(divide(Y, X)), Y)
% 4.05/0.86 = { by lemma 18 }
% 4.05/0.86 X
% 4.05/0.86
% 4.05/0.86 Lemma 27: multiply(divide(multiply(divide(X, Y), multiply(Y, divide(Z, W))), V), multiply(V, divide(W, Z))) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(divide(multiply(divide(X, Y), multiply(Y, divide(Z, W))), V), multiply(V, divide(W, Z)))
% 4.05/0.86 = { by lemma 25 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(X, Y), multiply(Y, divide(Z, W))), V), divide(V, divide(Z, W)))
% 4.05/0.86 = { by lemma 5 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(X, Y), multiply(Y, divide(Z, W))), V), divide(V, multiply(divide(divide(U, T), S), divide(S, divide(divide(W, Z), divide(T, U))))))
% 4.05/0.86 = { by lemma 25 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(X, Y), divide(Y, divide(W, Z))), V), divide(V, multiply(divide(divide(U, T), S), divide(S, divide(divide(W, Z), divide(T, U))))))
% 4.05/0.86 = { by lemma 10 }
% 4.05/0.86 X
% 4.05/0.86
% 4.05/0.86 Lemma 28: multiply(multiply(multiply(divide(multiply(X, Y), Z), divide(Z, W)), W), inverse(Y)) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(multiply(multiply(divide(multiply(X, Y), Z), divide(Z, W)), W), inverse(Y))
% 4.05/0.86 = { by axiom 1 (multiply) }
% 4.05/0.86 multiply(multiply(multiply(divide(divide(X, inverse(Y)), Z), divide(Z, W)), W), inverse(Y))
% 4.05/0.86 = { by lemma 14 }
% 4.05/0.86 X
% 4.05/0.86
% 4.05/0.86 Lemma 29: multiply(divide(multiply(divide(multiply(X, Y), Z), divide(Z, multiply(W, Y))), V), multiply(V, W)) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, Y), Z), divide(Z, multiply(W, Y))), V), multiply(V, W))
% 4.05/0.86 = { by axiom 1 (multiply) }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, Y), Z), divide(Z, divide(W, inverse(Y)))), V), multiply(V, W))
% 4.05/0.86 = { by lemma 21 R->L }
% 4.05/0.86 multiply(multiply(multiply(divide(multiply(X, Y), Z), divide(Z, divide(W, inverse(Y)))), divide(W, inverse(Y))), inverse(Y))
% 4.05/0.86 = { by lemma 28 }
% 4.05/0.86 X
% 4.05/0.86
% 4.05/0.86 Lemma 30: multiply(divide(multiply(divide(X, Y), divide(Y, multiply(Z, W))), V), multiply(V, Z)) = divide(X, W).
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(divide(multiply(divide(X, Y), divide(Y, multiply(Z, W))), V), multiply(V, Z))
% 4.05/0.86 = { by lemma 26 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(divide(X, W), W), Y), divide(Y, multiply(Z, W))), V), multiply(V, Z))
% 4.05/0.86 = { by lemma 29 }
% 4.05/0.86 divide(X, W)
% 4.05/0.86
% 4.05/0.86 Lemma 31: multiply(X, multiply(divide(Y, Z), divide(Z, Y))) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(X, multiply(divide(Y, Z), divide(Z, Y)))
% 4.05/0.86 = { by lemma 27 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, multiply(divide(Y, Z), divide(Z, Y))), W), multiply(W, divide(Y, Z))), V), multiply(V, divide(Z, Y)))
% 4.05/0.86 = { by lemma 25 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, multiply(divide(Y, Z), divide(Z, Y))), W), divide(W, divide(Z, Y))), V), multiply(V, divide(Z, Y)))
% 4.05/0.86 = { by lemma 30 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, multiply(divide(Y, Z), divide(Z, Y))), W), divide(W, multiply(divide(multiply(divide(Z, U), divide(U, multiply(T, Y))), S), multiply(S, T)))), V), multiply(V, divide(Z, Y)))
% 4.05/0.86 = { by lemma 6 R->L }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, multiply(divide(Y, Z), divide(Z, Y))), W), divide(W, multiply(divide(multiply(divide(multiply(multiply(divide(Z, Y), divide(divide(Y, Z), divide(Y, Z))), Y), U), divide(U, multiply(T, Y))), S), multiply(S, T)))), V), multiply(V, divide(Z, Y)))
% 4.05/0.86 = { by lemma 25 }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, multiply(divide(Y, Z), divide(Z, Y))), W), divide(W, multiply(divide(multiply(divide(multiply(multiply(divide(Z, Y), multiply(divide(Y, Z), divide(Z, Y))), Y), U), divide(U, multiply(T, Y))), S), multiply(S, T)))), V), multiply(V, divide(Z, Y)))
% 4.05/0.86 = { by lemma 29 }
% 4.05/0.86 multiply(divide(multiply(divide(multiply(X, multiply(divide(Y, Z), divide(Z, Y))), W), divide(W, multiply(divide(Z, Y), multiply(divide(Y, Z), divide(Z, Y))))), V), multiply(V, divide(Z, Y)))
% 4.05/0.86 = { by lemma 29 }
% 4.05/0.86 X
% 4.05/0.86
% 4.05/0.86 Lemma 32: multiply(divide(V, U), multiply(divide(U, V), divide(X, Y))) = multiply(divide(X, Y), multiply(divide(Z, W), divide(W, Z))).
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(divide(V, U), multiply(divide(U, V), divide(X, Y)))
% 4.05/0.86 = { by lemma 5 R->L }
% 4.05/0.86 multiply(divide(V, U), multiply(divide(U, V), multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T))))))
% 4.05/0.86 = { by axiom 1 (multiply) }
% 4.05/0.86 multiply(divide(V, U), divide(divide(U, V), inverse(multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T)))))))
% 4.05/0.86 = { by lemma 23 R->L }
% 4.05/0.86 multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), multiply(divide(divide(V, U), V2), divide(V2, divide(inverse(multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T))))), divide(U, V)))))
% 4.05/0.86 = { by lemma 7 }
% 4.05/0.86 multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), multiply(divide(divide(X, Y), W2), divide(W2, divide(inverse(multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T))))), divide(Y, X)))))
% 4.05/0.86 = { by lemma 23 }
% 4.05/0.86 multiply(divide(X, Y), divide(divide(Y, X), inverse(multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T)))))))
% 4.05/0.86 = { by axiom 1 (multiply) R->L }
% 4.05/0.86 multiply(divide(X, Y), multiply(divide(Y, X), multiply(divide(divide(T, S), X2), divide(X2, divide(divide(Y, X), divide(S, T))))))
% 4.05/0.86 = { by lemma 16 }
% 4.05/0.86 multiply(divide(X, Y), multiply(divide(Z, W), divide(W, Z)))
% 4.05/0.86
% 4.05/0.86 Lemma 33: multiply(divide(X, Y), multiply(divide(Y, X), Z)) = Z.
% 4.05/0.86 Proof:
% 4.05/0.86 multiply(divide(X, Y), multiply(divide(Y, X), Z))
% 4.05/0.86 = { by axiom 2 (single_axiom) R->L }
% 4.05/0.86 multiply(divide(X, Y), multiply(divide(Y, X), divide(inverse(divide(W, divide(Z, divide(V, U)))), divide(divide(U, V), W))))
% 4.05/0.86 = { by lemma 32 }
% 4.05/0.86 multiply(divide(inverse(divide(W, divide(Z, divide(V, U)))), divide(divide(U, V), W)), multiply(divide(T, S), divide(S, T)))
% 4.05/0.86 = { by axiom 2 (single_axiom) }
% 4.05/0.86 multiply(Z, multiply(divide(T, S), divide(S, T)))
% 4.05/0.86 = { by lemma 31 }
% 4.05/0.86 Z
% 4.05/0.86
% 4.05/0.86 Lemma 34: divide(X, multiply(divide(Y, Z), divide(Z, Y))) = X.
% 4.05/0.86 Proof:
% 4.05/0.86 divide(X, multiply(divide(Y, Z), divide(Z, Y)))
% 4.05/0.86 = { by lemma 33 R->L }
% 4.05/0.86 multiply(divide(W, V), multiply(divide(V, W), divide(X, multiply(divide(Y, Z), divide(Z, Y)))))
% 4.05/0.86 = { by lemma 32 }
% 4.05/0.86 multiply(divide(X, multiply(divide(Y, Z), divide(Z, Y))), multiply(divide(Y, Z), divide(Z, Y)))
% 4.05/0.86 = { by lemma 26 }
% 4.05/0.87 X
% 4.05/0.87
% 4.05/0.87 Lemma 35: divide(multiply(X, Y), Y) = X.
% 4.05/0.87 Proof:
% 4.05/0.87 divide(multiply(X, Y), Y)
% 4.05/0.87 = { by lemma 14 R->L }
% 4.05/0.87 multiply(multiply(multiply(divide(divide(divide(multiply(X, Y), Y), inverse(divide(Y, Z))), W), divide(W, divide(Y, Z))), divide(Y, Z)), inverse(divide(Y, Z)))
% 4.05/0.87 = { by lemma 26 R->L }
% 4.05/0.87 multiply(multiply(divide(multiply(multiply(divide(divide(divide(multiply(X, Y), Y), inverse(divide(Y, Z))), W), divide(W, divide(Y, Z))), divide(Y, Z)), V), V), inverse(divide(Y, Z)))
% 4.05/0.87 = { by lemma 31 R->L }
% 4.05/0.87 multiply(multiply(multiply(divide(multiply(multiply(divide(divide(divide(multiply(X, Y), Y), inverse(divide(Y, Z))), W), divide(W, divide(Y, Z))), divide(Y, Z)), V), V), multiply(divide(U, T), divide(T, U))), inverse(divide(Y, Z)))
% 4.05/0.87 = { by lemma 34 R->L }
% 4.05/0.87 multiply(multiply(multiply(divide(multiply(multiply(divide(divide(divide(multiply(X, Y), Y), inverse(divide(Y, Z))), W), divide(W, divide(Y, Z))), divide(Y, Z)), V), divide(V, multiply(divide(U, T), divide(T, U)))), multiply(divide(U, T), divide(T, U))), inverse(divide(Y, Z)))
% 4.05/0.87 = { by lemma 28 }
% 4.05/0.87 multiply(divide(divide(divide(multiply(X, Y), Y), inverse(divide(Y, Z))), W), divide(W, divide(Y, Z)))
% 4.05/0.87 = { by axiom 1 (multiply) R->L }
% 4.05/0.87 multiply(divide(multiply(divide(multiply(X, Y), Y), divide(Y, Z)), W), divide(W, divide(Y, Z)))
% 4.05/0.87 = { by lemma 27 R->L }
% 4.05/0.87 multiply(divide(multiply(divide(multiply(divide(multiply(divide(multiply(X, Y), Y), divide(Y, Z)), S), multiply(S, divide(Z, Y))), X2), multiply(X2, divide(Y, Z))), W), divide(W, divide(Y, Z)))
% 4.05/0.87 = { by lemma 26 R->L }
% 4.05/0.87 multiply(divide(multiply(divide(multiply(divide(multiply(divide(multiply(X, Y), Y), divide(Y, multiply(divide(Z, Y), Y))), S), multiply(S, divide(Z, Y))), X2), multiply(X2, divide(Y, Z))), W), divide(W, divide(Y, Z)))
% 4.05/0.87 = { by lemma 29 }
% 4.05/0.87 multiply(divide(multiply(divide(X, X2), multiply(X2, divide(Y, Z))), W), divide(W, divide(Y, Z)))
% 4.05/0.87 = { by lemma 25 }
% 4.05/0.87 multiply(divide(multiply(divide(X, X2), multiply(X2, divide(Y, Z))), W), multiply(W, divide(Z, Y)))
% 4.05/0.87 = { by lemma 27 }
% 4.05/0.87 X
% 4.05/0.87
% 4.05/0.87 Lemma 36: multiply(divide(X, Y), multiply(Y, Z)) = multiply(X, Z).
% 4.05/0.87 Proof:
% 4.05/0.87 multiply(divide(X, Y), multiply(Y, Z))
% 4.05/0.87 = { by lemma 21 R->L }
% 4.05/0.87 multiply(multiply(X, divide(Z, multiply(divide(W, V), divide(V, W)))), multiply(divide(W, V), divide(V, W)))
% 4.05/0.87 = { by lemma 34 }
% 4.05/0.87 multiply(multiply(X, Z), multiply(divide(W, V), divide(V, W)))
% 4.05/0.87 = { by lemma 31 }
% 4.05/0.87 multiply(X, Z)
% 4.05/0.87
% 4.05/0.87 Lemma 37: multiply(X, divide(Y, Y)) = X.
% 4.05/0.87 Proof:
% 4.05/0.87 multiply(X, divide(Y, Y))
% 4.05/0.87 = { by lemma 35 R->L }
% 4.05/0.87 divide(multiply(multiply(X, divide(Y, Y)), Y), Y)
% 4.05/0.87 = { by lemma 21 }
% 4.05/0.87 divide(multiply(divide(X, Z), multiply(Z, Y)), Y)
% 4.05/0.87 = { by lemma 36 }
% 4.05/0.87 divide(multiply(X, Y), Y)
% 4.05/0.87 = { by lemma 35 }
% 4.05/0.87 X
% 4.05/0.87
% 4.05/0.87 Lemma 38: multiply(X, multiply(inverse(X), Y)) = Y.
% 4.05/0.87 Proof:
% 4.05/0.87 multiply(X, multiply(inverse(X), Y))
% 4.05/0.87 = { by lemma 26 R->L }
% 4.05/0.87 multiply(multiply(divide(X, Z), Z), multiply(inverse(X), Y))
% 4.05/0.87 = { by lemma 36 R->L }
% 4.05/0.87 multiply(multiply(divide(divide(X, Z), W), multiply(W, Z)), multiply(inverse(X), Y))
% 4.05/0.87 = { by lemma 22 R->L }
% 4.05/0.87 multiply(multiply(multiply(divide(V, U), divide(U, V)), X), multiply(inverse(X), Y))
% 4.05/0.87 = { by axiom 1 (multiply) }
% 4.05/0.87 multiply(divide(multiply(divide(V, U), divide(U, V)), inverse(X)), multiply(inverse(X), Y))
% 4.05/0.87 = { by lemma 21 R->L }
% 4.05/0.87 multiply(multiply(multiply(divide(V, U), divide(U, V)), divide(Y, T)), T)
% 4.05/0.87 = { by lemma 15 }
% 4.05/0.87 Y
% 4.05/0.87
% 4.05/0.87 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 4.05/0.87 Proof:
% 4.05/0.87 multiply(multiply(a3, b3), c3)
% 4.05/0.87 = { by lemma 36 R->L }
% 4.05/0.87 multiply(multiply(divide(a3, X), multiply(X, b3)), c3)
% 4.05/0.87 = { by lemma 21 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(c3)), c3)
% 4.05/0.87 = { by lemma 38 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(c3)), multiply(Y, multiply(inverse(Y), c3)))
% 4.05/0.87 = { by lemma 38 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), multiply(Y, multiply(inverse(Y), c3)))
% 4.05/0.87 = { by axiom 1 (multiply) }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), divide(Y, inverse(multiply(inverse(Y), c3))))
% 4.05/0.87 = { by lemma 19 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y)))
% 4.05/0.87 = { by lemma 26 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), multiply(divide(divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y)), Z), Z))
% 4.05/0.87 = { by lemma 36 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), multiply(divide(divide(divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y)), Z), W), multiply(W, Z)))
% 4.05/0.87 = { by lemma 22 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), multiply(multiply(divide(Y, Y), divide(Y, Y)), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))))
% 4.05/0.87 = { by lemma 37 }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))))
% 4.05/0.87 = { by lemma 26 R->L }
% 4.05/0.87 multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 37 R->L }
% 4.05/0.87 multiply(multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), divide(Y, Y)), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 24 R->L }
% 4.05/0.87 multiply(multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), inverse(divide(Y, Y))), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 30 R->L }
% 4.05/0.87 multiply(multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), inverse(multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3))))))), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 36 R->L }
% 4.05/0.87 multiply(multiply(divide(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), V), multiply(V, inverse(multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))))))), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 21 R->L }
% 4.05/0.87 multiply(multiply(multiply(multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))), divide(inverse(multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))))), U)), U), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 33 R->L }
% 4.05/0.87 multiply(multiply(multiply(multiply(divide(multiply(a3, divide(b3, inverse(c3))), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3))))), multiply(divide(multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))), multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))))), divide(inverse(multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))))), U)), U), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 35 }
% 4.05/0.87 multiply(multiply(multiply(multiply(divide(multiply(a3, divide(b3, inverse(c3))), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3))))), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))))), divide(inverse(multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(multiply(a3, divide(b3, inverse(c3))), inverse(multiply(Y, multiply(inverse(Y), c3)))))), U)), U), multiply(divide(multiply(divide(Y, Y), divide(Y, multiply(inverse(multiply(Y, multiply(inverse(Y), c3))), Y))), multiply(a3, divide(b3, inverse(c3)))), multiply(a3, divide(b3, inverse(c3)))))
% 4.05/0.87 = { by lemma 17 }
% 4.05/0.87 multiply(a3, divide(b3, inverse(c3)))
% 4.05/0.87 = { by axiom 1 (multiply) R->L }
% 4.05/0.87 multiply(a3, multiply(b3, c3))
% 4.05/0.87 % SZS output end Proof
% 4.05/0.87
% 4.05/0.87 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------