TSTP Solution File: GRP469-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP469-1 : 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 01:18:33 EDT 2023
% Result : Unsatisfiable 2.31s 0.64s
% Output : Proof 2.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP469-1 : 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 22:25:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 2.31/0.64 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.31/0.64
% 2.31/0.64 % SZS status Unsatisfiable
% 2.31/0.64
% 2.31/0.70 % SZS output start Proof
% 2.31/0.70 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 2.31/0.70 Axiom 2 (single_axiom): divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)) = Y.
% 2.31/0.70
% 2.87/0.70 Lemma 3: divide(inverse(divide(X, divide(Y, multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), X)) = Y.
% 2.87/0.70 Proof:
% 2.87/0.70 divide(inverse(divide(X, divide(Y, multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), X))
% 2.87/0.70 = { by axiom 1 (multiply) }
% 2.87/0.70 divide(inverse(divide(X, divide(Y, multiply(inverse(Z), W)))), divide(divide(inverse(W), inverse(Z)), X))
% 2.87/0.70 = { by axiom 1 (multiply) }
% 2.87/0.70 divide(inverse(divide(X, divide(Y, divide(inverse(Z), inverse(W))))), divide(divide(inverse(W), inverse(Z)), X))
% 2.87/0.70 = { by axiom 2 (single_axiom) }
% 2.87/0.70 Y
% 2.87/0.70
% 2.87/0.70 Lemma 4: divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, divide(W, V))))) = divide(V, W).
% 2.87/0.70 Proof:
% 2.87/0.70 divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, divide(W, V)))))
% 2.87/0.70 = { by axiom 1 (multiply) }
% 2.87/0.70 divide(inverse(X), divide(multiply(inverse(Y), Z), inverse(divide(multiply(inverse(Z), Y), divide(X, divide(W, V))))))
% 2.87/0.70 = { by axiom 2 (single_axiom) R->L }
% 2.87/0.70 divide(inverse(divide(inverse(divide(multiply(inverse(Z), Y), divide(X, divide(W, V)))), divide(divide(V, W), multiply(inverse(Z), Y)))), divide(multiply(inverse(Y), Z), inverse(divide(multiply(inverse(Z), Y), divide(X, divide(W, V))))))
% 2.87/0.70 = { by lemma 3 }
% 2.87/0.70 divide(V, W)
% 2.87/0.70
% 2.87/0.70 Lemma 5: multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, W))), Z) = W.
% 2.87/0.70 Proof:
% 2.87/0.70 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, W))), Z)
% 2.87/0.70 = { by axiom 2 (single_axiom) R->L }
% 2.87/0.70 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))))), Z)
% 2.87/0.70 = { by axiom 1 (multiply) }
% 2.87/0.70 divide(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))))), inverse(Z))
% 2.87/0.70 = { by lemma 4 R->L }
% 2.87/0.70 divide(inverse(S), multiply(multiply(inverse(X2), Y2), divide(multiply(inverse(Y2), X2), divide(S, divide(inverse(Z), multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))))))))))
% 2.87/0.70 = { by lemma 4 }
% 2.87/0.70 divide(inverse(S), multiply(multiply(inverse(X2), Y2), divide(multiply(inverse(Y2), X2), divide(S, divide(divide(divide(T, U), V), inverse(divide(V, divide(W, divide(U, T)))))))))
% 2.87/0.70 = { by lemma 4 }
% 2.87/0.70 divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))
% 2.87/0.70 = { by axiom 2 (single_axiom) }
% 2.87/0.70 W
% 2.87/0.70
% 2.87/0.70 Lemma 6: multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, W))), inverse(V)) = multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(W, Z)))).
% 2.87/0.70 Proof:
% 2.87/0.70 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, W))), inverse(V))
% 2.87/0.70 = { by lemma 4 R->L }
% 2.87/0.70 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(W, Z))))))), inverse(V))
% 2.87/0.70 = { by lemma 5 }
% 2.87/0.70 multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(W, Z))))
% 2.87/0.70
% 2.87/0.70 Lemma 7: multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, divide(W, inverse(Z))))) = W.
% 2.87/0.70 Proof:
% 2.87/0.70 multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, divide(W, inverse(Z)))))
% 2.87/0.70 = { by lemma 6 R->L }
% 2.87/0.70 multiply(multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(inverse(Z), W))), inverse(Z))
% 2.87/0.70 = { by lemma 5 }
% 2.87/0.70 W
% 2.87/0.70
% 2.87/0.70 Lemma 8: multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), multiply(Z, W))), Z) = inverse(W).
% 2.87/0.70 Proof:
% 2.87/0.70 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), multiply(Z, W))), Z)
% 2.87/0.70 = { by axiom 1 (multiply) }
% 2.87/0.70 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, inverse(W)))), Z)
% 2.87/0.70 = { by lemma 5 }
% 2.87/0.70 inverse(W)
% 2.87/0.70
% 2.87/0.70 Lemma 9: divide(multiply(inverse(X), Y), multiply(multiply(multiply(inverse(Z), W), divide(multiply(inverse(W), Z), V)), multiply(inverse(X), Y))) = V.
% 2.87/0.70 Proof:
% 2.87/0.70 divide(multiply(inverse(X), Y), multiply(multiply(multiply(inverse(Z), W), divide(multiply(inverse(W), Z), V)), multiply(inverse(X), Y)))
% 2.87/0.70 = { by lemma 7 R->L }
% 2.87/0.70 divide(multiply(inverse(X), Y), multiply(multiply(multiply(inverse(Z), W), divide(multiply(inverse(W), Z), multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(U, divide(V, inverse(U))))))), multiply(inverse(X), Y)))
% 2.87/0.70 = { by lemma 8 }
% 2.87/0.70 divide(multiply(inverse(X), Y), inverse(divide(multiply(inverse(Y), X), divide(U, divide(V, inverse(U))))))
% 2.87/0.70 = { by axiom 1 (multiply) R->L }
% 2.87/0.70 multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(U, divide(V, inverse(U)))))
% 2.87/0.70 = { by lemma 7 }
% 2.87/0.70 V
% 2.87/0.70
% 2.87/0.70 Lemma 10: multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, multiply(W, Z)))) = W.
% 2.87/0.70 Proof:
% 2.87/0.70 multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, multiply(W, Z))))
% 2.87/0.70 = { by axiom 1 (multiply) }
% 2.87/0.70 multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, divide(W, inverse(Z)))))
% 2.87/0.70 = { by lemma 6 R->L }
% 2.87/0.70 multiply(multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(inverse(Z), W))), inverse(Z))
% 2.87/0.70 = { by lemma 5 }
% 2.87/0.70 W
% 2.87/0.70
% 2.87/0.70 Lemma 11: divide(Z, multiply(Y, Z)) = divide(X, multiply(Y, X)).
% 2.87/0.70 Proof:
% 2.87/0.70 divide(Z, multiply(Y, Z))
% 2.87/0.70 = { by lemma 9 R->L }
% 2.87/0.70 divide(multiply(inverse(W), V), multiply(multiply(multiply(inverse(S), X2), divide(multiply(inverse(X2), S), divide(Z, multiply(Y, Z)))), multiply(inverse(W), V)))
% 2.87/0.70 = { by lemma 10 }
% 2.87/0.70 divide(multiply(inverse(W), V), multiply(Y, multiply(inverse(W), V)))
% 2.87/0.70 = { by lemma 10 R->L }
% 2.87/0.70 divide(multiply(inverse(W), V), multiply(multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(X, multiply(Y, X)))), multiply(inverse(W), V)))
% 2.87/0.70 = { by lemma 9 }
% 2.87/0.70 divide(X, multiply(Y, X))
% 2.87/0.70
% 2.87/0.70 Lemma 12: divide(multiply(inverse(X), Y), multiply(Z, multiply(inverse(X), Y))) = divide(W, divide(Z, inverse(W))).
% 2.87/0.70 Proof:
% 2.87/0.70 divide(multiply(inverse(X), Y), multiply(Z, multiply(inverse(X), Y)))
% 2.87/0.70 = { by lemma 7 R->L }
% 2.87/0.70 divide(multiply(inverse(X), Y), multiply(multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(W, divide(Z, inverse(W))))), multiply(inverse(X), Y)))
% 2.87/0.70 = { by lemma 9 }
% 2.87/0.70 divide(W, divide(Z, inverse(W)))
% 2.87/0.70
% 2.87/0.70 Lemma 13: divide(X, divide(Y, inverse(X))) = divide(Z, multiply(Y, Z)).
% 2.87/0.70 Proof:
% 2.87/0.70 divide(X, divide(Y, inverse(X)))
% 2.87/0.70 = { by lemma 12 R->L }
% 2.87/0.70 divide(multiply(inverse(W), V), multiply(Y, multiply(inverse(W), V)))
% 2.87/0.70 = { by lemma 10 R->L }
% 2.87/0.70 divide(multiply(inverse(W), V), multiply(multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(Z, multiply(Y, Z)))), multiply(inverse(W), V)))
% 2.87/0.70 = { by lemma 9 }
% 2.87/0.70 divide(Z, multiply(Y, Z))
% 2.87/0.70
% 2.87/0.70 Lemma 14: inverse(divide(multiply(inverse(X), Y), divide(Z, multiply(W, Z)))) = divide(V, multiply(multiply(multiply(inverse(X), Y), W), V)).
% 2.87/0.70 Proof:
% 2.87/0.70 inverse(divide(multiply(inverse(X), Y), divide(Z, multiply(W, Z))))
% 2.87/0.70 = { by lemma 8 R->L }
% 2.87/0.70 multiply(multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), multiply(multiply(inverse(Y), X), divide(multiply(inverse(X), Y), divide(Z, multiply(W, Z)))))), multiply(inverse(Y), X))
% 2.87/0.70 = { by lemma 10 }
% 2.87/0.70 multiply(multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), W)), multiply(inverse(Y), X))
% 2.87/0.70 = { by lemma 9 R->L }
% 2.87/0.70 divide(multiply(inverse(S), X2), multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), multiply(multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), W)), multiply(inverse(Y), X)))), multiply(inverse(S), X2)))
% 2.87/0.70 = { by lemma 9 }
% 2.87/0.70 divide(multiply(inverse(S), X2), multiply(multiply(multiply(inverse(X), Y), W), multiply(inverse(S), X2)))
% 2.87/0.70 = { by lemma 12 }
% 2.87/0.70 divide(Y2, divide(multiply(multiply(inverse(X), Y), W), inverse(Y2)))
% 2.87/0.70 = { by lemma 13 }
% 2.87/0.70 divide(V, multiply(multiply(multiply(inverse(X), Y), W), V))
% 2.87/0.70
% 2.87/0.70 Lemma 15: divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X)) = inverse(divide(Z, divide(Y, divide(V, W)))).
% 2.87/0.70 Proof:
% 2.87/0.70 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X))
% 2.87/0.70 = { by axiom 2 (single_axiom) R->L }
% 2.87/0.70 divide(inverse(divide(X, divide(inverse(divide(Z, divide(Y, divide(V, W)))), divide(divide(W, V), Z)))), divide(divide(Z, divide(W, V)), X))
% 2.87/0.70 = { by axiom 2 (single_axiom) }
% 2.87/0.70 inverse(divide(Z, divide(Y, divide(V, W))))
% 2.87/0.70
% 2.87/0.71 Lemma 16: divide(inverse(divide(X, Y)), divide(divide(Z, multiply(W, V)), X)) = inverse(divide(Z, divide(Y, divide(inverse(V), W)))).
% 2.87/0.71 Proof:
% 2.87/0.71 divide(inverse(divide(X, Y)), divide(divide(Z, multiply(W, V)), X))
% 2.87/0.71 = { by axiom 1 (multiply) }
% 2.87/0.71 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, inverse(V))), X))
% 2.87/0.71 = { by lemma 15 }
% 2.87/0.71 inverse(divide(Z, divide(Y, divide(inverse(V), W))))
% 2.87/0.71
% 2.87/0.71 Lemma 17: divide(inverse(multiply(X, Y)), divide(divide(Z, divide(W, V)), X)) = inverse(divide(Z, divide(inverse(Y), divide(V, W)))).
% 2.87/0.71 Proof:
% 2.87/0.71 divide(inverse(multiply(X, Y)), divide(divide(Z, divide(W, V)), X))
% 2.87/0.71 = { by axiom 1 (multiply) }
% 2.87/0.71 divide(inverse(divide(X, inverse(Y))), divide(divide(Z, divide(W, V)), X))
% 2.87/0.71 = { by lemma 15 }
% 2.87/0.71 inverse(divide(Z, divide(inverse(Y), divide(V, W))))
% 2.87/0.71
% 2.87/0.71 Lemma 18: divide(inverse(divide(X, Y)), divide(divide(Z, multiply(inverse(W), V)), X)) = inverse(divide(Z, divide(Y, multiply(inverse(V), W)))).
% 2.87/0.71 Proof:
% 2.87/0.71 divide(inverse(divide(X, Y)), divide(divide(Z, multiply(inverse(W), V)), X))
% 2.87/0.71 = { by lemma 3 R->L }
% 2.87/0.71 divide(inverse(divide(X, divide(inverse(divide(Z, divide(Y, multiply(inverse(V), W)))), divide(multiply(inverse(W), V), Z)))), divide(divide(Z, multiply(inverse(W), V)), X))
% 2.87/0.71 = { by axiom 2 (single_axiom) }
% 2.87/0.71 inverse(divide(Z, divide(Y, multiply(inverse(V), W))))
% 2.87/0.71
% 2.87/0.71 Lemma 19: divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))) = Y.
% 2.87/0.71 Proof:
% 2.87/0.71 divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z)))
% 2.87/0.71 = { by lemma 4 R->L }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z)), X)))))
% 2.87/0.71 = { by lemma 4 R->L }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(inverse(S), multiply(multiply(inverse(X2), Y2), divide(multiply(inverse(Y2), X2), divide(S, divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z)))))))))))
% 2.87/0.71 = { by lemma 10 R->L }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(inverse(S), multiply(multiply(inverse(X2), Y2), divide(multiply(inverse(Y2), X2), divide(S, multiply(multiply(inverse(Z2), W2), divide(multiply(inverse(W2), Z2), divide(V2, multiply(divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))), V2))))))))))))
% 2.87/0.71 = { by axiom 1 (multiply) }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(inverse(S), multiply(multiply(inverse(X2), Y2), divide(multiply(inverse(Y2), X2), divide(S, divide(multiply(inverse(Z2), W2), inverse(divide(multiply(inverse(W2), Z2), divide(V2, multiply(divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))), V2)))))))))))))
% 2.87/0.71 = { by lemma 4 }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(inverse(divide(multiply(inverse(W2), Z2), divide(V2, multiply(divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))), V2)))), multiply(inverse(Z2), W2))))))
% 2.87/0.71 = { by lemma 14 }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(divide(U2, multiply(multiply(multiply(inverse(W2), Z2), divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z)))), U2)), multiply(inverse(Z2), W2))))))
% 2.87/0.71 = { by axiom 1 (multiply) }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(divide(U2, multiply(divide(multiply(inverse(W2), Z2), inverse(divide(X, divide(divide(inverse(Y), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))))), U2)), multiply(inverse(Z2), W2))))))
% 2.87/0.71 = { by lemma 18 R->L }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(divide(U2, multiply(divide(multiply(inverse(W2), Z2), divide(inverse(divide(T2, divide(inverse(Y), divide(multiply(inverse(Z), W), X)))), divide(divide(X, multiply(inverse(Z), W)), T2))), U2)), multiply(inverse(Z2), W2))))))
% 2.87/0.71 = { by axiom 2 (single_axiom) }
% 2.87/0.71 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(divide(U2, multiply(divide(multiply(inverse(W2), Z2), inverse(Y)), U2)), multiply(inverse(Z2), W2))))))
% 2.87/0.71 = { by lemma 4 }
% 2.87/0.71 divide(multiply(inverse(Z2), W2), divide(U2, multiply(divide(multiply(inverse(W2), Z2), inverse(Y)), U2)))
% 2.87/0.71 = { by axiom 1 (multiply) R->L }
% 2.87/0.71 divide(multiply(inverse(Z2), W2), divide(U2, multiply(multiply(multiply(inverse(W2), Z2), Y), U2)))
% 2.87/0.71 = { by lemma 14 R->L }
% 2.87/0.71 divide(multiply(inverse(Z2), W2), inverse(divide(multiply(inverse(W2), Z2), divide(S2, multiply(Y, S2)))))
% 2.87/0.71 = { by axiom 1 (multiply) R->L }
% 2.87/0.71 multiply(multiply(inverse(Z2), W2), divide(multiply(inverse(W2), Z2), divide(S2, multiply(Y, S2))))
% 2.87/0.71 = { by lemma 10 }
% 2.87/0.71 Y
% 2.87/0.71
% 2.87/0.71 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 2.87/0.71 Proof:
% 2.87/0.71 multiply(inverse(a1), a1)
% 2.87/0.71 = { by lemma 19 R->L }
% 2.87/0.71 divide(X, divide(divide(inverse(multiply(inverse(a1), a1)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by axiom 2 (single_axiom) R->L }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(a1), a1)), divide(divide(V, multiply(inverse(inverse(a1)), V)), inverse(a1))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 4 R->L }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(a1), a1)), divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 19 R->L }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(a1), a1)), divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(X2, divide(divide(inverse(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V)))), divide(multiply(inverse(Y2), Z2), X2)), multiply(inverse(Z2), Y2)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 18 R->L }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(a1), a1)), divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(X2, divide(divide(divide(inverse(divide(W2, V)), divide(divide(inverse(a1), multiply(inverse(V), inverse(a1))), W2)), divide(multiply(inverse(Y2), Z2), X2)), multiply(inverse(Z2), Y2)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 16 }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(a1), a1)), divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(X2, divide(divide(inverse(divide(inverse(a1), divide(V, divide(inverse(inverse(a1)), inverse(V))))), divide(multiply(inverse(Y2), Z2), X2)), multiply(inverse(Z2), Y2)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 19 }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(a1), a1)), divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(inverse(a1), divide(V, divide(inverse(inverse(a1)), inverse(V))))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 4 }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(a1), a1)), divide(divide(V, divide(inverse(inverse(a1)), inverse(V))), inverse(a1))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 17 }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, inverse(divide(V, divide(inverse(a1), divide(inverse(V), inverse(inverse(a1)))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by axiom 1 (multiply) R->L }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, inverse(divide(V, divide(inverse(a1), multiply(inverse(V), inverse(a1))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by lemma 11 }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, inverse(divide(V, divide(inverse(b1), multiply(inverse(V), inverse(b1))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.71 = { by axiom 1 (multiply) }
% 2.87/0.71 divide(X, divide(divide(divide(inverse(divide(W, inverse(divide(V, divide(inverse(b1), divide(inverse(V), inverse(inverse(b1)))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 17 R->L }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(divide(V, divide(inverse(inverse(b1)), inverse(V))), inverse(b1))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 4 R->L }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(inverse(V2), multiply(multiply(inverse(U2), T2), divide(multiply(inverse(T2), U2), divide(V2, divide(inverse(b1), divide(V, divide(inverse(inverse(b1)), inverse(V))))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 19 R->L }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(inverse(V2), multiply(multiply(inverse(U2), T2), divide(multiply(inverse(T2), U2), divide(V2, divide(S2, divide(divide(inverse(divide(inverse(b1), divide(V, divide(inverse(inverse(b1)), inverse(V))))), divide(multiply(inverse(X3), Y3), S2)), multiply(inverse(Y3), X3)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 16 R->L }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(inverse(V2), multiply(multiply(inverse(U2), T2), divide(multiply(inverse(T2), U2), divide(V2, divide(S2, divide(divide(divide(inverse(divide(Z3, V)), divide(divide(inverse(b1), multiply(inverse(V), inverse(b1))), Z3)), divide(multiply(inverse(X3), Y3), S2)), multiply(inverse(Y3), X3)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 11 R->L }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(inverse(V2), multiply(multiply(inverse(U2), T2), divide(multiply(inverse(T2), U2), divide(V2, divide(S2, divide(divide(divide(inverse(divide(Z3, V)), divide(divide(inverse(a1), multiply(inverse(V), inverse(a1))), Z3)), divide(multiply(inverse(X3), Y3), S2)), multiply(inverse(Y3), X3)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 16 }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(inverse(V2), multiply(multiply(inverse(U2), T2), divide(multiply(inverse(T2), U2), divide(V2, divide(S2, divide(divide(inverse(divide(inverse(a1), divide(V, divide(inverse(inverse(a1)), inverse(V))))), divide(multiply(inverse(X3), Y3), S2)), multiply(inverse(Y3), X3)))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 19 }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(inverse(V2), multiply(multiply(inverse(U2), T2), divide(multiply(inverse(T2), U2), divide(V2, divide(inverse(a1), divide(V, divide(inverse(inverse(a1)), inverse(V))))))))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 4 }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(divide(V, divide(inverse(inverse(a1)), inverse(V))), inverse(a1))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 13 }
% 2.87/0.72 divide(X, divide(divide(divide(inverse(divide(W, divide(inverse(multiply(inverse(b1), b1)), divide(divide(V, multiply(inverse(inverse(a1)), V)), inverse(a1))))), divide(divide(inverse(a1), divide(V, multiply(inverse(inverse(a1)), V))), W)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by axiom 2 (single_axiom) }
% 2.87/0.72 divide(X, divide(divide(inverse(multiply(inverse(b1), b1)), divide(multiply(inverse(Y), Z), X)), multiply(inverse(Z), Y)))
% 2.87/0.72 = { by lemma 19 }
% 2.87/0.72 multiply(inverse(b1), b1)
% 2.87/0.72 % SZS output end Proof
% 2.87/0.72
% 2.87/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
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