TSTP Solution File: GRP478-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP478-1 : 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 : n014.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 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP478-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:12:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.20/0.50 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, W)))), W) = Z.
% 0.20/0.50
% 0.20/0.50 Lemma 3: multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, multiply(Y, W)))), W) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, multiply(Y, W)))), W)
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, inverse(W))))), W)
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, inverse(W))))), inverse(W))
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 4: inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, multiply(W, V))))) = multiply(inverse(divide(divide(divide(U, U), W), Z)), V).
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, multiply(W, V)))))
% 0.20/0.50 = { by lemma 3 R->L }
% 0.20/0.50 multiply(inverse(divide(divide(divide(U, U), W), divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, multiply(W, V))))), multiply(W, V)))), V)
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 multiply(inverse(divide(divide(divide(U, U), W), Z)), V)
% 0.20/0.50
% 0.20/0.50 Lemma 5: divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), divide(Y, W)) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), divide(Y, W))
% 0.20/0.50 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.50 divide(divide(inverse(divide(divide(divide(X, X), Y), divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, divide(Y, W))))), divide(Y, W)))), W), divide(Y, W))
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, divide(Y, W))))), divide(Y, W))
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 6: divide(divide(multiply(inverse(divide(divide(divide(X, X), Y), Z)), W), V), divide(U, V)) = divide(Z, divide(U, multiply(Y, W))).
% 0.20/0.50 Proof:
% 0.20/0.50 divide(divide(multiply(inverse(divide(divide(divide(X, X), Y), Z)), W), V), divide(U, V))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 divide(divide(inverse(divide(divide(divide(T, T), U), divide(Z, divide(U, multiply(Y, W))))), V), divide(U, V))
% 0.20/0.50 = { by lemma 5 }
% 0.20/0.50 divide(Z, divide(U, multiply(Y, W)))
% 0.20/0.50
% 0.20/0.50 Lemma 7: divide(divide(X, W), divide(Z, W)) = divide(divide(X, Y), divide(Z, Y)).
% 0.20/0.50 Proof:
% 0.20/0.50 divide(divide(X, W), divide(Z, W))
% 0.20/0.50 = { by lemma 3 R->L }
% 0.20/0.50 divide(divide(multiply(inverse(divide(divide(divide(S, S), U), divide(X, multiply(U, T)))), T), W), divide(Z, W))
% 0.20/0.50 = { by lemma 6 }
% 0.20/0.50 divide(divide(X, multiply(U, T)), divide(Z, multiply(U, T)))
% 0.20/0.50 = { by lemma 6 R->L }
% 0.20/0.50 divide(divide(multiply(inverse(divide(divide(divide(V, V), U), divide(X, multiply(U, T)))), T), Y), divide(Z, Y))
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 divide(divide(X, Y), divide(Z, Y))
% 0.20/0.50
% 0.20/0.50 Lemma 8: divide(divide(X, Y), divide(Z, Y)) = divide(multiply(X, W), multiply(Z, W)).
% 0.20/0.50 Proof:
% 0.20/0.50 divide(divide(X, Y), divide(Z, Y))
% 0.20/0.50 = { by lemma 7 }
% 0.20/0.50 divide(divide(X, inverse(W)), divide(Z, inverse(W)))
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 divide(multiply(X, W), divide(Z, inverse(W)))
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 divide(multiply(X, W), multiply(Z, W))
% 0.20/0.50
% 0.20/0.50 Lemma 9: divide(multiply(inverse(divide(divide(divide(X, X), Y), Z)), W), multiply(Y, W)) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 divide(multiply(inverse(divide(divide(divide(X, X), Y), Z)), W), multiply(Y, W))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, multiply(Y, W))))), multiply(Y, W))
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 10: multiply(inverse(X), divide(multiply(divide(Y, Y), Z), multiply(divide(W, W), Z))) = inverse(X).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(X), divide(multiply(divide(Y, Y), Z), multiply(divide(W, W), Z)))
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(inverse(X), divide(multiply(divide(Y, Y), Z), divide(divide(W, W), inverse(Z))))
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(inverse(X), divide(divide(divide(Y, Y), inverse(Z)), divide(divide(W, W), inverse(Z))))
% 0.20/0.50 = { by lemma 7 R->L }
% 0.20/0.50 multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), divide(divide(W, W), inverse(X))))
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 multiply(inverse(X), divide(multiply(divide(Y, Y), X), divide(divide(W, W), inverse(X))))
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 multiply(inverse(X), divide(multiply(divide(Y, Y), X), multiply(divide(W, W), X)))
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X)))
% 0.20/0.50 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.50 divide(inverse(divide(divide(divide(V, V), U), divide(multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), divide(U, T)))), T)
% 0.20/0.50 = { by lemma 5 R->L }
% 0.20/0.50 divide(inverse(divide(divide(inverse(divide(divide(divide(W, W), inverse(X)), divide(divide(divide(V, V), U), divide(multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), divide(U, T))))), divide(U, T)), divide(inverse(X), divide(U, T)))), T)
% 0.20/0.50 = { by axiom 1 (multiply) R->L }
% 0.20/0.50 divide(inverse(divide(divide(inverse(divide(multiply(divide(W, W), X), divide(divide(divide(V, V), U), divide(multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), divide(U, T))))), divide(U, T)), divide(inverse(X), divide(U, T)))), T)
% 0.20/0.50 = { by lemma 9 R->L }
% 0.20/0.50 divide(inverse(divide(divide(inverse(divide(divide(multiply(inverse(divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X)))), divide(divide(divide(V, V), U), divide(multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), divide(U, T))))), divide(U, T)), divide(inverse(X), divide(U, T)))), T)
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 divide(inverse(divide(divide(inverse(divide(divide(divide(inverse(divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), inverse(divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X)))), multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X)))), divide(divide(divide(V, V), U), divide(multiply(inverse(X), divide(divide(divide(Y, Y), inverse(X)), multiply(divide(W, W), X))), divide(U, T))))), divide(U, T)), divide(inverse(X), divide(U, T)))), T)
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 divide(inverse(divide(divide(divide(V, V), U), divide(inverse(X), divide(U, T)))), T)
% 0.20/0.50 = { by axiom 2 (single_axiom) }
% 0.20/0.50 inverse(X)
% 0.20/0.50
% 0.20/0.50 Lemma 11: inverse(divide(multiply(divide(X, X), Y), multiply(Z, Y))) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(divide(multiply(divide(X, X), Y), multiply(Z, Y)))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 inverse(divide(divide(divide(X, X), inverse(W)), divide(Z, inverse(W))))
% 0.20/0.50 = { by lemma 10 R->L }
% 0.20/0.50 multiply(inverse(divide(divide(divide(X, X), inverse(W)), divide(Z, inverse(W)))), divide(multiply(divide(V, V), U), multiply(divide(T, T), U)))
% 0.20/0.50 = { by lemma 10 R->L }
% 0.20/0.50 multiply(inverse(divide(divide(divide(X, X), inverse(W)), divide(Z, multiply(inverse(W), divide(multiply(divide(V, V), U), multiply(divide(T, T), U)))))), divide(multiply(divide(V, V), U), multiply(divide(T, T), U)))
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 12: inverse(divide(divide(divide(X, X), Y), divide(multiply(Z, W), multiply(Y, W)))) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(divide(divide(divide(X, X), Y), divide(multiply(Z, W), multiply(Y, W))))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 inverse(divide(divide(divide(X, X), Y), divide(divide(Z, multiply(V, U)), divide(Y, multiply(V, U)))))
% 0.20/0.50 = { by lemma 4 }
% 0.20/0.50 multiply(inverse(divide(divide(divide(T, T), V), divide(Z, multiply(V, U)))), U)
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 13: multiply(inverse(divide(multiply(divide(X, X), Y), Z)), Y) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(divide(multiply(divide(X, X), Y), Z)), Y)
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(inverse(divide(divide(divide(X, X), inverse(Y)), Z)), Y)
% 0.20/0.50 = { by lemma 10 R->L }
% 0.20/0.50 multiply(multiply(inverse(divide(divide(divide(X, X), inverse(Y)), Z)), divide(multiply(divide(W, W), V), multiply(divide(U, U), V))), Y)
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 divide(multiply(inverse(divide(divide(divide(X, X), inverse(Y)), Z)), divide(multiply(divide(W, W), V), multiply(divide(U, U), V))), inverse(Y))
% 0.20/0.50 = { by lemma 10 R->L }
% 0.20/0.50 divide(multiply(inverse(divide(divide(divide(X, X), inverse(Y)), Z)), divide(multiply(divide(W, W), V), multiply(divide(U, U), V))), multiply(inverse(Y), divide(multiply(divide(W, W), V), multiply(divide(U, U), V))))
% 0.20/0.50 = { by lemma 9 }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 14: divide(multiply(X, Y), multiply(Z, Y)) = divide(X, Z).
% 0.20/0.50 Proof:
% 0.20/0.50 divide(multiply(X, Y), multiply(Z, Y))
% 0.20/0.50 = { by lemma 13 R->L }
% 0.20/0.50 divide(multiply(inverse(divide(multiply(divide(W, W), Y), multiply(X, Y))), Y), multiply(Z, Y))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 divide(multiply(inverse(divide(divide(divide(W, W), Z), divide(X, Z))), Y), multiply(Z, Y))
% 0.20/0.50 = { by lemma 9 }
% 0.20/0.50 divide(X, Z)
% 0.20/0.50
% 0.20/0.50 Lemma 15: multiply(X, divide(Y, Y)) = X.
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(X, divide(Y, Y))
% 0.20/0.50 = { by lemma 12 R->L }
% 0.20/0.50 multiply(inverse(divide(divide(divide(Z, Z), W), divide(multiply(X, V), multiply(W, V)))), divide(Y, Y))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 multiply(inverse(divide(divide(divide(Z, Z), W), divide(multiply(X, V), multiply(W, V)))), divide(multiply(Y, U), multiply(Y, U)))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 multiply(inverse(divide(divide(divide(Z, Z), W), divide(multiply(X, V), multiply(W, V)))), divide(divide(Y, Y), divide(Y, Y)))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 multiply(inverse(divide(divide(divide(Z, Z), W), divide(multiply(X, V), multiply(W, V)))), divide(multiply(divide(Y, Y), T), multiply(divide(Y, Y), T)))
% 0.20/0.50 = { by lemma 10 }
% 0.20/0.50 inverse(divide(divide(divide(Z, Z), W), divide(multiply(X, V), multiply(W, V))))
% 0.20/0.50 = { by lemma 12 }
% 0.20/0.50 X
% 0.20/0.50
% 0.20/0.50 Lemma 16: divide(X, multiply(inverse(Y), Y)) = X.
% 0.20/0.50 Proof:
% 0.20/0.50 divide(X, multiply(inverse(Y), Y))
% 0.20/0.50 = { by lemma 13 R->L }
% 0.20/0.50 multiply(inverse(divide(multiply(divide(Z, Z), Y), divide(X, multiply(inverse(Y), Y)))), Y)
% 0.20/0.50 = { by axiom 1 (multiply) }
% 0.20/0.50 multiply(inverse(divide(divide(divide(Z, Z), inverse(Y)), divide(X, multiply(inverse(Y), Y)))), Y)
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 X
% 0.20/0.50
% 0.20/0.51 Lemma 17: divide(inverse(divide(multiply(divide(X, X), divide(divide(divide(Y, Y), Z), divide(inverse(W), divide(Z, V)))), multiply(U, W))), V) = U.
% 0.20/0.51 Proof:
% 0.20/0.51 divide(inverse(divide(multiply(divide(X, X), divide(divide(divide(Y, Y), Z), divide(inverse(W), divide(Z, V)))), multiply(U, W))), V)
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 divide(inverse(divide(multiply(divide(X, X), divide(divide(divide(Y, Y), Z), divide(inverse(W), divide(Z, V)))), divide(U, inverse(W)))), V)
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 divide(inverse(divide(divide(divide(X, X), inverse(divide(divide(divide(Y, Y), Z), divide(inverse(W), divide(Z, V))))), divide(U, inverse(W)))), V)
% 0.20/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.51 divide(inverse(divide(divide(divide(X, X), inverse(divide(divide(divide(Y, Y), Z), divide(inverse(W), divide(Z, V))))), divide(U, divide(inverse(divide(divide(divide(Y, Y), Z), divide(inverse(W), divide(Z, V)))), V)))), V)
% 0.20/0.51 = { by axiom 2 (single_axiom) }
% 0.20/0.51 U
% 0.20/0.51
% 0.20/0.51 Lemma 18: multiply(inverse(X), X) = divide(Y, Y).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(inverse(X), X)
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 divide(inverse(X), inverse(X))
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 inverse(divide(multiply(divide(inverse(X), inverse(X)), Z), multiply(divide(inverse(X), inverse(X)), Z)))
% 0.20/0.51 = { by lemma 15 R->L }
% 0.20/0.51 inverse(multiply(divide(multiply(divide(inverse(X), inverse(X)), Z), multiply(divide(inverse(X), inverse(X)), Z)), divide(W, W)))
% 0.20/0.51 = { by lemma 16 R->L }
% 0.20/0.51 inverse(divide(multiply(divide(multiply(divide(inverse(X), inverse(X)), Z), multiply(divide(inverse(X), inverse(X)), Z)), divide(W, W)), multiply(inverse(V), V)))
% 0.20/0.51 = { by lemma 17 R->L }
% 0.20/0.51 divide(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), divide(S, Y2)))), multiply(inverse(divide(multiply(divide(multiply(divide(inverse(X), inverse(X)), Z), multiply(divide(inverse(X), inverse(X)), Z)), divide(W, W)), multiply(inverse(V), V))), X2))), Y2)
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 divide(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), divide(S, Y2)))), multiply(inverse(divide(divide(divide(multiply(divide(inverse(X), inverse(X)), Z), multiply(divide(inverse(X), inverse(X)), Z)), inverse(divide(W, W))), multiply(inverse(V), V))), X2))), Y2)
% 0.20/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.20/0.51 divide(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), divide(S, Y2)))), multiply(inverse(divide(divide(divide(multiply(divide(inverse(X), inverse(X)), Z), multiply(divide(inverse(X), inverse(X)), Z)), inverse(divide(W, W))), divide(inverse(divide(divide(divide(Z2, Z2), W2), divide(multiply(inverse(V), V), divide(W2, multiply(inverse(divide(W, W)), X2))))), multiply(inverse(divide(W, W)), X2)))), X2))), Y2)
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 divide(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), divide(S, Y2)))), inverse(divide(divide(divide(Z2, Z2), W2), divide(multiply(inverse(V), V), divide(W2, multiply(inverse(divide(W, W)), X2))))))), Y2)
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 divide(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), divide(S, Y2)))), multiply(inverse(divide(divide(divide(multiply(divide(Y, Y), V2), multiply(divide(Y, Y), V2)), inverse(divide(W, W))), divide(inverse(divide(divide(divide(Z2, Z2), W2), divide(multiply(inverse(V), V), divide(W2, multiply(inverse(divide(W, W)), X2))))), multiply(inverse(divide(W, W)), X2)))), X2))), Y2)
% 0.20/0.51 = { by axiom 2 (single_axiom) }
% 0.20/0.51 divide(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), divide(S, Y2)))), multiply(inverse(divide(divide(divide(multiply(divide(Y, Y), V2), multiply(divide(Y, Y), V2)), inverse(divide(W, W))), multiply(inverse(V), V))), X2))), Y2)
% 0.20/0.51 = { by axiom 1 (multiply) R->L }
% 0.20/0.51 divide(inverse(divide(multiply(divide(U, U), divide(divide(divide(T, T), S), divide(inverse(X2), divide(S, Y2)))), multiply(inverse(divide(multiply(divide(multiply(divide(Y, Y), V2), multiply(divide(Y, Y), V2)), divide(W, W)), multiply(inverse(V), V))), X2))), Y2)
% 0.20/0.51 = { by lemma 17 }
% 0.20/0.51 inverse(divide(multiply(divide(multiply(divide(Y, Y), V2), multiply(divide(Y, Y), V2)), divide(W, W)), multiply(inverse(V), V)))
% 0.20/0.51 = { by lemma 16 }
% 0.20/0.51 inverse(multiply(divide(multiply(divide(Y, Y), V2), multiply(divide(Y, Y), V2)), divide(W, W)))
% 0.20/0.51 = { by lemma 15 }
% 0.20/0.51 inverse(divide(multiply(divide(Y, Y), V2), multiply(divide(Y, Y), V2)))
% 0.20/0.51 = { by lemma 11 }
% 0.20/0.51 divide(Y, Y)
% 0.20/0.51
% 0.20/0.51 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(inverse(a1), a1)
% 0.20/0.51 = { by lemma 18 }
% 0.20/0.51 divide(X, X)
% 0.20/0.51 = { by lemma 18 R->L }
% 0.20/0.51 multiply(inverse(b1), b1)
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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