%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP071-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:12 AM UTC 2026
% Result : Unsatisfiable 0.48s 0.52s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP071-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:17:51 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.52 Command-line arguments: --no-flatten-goal
% 0.48/0.52
% 0.48/0.52 % SZS status Unsatisfiable
% 0.48/0.52
% 0.48/0.58 % SZS output start Proof
% 0.48/0.58 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.48/0.58 Axiom 2 (single_axiom): divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)) = Y.
% 0.48/0.58
% 0.48/0.58 Lemma 3: divide(inverse(X), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, divide(W, V)))))) = divide(V, W).
% 0.48/0.58 Proof:
% 0.48/0.58 divide(inverse(X), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, divide(W, V))))))
% 0.48/0.58 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.58 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))))))
% 0.48/0.58 = { by axiom 2 (single_axiom) }
% 0.48/0.58 divide(V, W)
% 0.48/0.58
% 0.48/0.58 Lemma 4: divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X)) = inverse(divide(Z, divide(Y, divide(V, W)))).
% 0.48/0.58 Proof:
% 0.48/0.58 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X))
% 0.48/0.58 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.58 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))
% 0.48/0.58 = { by axiom 2 (single_axiom) }
% 0.48/0.58 inverse(divide(Z, divide(Y, divide(V, W))))
% 0.48/0.58
% 0.48/0.58 Lemma 5: inverse(divide(X, divide(divide(Y, divide(divide(Z, W), X)), divide(W, Z)))) = Y.
% 0.48/0.58 Proof:
% 0.48/0.58 inverse(divide(X, divide(divide(Y, divide(divide(Z, W), X)), divide(W, Z))))
% 0.48/0.58 = { by lemma 4 R->L }
% 0.48/0.58 divide(inverse(divide(V, divide(Y, divide(divide(Z, W), X)))), divide(divide(X, divide(Z, W)), V))
% 0.48/0.58 = { by axiom 2 (single_axiom) }
% 0.48/0.58 Y
% 0.48/0.58
% 0.48/0.58 Lemma 6: divide(divide(divide(X, Y), inverse(divide(divide(Y, X), divide(Z, divide(W, V))))), inverse(Z)) = divide(W, V).
% 0.48/0.58 Proof:
% 0.48/0.58 divide(divide(divide(X, Y), inverse(divide(divide(Y, X), divide(Z, divide(W, V))))), inverse(Z))
% 0.48/0.58 = { by lemma 3 R->L }
% 0.48/0.58 divide(inverse(U), divide(divide(T, S), inverse(divide(divide(S, T), divide(U, divide(inverse(Z), divide(divide(X, Y), inverse(divide(divide(Y, X), divide(Z, divide(W, V)))))))))))
% 0.48/0.58 = { by lemma 3 }
% 0.48/0.58 divide(inverse(U), divide(divide(T, S), inverse(divide(divide(S, T), divide(U, divide(V, W))))))
% 0.48/0.58 = { by lemma 3 }
% 0.48/0.58 divide(W, V)
% 0.48/0.58
% 0.48/0.58 Lemma 7: divide(divide(divide(X, Y), Z), inverse(divide(Z, divide(divide(W, V), divide(Y, X))))) = divide(V, W).
% 0.48/0.58 Proof:
% 0.48/0.58 divide(divide(divide(X, Y), Z), inverse(divide(Z, divide(divide(W, V), divide(Y, X)))))
% 0.48/0.58 = { by lemma 5 R->L }
% 0.48/0.58 divide(divide(divide(X, Y), inverse(divide(divide(Y, X), divide(divide(Z, divide(divide(W, V), divide(Y, X))), divide(V, W))))), inverse(divide(Z, divide(divide(W, V), divide(Y, X)))))
% 0.48/0.58 = { by lemma 6 }
% 0.48/0.58 divide(V, W)
% 0.48/0.58
% 0.48/0.58 Lemma 8: inverse(divide(X, divide(divide(X, divide(Y, Z)), divide(Z, Y)))) = divide(inverse(divide(W, V)), divide(V, W)).
% 0.48/0.58 Proof:
% 0.48/0.58 inverse(divide(X, divide(divide(X, divide(Y, Z)), divide(Z, Y))))
% 0.48/0.58 = { by lemma 4 R->L }
% 0.48/0.58 divide(inverse(divide(U, divide(X, divide(Y, Z)))), divide(divide(X, divide(Y, Z)), U))
% 0.48/0.58 = { by lemma 7 R->L }
% 0.48/0.58 divide(inverse(divide(U, divide(X, divide(Y, Z)))), divide(divide(divide(T, S), X2), inverse(divide(X2, divide(divide(U, divide(X, divide(Y, Z))), divide(S, T))))))
% 0.48/0.58 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.58 divide(inverse(divide(inverse(divide(X2, divide(divide(U, divide(X, divide(Y, Z))), divide(S, T)))), divide(divide(T, S), X2))), divide(divide(divide(T, S), X2), inverse(divide(X2, divide(divide(U, divide(X, divide(Y, Z))), divide(S, T))))))
% 0.48/0.58 = { by lemma 5 R->L }
% 0.48/0.58 divide(inverse(divide(inverse(divide(X2, divide(divide(U, divide(X, divide(Y, Z))), divide(S, T)))), divide(divide(T, S), X2))), divide(inverse(divide(Y2, divide(divide(divide(divide(T, S), X2), divide(divide(Z2, W2), Y2)), divide(W2, Z2)))), inverse(divide(X2, divide(divide(U, divide(X, divide(Y, Z))), divide(S, T))))))
% 0.48/0.58 = { by lemma 4 R->L }
% 0.48/0.58 divide(inverse(divide(inverse(divide(X2, divide(divide(U, divide(X, divide(Y, Z))), divide(S, T)))), divide(divide(T, S), X2))), divide(divide(inverse(divide(V2, divide(divide(divide(T, S), X2), divide(divide(Z2, W2), Y2)))), divide(divide(Y2, divide(Z2, W2)), V2)), inverse(divide(X2, divide(divide(U, divide(X, divide(Y, Z))), divide(S, T))))))
% 0.48/0.58 = { by lemma 4 }
% 0.48/0.58 inverse(divide(inverse(divide(V2, divide(divide(divide(T, S), X2), divide(divide(Z2, W2), Y2)))), divide(divide(divide(T, S), X2), divide(V2, divide(Y2, divide(Z2, W2))))))
% 0.48/0.58 = { by lemma 4 R->L }
% 0.48/0.58 divide(inverse(divide(inverse(divide(X2, divide(divide(W, V), divide(S, T)))), divide(divide(T, S), X2))), divide(divide(inverse(divide(V2, divide(divide(divide(T, S), X2), divide(divide(Z2, W2), Y2)))), divide(divide(Y2, divide(Z2, W2)), V2)), inverse(divide(X2, divide(divide(W, V), divide(S, T))))))
% 0.48/0.58 = { by lemma 4 }
% 0.48/0.58 divide(inverse(divide(inverse(divide(X2, divide(divide(W, V), divide(S, T)))), divide(divide(T, S), X2))), divide(inverse(divide(Y2, divide(divide(divide(divide(T, S), X2), divide(divide(Z2, W2), Y2)), divide(W2, Z2)))), inverse(divide(X2, divide(divide(W, V), divide(S, T))))))
% 0.48/0.58 = { by lemma 5 }
% 0.48/0.58 divide(inverse(divide(inverse(divide(X2, divide(divide(W, V), divide(S, T)))), divide(divide(T, S), X2))), divide(divide(divide(T, S), X2), inverse(divide(X2, divide(divide(W, V), divide(S, T))))))
% 0.48/0.58 = { by axiom 2 (single_axiom) }
% 0.48/0.58 divide(inverse(divide(W, V)), divide(divide(divide(T, S), X2), inverse(divide(X2, divide(divide(W, V), divide(S, T))))))
% 0.48/0.58 = { by lemma 7 }
% 0.48/0.58 divide(inverse(divide(W, V)), divide(V, W))
% 0.48/0.58
% 0.48/0.58 Lemma 9: divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(divide(Z, W), V)) = divide(V, divide(Z, W)).
% 0.48/0.58 Proof:
% 0.48/0.58 divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(divide(Z, W), V))
% 0.48/0.58 = { by lemma 8 R->L }
% 0.48/0.58 divide(inverse(divide(V, divide(divide(V, divide(Z, W)), divide(W, Z)))), divide(divide(Z, W), V))
% 0.48/0.58 = { by axiom 2 (single_axiom) }
% 0.48/0.58 divide(V, divide(Z, W))
% 0.48/0.58
% 0.48/0.58 Lemma 10: inverse(divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z)))) = divide(inverse(divide(W, V)), divide(V, W)).
% 0.48/0.58 Proof:
% 0.48/0.58 inverse(divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z))))
% 0.48/0.58 = { by lemma 9 R->L }
% 0.48/0.58 inverse(divide(divide(inverse(divide(U, T)), divide(T, U)), divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z)))))
% 0.48/0.58 = { by lemma 9 R->L }
% 0.48/0.58 inverse(divide(divide(inverse(divide(U, T)), divide(T, U)), divide(divide(divide(inverse(divide(U, T)), divide(T, U)), divide(divide(Y, Z), X)), divide(X, divide(Y, Z)))))
% 0.48/0.58 = { by lemma 8 }
% 0.48/0.58 divide(inverse(divide(W, V)), divide(V, W))
% 0.48/0.58
% 0.48/0.58 Lemma 11: divide(divide(X, divide(Y, Z)), divide(Z, Y)) = X.
% 0.48/0.58 Proof:
% 0.48/0.58 divide(divide(X, divide(Y, Z)), divide(Z, Y))
% 0.48/0.58 = { by lemma 9 R->L }
% 0.48/0.58 divide(divide(inverse(divide(W, V)), divide(V, W)), divide(divide(Z, Y), divide(X, divide(Y, Z))))
% 0.48/0.58 = { by lemma 10 R->L }
% 0.48/0.59 divide(inverse(divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z)))), divide(divide(Z, Y), divide(X, divide(Y, Z))))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 X
% 0.48/0.59
% 0.48/0.59 Lemma 12: divide(inverse(divide(X, Y)), divide(Y, X)) = inverse(divide(Z, Z)).
% 0.48/0.59 Proof:
% 0.48/0.59 divide(inverse(divide(X, Y)), divide(Y, X))
% 0.48/0.59 = { by lemma 10 R->L }
% 0.48/0.59 inverse(divide(divide(inverse(divide(W, divide(Z, divide(V, U)))), divide(divide(U, V), W)), divide(inverse(divide(W, divide(Z, divide(V, U)))), divide(divide(U, V), W))))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 inverse(divide(Z, divide(inverse(divide(W, divide(Z, divide(V, U)))), divide(divide(U, V), W))))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 inverse(divide(Z, Z))
% 0.48/0.59
% 0.48/0.59 Lemma 13: divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z))) = inverse(divide(W, W)).
% 0.48/0.59 Proof:
% 0.48/0.59 divide(divide(X, divide(Y, Z)), divide(X, divide(Y, Z)))
% 0.48/0.59 = { by lemma 9 R->L }
% 0.48/0.59 divide(divide(divide(inverse(divide(V, U)), divide(U, V)), divide(divide(Y, Z), X)), divide(X, divide(Y, Z)))
% 0.48/0.59 = { by lemma 11 }
% 0.48/0.59 divide(inverse(divide(V, U)), divide(U, V))
% 0.48/0.59 = { by lemma 12 }
% 0.48/0.59 inverse(divide(W, W))
% 0.48/0.59
% 0.48/0.59 Lemma 14: inverse(divide(X, X)) = divide(Y, Y).
% 0.48/0.59 Proof:
% 0.48/0.59 inverse(divide(X, X))
% 0.48/0.59 = { by lemma 13 R->L }
% 0.48/0.59 divide(divide(inverse(divide(Z, divide(Y, divide(W, V)))), divide(divide(V, W), Z)), divide(inverse(divide(Z, divide(Y, divide(W, V)))), divide(divide(V, W), Z)))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 divide(Y, divide(inverse(divide(Z, divide(Y, divide(W, V)))), divide(divide(V, W), Z)))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 divide(Y, Y)
% 0.48/0.59
% 0.48/0.59 Lemma 15: divide(divide(X, X), divide(Y, Z)) = divide(Z, Y).
% 0.48/0.59 Proof:
% 0.48/0.59 divide(divide(X, X), divide(Y, Z))
% 0.48/0.59 = { by lemma 14 R->L }
% 0.48/0.59 divide(inverse(divide(W, W)), divide(Y, Z))
% 0.48/0.59 = { by lemma 12 R->L }
% 0.48/0.59 divide(divide(inverse(divide(V, U)), divide(U, V)), divide(Y, Z))
% 0.48/0.59 = { by lemma 11 R->L }
% 0.48/0.59 divide(divide(inverse(divide(V, U)), divide(U, V)), divide(divide(divide(Y, divide(T, S)), divide(S, T)), Z))
% 0.48/0.59 = { by lemma 9 }
% 0.48/0.59 divide(Z, divide(divide(Y, divide(T, S)), divide(S, T)))
% 0.48/0.59 = { by lemma 11 }
% 0.48/0.59 divide(Z, Y)
% 0.48/0.59
% 0.48/0.59 Lemma 16: divide(divide(X, Y), divide(Z, Z)) = divide(X, Y).
% 0.48/0.59 Proof:
% 0.48/0.59 divide(divide(X, Y), divide(Z, Z))
% 0.48/0.59 = { by lemma 3 R->L }
% 0.48/0.59 divide(inverse(W), divide(divide(V, U), inverse(divide(divide(U, V), divide(W, divide(divide(Z, Z), divide(X, Y)))))))
% 0.48/0.59 = { by lemma 15 }
% 0.48/0.59 divide(inverse(W), divide(divide(V, U), inverse(divide(divide(U, V), divide(W, divide(Y, X))))))
% 0.48/0.59 = { by lemma 3 }
% 0.48/0.59 divide(X, Y)
% 0.48/0.59
% 0.48/0.59 Lemma 17: divide(X, divide(Y, Y)) = X.
% 0.48/0.59 Proof:
% 0.48/0.59 divide(X, divide(Y, Y))
% 0.48/0.59 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.59 divide(divide(inverse(divide(Z, divide(X, divide(W, V)))), divide(divide(V, W), Z)), divide(Y, Y))
% 0.48/0.59 = { by lemma 16 }
% 0.48/0.59 divide(inverse(divide(Z, divide(X, divide(W, V)))), divide(divide(V, W), Z))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 X
% 0.48/0.59
% 0.48/0.59 Lemma 18: inverse(inverse(X)) = X.
% 0.48/0.59 Proof:
% 0.48/0.59 inverse(inverse(X))
% 0.48/0.59 = { by lemma 17 R->L }
% 0.48/0.59 inverse(inverse(divide(X, divide(Y, Y))))
% 0.48/0.59 = { by lemma 15 R->L }
% 0.48/0.59 inverse(inverse(divide(X, divide(divide(Z, Z), divide(Y, Y)))))
% 0.48/0.59 = { by lemma 14 R->L }
% 0.48/0.59 inverse(inverse(divide(X, divide(divide(Z, Z), inverse(divide(Z, Z))))))
% 0.48/0.59 = { by lemma 15 R->L }
% 0.48/0.59 inverse(inverse(divide(X, divide(divide(W, W), divide(inverse(divide(Z, Z)), divide(Z, Z))))))
% 0.48/0.59 = { by lemma 17 R->L }
% 0.48/0.59 inverse(inverse(divide(X, divide(divide(W, W), divide(inverse(divide(divide(Z, Z), divide(W, W))), divide(Z, Z))))))
% 0.48/0.59 = { by lemma 4 R->L }
% 0.48/0.59 inverse(divide(inverse(divide(divide(Z, Z), divide(W, W))), divide(divide(X, divide(divide(Z, Z), inverse(divide(divide(Z, Z), divide(W, W))))), divide(Z, Z))))
% 0.48/0.59 = { by lemma 5 }
% 0.48/0.59 X
% 0.48/0.59
% 0.48/0.59 Lemma 19: divide(divide(divide(X, Y), inverse(divide(divide(Y, X), divide(Z, W)))), inverse(Z)) = W.
% 0.48/0.59 Proof:
% 0.48/0.59 divide(divide(divide(X, Y), inverse(divide(divide(Y, X), divide(Z, W)))), inverse(Z))
% 0.48/0.59 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.59 divide(divide(divide(X, Y), inverse(divide(divide(Y, X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V)))))), inverse(Z))
% 0.48/0.59 = { by lemma 6 }
% 0.48/0.59 divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 W
% 0.48/0.59
% 0.48/0.59 Lemma 20: divide(divide(X, X), inverse(Y)) = Y.
% 0.48/0.59 Proof:
% 0.48/0.59 divide(divide(X, X), inverse(Y))
% 0.48/0.59 = { by lemma 15 R->L }
% 0.48/0.59 divide(divide(divide(Z, Z), divide(X, X)), inverse(Y))
% 0.48/0.59 = { by lemma 14 R->L }
% 0.48/0.59 divide(divide(divide(Z, Z), inverse(divide(Z, Z))), inverse(Y))
% 0.48/0.59 = { by lemma 16 R->L }
% 0.48/0.59 divide(divide(divide(Z, Z), inverse(divide(divide(Z, Z), divide(Y, Y)))), inverse(Y))
% 0.48/0.59 = { by lemma 19 }
% 0.48/0.59 Y
% 0.48/0.59
% 0.48/0.59 Lemma 21: inverse(divide(inverse(X), divide(Y, X))) = Y.
% 0.48/0.59 Proof:
% 0.48/0.59 inverse(divide(inverse(X), divide(Y, X)))
% 0.48/0.59 = { by lemma 16 R->L }
% 0.48/0.59 inverse(divide(inverse(X), divide(divide(Y, X), divide(Z, Z))))
% 0.48/0.59 = { by lemma 4 R->L }
% 0.48/0.59 divide(inverse(divide(W, divide(Y, X))), divide(divide(inverse(X), divide(Z, Z)), W))
% 0.48/0.59 = { by lemma 20 R->L }
% 0.48/0.59 divide(inverse(divide(W, divide(Y, divide(divide(Z, Z), inverse(X))))), divide(divide(inverse(X), divide(Z, Z)), W))
% 0.48/0.59 = { by axiom 2 (single_axiom) }
% 0.48/0.59 Y
% 0.48/0.59
% 0.48/0.59 Lemma 22: inverse(divide(X, Y)) = divide(Y, X).
% 0.48/0.59 Proof:
% 0.48/0.59 inverse(divide(X, Y))
% 0.48/0.59 = { by lemma 3 R->L }
% 0.48/0.59 inverse(divide(inverse(Z), divide(divide(W, V), inverse(divide(divide(V, W), divide(Z, divide(Y, X)))))))
% 0.48/0.59 = { by lemma 11 R->L }
% 0.48/0.59 inverse(divide(inverse(Z), divide(divide(divide(divide(W, V), inverse(divide(divide(V, W), divide(Z, divide(Y, X))))), divide(inverse(Z), divide(U, U))), divide(divide(U, U), inverse(Z)))))
% 0.48/0.59 = { by lemma 20 }
% 0.48/0.59 inverse(divide(inverse(Z), divide(divide(divide(divide(W, V), inverse(divide(divide(V, W), divide(Z, divide(Y, X))))), divide(inverse(Z), divide(U, U))), Z)))
% 0.48/0.59 = { by lemma 17 }
% 0.48/0.59 inverse(divide(inverse(Z), divide(divide(divide(divide(W, V), inverse(divide(divide(V, W), divide(Z, divide(Y, X))))), inverse(Z)), Z)))
% 0.48/0.59 = { by lemma 21 }
% 0.48/0.59 divide(divide(divide(W, V), inverse(divide(divide(V, W), divide(Z, divide(Y, X))))), inverse(Z))
% 0.48/0.59 = { by lemma 19 }
% 0.48/0.59 divide(Y, X)
% 0.48/0.59
% 0.48/0.59 Lemma 23: divide(divide(X, X), Y) = inverse(Y).
% 0.48/0.59 Proof:
% 0.48/0.59 divide(divide(X, X), Y)
% 0.48/0.59 = { by lemma 22 R->L }
% 0.48/0.59 inverse(divide(Y, divide(X, X)))
% 0.48/0.59 = { by lemma 17 }
% 0.48/0.59 inverse(Y)
% 0.48/0.59
% 0.48/0.59 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.48/0.59 Proof:
% 0.48/0.59 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.48/0.59 = { by axiom 1 (multiply) }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.48/0.60 = { by axiom 1 (multiply) }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3))
% 0.48/0.60 = { by axiom 1 (multiply) }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.48/0.60 = { by axiom 1 (multiply) }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(divide(a3, inverse(b3)), c3))
% 0.48/0.60 = { by axiom 1 (multiply) }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.48/0.60 = { by lemma 23 }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.48/0.60 = { by lemma 18 }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.48/0.60 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, divide(inverse(divide(X, divide(inverse(b3), divide(Y, Z)))), divide(divide(Z, Y), X))), inverse(c3)))
% 0.48/0.60 = { by lemma 22 R->L }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, inverse(divide(inverse(c3), divide(a3, divide(inverse(divide(X, divide(inverse(b3), divide(Y, Z)))), divide(divide(Z, Y), X))))))
% 0.48/0.60 = { by lemma 11 R->L }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(inverse(divide(inverse(c3), divide(a3, divide(inverse(divide(X, divide(inverse(b3), divide(Y, Z)))), divide(divide(Z, Y), X))))), divide(divide(divide(divide(Z, Y), X), inverse(divide(X, divide(inverse(b3), divide(Y, Z))))), inverse(c3))), divide(inverse(c3), divide(divide(divide(Z, Y), X), inverse(divide(X, divide(inverse(b3), divide(Y, Z))))))))
% 0.48/0.60 = { by axiom 2 (single_axiom) }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), divide(divide(divide(Z, Y), X), inverse(divide(X, divide(inverse(b3), divide(Y, Z))))))))
% 0.48/0.60 = { by lemma 3 R->L }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), divide(inverse(W), divide(divide(V, V), inverse(divide(divide(V, V), divide(W, divide(inverse(divide(X, divide(inverse(b3), divide(Y, Z)))), divide(divide(Z, Y), X))))))))))
% 0.48/0.60 = { by axiom 2 (single_axiom) }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), divide(inverse(W), divide(divide(V, V), inverse(divide(divide(V, V), divide(W, inverse(b3)))))))))
% 0.48/0.60 = { by lemma 23 }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), divide(inverse(W), inverse(inverse(divide(divide(V, V), divide(W, inverse(b3)))))))))
% 0.48/0.60 = { by lemma 18 }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), divide(inverse(W), divide(divide(V, V), divide(W, inverse(b3)))))))
% 0.48/0.60 = { by lemma 15 }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), divide(inverse(W), divide(inverse(b3), W)))))
% 0.48/0.60 = { by lemma 18 R->L }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), inverse(inverse(divide(inverse(W), divide(inverse(b3), W)))))))
% 0.48/0.60 = { by lemma 21 }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), inverse(inverse(b3)))))
% 0.48/0.60 = { by lemma 18 }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), b3)))
% 0.48/0.60 = { by lemma 22 R->L }
% 0.48/0.60 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.48/0.60 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.60 tuple(divide(inverse(a1), divide(inverse(divide(U, divide(inverse(a1), divide(T, S)))), divide(divide(S, T), U))), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.48/0.60 = { by axiom 2 (single_axiom) R->L }
% 0.48/0.60 tuple(divide(divide(inverse(divide(U, divide(inverse(a1), divide(T, S)))), divide(divide(S, T), U)), divide(inverse(divide(U, divide(inverse(a1), divide(T, S)))), divide(divide(S, T), U))), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.48/0.60 = { by lemma 13 }
% 0.48/0.60 tuple(inverse(divide(X2, X2)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.48/0.60 = { by lemma 13 R->L }
% 0.48/0.60 tuple(divide(divide(inverse(divide(Y2, divide(inverse(b1), divide(Z2, W2)))), divide(divide(W2, Z2), Y2)), divide(inverse(divide(Y2, divide(inverse(b1), divide(Z2, W2)))), divide(divide(W2, Z2), Y2))), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.48/0.60 = { by axiom 2 (single_axiom) }
% 0.48/0.60 tuple(divide(inverse(b1), divide(inverse(divide(Y2, divide(inverse(b1), divide(Z2, W2)))), divide(divide(W2, Z2), Y2))), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.48/0.60 = { by axiom 2 (single_axiom) }
% 0.48/0.60 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.48/0.60 = { by axiom 1 (multiply) R->L }
% 0.48/0.60 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, divide(b3, inverse(c3))))
% 0.48/0.60 = { by axiom 1 (multiply) R->L }
% 0.48/0.60 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, multiply(b3, c3)))
% 0.48/0.60 = { by axiom 1 (multiply) R->L }
% 0.48/0.60 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.48/0.60 % SZS output end Proof
% 0.48/0.60
% 0.48/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------