%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP072-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 0.53s 0.54s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP072-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:23:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.54 Command-line arguments: --no-flatten-goal
% 0.53/0.54
% 0.53/0.54 % SZS status Unsatisfiable
% 0.53/0.54
% 0.53/0.62 % SZS output start Proof
% 0.53/0.62 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.53/0.62 Axiom 2 (single_axiom): divide(divide(inverse(divide(X, Y)), divide(divide(Z, W), X)), divide(W, Z)) = Y.
% 0.53/0.62
% 0.53/0.62 Lemma 3: divide(divide(inverse(X), divide(divide(Y, Z), divide(inverse(divide(W, X)), divide(divide(V, U), W)))), divide(Z, Y)) = divide(U, V).
% 0.53/0.62 Proof:
% 0.53/0.62 divide(divide(inverse(X), divide(divide(Y, Z), divide(inverse(divide(W, X)), divide(divide(V, U), W)))), divide(Z, Y))
% 0.53/0.62 = { by axiom 2 (single_axiom) R->L }
% 0.53/0.62 divide(divide(inverse(divide(divide(inverse(divide(W, X)), divide(divide(V, U), W)), divide(U, V))), divide(divide(Y, Z), divide(inverse(divide(W, X)), divide(divide(V, U), W)))), divide(Z, Y))
% 0.53/0.62 = { by axiom 2 (single_axiom) }
% 0.53/0.62 divide(U, V)
% 0.53/0.62
% 0.53/0.62 Lemma 4: divide(divide(inverse(divide(divide(X, Y), Z)), W), divide(divide(divide(Y, X), V), inverse(divide(V, W)))) = Z.
% 0.53/0.62 Proof:
% 0.53/0.62 divide(divide(inverse(divide(divide(X, Y), Z)), W), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 0.53/0.62 = { by axiom 2 (single_axiom) R->L }
% 0.53/0.62 divide(divide(inverse(divide(divide(X, Y), Z)), divide(divide(inverse(divide(V, W)), divide(divide(Y, X), V)), divide(X, Y))), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 0.53/0.62 = { by axiom 2 (single_axiom) }
% 0.53/0.62 Z
% 0.53/0.62
% 0.53/0.62 Lemma 5: divide(divide(divide(X, Y), Z), inverse(divide(Z, divide(divide(W, V), divide(Y, X))))) = divide(V, W).
% 0.53/0.62 Proof:
% 0.53/0.62 divide(divide(divide(X, Y), Z), inverse(divide(Z, divide(divide(W, V), divide(Y, X)))))
% 0.53/0.62 = { by axiom 2 (single_axiom) R->L }
% 0.53/0.62 divide(divide(inverse(divide(divide(inverse(divide(divide(Y, X), U)), divide(divide(W, V), divide(Y, X))), divide(divide(divide(X, Y), Z), inverse(divide(Z, divide(divide(W, V), divide(Y, X))))))), divide(divide(T, S), divide(inverse(divide(divide(Y, X), U)), divide(divide(W, V), divide(Y, X))))), divide(S, T))
% 0.53/0.62 = { by lemma 4 }
% 0.53/0.62 divide(divide(inverse(U), divide(divide(T, S), divide(inverse(divide(divide(Y, X), U)), divide(divide(W, V), divide(Y, X))))), divide(S, T))
% 0.53/0.62 = { by lemma 3 }
% 0.53/0.62 divide(V, W)
% 0.53/0.62
% 0.53/0.62 Lemma 6: divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)) = Y.
% 0.53/0.62 Proof:
% 0.53/0.62 divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X))
% 0.53/0.62 = { by axiom 2 (single_axiom) R->L }
% 0.53/0.62 divide(inverse(divide(X, divide(divide(divide(inverse(divide(V, Y)), divide(divide(U, T), V)), divide(T, U)), divide(Z, W)))), divide(divide(W, Z), X))
% 0.53/0.62 = { by lemma 3 R->L }
% 0.53/0.62 divide(divide(inverse(S), divide(divide(X2, Y2), divide(inverse(divide(Z2, S)), divide(divide(divide(divide(W, Z), X), inverse(divide(X, divide(divide(divide(inverse(divide(V, Y)), divide(divide(U, T), V)), divide(T, U)), divide(Z, W))))), Z2)))), divide(Y2, X2))
% 0.53/0.62 = { by lemma 5 }
% 0.53/0.62 divide(divide(inverse(S), divide(divide(X2, Y2), divide(inverse(divide(Z2, S)), divide(divide(divide(T, U), divide(inverse(divide(V, Y)), divide(divide(U, T), V))), Z2)))), divide(Y2, X2))
% 0.53/0.62 = { by lemma 3 }
% 0.53/0.62 divide(divide(inverse(divide(V, Y)), divide(divide(U, T), V)), divide(T, U))
% 0.53/0.62 = { by axiom 2 (single_axiom) }
% 0.53/0.62 Y
% 0.53/0.62
% 0.53/0.63 Lemma 7: divide(divide(X, W), inverse(divide(W, Z))) = divide(divide(X, Y), inverse(divide(Y, Z))).
% 0.53/0.63 Proof:
% 0.53/0.63 divide(divide(X, W), inverse(divide(W, Z)))
% 0.53/0.63 = { by axiom 2 (single_axiom) R->L }
% 0.53/0.63 divide(divide(divide(divide(inverse(divide(V, X)), divide(divide(U, T), V)), divide(T, U)), W), inverse(divide(W, Z)))
% 0.53/0.63 = { by axiom 2 (single_axiom) R->L }
% 0.53/0.63 divide(divide(inverse(divide(divide(inverse(divide(divide(divide(T, U), divide(inverse(divide(V, X)), divide(divide(U, T), V))), S)), Z), divide(divide(divide(divide(inverse(divide(V, X)), divide(divide(U, T), V)), divide(T, U)), W), inverse(divide(W, Z))))), divide(divide(X2, Y2), divide(inverse(divide(divide(divide(T, U), divide(inverse(divide(V, X)), divide(divide(U, T), V))), S)), Z))), divide(Y2, X2))
% 0.53/0.63 = { by lemma 4 }
% 0.53/0.63 divide(divide(inverse(S), divide(divide(X2, Y2), divide(inverse(divide(divide(divide(T, U), divide(inverse(divide(V, X)), divide(divide(U, T), V))), S)), Z))), divide(Y2, X2))
% 0.53/0.63 = { by lemma 4 R->L }
% 0.53/0.63 divide(divide(inverse(divide(divide(inverse(divide(divide(divide(T, U), divide(inverse(divide(V, X)), divide(divide(U, T), V))), S)), Z), divide(divide(divide(divide(inverse(divide(V, X)), divide(divide(U, T), V)), divide(T, U)), Y), inverse(divide(Y, Z))))), divide(divide(X2, Y2), divide(inverse(divide(divide(divide(T, U), divide(inverse(divide(V, X)), divide(divide(U, T), V))), S)), Z))), divide(Y2, X2))
% 0.53/0.63 = { by axiom 2 (single_axiom) }
% 0.53/0.63 divide(divide(divide(divide(inverse(divide(V, X)), divide(divide(U, T), V)), divide(T, U)), Y), inverse(divide(Y, Z)))
% 0.53/0.63 = { by axiom 2 (single_axiom) }
% 0.53/0.63 divide(divide(X, Y), inverse(divide(Y, Z)))
% 0.53/0.63
% 0.53/0.63 Lemma 8: divide(divide(X, inverse(divide(Y, divide(Z, divide(W, V))))), inverse(Z)) = divide(divide(X, U), inverse(divide(U, divide(divide(V, W), Y)))).
% 0.53/0.63 Proof:
% 0.53/0.63 divide(divide(X, inverse(divide(Y, divide(Z, divide(W, V))))), inverse(Z))
% 0.53/0.63 = { by lemma 6 R->L }
% 0.53/0.63 divide(divide(X, inverse(divide(Y, divide(Z, divide(W, V))))), inverse(divide(inverse(divide(Y, divide(Z, divide(W, V)))), divide(divide(V, W), Y))))
% 0.53/0.63 = { by lemma 7 R->L }
% 0.53/0.63 divide(divide(X, U), inverse(divide(U, divide(divide(V, W), Y))))
% 0.53/0.63
% 0.53/0.63 Lemma 9: divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Z, W)) = divide(W, Z).
% 0.53/0.63 Proof:
% 0.53/0.63 divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Z, W))
% 0.53/0.63 = { by lemma 3 R->L }
% 0.53/0.63 divide(divide(divide(inverse(V), divide(divide(U, T), divide(inverse(divide(S, V)), divide(divide(divide(Y, X), inverse(divide(X, Y))), S)))), divide(T, U)), divide(Z, W))
% 0.53/0.63 = { by lemma 5 R->L }
% 0.53/0.63 divide(divide(divide(inverse(V), divide(divide(U, T), divide(inverse(divide(S, V)), divide(divide(divide(divide(divide(X2, Y2), Z2), inverse(divide(Z2, divide(divide(X, Y), divide(Y2, X2))))), inverse(divide(X, Y))), S)))), divide(T, U)), divide(Z, W))
% 0.53/0.63 = { by lemma 8 }
% 0.53/0.63 divide(divide(divide(inverse(V), divide(divide(U, T), divide(inverse(divide(S, V)), divide(divide(divide(divide(divide(X2, Y2), Z2), W2), inverse(divide(W2, divide(divide(X2, Y2), Z2)))), S)))), divide(T, U)), divide(Z, W))
% 0.53/0.63 = { by lemma 8 R->L }
% 0.53/0.63 divide(divide(divide(inverse(V), divide(divide(U, T), divide(inverse(divide(S, V)), divide(divide(divide(divide(divide(X2, Y2), Z2), inverse(divide(Z2, divide(divide(V2, divide(W, Z)), divide(Y2, X2))))), inverse(divide(V2, divide(W, Z)))), S)))), divide(T, U)), divide(Z, W))
% 0.53/0.63 = { by lemma 5 }
% 1.53/0.63 divide(divide(divide(inverse(V), divide(divide(U, T), divide(inverse(divide(S, V)), divide(divide(divide(divide(W, Z), V2), inverse(divide(V2, divide(W, Z)))), S)))), divide(T, U)), divide(Z, W))
% 1.53/0.63 = { by lemma 3 }
% 1.53/0.63 divide(divide(inverse(divide(V2, divide(W, Z))), divide(divide(W, Z), V2)), divide(Z, W))
% 1.53/0.63 = { by axiom 2 (single_axiom) }
% 1.53/0.63 divide(W, Z)
% 1.53/0.63
% 1.53/0.63 Lemma 10: divide(divide(X, Y), divide(inverse(divide(Z, W)), divide(W, Z))) = divide(X, Y).
% 1.53/0.63 Proof:
% 1.53/0.63 divide(divide(X, Y), divide(inverse(divide(Z, W)), divide(W, Z)))
% 1.53/0.63 = { by lemma 3 R->L }
% 1.53/0.63 divide(divide(inverse(V), divide(divide(U, T), divide(inverse(divide(S, V)), divide(divide(divide(inverse(divide(Z, W)), divide(W, Z)), divide(X, Y)), S)))), divide(T, U))
% 1.53/0.63 = { by lemma 9 }
% 1.53/0.63 divide(divide(inverse(V), divide(divide(U, T), divide(inverse(divide(S, V)), divide(divide(Y, X), S)))), divide(T, U))
% 1.53/0.63 = { by lemma 3 }
% 1.53/0.63 divide(X, Y)
% 1.53/0.63
% 1.53/0.63 Lemma 11: divide(inverse(divide(X, Y)), divide(Y, X)) = divide(divide(Z, W), inverse(divide(W, Z))).
% 1.53/0.63 Proof:
% 1.53/0.63 divide(inverse(divide(X, Y)), divide(Y, X))
% 1.53/0.63 = { by lemma 10 R->L }
% 1.53/0.63 divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(inverse(divide(W, Z)), divide(Z, W)))
% 1.53/0.63 = { by lemma 9 }
% 1.53/0.63 divide(divide(Z, W), inverse(divide(W, Z)))
% 1.53/0.63
% 1.53/0.63 Lemma 12: divide(X, divide(divide(Y, Z), inverse(divide(Z, Y)))) = X.
% 1.53/0.63 Proof:
% 1.53/0.63 divide(X, divide(divide(Y, Z), inverse(divide(Z, Y))))
% 1.53/0.63 = { by lemma 11 R->L }
% 1.53/0.63 divide(X, divide(inverse(divide(W, V)), divide(V, W)))
% 1.53/0.63 = { by axiom 2 (single_axiom) R->L }
% 1.53/0.63 divide(divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T)), divide(inverse(divide(W, V)), divide(V, W)))
% 1.53/0.63 = { by lemma 10 }
% 1.53/0.63 divide(divide(inverse(divide(U, X)), divide(divide(T, S), U)), divide(S, T))
% 1.53/0.63 = { by axiom 2 (single_axiom) }
% 1.53/0.63 X
% 1.53/0.63
% 1.53/0.63 Lemma 13: divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X)) = inverse(divide(Z, divide(Y, divide(V, W)))).
% 1.53/0.63 Proof:
% 1.53/0.63 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X))
% 1.53/0.63 = { by lemma 6 R->L }
% 1.53/0.63 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))
% 1.53/0.63 = { by lemma 6 }
% 1.53/0.63 inverse(divide(Z, divide(Y, divide(V, W))))
% 1.53/0.63
% 1.53/0.63 Lemma 14: divide(inverse(divide(X, Y)), divide(Z, X)) = inverse(divide(Z, Y)).
% 1.53/0.63 Proof:
% 1.53/0.63 divide(inverse(divide(X, Y)), divide(Z, X))
% 1.53/0.63 = { by lemma 12 R->L }
% 1.53/0.63 divide(inverse(divide(X, Y)), divide(divide(Z, divide(divide(W, V), inverse(divide(V, W)))), X))
% 1.53/0.63 = { by lemma 13 }
% 1.53/0.63 inverse(divide(Z, divide(Y, divide(inverse(divide(V, W)), divide(W, V)))))
% 1.53/0.63 = { by lemma 11 }
% 1.53/0.63 inverse(divide(Z, divide(Y, divide(divide(U, T), inverse(divide(T, U))))))
% 1.53/0.63 = { by lemma 12 }
% 1.53/0.63 inverse(divide(Z, Y))
% 1.53/0.63
% 1.53/0.63 Lemma 15: divide(divide(X, Y), inverse(divide(Y, X))) = inverse(divide(Z, Z)).
% 1.53/0.63 Proof:
% 1.53/0.63 divide(divide(X, Y), inverse(divide(Y, X)))
% 1.53/0.63 = { by lemma 11 R->L }
% 1.53/0.63 divide(inverse(divide(W, Z)), divide(Z, W))
% 1.53/0.63 = { by lemma 14 }
% 1.53/0.63 inverse(divide(Z, Z))
% 1.53/0.63
% 1.53/0.63 Lemma 16: divide(X, inverse(divide(Y, Y))) = X.
% 1.53/0.63 Proof:
% 1.53/0.63 divide(X, inverse(divide(Y, Y)))
% 1.53/0.63 = { by lemma 15 R->L }
% 1.53/0.63 divide(X, divide(divide(Z, W), inverse(divide(W, Z))))
% 1.53/0.63 = { by lemma 12 }
% 1.53/0.63 X
% 1.53/0.63
% 1.53/0.63 Lemma 17: inverse(divide(X, divide(divide(Y, divide(divide(Z, W), X)), divide(W, Z)))) = Y.
% 1.53/0.63 Proof:
% 1.53/0.63 inverse(divide(X, divide(divide(Y, divide(divide(Z, W), X)), divide(W, Z))))
% 1.53/0.63 = { by lemma 13 R->L }
% 1.53/0.63 divide(inverse(divide(V, divide(Y, divide(divide(Z, W), X)))), divide(divide(X, divide(Z, W)), V))
% 1.53/0.63 = { by lemma 6 }
% 1.53/0.63 Y
% 1.53/0.63
% 1.53/0.63 Lemma 18: divide(X, divide(Y, Y)) = X.
% 1.53/0.63 Proof:
% 1.53/0.63 divide(X, divide(Y, Y))
% 1.53/0.63 = { by lemma 17 R->L }
% 1.53/0.63 divide(inverse(divide(Y, divide(divide(X, divide(divide(Z, W), Y)), divide(W, Z)))), divide(Y, Y))
% 1.53/0.63 = { by lemma 14 }
% 1.53/0.63 inverse(divide(Y, divide(divide(X, divide(divide(Z, W), Y)), divide(W, Z))))
% 1.53/0.63 = { by lemma 17 }
% 1.53/0.63 X
% 1.53/0.63
% 1.53/0.63 Lemma 19: divide(divide(X, Y), inverse(Y)) = X.
% 1.53/0.63 Proof:
% 1.53/0.63 divide(divide(X, Y), inverse(Y))
% 1.53/0.63 = { by lemma 12 R->L }
% 1.53/0.63 divide(divide(X, Y), inverse(divide(Y, divide(divide(Z, W), inverse(divide(W, Z))))))
% 1.53/0.63 = { by lemma 7 }
% 1.53/0.64 divide(divide(X, divide(V, V)), inverse(divide(divide(V, V), divide(divide(Z, W), inverse(divide(W, Z))))))
% 1.53/0.64 = { by lemma 12 }
% 1.53/0.64 divide(divide(X, divide(V, V)), inverse(divide(V, V)))
% 1.53/0.64 = { by lemma 16 }
% 1.53/0.64 divide(X, divide(V, V))
% 1.53/0.64 = { by lemma 18 }
% 1.53/0.64 X
% 1.53/0.64
% 1.53/0.64 Lemma 20: inverse(divide(X, X)) = divide(Y, Y).
% 1.53/0.64 Proof:
% 1.53/0.64 inverse(divide(X, X))
% 1.53/0.64 = { by lemma 15 R->L }
% 1.53/0.64 divide(divide(Y, Y), inverse(divide(Y, Y)))
% 1.53/0.64 = { by lemma 16 }
% 1.53/0.64 divide(Y, Y)
% 1.53/0.64
% 1.53/0.64 Lemma 21: divide(divide(X, X), Y) = divide(inverse(Z), divide(Y, Z)).
% 1.53/0.64 Proof:
% 1.53/0.64 divide(divide(X, X), Y)
% 1.53/0.64 = { by lemma 20 R->L }
% 1.53/0.64 divide(inverse(divide(W, W)), Y)
% 1.53/0.64 = { by lemma 18 R->L }
% 1.53/0.64 divide(inverse(divide(W, W)), divide(Y, divide(W, W)))
% 1.53/0.64 = { by lemma 12 R->L }
% 1.53/0.64 divide(inverse(divide(divide(W, W), divide(divide(V, U), inverse(divide(U, V))))), divide(Y, divide(W, W)))
% 1.53/0.64 = { by lemma 3 R->L }
% 1.53/0.64 divide(divide(inverse(T), divide(divide(S, X2), divide(inverse(divide(Y2, T)), divide(divide(divide(Y, divide(W, W)), inverse(divide(divide(W, W), divide(divide(V, U), inverse(divide(U, V)))))), Y2)))), divide(X2, S))
% 1.53/0.64 = { by lemma 7 R->L }
% 1.53/0.64 divide(divide(inverse(T), divide(divide(S, X2), divide(inverse(divide(Y2, T)), divide(divide(divide(Y, Z), inverse(divide(Z, divide(divide(V, U), inverse(divide(U, V)))))), Y2)))), divide(X2, S))
% 1.53/0.64 = { by lemma 3 }
% 1.53/0.64 divide(inverse(divide(Z, divide(divide(V, U), inverse(divide(U, V))))), divide(Y, Z))
% 1.53/0.64 = { by lemma 12 }
% 1.53/0.64 divide(inverse(Z), divide(Y, Z))
% 1.53/0.64
% 1.53/0.64 Lemma 22: divide(X, inverse(inverse(Y))) = divide(X, Y).
% 1.53/0.64 Proof:
% 1.53/0.64 divide(X, inverse(inverse(Y)))
% 1.53/0.64 = { by lemma 19 R->L }
% 1.53/0.64 divide(divide(divide(X, Y), inverse(Y)), inverse(inverse(Y)))
% 1.53/0.64 = { by lemma 19 }
% 1.53/0.64 divide(X, Y)
% 1.53/0.64
% 1.53/0.64 Lemma 23: inverse(divide(X, Y)) = divide(Y, X).
% 1.53/0.64 Proof:
% 1.53/0.64 inverse(divide(X, Y))
% 1.53/0.64 = { by lemma 19 R->L }
% 1.53/0.64 divide(divide(inverse(divide(X, Y)), inverse(X)), inverse(inverse(X)))
% 1.53/0.64 = { by lemma 18 R->L }
% 1.53/0.64 divide(divide(inverse(divide(X, Y)), divide(inverse(X), divide(X, X))), inverse(inverse(X)))
% 1.53/0.64 = { by lemma 18 R->L }
% 1.53/0.64 divide(divide(inverse(divide(X, divide(Y, divide(Z, Z)))), divide(inverse(X), divide(X, X))), inverse(inverse(X)))
% 1.53/0.64 = { by lemma 21 R->L }
% 1.53/0.64 divide(divide(inverse(divide(X, divide(Y, divide(Z, Z)))), divide(divide(Z, Z), X)), inverse(inverse(X)))
% 1.53/0.64 = { by lemma 6 }
% 1.53/0.64 divide(Y, inverse(inverse(X)))
% 1.53/0.64 = { by lemma 22 }
% 1.53/0.64 divide(Y, X)
% 1.53/0.64
% 1.53/0.64 Lemma 24: divide(inverse(X), divide(Y, X)) = inverse(Y).
% 1.53/0.64 Proof:
% 1.53/0.64 divide(inverse(X), divide(Y, X))
% 1.53/0.64 = { by lemma 23 R->L }
% 1.53/0.64 divide(inverse(X), inverse(divide(X, Y)))
% 1.53/0.64 = { by lemma 18 R->L }
% 1.53/0.64 divide(divide(inverse(X), divide(X, X)), inverse(divide(X, Y)))
% 1.53/0.64 = { by lemma 21 R->L }
% 1.53/0.64 divide(divide(divide(Z, Z), X), inverse(divide(X, Y)))
% 1.53/0.64 = { by lemma 9 R->L }
% 1.53/0.64 divide(divide(inverse(divide(W, V)), divide(V, W)), divide(inverse(divide(X, Y)), divide(divide(Z, Z), X)))
% 1.53/0.64 = { by lemma 14 }
% 1.53/0.64 divide(inverse(divide(V, V)), divide(inverse(divide(X, Y)), divide(divide(Z, Z), X)))
% 1.53/0.64 = { by lemma 20 }
% 1.53/0.64 divide(divide(Z, Z), divide(inverse(divide(X, Y)), divide(divide(Z, Z), X)))
% 1.53/0.64 = { by lemma 23 R->L }
% 1.53/0.64 inverse(divide(divide(inverse(divide(X, Y)), divide(divide(Z, Z), X)), divide(Z, Z)))
% 1.53/0.64 = { by axiom 2 (single_axiom) }
% 1.53/0.64 inverse(Y)
% 1.53/0.64
% 1.53/0.64 Lemma 25: inverse(inverse(X)) = X.
% 1.53/0.64 Proof:
% 1.53/0.64 inverse(inverse(X))
% 1.53/0.64 = { by lemma 24 R->L }
% 1.53/0.64 divide(inverse(Y), divide(inverse(X), Y))
% 1.53/0.64 = { by lemma 21 R->L }
% 1.53/0.64 divide(divide(Z, Z), inverse(X))
% 1.53/0.64 = { by lemma 20 R->L }
% 1.53/0.64 divide(inverse(divide(W, W)), inverse(X))
% 1.53/0.64 = { by lemma 15 R->L }
% 1.53/0.64 divide(divide(divide(V, U), inverse(divide(U, V))), inverse(X))
% 1.53/0.64 = { by lemma 11 R->L }
% 1.53/0.64 divide(divide(inverse(divide(T, S)), divide(S, T)), inverse(X))
% 1.53/0.64 = { by lemma 24 R->L }
% 1.53/0.64 divide(divide(inverse(divide(T, S)), divide(S, T)), divide(inverse(X2), divide(X, X2)))
% 1.53/0.64 = { by lemma 9 }
% 1.53/0.64 divide(divide(X, X2), inverse(X2))
% 1.53/0.64 = { by lemma 19 }
% 1.53/0.64 X
% 1.53/0.64
% 1.53/0.64 Lemma 26: divide(divide(X, inverse(Y)), Y) = X.
% 1.53/0.64 Proof:
% 1.53/0.64 divide(divide(X, inverse(Y)), Y)
% 1.53/0.64 = { by lemma 22 R->L }
% 1.53/0.64 divide(divide(X, inverse(Y)), inverse(inverse(Y)))
% 1.53/0.64 = { by lemma 19 }
% 1.53/0.64 X
% 1.53/0.64
% 1.53/0.64 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))).
% 1.53/0.64 Proof:
% 1.53/0.64 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 1.53/0.64 = { by axiom 1 (multiply) }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 1.53/0.64 = { by axiom 1 (multiply) }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3))
% 1.53/0.64 = { by axiom 1 (multiply) }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3))
% 1.53/0.64 = { by axiom 1 (multiply) }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(divide(a3, inverse(b3)), c3))
% 1.53/0.64 = { by axiom 1 (multiply) }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 1.53/0.64 = { by lemma 21 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(X), divide(inverse(a2), X)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 1.53/0.64 = { by lemma 24 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 1.53/0.64 = { by lemma 25 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), inverse(c3)))
% 1.53/0.64 = { by lemma 26 R->L }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), divide(divide(inverse(c3), inverse(inverse(b3))), inverse(b3))))
% 1.53/0.64 = { by lemma 23 R->L }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), inverse(divide(inverse(b3), divide(inverse(c3), inverse(inverse(b3)))))))
% 1.53/0.64 = { by lemma 7 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, divide(divide(Y, Z), inverse(divide(Z, Y)))), inverse(divide(divide(divide(Y, Z), inverse(divide(Z, Y))), divide(inverse(c3), inverse(inverse(b3)))))))
% 1.53/0.64 = { by lemma 23 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, divide(divide(Y, Z), inverse(divide(Z, Y)))), divide(divide(inverse(c3), inverse(inverse(b3))), divide(divide(Y, Z), inverse(divide(Z, Y))))))
% 1.53/0.64 = { by lemma 12 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(divide(inverse(c3), inverse(inverse(b3))), divide(divide(Y, Z), inverse(divide(Z, Y))))))
% 1.53/0.64 = { by lemma 12 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), inverse(inverse(b3)))))
% 1.53/0.64 = { by lemma 25 }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), b3)))
% 1.53/0.64 = { by lemma 23 R->L }
% 1.53/0.64 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by lemma 26 R->L }
% 1.53/0.64 tuple(divide(inverse(a1), divide(divide(inverse(a1), inverse(W)), W)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by lemma 26 R->L }
% 1.53/0.64 tuple(divide(divide(divide(inverse(a1), inverse(W)), W), divide(divide(inverse(a1), inverse(W)), W)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by lemma 23 R->L }
% 1.53/0.64 tuple(divide(divide(divide(inverse(a1), inverse(W)), W), inverse(divide(W, divide(inverse(a1), inverse(W))))), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by lemma 15 }
% 1.53/0.64 tuple(inverse(divide(V, V)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by lemma 20 }
% 1.53/0.64 tuple(divide(divide(divide(inverse(b1), inverse(U)), U), divide(divide(inverse(b1), inverse(U)), U)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by lemma 26 }
% 1.53/0.64 tuple(divide(inverse(b1), divide(divide(inverse(b1), inverse(U)), U)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by lemma 26 }
% 1.53/0.64 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 1.53/0.64 = { by axiom 1 (multiply) R->L }
% 1.53/0.64 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, divide(b3, inverse(c3))))
% 1.53/0.65 = { by axiom 1 (multiply) R->L }
% 1.53/0.65 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, multiply(b3, c3)))
% 1.53/0.65 = { by axiom 1 (multiply) R->L }
% 1.53/0.65 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 1.53/0.65 % SZS output end Proof
% 1.53/0.65
% 1.53/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------