%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:09:11 AM UTC 2026
% Result : Unsatisfiable 13.89s 2.17s
% Output : Proof 14.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n005.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 27 09:17:31 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.89/2.17 Command-line arguments: --no-flatten-goal
% 13.89/2.17
% 13.89/2.17 % SZS status Unsatisfiable
% 13.89/2.17
% 14.19/2.29 % SZS output start Proof
% 14.19/2.30 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z))))))) = W.
% 14.19/2.30
% 14.19/2.30 Lemma 2: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W)))) = V.
% 14.19/2.30 Proof:
% 14.19/2.30 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W))))
% 14.19/2.30 = { by axiom 1 (single_axiom) R->L }
% 14.19/2.30 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z)))))))))))
% 14.19/2.30 = { by axiom 1 (single_axiom) }
% 14.19/2.30 V
% 14.19/2.30
% 14.19/2.30 Lemma 3: inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, U), inverse(multiply(T, multiply(X, U))))))) = T.
% 14.19/2.30 Proof:
% 14.19/2.30 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, U), inverse(multiply(T, multiply(X, U)))))))
% 14.19/2.30 = { by axiom 1 (single_axiom) R->L }
% 14.19/2.30 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W))))))), U), inverse(multiply(T, multiply(X, U)))))))
% 14.19/2.30 = { by axiom 1 (single_axiom) }
% 14.19/2.30 T
% 14.19/2.30
% 14.19/2.30 Lemma 4: multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))) = W.
% 14.19/2.30 Proof:
% 14.19/2.30 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z))))))
% 14.19/2.30 = { by lemma 2 R->L }
% 14.19/2.30 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 14.19/2.30 = { by lemma 3 }
% 14.19/2.30 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 14.19/2.30 = { by lemma 2 R->L }
% 14.19/2.30 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), S)), inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), S))))))))
% 14.19/2.30 = { by axiom 1 (single_axiom) }
% 14.97/2.30 W
% 14.97/2.30
% 14.97/2.30 Lemma 5: multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(W, multiply(V, T)))))) = multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z)))))).
% 14.97/2.30 Proof:
% 14.97/2.30 multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(W, multiply(V, T))))))
% 14.97/2.30 = { by lemma 2 R->L }
% 14.97/2.31 inverse(multiply(S, multiply(X2, multiply(multiply(inverse(X2), multiply(multiply(inverse(S), multiply(multiply(W, Y2), inverse(multiply(Z2, multiply(W2, Y2))))), inverse(multiply(W2, multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(W, multiply(V, T)))))), multiply(multiply(W, Y2), inverse(multiply(Z2, multiply(W2, Y2))))))))), W2))))
% 14.97/2.31 = { by lemma 3 }
% 14.97/2.31 inverse(multiply(S, multiply(X2, multiply(multiply(inverse(X2), multiply(multiply(inverse(S), multiply(multiply(W, Y2), inverse(multiply(Z2, multiply(W2, Y2))))), Z2)), W2))))
% 14.97/2.31 = { by lemma 3 R->L }
% 14.97/2.31 inverse(multiply(S, multiply(X2, multiply(multiply(inverse(X2), multiply(multiply(inverse(S), multiply(multiply(W, Y2), inverse(multiply(Z2, multiply(W2, Y2))))), inverse(multiply(W2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z)))))), multiply(multiply(W, Y2), inverse(multiply(Z2, multiply(W2, Y2))))))))), W2))))
% 14.97/2.31 = { by lemma 2 }
% 14.97/2.31 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z))))))
% 14.97/2.31
% 14.97/2.31 Lemma 6: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(X, W)))))), inverse(multiply(U, multiply(T, multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(V, multiply(T, X2)))))))))))) = U.
% 14.97/2.31 Proof:
% 14.97/2.31 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(X, W)))))), inverse(multiply(U, multiply(T, multiply(S, multiply(multiply(inverse(S), X2), inverse(multiply(V, multiply(T, X2))))))))))))
% 14.97/2.31 = { by lemma 5 }
% 14.97/2.31 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(X, W)))))), inverse(multiply(U, multiply(X, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(X, W))))))))))))
% 14.97/2.31 = { by axiom 1 (single_axiom) }
% 14.97/2.31 U
% 14.97/2.31
% 14.97/2.31 Lemma 7: inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y)))))) = Z.
% 14.97/2.31 Proof:
% 14.97/2.31 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y))))))
% 14.97/2.31 = { by lemma 4 R->L }
% 14.97/2.31 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(Y), multiply(W, U))))))))))))
% 14.97/2.31 = { by lemma 4 R->L }
% 14.97/2.31 inverse(multiply(inverse(X), multiply(X, multiply(multiply(inverse(X), multiply(T, multiply(multiply(inverse(T), S), inverse(multiply(inverse(Y), multiply(inverse(X), S)))))), inverse(multiply(Z, multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(Y), multiply(W, U))))))))))))
% 14.97/2.31 = { by lemma 6 }
% 14.97/2.31 Z
% 14.97/2.31
% 14.97/2.31 Lemma 8: multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W))) = X.
% 14.97/2.31 Proof:
% 14.97/2.31 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W)))
% 14.97/2.31 = { by lemma 7 R->L }
% 14.97/2.31 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), inverse(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(W, Z)))))))))
% 14.97/2.31 = { by lemma 5 R->L }
% 14.97/2.31 multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(inverse(X), multiply(V, T))))))
% 14.97/2.31 = { by lemma 4 }
% 14.97/2.31 X
% 14.97/2.31
% 14.97/2.31 Lemma 9: inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X)))))) = Z.
% 14.97/2.31 Proof:
% 14.97/2.31 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X))))))
% 14.97/2.31 = { by lemma 4 R->L }
% 14.97/2.31 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(X), multiply(W, U))))))))))))
% 14.97/2.31 = { by lemma 8 R->L }
% 14.97/2.31 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(T, multiply(multiply(inverse(T), multiply(S, inverse(multiply(X2, S)))), X2))), inverse(multiply(Z, multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(X), multiply(W, U))))))))))))
% 14.97/2.31 = { by lemma 7 R->L }
% 14.97/2.31 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(T, multiply(multiply(inverse(T), multiply(S, inverse(multiply(X2, S)))), inverse(multiply(inverse(X), multiply(X, multiply(S, inverse(multiply(X2, S))))))))), inverse(multiply(Z, multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(X), multiply(W, U))))))))))))
% 14.97/2.31 = { by lemma 6 }
% 14.97/2.31 Z
% 14.97/2.31
% 14.97/2.31 Lemma 10: inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(Z, W)))), Z)))) = W.
% 14.97/2.31 Proof:
% 14.97/2.31 inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(Z, W)))), Z))))
% 14.97/2.31 = { by lemma 9 R->L }
% 14.97/2.31 inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(Z, W)))), inverse(multiply(W, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, W))))))))))
% 14.97/2.31 = { by lemma 7 }
% 14.97/2.31 W
% 14.97/2.31
% 14.97/2.31 Lemma 11: inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), W)))) = multiply(V, multiply(inverse(V), inverse(multiply(Z, W)))).
% 14.97/2.31 Proof:
% 14.97/2.31 inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(inverse(Y), Z)), W))))
% 14.97/2.31 = { by lemma 9 R->L }
% 14.97/2.31 inverse(multiply(inverse(X), multiply(X, multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(W, multiply(V, multiply(inverse(V), inverse(multiply(Z, W)))))))), W))))
% 14.97/2.31 = { by lemma 10 }
% 14.97/2.31 multiply(V, multiply(inverse(V), inverse(multiply(Z, W))))
% 14.97/2.31
% 14.97/2.31 Lemma 12: multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, Z)), Y)))) = Z.
% 14.97/2.31 Proof:
% 14.97/2.31 multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, Z)), Y))))
% 14.97/2.31 = { by lemma 11 R->L }
% 14.97/2.31 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(Y, Z)))), Y))))
% 14.97/2.31 = { by lemma 10 }
% 14.97/2.31 Z
% 14.97/2.31
% 14.97/2.31 Lemma 13: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y))))) = Z.
% 14.97/2.31 Proof:
% 14.97/2.31 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y)))))
% 14.97/2.31 = { by lemma 4 R->L }
% 14.97/2.31 multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y)))))), multiply(W, U))))))
% 14.97/2.31 = { by lemma 7 }
% 14.97/2.31 multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(Z), multiply(W, U))))))
% 14.97/2.31 = { by lemma 4 }
% 14.97/2.31 Z
% 14.97/2.31
% 14.97/2.31 Lemma 14: inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, multiply(multiply(inverse(X), multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(X2, T))))), S)), X2)))) = U.
% 14.97/2.31 Proof:
% 14.97/2.31 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, multiply(multiply(inverse(X), multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 14.97/2.31 = { by lemma 2 R->L }
% 14.97/2.31 inverse(multiply(X, multiply(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), inverse(multiply(V, multiply(Y, W)))))), multiply(multiply(V, multiply(multiply(inverse(X), multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(X2, T))))), S)), inverse(multiply(U, multiply(X, multiply(multiply(inverse(X), multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(X2, T))))), S))))))))
% 14.97/2.31 = { by lemma 3 }
% 14.97/2.31 U
% 14.97/2.31
% 14.97/2.31 Lemma 15: multiply(Z, multiply(inverse(Z), Y)) = multiply(X, multiply(inverse(X), Y)).
% 14.97/2.31 Proof:
% 14.97/2.31 multiply(Z, multiply(inverse(Z), Y))
% 14.97/2.31 = { by lemma 14 R->L }
% 14.97/2.31 multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2))))))
% 14.97/2.31 = { by lemma 10 R->L }
% 14.97/2.31 inverse(multiply(inverse(W2), multiply(W2, multiply(multiply(V2, multiply(inverse(V2), inverse(multiply(multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2)), multiply(Z, multiply(inverse(Z), inverse(multiply(W, multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2)))))))))), multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2))))))
% 14.97/2.31 = { by lemma 9 }
% 14.97/2.31 inverse(multiply(inverse(W2), multiply(W2, multiply(multiply(V2, multiply(inverse(V2), W)), multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2))))))
% 14.97/2.31 = { by lemma 9 R->L }
% 14.97/2.31 inverse(multiply(inverse(W2), multiply(W2, multiply(multiply(V2, multiply(inverse(V2), inverse(multiply(multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2)), multiply(X, multiply(inverse(X), inverse(multiply(W, multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2)))))))))), multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2))))))
% 14.97/2.31 = { by lemma 10 }
% 14.97/2.31 multiply(X, multiply(inverse(X), inverse(multiply(W, multiply(multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(S, multiply(V, T)))))), multiply(multiply(S, multiply(multiply(inverse(W), multiply(multiply(inverse(Y), X2), inverse(multiply(Y2, multiply(Z2, X2))))), Y2)), Z2))))))
% 14.97/2.31 = { by lemma 14 }
% 14.97/2.31 multiply(X, multiply(inverse(X), Y))
% 14.97/2.31
% 14.97/2.31 Lemma 16: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 14.97/2.31 Proof:
% 14.97/2.31 multiply(Y, inverse(Y))
% 14.97/2.31 = { by lemma 8 R->L }
% 14.97/2.31 multiply(Y, multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 14.97/2.31 = { by lemma 15 }
% 14.97/2.31 multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 14.97/2.31 = { by lemma 8 }
% 14.97/2.31 multiply(X, inverse(X))
% 14.97/2.31
% 14.97/2.31 Lemma 17: multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, inverse(Y))), Z)))) = inverse(Z).
% 14.97/2.31 Proof:
% 14.97/2.31 multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, inverse(Y))), Z))))
% 14.97/2.31 = { by lemma 11 R->L }
% 14.97/2.31 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(Y, inverse(Y))))), Z))))
% 14.97/2.31 = { by lemma 16 }
% 14.97/2.31 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(Z, inverse(Z))))), Z))))
% 14.97/2.31 = { by lemma 10 }
% 14.97/2.32 inverse(Z)
% 14.97/2.32
% 14.97/2.32 Lemma 18: multiply(X, multiply(Y, inverse(multiply(X, Y)))) = inverse(inverse(inverse(multiply(Z, inverse(Z))))).
% 14.97/2.32 Proof:
% 14.97/2.32 multiply(X, multiply(Y, inverse(multiply(X, Y))))
% 14.97/2.32 = { by lemma 10 R->L }
% 14.97/2.32 multiply(X, inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(X, multiply(Y, inverse(multiply(X, Y))))))), X)))))
% 14.97/2.32 = { by lemma 12 R->L }
% 14.97/2.32 multiply(X, inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(X, Y)))))), inverse(X)))))))), X)))))
% 14.97/2.32 = { by lemma 9 R->L }
% 14.97/2.32 multiply(X, inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(multiply(U, multiply(T, multiply(inverse(T), inverse(multiply(X, U)))))), Y)))))), inverse(X)))))))), X)))))
% 14.97/2.32 = { by lemma 13 }
% 14.97/2.32 multiply(X, inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(U, multiply(T, multiply(inverse(T), inverse(multiply(X, U)))))), inverse(X)))))))), X)))))
% 14.97/2.32 = { by lemma 9 }
% 14.97/2.32 multiply(X, inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(X, multiply(inverse(X), inverse(multiply(X, inverse(X)))))))), X)))))
% 14.97/2.32 = { by lemma 10 }
% 14.97/2.32 multiply(X, multiply(inverse(X), inverse(multiply(X, inverse(X)))))
% 14.97/2.32 = { by lemma 16 }
% 14.97/2.32 multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(multiply(Z, inverse(Z))))))))
% 14.97/2.32 = { by lemma 17 }
% 14.97/2.32 inverse(inverse(inverse(multiply(Z, inverse(Z)))))
% 14.97/2.32
% 14.97/2.32 Lemma 19: inverse(multiply(inverse(X), inverse(inverse(inverse(multiply(Y, inverse(Y))))))) = X.
% 14.97/2.32 Proof:
% 14.97/2.32 inverse(multiply(inverse(X), inverse(inverse(inverse(multiply(Y, inverse(Y)))))))
% 14.97/2.32 = { by lemma 18 R->L }
% 14.97/2.32 inverse(multiply(inverse(X), multiply(X, multiply(inverse(X), inverse(multiply(X, inverse(X)))))))
% 14.97/2.32 = { by lemma 9 }
% 14.97/2.32 X
% 14.97/2.32
% 14.97/2.32 Lemma 20: multiply(Z, inverse(multiply(Y, Z))) = multiply(X, inverse(multiply(Y, X))).
% 14.97/2.32 Proof:
% 14.97/2.32 multiply(Z, inverse(multiply(Y, Z)))
% 14.97/2.32 = { by lemma 10 R->L }
% 14.97/2.32 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(U, multiply(Z, inverse(multiply(Y, Z))))))), U))))
% 14.97/2.32 = { by lemma 12 R->L }
% 14.97/2.32 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(T, multiply(inverse(T), inverse(multiply(inverse(multiply(inverse(U), multiply(U, multiply(Z, inverse(multiply(Y, Z)))))), inverse(U)))))))), U))))
% 14.97/2.32 = { by lemma 7 }
% 14.97/2.32 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(T, multiply(inverse(T), inverse(multiply(Y, inverse(U)))))))), U))))
% 14.97/2.32 = { by lemma 7 R->L }
% 14.97/2.32 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(T, multiply(inverse(T), inverse(multiply(inverse(multiply(inverse(U), multiply(U, multiply(X, inverse(multiply(Y, X)))))), inverse(U)))))))), U))))
% 14.97/2.32 = { by lemma 12 }
% 14.97/2.32 inverse(multiply(inverse(W), multiply(W, multiply(multiply(V, multiply(inverse(V), inverse(multiply(U, multiply(X, inverse(multiply(Y, X))))))), U))))
% 14.97/2.32 = { by lemma 10 }
% 14.97/2.32 multiply(X, inverse(multiply(Y, X)))
% 14.97/2.32
% 14.97/2.32 Lemma 21: multiply(inverse(inverse(inverse(multiply(X, inverse(X))))), Y) = multiply(Z, inverse(multiply(inverse(Y), Z))).
% 14.97/2.32 Proof:
% 14.97/2.32 multiply(inverse(inverse(inverse(multiply(X, inverse(X))))), Y)
% 14.97/2.32 = { by lemma 18 R->L }
% 14.97/2.32 multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(Y, inverse(Y))))), Y)
% 14.97/2.32 = { by lemma 9 R->L }
% 14.97/2.32 multiply(multiply(Y, multiply(inverse(Y), inverse(multiply(Y, inverse(Y))))), inverse(multiply(inverse(Y), multiply(Y, multiply(inverse(Y), inverse(multiply(Y, inverse(Y))))))))
% 14.97/2.32 = { by lemma 20 R->L }
% 14.97/2.32 multiply(Z, inverse(multiply(inverse(Y), Z)))
% 14.97/2.32
% 14.97/2.32 Lemma 22: multiply(inverse(X), multiply(X, Y)) = multiply(Z, multiply(inverse(Z), Y)).
% 14.97/2.32 Proof:
% 14.97/2.32 multiply(inverse(X), multiply(X, Y))
% 14.97/2.32 = { by lemma 4 R->L }
% 14.97/2.32 multiply(inverse(X), multiply(X, multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(Y), multiply(W, U))))))))
% 14.97/2.32 = { by lemma 9 R->L }
% 14.97/2.32 multiply(inverse(X), multiply(X, multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(T, inverse(T))))), multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(Y), inverse(inverse(inverse(multiply(T, inverse(T))))))))))), multiply(W, U))))))))
% 14.97/2.32 = { by lemma 4 }
% 14.97/2.32 multiply(inverse(X), multiply(X, multiply(inverse(inverse(inverse(multiply(T, inverse(T))))), multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(Y), inverse(inverse(inverse(multiply(T, inverse(T))))))))))))
% 14.97/2.32 = { by lemma 19 }
% 14.97/2.32 multiply(inverse(X), multiply(X, multiply(inverse(inverse(inverse(multiply(T, inverse(T))))), multiply(Z, multiply(inverse(Z), Y)))))
% 14.97/2.32 = { by lemma 21 }
% 14.97/2.32 multiply(inverse(X), multiply(X, multiply(S, inverse(multiply(inverse(multiply(Z, multiply(inverse(Z), Y))), S)))))
% 14.97/2.32 = { by lemma 4 R->L }
% 14.97/2.32 multiply(inverse(X2), multiply(X2, multiply(multiply(inverse(X2), Y2), inverse(multiply(inverse(multiply(inverse(X), multiply(X, multiply(S, inverse(multiply(inverse(multiply(Z, multiply(inverse(Z), Y))), S)))))), multiply(inverse(X2), Y2))))))
% 14.97/2.32 = { by lemma 7 }
% 14.97/2.32 multiply(inverse(X2), multiply(X2, multiply(multiply(inverse(X2), Y2), inverse(multiply(inverse(multiply(Z, multiply(inverse(Z), Y))), multiply(inverse(X2), Y2))))))
% 14.97/2.32 = { by lemma 13 }
% 14.97/2.32 multiply(Z, multiply(inverse(Z), Y))
% 14.97/2.32
% 14.97/2.32 Lemma 23: inverse(inverse(X)) = X.
% 14.97/2.32 Proof:
% 14.97/2.32 inverse(inverse(X))
% 14.97/2.32 = { by lemma 7 R->L }
% 14.97/2.32 inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(X), multiply(X, inverse(multiply(Z, X)))), inverse(multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, inverse(multiply(Z, X))))))))))
% 14.97/2.32 = { by lemma 7 }
% 14.97/2.32 inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(X), multiply(X, inverse(multiply(Z, X)))), Z))))
% 14.97/2.32 = { by lemma 22 }
% 14.97/2.32 inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(W, multiply(inverse(W), inverse(multiply(Z, X)))), Z))))
% 14.97/2.32 = { by lemma 11 }
% 14.97/2.32 multiply(V, multiply(inverse(V), inverse(multiply(inverse(multiply(Z, X)), Z))))
% 14.97/2.32 = { by lemma 12 }
% 14.97/2.32 X
% 14.97/2.32
% 14.97/2.32 Lemma 24: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 14.97/2.32 Proof:
% 14.97/2.32 multiply(inverse(X), X)
% 14.97/2.32 = { by lemma 8 R->L }
% 14.97/2.33 multiply(inverse(X), multiply(X, multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 14.97/2.33 = { by lemma 22 }
% 14.97/2.33 multiply(Y, multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(V, W)))), V))))
% 14.97/2.33 = { by lemma 8 }
% 14.97/2.33 multiply(Y, inverse(Y))
% 14.97/2.33
% 14.97/2.33 Lemma 25: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 14.97/2.33 Proof:
% 14.97/2.33 inverse(multiply(X, inverse(X)))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 inverse(inverse(inverse(multiply(X, inverse(X)))))
% 14.97/2.33 = { by lemma 18 R->L }
% 14.97/2.33 multiply(inverse(Z), multiply(inverse(inverse(Z)), inverse(multiply(inverse(Z), inverse(inverse(Z))))))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 multiply(inverse(Z), multiply(inverse(inverse(Z)), inverse(inverse(inverse(multiply(inverse(Z), inverse(inverse(Z))))))))
% 14.97/2.33 = { by lemma 18 R->L }
% 14.97/2.33 multiply(inverse(Z), multiply(inverse(inverse(Z)), multiply(W, multiply(inverse(W), inverse(multiply(W, inverse(W)))))))
% 14.97/2.33 = { by lemma 17 R->L }
% 14.97/2.33 multiply(inverse(Z), multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(multiply(W, inverse(W))), inverse(Z))))), multiply(W, multiply(inverse(W), inverse(multiply(W, inverse(W)))))))
% 14.97/2.33 = { by lemma 4 R->L }
% 14.97/2.33 multiply(inverse(Z), multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(multiply(W, inverse(W))), inverse(Z))))), multiply(W, multiply(inverse(W), inverse(multiply(W, inverse(W))))))), multiply(V, T)))))))
% 14.97/2.33 = { by lemma 7 R->L }
% 14.97/2.33 multiply(inverse(Z), multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(inverse(multiply(multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(multiply(W, inverse(W))), inverse(Z))))), multiply(W, multiply(inverse(W), inverse(multiply(inverse(Z), multiply(Z, multiply(inverse(Z), inverse(multiply(inverse(multiply(W, inverse(W))), inverse(Z))))))))))), multiply(V, T)))))))
% 14.97/2.33 = { by lemma 9 }
% 14.97/2.33 multiply(inverse(Z), multiply(V, multiply(U, multiply(multiply(inverse(U), T), inverse(multiply(inverse(Z), multiply(V, T)))))))
% 14.97/2.33 = { by lemma 4 }
% 14.97/2.33 multiply(inverse(Z), Z)
% 14.97/2.33 = { by lemma 24 }
% 14.97/2.33 multiply(Y, inverse(Y))
% 14.97/2.33
% 14.97/2.33 Lemma 26: multiply(X, multiply(inverse(X), Y)) = Y.
% 14.97/2.33 Proof:
% 14.97/2.33 multiply(X, multiply(inverse(X), Y))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 multiply(X, multiply(inverse(X), inverse(inverse(Y))))
% 14.97/2.33 = { by lemma 15 }
% 14.97/2.33 multiply(Y, multiply(inverse(Y), inverse(inverse(Y))))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 multiply(Y, inverse(inverse(multiply(inverse(Y), inverse(inverse(Y))))))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 inverse(inverse(multiply(Y, inverse(inverse(multiply(inverse(Y), inverse(inverse(Y))))))))
% 14.97/2.33 = { by lemma 25 R->L }
% 14.97/2.33 inverse(inverse(multiply(Y, inverse(inverse(inverse(multiply(Z, inverse(Z))))))))
% 14.97/2.33 = { by lemma 7 R->L }
% 14.97/2.33 inverse(multiply(inverse(W), multiply(W, multiply(V, inverse(multiply(inverse(inverse(multiply(Y, inverse(inverse(inverse(multiply(Z, inverse(Z)))))))), V))))))
% 14.97/2.33 = { by lemma 21 R->L }
% 14.97/2.33 inverse(multiply(inverse(W), multiply(W, multiply(inverse(inverse(inverse(multiply(Z, inverse(Z))))), inverse(multiply(Y, inverse(inverse(inverse(multiply(Z, inverse(Z)))))))))))
% 14.97/2.33 = { by lemma 7 }
% 14.97/2.33 Y
% 14.97/2.33
% 14.97/2.33 Lemma 27: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 14.97/2.33 Proof:
% 14.97/2.33 multiply(X, inverse(multiply(Y, X)))
% 14.97/2.33 = { by lemma 20 }
% 14.97/2.33 multiply(inverse(Y), inverse(multiply(Y, inverse(Y))))
% 14.97/2.33 = { by lemma 16 R->L }
% 14.97/2.33 multiply(inverse(Y), inverse(multiply(Z, inverse(Z))))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 multiply(inverse(Y), inverse(inverse(inverse(multiply(Z, inverse(Z))))))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 inverse(inverse(multiply(inverse(Y), inverse(inverse(inverse(multiply(Z, inverse(Z))))))))
% 14.97/2.33 = { by lemma 19 }
% 14.97/2.33 inverse(Y)
% 14.97/2.33
% 14.97/2.33 Lemma 28: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 14.97/2.33 Proof:
% 14.97/2.33 inverse(multiply(X, inverse(Y)))
% 14.97/2.33 = { by lemma 26 R->L }
% 14.97/2.33 multiply(Y, multiply(inverse(Y), inverse(multiply(X, inverse(Y)))))
% 14.97/2.33 = { by lemma 27 }
% 14.97/2.33 multiply(Y, inverse(X))
% 14.97/2.33
% 14.97/2.33 Lemma 29: multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z)))))) = multiply(V, multiply(U, multiply(inverse(U), inverse(multiply(W, V))))).
% 14.97/2.33 Proof:
% 14.97/2.33 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z))))))
% 14.97/2.33 = { by lemma 9 R->L }
% 14.97/2.33 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(multiply(V, multiply(U, multiply(inverse(U), inverse(multiply(W, V)))))), multiply(X, Z))))))
% 14.97/2.33 = { by lemma 4 }
% 14.97/2.33 multiply(V, multiply(U, multiply(inverse(U), inverse(multiply(W, V)))))
% 14.97/2.33
% 14.97/2.33 Lemma 30: inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 14.97/2.33 Proof:
% 14.97/2.33 inverse(multiply(X, Y))
% 14.97/2.33 = { by axiom 1 (single_axiom) R->L }
% 14.97/2.33 inverse(multiply(X, inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(Y, multiply(Z, V)))))))))
% 14.97/2.33 = { by lemma 28 }
% 14.97/2.33 multiply(multiply(Z, multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(Y, multiply(Z, V)))))), inverse(X))
% 14.97/2.33 = { by lemma 29 }
% 14.97/2.33 multiply(multiply(U, multiply(T, multiply(inverse(T), inverse(multiply(Y, U))))), inverse(X))
% 14.97/2.33 = { by lemma 26 }
% 14.97/2.33 multiply(multiply(U, inverse(multiply(Y, U))), inverse(X))
% 14.97/2.33 = { by lemma 27 }
% 14.97/2.33 multiply(inverse(Y), inverse(X))
% 14.97/2.33
% 14.97/2.33 Lemma 31: multiply(multiply(X, inverse(X)), Y) = Y.
% 14.97/2.33 Proof:
% 14.97/2.33 multiply(multiply(X, inverse(X)), Y)
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 multiply(multiply(X, inverse(X)), inverse(inverse(Y)))
% 14.97/2.33 = { by lemma 28 R->L }
% 14.97/2.33 inverse(multiply(inverse(Y), inverse(multiply(X, inverse(X)))))
% 14.97/2.33 = { by lemma 23 R->L }
% 14.97/2.33 inverse(multiply(inverse(Y), inverse(inverse(inverse(multiply(X, inverse(X)))))))
% 14.97/2.34 = { by lemma 19 }
% 14.97/2.34 Y
% 14.97/2.34
% 14.97/2.34 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))).
% 14.97/2.34 Proof:
% 14.97/2.34 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 14.97/2.34 = { by lemma 24 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 14.97/2.34 = { by lemma 24 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3))
% 14.97/2.34 = { by lemma 31 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 14.97/2.34 = { by lemma 14 R->L }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), inverse(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))))))
% 14.97/2.34 = { by lemma 23 R->L }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, inverse(inverse(b3))), inverse(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))))))
% 14.97/2.34 = { by lemma 28 R->L }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))))))
% 14.97/2.34 = { by lemma 30 R->L }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3)))))
% 14.97/2.34 = { by lemma 27 R->L }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(Z2, inverse(multiply(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))), Z2))))
% 14.97/2.34 = { by lemma 26 R->L }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(Z2, multiply(W2, multiply(inverse(W2), inverse(multiply(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))), Z2))))))
% 14.97/2.34 = { by lemma 29 R->L }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(V2, inverse(V2)), multiply(multiply(inverse(multiply(V2, inverse(V2))), b3), inverse(multiply(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))), multiply(a3, b3)))))))
% 14.97/2.34 = { by lemma 31 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(inverse(multiply(V2, inverse(V2))), b3), inverse(multiply(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))), multiply(a3, b3))))))
% 14.97/2.34 = { by lemma 25 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(multiply(U2, inverse(U2)), b3), inverse(multiply(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))), multiply(a3, b3))))))
% 14.97/2.34 = { by lemma 31 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, inverse(multiply(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))), multiply(a3, b3))))))
% 14.97/2.34 = { by lemma 30 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, multiply(inverse(multiply(a3, b3)), inverse(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))))))))
% 14.97/2.34 = { by lemma 30 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, multiply(multiply(inverse(b3), inverse(a3)), inverse(multiply(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2))), multiply(inverse(b3), inverse(a3))))))))
% 14.97/2.34 = { by lemma 27 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, inverse(multiply(Z, multiply(multiply(W, multiply(V, multiply(multiply(inverse(V), U), inverse(multiply(T, multiply(W, U)))))), multiply(multiply(T, multiply(multiply(inverse(Z), multiply(multiply(inverse(c3), S), inverse(multiply(X2, multiply(Y2, S))))), X2)), Y2)))))))
% 14.97/2.34 = { by lemma 14 }
% 14.97/2.34 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 14.97/2.34 = { by lemma 24 R->L }
% 14.97/2.34 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 14.97/2.34 % SZS output end Proof
% 14.97/2.34
% 14.97/2.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------