%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP060-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 1.82s 0.61s
% Output : Proof 2.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP060-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 09:17:19 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.82/0.61 Command-line arguments: --no-flatten-goal
% 1.82/0.61
% 1.82/0.61 % SZS status Unsatisfiable
% 1.82/0.61
% 2.79/0.73 % SZS output start Proof
% 2.79/0.74 Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), X))))) = W.
% 2.79/0.74
% 2.79/0.74 Lemma 2: multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X))))) = W.
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) R->L }
% 2.79/0.74 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(W, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V)))))), X)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 W
% 2.79/0.74
% 2.79/0.74 Lemma 3: multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(W))), multiply(W, multiply(V, X))))) = multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(W))), multiply(W, multiply(V, X)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) R->L }
% 2.79/0.74 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y)))))), inverse(W))), multiply(W, multiply(V, X)))))
% 2.79/0.74 = { by lemma 2 }
% 2.79/0.74 multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y)))
% 2.79/0.74
% 2.79/0.74 Lemma 4: multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y))) = W.
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y)))
% 2.79/0.74 = { by lemma 3 R->L }
% 2.79/0.74 multiply(V, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(U))), multiply(U, multiply(Z, V)))))
% 2.79/0.74 = { by lemma 2 }
% 2.79/0.74 W
% 2.79/0.74
% 2.79/0.74 Lemma 5: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))) = multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(Z)), W))), inverse(U))).
% 2.79/0.74 Proof:
% 2.79/0.74 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W))))
% 2.79/0.74 = { by lemma 4 R->L }
% 2.79/0.74 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(multiply(W, inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W))))))), W))), inverse(U)))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(Z)), W))), inverse(U)))
% 2.79/0.74
% 2.79/0.74 Lemma 6: multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(multiply(inverse(Z), inverse(W)), X))), inverse(Z)))) = W.
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(multiply(inverse(Z), inverse(W)), X))), inverse(Z))))
% 2.79/0.74 = { by lemma 5 R->L }
% 2.79/0.74 multiply(X, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), inverse(multiply(W, V))), X)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 W
% 2.79/0.74
% 2.79/0.74 Lemma 7: multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, Z))), inverse(W))) = multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, Z))), inverse(W)))
% 2.79/0.74 = { by lemma 2 R->L }
% 2.79/0.74 multiply(U, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(Z, multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, Z))), inverse(W)))))), inverse(T))), multiply(T, multiply(Z, U)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 multiply(U, inverse(multiply(multiply(W, multiply(Y, inverse(T))), multiply(T, multiply(Z, U)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) R->L }
% 2.79/0.74 multiply(U, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(Z, multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W)))))), inverse(T))), multiply(T, multiply(Z, U)))))
% 2.79/0.74 = { by lemma 2 }
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W)))
% 2.79/0.74
% 2.79/0.74 Lemma 8: multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V))) = W.
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V)))
% 2.79/0.74 = { by lemma 3 R->L }
% 2.79/0.74 multiply(U, inverse(multiply(multiply(V, multiply(Y, inverse(Z))), multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z)))))), U)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 W
% 2.79/0.74
% 2.79/0.74 Lemma 9: multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X)))))) = multiply(V, inverse(multiply(Y, multiply(Z, multiply(W, V))))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))
% 2.79/0.74 = { by lemma 2 R->L }
% 2.79/0.74 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(W, multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))))), inverse(Z))), multiply(Z, multiply(W, V)))))
% 2.79/0.74 = { by lemma 8 }
% 2.79/0.74 multiply(V, inverse(multiply(Y, multiply(Z, multiply(W, V)))))
% 2.79/0.74
% 2.79/0.74 Lemma 10: multiply(X, multiply(multiply(inverse(X), inverse(multiply(inverse(Y), multiply(Z, multiply(W, inverse(V)))))), inverse(Y))) = multiply(V, multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(W, U))), inverse(Z))))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(multiply(inverse(Y), multiply(Z, multiply(W, inverse(V)))))), inverse(Y)))
% 2.79/0.74 = { by lemma 7 }
% 2.79/0.74 multiply(V, multiply(multiply(inverse(V), inverse(multiply(inverse(Y), multiply(Z, multiply(W, inverse(V)))))), inverse(Y)))
% 2.79/0.74 = { by lemma 6 R->L }
% 2.79/0.74 multiply(V, multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(V), inverse(multiply(inverse(Y), multiply(Z, multiply(W, inverse(V)))))), inverse(Y)))), U))), inverse(Z)))))
% 2.79/0.74 = { by lemma 9 R->L }
% 2.79/0.74 multiply(V, multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(S), inverse(multiply(inverse(Y), multiply(Z, multiply(W, inverse(S)))))), inverse(Y)))), U))), inverse(Z)))))
% 2.79/0.74 = { by lemma 8 R->L }
% 2.79/0.74 multiply(V, multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(S), inverse(multiply(inverse(Y), multiply(Z, multiply(W, inverse(S)))))), multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(W, multiply(inverse(S), inverse(multiply(inverse(Y), multiply(Z, multiply(W, inverse(S))))))))), inverse(Z)))))), U))), inverse(Z)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 multiply(V, multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(W, U))), inverse(Z)))))
% 2.79/0.74
% 2.79/0.74 Lemma 11: multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V)) = multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y)).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))
% 2.79/0.74 = { by lemma 6 R->L }
% 2.79/0.74 multiply(W, multiply(W2, multiply(V2, multiply(multiply(inverse(V2), inverse(multiply(multiply(inverse(Z2), inverse(multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))), W2))), inverse(Z2)))))
% 2.79/0.74 = { by lemma 10 R->L }
% 2.79/0.74 multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), multiply(Z2, multiply(multiply(inverse(Z2), inverse(multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))), inverse(W)))))), inverse(Y2)))
% 2.79/0.74 = { by lemma 4 }
% 2.79/0.74 multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), Z))), inverse(Y2)))
% 2.79/0.74 = { by lemma 4 R->L }
% 2.79/0.74 multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X)))))), inverse(Y2)))
% 2.79/0.74 = { by lemma 10 }
% 2.79/0.74 multiply(X, multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(multiply(inverse(S), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), U))), inverse(S)))))
% 2.79/0.74 = { by lemma 6 }
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))
% 2.79/0.74
% 2.79/0.74 Lemma 12: multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(multiply(inverse(Z), inverse(W)), W))), inverse(Z)))) = X.
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(multiply(inverse(Z), inverse(W)), W))), inverse(Z))))
% 2.79/0.74 = { by lemma 5 R->L }
% 2.79/0.74 multiply(X, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), inverse(multiply(W, V))), W)))))
% 2.79/0.74 = { by lemma 11 }
% 2.79/0.74 multiply(X, inverse(multiply(V, multiply(T, multiply(multiply(inverse(T), inverse(multiply(X, V))), X)))))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 X
% 2.79/0.74
% 2.79/0.74 Lemma 13: multiply(Z, multiply(inverse(Z), Y)) = multiply(X, multiply(inverse(X), Y)).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(Z, multiply(inverse(Z), Y))
% 2.79/0.74 = { by lemma 6 R->L }
% 2.79/0.74 multiply(Z, multiply(Y2, multiply(Z2, multiply(multiply(inverse(Z2), inverse(multiply(multiply(inverse(X2), inverse(multiply(inverse(Z), Y))), Y2))), inverse(X2)))))
% 2.79/0.74 = { by lemma 10 R->L }
% 2.79/0.74 multiply(T, multiply(multiply(inverse(T), inverse(multiply(inverse(S), multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Z), Y))), inverse(Z)))))), inverse(S)))
% 2.79/0.74 = { by lemma 11 }
% 2.79/0.74 multiply(T, multiply(multiply(inverse(T), inverse(multiply(inverse(S), multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(X), Y))), inverse(X)))))), inverse(S)))
% 2.79/0.74 = { by lemma 10 }
% 2.79/0.74 multiply(X, multiply(W, multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(multiply(inverse(X), Y))), W))), inverse(U)))))
% 2.79/0.74 = { by lemma 6 }
% 2.79/0.74 multiply(X, multiply(inverse(X), Y))
% 2.79/0.74
% 2.79/0.74 Lemma 14: multiply(multiply(inverse(X), inverse(multiply(W, Z))), W) = multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(multiply(inverse(X), inverse(multiply(W, Z))), W)
% 2.79/0.74 = { by lemma 2 R->L }
% 2.79/0.74 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(X, multiply(multiply(inverse(X), inverse(multiply(W, Z))), W)))), inverse(T))), multiply(T, multiply(X, V)))))
% 2.79/0.74 = { by lemma 11 }
% 2.79/0.74 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y)))), inverse(T))), multiply(T, multiply(X, V)))))
% 2.79/0.74 = { by lemma 2 }
% 2.79/0.74 multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y)
% 2.79/0.74
% 2.79/0.74 Lemma 15: multiply(multiply(inverse(X), inverse(Z)), Z) = multiply(multiply(inverse(X), inverse(Y)), Y).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(multiply(inverse(X), inverse(Z)), Z)
% 2.79/0.74 = { by lemma 12 R->L }
% 2.79/0.74 multiply(multiply(inverse(X), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(V), inverse(U)), U))), inverse(V)))))), Z)
% 2.79/0.74 = { by lemma 14 }
% 2.79/0.74 multiply(multiply(inverse(X), inverse(multiply(Y, multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(V), inverse(U)), U))), inverse(V)))))), Y)
% 2.79/0.74 = { by lemma 12 }
% 2.79/0.74 multiply(multiply(inverse(X), inverse(Y)), Y)
% 2.79/0.74
% 2.79/0.74 Lemma 16: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(Y, inverse(Y))
% 2.79/0.74 = { by lemma 12 R->L }
% 2.79/0.74 multiply(Y, multiply(inverse(Y), multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(W), inverse(V)), V))), inverse(W)))))
% 2.79/0.74 = { by lemma 13 }
% 2.79/0.74 multiply(X, multiply(inverse(X), multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(W), inverse(V)), V))), inverse(W)))))
% 2.79/0.74 = { by lemma 12 }
% 2.79/0.74 multiply(X, inverse(X))
% 2.79/0.74
% 2.79/0.74 Lemma 17: multiply(multiply(inverse(X), inverse(Y)), Y) = multiply(multiply(Z, inverse(Z)), inverse(X)).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(multiply(inverse(X), inverse(Y)), Y)
% 2.79/0.74 = { by lemma 15 }
% 2.79/0.74 multiply(multiply(inverse(X), inverse(inverse(X))), inverse(X))
% 2.79/0.74 = { by lemma 16 R->L }
% 2.79/0.74 multiply(multiply(Z, inverse(Z)), inverse(X))
% 2.79/0.74
% 2.79/0.74 Lemma 18: multiply(W, multiply(multiply(inverse(W), inverse(Y)), inverse(Z))) = multiply(X, multiply(multiply(inverse(X), inverse(Y)), inverse(Z))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(W, multiply(multiply(inverse(W), inverse(Y)), inverse(Z)))
% 2.79/0.74 = { by axiom 1 (single_axiom) R->L }
% 2.79/0.74 multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(Y, U))), V))))))), inverse(Z)))
% 2.79/0.74 = { by lemma 7 }
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(Y, U))), V))))))), inverse(Z)))
% 2.79/0.74 = { by axiom 1 (single_axiom) }
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(Y)), inverse(Z)))
% 2.79/0.74
% 2.79/0.74 Lemma 19: multiply(Y, multiply(Z, inverse(Z))) = multiply(X, multiply(inverse(X), inverse(inverse(Y)))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(Y, multiply(Z, inverse(Z)))
% 2.79/0.74 = { by lemma 12 R->L }
% 2.79/0.74 multiply(Y, multiply(Z, multiply(inverse(Z), multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(V), inverse(U)), U))), inverse(V))))))
% 2.79/0.74 = { by lemma 13 }
% 2.79/0.74 multiply(Y, multiply(inverse(Y), multiply(inverse(inverse(Y)), multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(V), inverse(U)), U))), inverse(V))))))
% 2.79/0.74 = { by lemma 13 R->L }
% 2.79/0.74 multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(V), inverse(U)), U))), inverse(V))))))
% 2.79/0.74 = { by lemma 12 }
% 2.79/0.74 multiply(X, multiply(inverse(X), inverse(inverse(Y))))
% 2.79/0.74
% 2.79/0.74 Lemma 20: multiply(multiply(X, inverse(X)), inverse(Y)) = multiply(inverse(Y), inverse(inverse(multiply(Z, inverse(Z))))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(multiply(X, inverse(X)), inverse(Y))
% 2.79/0.74 = { by lemma 2 R->L }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, multiply(multiply(X, inverse(X)), inverse(Y))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 17 R->L }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, multiply(multiply(inverse(Y), inverse(inverse(T))), inverse(T))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 2 R->L }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(S, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(Y2, multiply(Y, multiply(multiply(inverse(Y), inverse(inverse(T))), inverse(T)))))), inverse(Z2))), multiply(Z2, multiply(Y2, S))))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 2 R->L }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(S, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), multiply(W2, inverse(multiply(multiply(V2, multiply(multiply(inverse(V2), inverse(multiply(U2, inverse(multiply(Y2, multiply(Y, multiply(multiply(inverse(Y), inverse(inverse(T))), inverse(T)))))))), inverse(T2))), multiply(T2, multiply(U2, W2)))))), inverse(Z2))), multiply(Z2, multiply(Y2, S))))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 18 }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(S, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), multiply(W2, inverse(multiply(multiply(V2, multiply(multiply(inverse(V2), inverse(multiply(U2, inverse(multiply(Y2, multiply(multiply(Z, inverse(Z)), multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(T))), inverse(T)))))))), inverse(T2))), multiply(T2, multiply(U2, W2)))))), inverse(Z2))), multiply(Z2, multiply(Y2, S))))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 2 }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(S, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(Y2, multiply(multiply(Z, inverse(Z)), multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(T))), inverse(T)))))), inverse(Z2))), multiply(Z2, multiply(Y2, S))))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 2 }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(Z, inverse(Z)), multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(T))), inverse(T))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 17 }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(Z, inverse(Z)), multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z))))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 19 }
% 2.79/0.74 multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(multiply(Z, inverse(Z)))))))), inverse(U))), multiply(U, multiply(Y, W)))))
% 2.79/0.74 = { by lemma 2 }
% 2.79/0.74 multiply(inverse(Y), inverse(inverse(multiply(Z, inverse(Z)))))
% 2.79/0.74
% 2.79/0.74 Lemma 21: multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, inverse(Y)))), inverse(multiply(Z, inverse(Z))))) = inverse(multiply(W, inverse(W))).
% 2.79/0.74 Proof:
% 2.79/0.74 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, inverse(Y)))), inverse(multiply(Z, inverse(Z)))))
% 2.79/0.74 = { by lemma 12 R->L }
% 2.79/0.75 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Y), multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(T)), T))), inverse(U))))))), inverse(multiply(Z, inverse(Z)))))
% 2.79/0.75 = { by lemma 13 }
% 2.79/0.75 multiply(X, multiply(multiply(inverse(X), inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(inverse(multiply(Z, inverse(Z)))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(T)), T))), inverse(U))))))), inverse(multiply(Z, inverse(Z)))))
% 2.79/0.75 = { by lemma 12 }
% 2.79/0.75 multiply(X, multiply(multiply(inverse(X), inverse(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(multiply(Z, inverse(Z))))))), inverse(multiply(Z, inverse(Z)))))
% 2.79/0.75 = { by lemma 11 }
% 2.79/0.75 multiply(S, multiply(multiply(inverse(S), inverse(multiply(inverse(X2), inverse(inverse(multiply(Z, inverse(Z))))))), inverse(X2)))
% 2.79/0.75 = { by lemma 20 R->L }
% 2.79/0.75 multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(inverse(X2), inverse(inverse(X2))), inverse(X2)))), inverse(X2)))
% 2.79/0.75 = { by lemma 15 }
% 2.79/0.75 multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), inverse(inverse(Y2))))), multiply(inverse(Y2), inverse(inverse(Y2)))))), inverse(X2)))
% 2.79/0.75 = { by lemma 3 R->L }
% 2.79/0.75 multiply(Z2, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), inverse(inverse(Y2))))), inverse(W2))), multiply(W2, multiply(multiply(inverse(Y2), inverse(inverse(Y2))), Z2)))))
% 2.79/0.75 = { by lemma 2 R->L }
% 2.79/0.75 multiply(Z2, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(V2, inverse(multiply(multiply(U2, multiply(multiply(inverse(U2), inverse(multiply(Y2, multiply(inverse(Y2), inverse(inverse(Y2)))))), inverse(T2))), multiply(T2, multiply(Y2, V2))))))), inverse(W2))), multiply(W2, multiply(multiply(inverse(Y2), inverse(inverse(Y2))), Z2)))))
% 2.79/0.75 = { by lemma 19 R->L }
% 2.79/0.75 multiply(Z2, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(V2, inverse(multiply(multiply(U2, multiply(multiply(inverse(U2), inverse(multiply(Y2, multiply(multiply(inverse(Y2), inverse(inverse(Y2))), inverse(multiply(inverse(Y2), inverse(inverse(Y2)))))))), inverse(T2))), multiply(T2, multiply(Y2, V2))))))), inverse(W2))), multiply(W2, multiply(multiply(inverse(Y2), inverse(inverse(Y2))), Z2)))))
% 2.79/0.75 = { by lemma 2 }
% 2.79/0.75 multiply(Z2, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(multiply(inverse(Y2), inverse(inverse(Y2))), inverse(multiply(inverse(Y2), inverse(inverse(Y2))))))), inverse(W2))), multiply(W2, multiply(multiply(inverse(Y2), inverse(inverse(Y2))), Z2)))))
% 2.79/0.75 = { by lemma 16 R->L }
% 2.79/0.75 multiply(Z2, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(multiply(inverse(Y2), inverse(inverse(Y2))), inverse(multiply(W, inverse(W)))))), inverse(W2))), multiply(W2, multiply(multiply(inverse(Y2), inverse(inverse(Y2))), Z2)))))
% 2.79/0.75 = { by lemma 2 }
% 2.79/0.75 inverse(multiply(W, inverse(W)))
% 2.79/0.75
% 2.79/0.75 Lemma 22: multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Y))))) = multiply(Z, inverse(Z)).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Y)))))
% 2.79/0.75 = { by axiom 1 (single_axiom) R->L }
% 2.79/0.75 multiply(multiply(inverse(multiply(W, inverse(W))), inverse(multiply(inverse(X), multiply(V, multiply(multiply(inverse(V), inverse(multiply(X, inverse(X)))), inverse(multiply(W, inverse(W)))))))), multiply(inverse(X), inverse(multiply(Y, inverse(Y)))))
% 2.79/0.75 = { by lemma 21 }
% 2.79/0.75 multiply(multiply(inverse(multiply(W, inverse(W))), inverse(multiply(inverse(X), inverse(multiply(Y, inverse(Y)))))), multiply(inverse(X), inverse(multiply(Y, inverse(Y)))))
% 2.79/0.75 = { by lemma 17 }
% 2.79/0.75 multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W))))
% 2.79/0.75 = { by lemma 16 R->L }
% 2.79/0.75 multiply(Z, inverse(Z))
% 2.79/0.75
% 2.79/0.75 Lemma 23: multiply(inverse(X), inverse(multiply(Y, inverse(Y)))) = inverse(X).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(inverse(X), inverse(multiply(Y, inverse(Y))))
% 2.79/0.75 = { by lemma 2 R->L }
% 2.79/0.75 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Y))))))), inverse(V))), multiply(V, multiply(X, Z)))))
% 2.79/0.75 = { by lemma 22 }
% 2.79/0.75 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(X, inverse(X)))), inverse(V))), multiply(V, multiply(X, Z)))))
% 2.79/0.75 = { by lemma 3 }
% 2.79/0.75 multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(inverse(W), inverse(multiply(X, inverse(X)))), X))), inverse(W)))
% 2.79/0.75 = { by lemma 4 }
% 2.79/0.75 inverse(X)
% 2.79/0.75
% 2.79/0.75 Lemma 24: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 2.79/0.75 Proof:
% 2.79/0.75 inverse(multiply(X, inverse(X)))
% 2.79/0.75 = { by lemma 21 R->L }
% 2.79/0.75 multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, inverse(W)))), inverse(multiply(V, inverse(V)))))
% 2.79/0.75 = { by lemma 23 }
% 2.79/0.75 multiply(Z, multiply(inverse(Z), inverse(multiply(V, inverse(V)))))
% 2.79/0.75 = { by lemma 22 }
% 2.79/0.75 multiply(Y, inverse(Y))
% 2.79/0.75
% 2.79/0.75 Lemma 25: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(inverse(X), X)
% 2.79/0.75 = { by lemma 23 R->L }
% 2.79/0.75 multiply(multiply(inverse(X), inverse(multiply(Z, inverse(Z)))), X)
% 2.79/0.75 = { by lemma 24 R->L }
% 2.79/0.75 multiply(multiply(inverse(X), inverse(inverse(multiply(W, inverse(W))))), X)
% 2.79/0.75 = { by lemma 20 R->L }
% 2.79/0.75 multiply(multiply(multiply(V, inverse(V)), inverse(X)), X)
% 2.79/0.75 = { by lemma 24 R->L }
% 2.79/0.75 multiply(multiply(inverse(multiply(U, inverse(U))), inverse(X)), X)
% 2.79/0.75 = { by lemma 17 }
% 2.79/0.75 multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))
% 2.79/0.75 = { by lemma 16 R->L }
% 2.79/0.75 multiply(Y, inverse(Y))
% 2.79/0.75
% 2.79/0.75 Lemma 26: multiply(X, multiply(Y, inverse(Y))) = X.
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(X, multiply(Y, inverse(Y)))
% 2.79/0.75 = { by lemma 25 R->L }
% 2.79/0.75 multiply(X, multiply(inverse(X), X))
% 2.79/0.75 = { by lemma 23 R->L }
% 2.79/0.75 multiply(X, multiply(multiply(inverse(X), inverse(multiply(X, inverse(X)))), X))
% 2.79/0.75 = { by lemma 11 }
% 2.79/0.75 multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(W), inverse(X)))), inverse(W)))
% 2.79/0.75 = { by lemma 23 R->L }
% 2.79/0.75 multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(W), inverse(multiply(V, inverse(V)))), inverse(X)))), inverse(W)))
% 2.79/0.75 = { by lemma 3 R->L }
% 2.79/0.75 multiply(U, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, inverse(V)))), inverse(T))), multiply(T, multiply(inverse(X), U)))))
% 2.79/0.75 = { by lemma 25 R->L }
% 2.79/0.75 multiply(U, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(inverse(X), X))), inverse(T))), multiply(T, multiply(inverse(X), U)))))
% 2.79/0.75 = { by lemma 2 }
% 2.79/0.75 X
% 2.79/0.75
% 2.79/0.75 Lemma 27: multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y)) = multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(W)), X))), inverse(U))).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y))
% 2.79/0.75 = { by lemma 2 R->L }
% 2.79/0.75 multiply(T, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y))))), inverse(S))), multiply(S, multiply(X, T)))))
% 2.79/0.75 = { by lemma 4 }
% 2.79/0.75 multiply(T, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(W)), inverse(S))), multiply(S, multiply(X, T)))))
% 2.79/0.75 = { by lemma 3 }
% 2.79/0.75 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(U), inverse(W)), X))), inverse(U)))
% 2.79/0.75
% 2.79/0.75 Lemma 28: inverse(inverse(X)) = X.
% 2.79/0.75 Proof:
% 2.79/0.75 inverse(inverse(X))
% 2.79/0.75 = { by lemma 23 R->L }
% 2.79/0.75 inverse(multiply(inverse(X), inverse(multiply(Y, inverse(Y)))))
% 2.79/0.75 = { by lemma 23 R->L }
% 2.79/0.75 inverse(multiply(multiply(inverse(X), inverse(multiply(inverse(multiply(Y, inverse(Y))), inverse(inverse(multiply(Y, inverse(Y))))))), inverse(multiply(Y, inverse(Y)))))
% 2.79/0.75 = { by lemma 20 R->L }
% 2.79/0.75 inverse(multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(Y, inverse(Y))), inverse(inverse(multiply(Y, inverse(Y))))), inverse(multiply(Y, inverse(Y)))))), inverse(multiply(Y, inverse(Y)))))
% 2.79/0.75 = { by lemma 26 R->L }
% 2.79/0.75 inverse(multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(Y, inverse(Y))), inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(X, inverse(X))))), inverse(multiply(Y, inverse(Y)))))), inverse(multiply(Y, inverse(Y)))))
% 2.79/0.75 = { by lemma 27 }
% 2.79/0.75 inverse(multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(W), inverse(multiply(X, inverse(X)))), X))), inverse(W))))
% 2.79/0.75 = { by lemma 27 }
% 2.79/0.75 inverse(multiply(Z, multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(X), inverse(inverse(X))), Z))), inverse(X)))))
% 2.79/0.75 = { by lemma 5 }
% 2.79/0.75 multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(inverse(T), inverse(multiply(inverse(X), inverse(inverse(X))))), inverse(X)))), inverse(T)))
% 2.79/0.75 = { by lemma 23 }
% 2.79/0.75 multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(X)))), inverse(T)))
% 2.79/0.75 = { by lemma 11 R->L }
% 2.79/0.75 multiply(X, multiply(multiply(inverse(X), inverse(multiply(X, inverse(X)))), X))
% 2.79/0.75 = { by lemma 23 }
% 2.79/0.75 multiply(X, multiply(inverse(X), X))
% 2.79/0.75 = { by lemma 25 }
% 2.79/0.75 multiply(X, multiply(S, inverse(S)))
% 2.79/0.75 = { by lemma 26 }
% 2.79/0.75 X
% 2.79/0.75
% 2.79/0.75 Lemma 29: multiply(X, multiply(inverse(X), inverse(inverse(inverse(Y))))) = inverse(Y).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(X, multiply(inverse(X), inverse(inverse(inverse(Y)))))
% 2.79/0.75 = { by lemma 19 R->L }
% 2.79/0.75 multiply(inverse(Y), multiply(Z, inverse(Z)))
% 2.79/0.75 = { by lemma 24 R->L }
% 2.79/0.75 multiply(inverse(Y), inverse(multiply(W, inverse(W))))
% 2.79/0.75 = { by lemma 23 }
% 2.79/0.75 inverse(Y)
% 2.79/0.75
% 2.79/0.75 Lemma 30: multiply(X, multiply(inverse(X), inverse(Y))) = inverse(Y).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(X, multiply(inverse(X), inverse(Y)))
% 2.79/0.75 = { by lemma 28 R->L }
% 2.79/0.75 multiply(X, multiply(inverse(X), inverse(inverse(inverse(Y)))))
% 2.79/0.75 = { by lemma 29 }
% 2.79/0.75 inverse(Y)
% 2.79/0.75
% 2.79/0.75 Lemma 31: multiply(multiply(inverse(X), inverse(Y)), Y) = inverse(X).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(multiply(inverse(X), inverse(Y)), Y)
% 2.79/0.75 = { by lemma 15 }
% 2.79/0.75 multiply(multiply(inverse(X), inverse(multiply(inverse(inverse(X)), inverse(inverse(inverse(X)))))), multiply(inverse(inverse(X)), inverse(inverse(inverse(X)))))
% 2.79/0.75 = { by lemma 23 }
% 2.79/0.75 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(inverse(inverse(X)))))
% 2.79/0.75 = { by lemma 29 }
% 2.79/0.75 inverse(X)
% 2.79/0.75
% 2.79/0.75 Lemma 32: multiply(X, multiply(inverse(X), inverse(inverse(Y)))) = Y.
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(X, multiply(inverse(X), inverse(inverse(Y))))
% 2.79/0.75 = { by lemma 19 R->L }
% 2.79/0.75 multiply(Y, multiply(Z, inverse(Z)))
% 2.79/0.75 = { by lemma 31 R->L }
% 2.79/0.75 multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(inverse(W))), inverse(W))))
% 2.79/0.75 = { by lemma 31 R->L }
% 2.79/0.75 multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(W), inverse(V)), V))), inverse(W))))
% 2.79/0.75 = { by lemma 12 }
% 2.79/0.75 Y
% 2.79/0.75
% 2.79/0.75 Lemma 33: multiply(inverse(inverse(X)), inverse(multiply(Y, X))) = multiply(Z, inverse(multiply(Y, Z))).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(inverse(inverse(X)), inverse(multiply(Y, X)))
% 2.79/0.75 = { by lemma 32 R->L }
% 2.79/0.75 multiply(inverse(inverse(X)), inverse(multiply(Y, multiply(Z, multiply(inverse(Z), inverse(inverse(X)))))))
% 2.79/0.75 = { by lemma 9 }
% 2.79/0.75 multiply(Z, inverse(multiply(Y, multiply(Z, multiply(inverse(Z), Z)))))
% 2.79/0.75 = { by lemma 25 }
% 2.79/0.75 multiply(Z, inverse(multiply(Y, multiply(Z, multiply(W, inverse(W))))))
% 2.79/0.75 = { by lemma 26 }
% 2.79/0.75 multiply(Z, inverse(multiply(Y, Z)))
% 2.79/0.75
% 2.79/0.75 Lemma 34: multiply(X, multiply(Y, inverse(multiply(Z, multiply(W, multiply(X, Y)))))) = multiply(multiply(inverse(W), inverse(multiply(V, Z))), V).
% 2.79/0.75 Proof:
% 2.79/0.75 multiply(X, multiply(Y, inverse(multiply(Z, multiply(W, multiply(X, Y))))))
% 2.79/0.75 = { by lemma 8 R->L }
% 2.79/0.75 multiply(X, multiply(Y, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(X, multiply(inverse(T), inverse(multiply(Z, multiply(W, multiply(X, inverse(T))))))))), inverse(W))), multiply(W, multiply(X, Y))))))
% 2.79/0.75 = { by lemma 2 }
% 2.79/0.75 multiply(X, multiply(inverse(T), inverse(multiply(Z, multiply(W, multiply(X, inverse(T)))))))
% 2.79/0.75 = { by lemma 2 R->L }
% 2.79/0.75 multiply(X, multiply(multiply(inverse(X), inverse(S)), inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(X, multiply(inverse(T), inverse(multiply(Z, multiply(W, multiply(X, inverse(T))))))))), inverse(W))), multiply(W, multiply(X, multiply(inverse(X), inverse(S))))))))
% 2.79/0.75 = { by lemma 8 }
% 2.79/0.75 multiply(X, multiply(multiply(inverse(X), inverse(S)), inverse(multiply(Z, multiply(W, multiply(X, multiply(inverse(X), inverse(S))))))))
% 2.79/0.75 = { by lemma 18 R->L }
% 2.79/0.76 multiply(multiply(inverse(W), inverse(multiply(V, Z))), multiply(multiply(inverse(multiply(inverse(W), inverse(multiply(V, Z)))), inverse(S)), inverse(multiply(Z, multiply(W, multiply(X, multiply(inverse(X), inverse(S))))))))
% 2.79/0.76 = { by lemma 13 }
% 2.79/0.76 multiply(multiply(inverse(W), inverse(multiply(V, Z))), multiply(multiply(inverse(multiply(inverse(W), inverse(multiply(V, Z)))), inverse(S)), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), multiply(inverse(multiply(inverse(W), inverse(multiply(V, Z)))), inverse(S))))))))
% 2.79/0.76 = { by axiom 1 (single_axiom) }
% 2.79/0.76 multiply(multiply(inverse(W), inverse(multiply(V, Z))), V)
% 2.79/0.76
% 2.79/0.76 Lemma 35: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 2.79/0.76 Proof:
% 2.79/0.76 multiply(X, inverse(multiply(Y, X)))
% 2.79/0.76 = { by lemma 28 R->L }
% 2.79/0.76 multiply(inverse(inverse(X)), inverse(multiply(Y, X)))
% 2.79/0.76 = { by axiom 1 (single_axiom) R->L }
% 2.79/0.76 multiply(Z, inverse(multiply(Y, multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(inverse(X)), inverse(multiply(Y, X))), Y))), Z)))))
% 2.79/0.76 = { by lemma 34 R->L }
% 2.79/0.76 multiply(Z, inverse(multiply(Y, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(U, inverse(multiply(X, multiply(inverse(X), multiply(V, U)))))))), Z)))))
% 2.79/0.76 = { by lemma 13 }
% 2.79/0.76 multiply(Z, inverse(multiply(Y, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(U, inverse(multiply(inverse(Y), multiply(inverse(inverse(Y)), multiply(V, U)))))))), Z)))))
% 2.79/0.76 = { by lemma 34 }
% 2.79/0.76 multiply(Z, inverse(multiply(Y, multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(inverse(inverse(inverse(Y))), inverse(multiply(Y, inverse(Y)))), Y))), Z)))))
% 2.79/0.76 = { by axiom 1 (single_axiom) }
% 2.79/0.76 multiply(inverse(inverse(inverse(Y))), inverse(multiply(Y, inverse(Y))))
% 2.79/0.76 = { by lemma 28 }
% 2.79/0.76 multiply(inverse(Y), inverse(multiply(Y, inverse(Y))))
% 2.79/0.76 = { by lemma 23 }
% 2.79/0.76 inverse(Y)
% 2.79/0.76
% 2.79/0.76 Lemma 36: inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 2.79/0.76 Proof:
% 2.79/0.76 inverse(multiply(X, Y))
% 2.79/0.76 = { by lemma 28 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(inverse(Y))))
% 2.79/0.76 = { by lemma 30 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(Y))))))
% 2.79/0.76 = { by lemma 31 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(inverse(Y)), multiply(multiply(inverse(Y), inverse(X)), X))))))
% 2.79/0.76 = { by lemma 28 }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(X)), X))))))
% 2.79/0.76 = { by lemma 26 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(X, multiply(Z, inverse(Z))))), X))))))
% 2.79/0.76 = { by lemma 25 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(X, multiply(inverse(X), X)))), X))))))
% 2.79/0.76 = { by lemma 13 }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), inverse(X))), multiply(inverse(inverse(multiply(inverse(Y), inverse(X)))), X)))), X))))))
% 2.79/0.76 = { by lemma 28 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), inverse(X))), multiply(inverse(inverse(multiply(inverse(Y), inverse(inverse(inverse(X)))))), X)))), X))))))
% 2.79/0.76 = { by lemma 28 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), inverse(X))), multiply(inverse(inverse(multiply(inverse(Y), inverse(inverse(inverse(X)))))), inverse(inverse(X)))))), X))))))
% 2.79/0.76 = { by lemma 29 R->L }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), inverse(X))), multiply(inverse(inverse(multiply(inverse(Y), inverse(inverse(inverse(X)))))), inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(inverse(X)))))))))), X))))))
% 2.79/0.76 = { by lemma 33 }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), inverse(X))), multiply(W, inverse(multiply(Y, W)))))), X))))))
% 2.79/0.76 = { by lemma 35 }
% 2.79/0.76 inverse(multiply(X, inverse(multiply(inverse(Y), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Y), inverse(X))), inverse(Y)))), X))))))
% 2.79/0.76 = { by axiom 1 (single_axiom) }
% 2.79/0.76 inverse(inverse(multiply(inverse(Y), inverse(X))))
% 2.79/0.76 = { by lemma 28 }
% 2.79/0.76 multiply(inverse(Y), inverse(X))
% 2.79/0.76
% 2.79/0.76 Lemma 37: multiply(multiply(X, inverse(X)), Y) = Y.
% 2.79/0.76 Proof:
% 2.79/0.76 multiply(multiply(X, inverse(X)), Y)
% 2.79/0.76 = { by lemma 2 R->L }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(multiply(X, inverse(X)), Y)))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 16 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(multiply(inverse(V), inverse(inverse(V))), Y)))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 30 R->L }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, multiply(inverse(Y), inverse(V))))), Y)))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 11 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(T, multiply(multiply(inverse(T), inverse(multiply(inverse(S), multiply(inverse(Y), inverse(V))))), inverse(S))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 35 R->L }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(T, multiply(multiply(inverse(T), inverse(multiply(inverse(S), multiply(inverse(Y), multiply(X2, inverse(multiply(V, X2))))))), inverse(S))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 33 R->L }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(T, multiply(multiply(inverse(T), inverse(multiply(inverse(S), multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(multiply(V, Y))))))), inverse(S))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 10 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(V, Y), multiply(inverse(multiply(V, Y)), multiply(Y2, multiply(multiply(inverse(Y2), inverse(multiply(inverse(inverse(Y)), inverse(multiply(V, Y))))), inverse(inverse(Y)))))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 14 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(V, Y), multiply(inverse(multiply(V, Y)), multiply(Y2, multiply(multiply(inverse(Y2), inverse(multiply(inverse(inverse(multiply(V, Y))), inverse(multiply(V, Y))))), inverse(inverse(multiply(V, Y))))))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 25 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(V, Y), multiply(inverse(multiply(V, Y)), multiply(Y2, multiply(multiply(inverse(Y2), inverse(multiply(Z2, inverse(Z2)))), inverse(inverse(multiply(V, Y))))))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 23 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(V, Y), multiply(inverse(multiply(V, Y)), multiply(Y2, multiply(inverse(Y2), inverse(inverse(multiply(V, Y))))))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 30 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(V, Y), multiply(inverse(multiply(V, Y)), inverse(inverse(multiply(V, Y))))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 32 }
% 2.79/0.76 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Y))), inverse(U))), multiply(U, multiply(V, Z)))))
% 2.79/0.76 = { by lemma 3 }
% 2.79/0.76 multiply(W2, multiply(multiply(inverse(W2), inverse(multiply(multiply(inverse(W), inverse(multiply(V, Y))), V))), inverse(W)))
% 2.79/0.76 = { by lemma 4 }
% 2.79/0.76 Y
% 2.79/0.76
% 2.79/0.76 Lemma 38: multiply(X, multiply(inverse(X), Y)) = Y.
% 2.79/0.76 Proof:
% 2.79/0.76 multiply(X, multiply(inverse(X), Y))
% 2.79/0.76 = { by lemma 13 }
% 2.79/0.76 multiply(multiply(Z, inverse(Z)), multiply(inverse(multiply(Z, inverse(Z))), Y))
% 2.79/0.76 = { by lemma 37 }
% 2.79/0.76 multiply(inverse(multiply(Z, inverse(Z))), Y)
% 2.79/0.76 = { by lemma 24 }
% 2.79/0.76 multiply(multiply(W, inverse(W)), Y)
% 2.79/0.77 = { by lemma 37 }
% 2.79/0.77 Y
% 2.79/0.77
% 2.79/0.77 Lemma 39: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 2.79/0.77 Proof:
% 2.79/0.77 inverse(multiply(X, inverse(Y)))
% 2.79/0.77 = { by lemma 38 R->L }
% 2.79/0.77 multiply(Y, multiply(inverse(Y), inverse(multiply(X, inverse(Y)))))
% 2.79/0.77 = { by lemma 35 }
% 2.79/0.77 multiply(Y, inverse(X))
% 2.79/0.77
% 2.79/0.77 Lemma 40: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 2.79/0.77 Proof:
% 2.79/0.77 multiply(inverse(multiply(X, Y)), X)
% 2.79/0.77 = { by lemma 28 R->L }
% 2.79/0.77 multiply(inverse(multiply(X, Y)), inverse(inverse(X)))
% 2.79/0.77 = { by lemma 35 R->L }
% 2.79/0.77 multiply(inverse(multiply(X, Y)), inverse(multiply(Y, inverse(multiply(X, Y)))))
% 2.79/0.77 = { by lemma 35 }
% 2.79/0.77 inverse(Y)
% 2.79/0.77
% 2.79/0.77 Lemma 41: multiply(multiply(inverse(X), Y), Z) = multiply(inverse(X), multiply(Y, Z)).
% 2.79/0.77 Proof:
% 2.79/0.77 multiply(multiply(inverse(X), Y), Z)
% 2.79/0.77 = { by lemma 28 R->L }
% 2.79/0.77 multiply(multiply(inverse(X), inverse(inverse(Y))), Z)
% 2.79/0.77 = { by lemma 35 R->L }
% 2.79/0.77 multiply(multiply(inverse(X), inverse(multiply(Z, inverse(multiply(Y, Z))))), Z)
% 2.79/0.77 = { by lemma 14 R->L }
% 2.79/0.77 multiply(multiply(inverse(X), inverse(multiply(multiply(Y, Z), inverse(multiply(Y, Z))))), multiply(Y, Z))
% 2.79/0.77 = { by lemma 23 }
% 2.79/0.77 multiply(inverse(X), multiply(Y, Z))
% 2.79/0.77
% 2.79/0.77 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1)).
% 2.79/0.77 Proof:
% 2.79/0.77 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 2.79/0.77 = { by lemma 25 }
% 2.79/0.77 tuple(multiply(multiply(X, inverse(X)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 2.79/0.77 = { by lemma 37 }
% 2.79/0.77 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 2.79/0.77 = { by lemma 25 }
% 2.79/0.77 tuple(a2, multiply(multiply(a3, b3), c3), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 28 R->L }
% 2.79/0.77 tuple(a2, multiply(multiply(a3, b3), inverse(inverse(c3))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 28 R->L }
% 2.79/0.77 tuple(a2, multiply(multiply(inverse(inverse(a3)), b3), inverse(inverse(c3))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 40 R->L }
% 2.79/0.77 tuple(a2, multiply(multiply(multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(b3)), b3), inverse(inverse(c3))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 36 R->L }
% 2.79/0.77 tuple(a2, multiply(multiply(inverse(multiply(b3, multiply(inverse(b3), inverse(a3)))), b3), inverse(inverse(c3))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 40 }
% 2.79/0.77 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(inverse(c3))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 38 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(inverse(Z), multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(inverse(c3))))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 41 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(b3), inverse(a3)))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 32 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(b3), inverse(a3)), multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(inverse(multiply(inverse(b3), inverse(a3)))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 24 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(inverse(b3), inverse(a3)), inverse(multiply(W, inverse(W)))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 38 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), multiply(inverse(inverse(inverse(c3))), multiply(multiply(inverse(b3), inverse(a3)), inverse(multiply(W, inverse(W)))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 41 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), multiply(multiply(inverse(inverse(inverse(c3))), multiply(inverse(b3), inverse(a3))), inverse(multiply(W, inverse(W))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 41 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), multiply(multiply(multiply(inverse(inverse(inverse(c3))), inverse(b3)), inverse(a3)), inverse(multiply(W, inverse(W))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 36 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), multiply(multiply(inverse(multiply(b3, inverse(inverse(c3)))), inverse(a3)), inverse(multiply(W, inverse(W))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 36 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), multiply(inverse(multiply(a3, multiply(b3, inverse(inverse(c3))))), inverse(multiply(W, inverse(W))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 36 R->L }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), inverse(multiply(multiply(W, inverse(W)), multiply(a3, multiply(b3, inverse(inverse(c3))))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 37 }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), inverse(multiply(a3, multiply(b3, inverse(inverse(c3)))))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 36 }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), multiply(inverse(multiply(b3, inverse(inverse(c3)))), inverse(a3))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 39 }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(inverse(c3)), multiply(multiply(inverse(c3), inverse(b3)), inverse(a3))))), inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 41 }
% 2.79/0.77 tuple(a2, multiply(Z, multiply(inverse(Z), multiply(inverse(multiply(inverse(inverse(c3)), multiply(multiply(inverse(c3), inverse(b3)), inverse(a3)))), inverse(inverse(c3))))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 38 }
% 2.79/0.77 tuple(a2, multiply(inverse(multiply(inverse(inverse(c3)), multiply(multiply(inverse(c3), inverse(b3)), inverse(a3)))), inverse(inverse(c3))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 40 }
% 2.79/0.77 tuple(a2, inverse(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 39 }
% 2.79/0.77 tuple(a2, multiply(a3, inverse(multiply(inverse(c3), inverse(b3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 39 }
% 2.79/0.77 tuple(a2, multiply(a3, multiply(b3, inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 28 }
% 2.79/0.77 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(Y, inverse(Y)))
% 2.79/0.77 = { by lemma 25 R->L }
% 2.79/0.77 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 2.79/0.77 % SZS output end Proof
% 2.79/0.77
% 2.79/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------