%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.42s 0.50s
% Output : Proof 1.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:20:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.50 Command-line arguments: --no-flatten-goal
% 0.42/0.50
% 0.42/0.50 % SZS status Unsatisfiable
% 0.42/0.50
% 0.42/0.60 % SZS output start Proof
% 0.42/0.60 Axiom 1 (single_axiom): inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), Z)), X), Y), multiply(W, inverse(W)))) = Z.
% 0.42/0.60
% 0.42/0.60 Lemma 2: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.42/0.60 Proof:
% 0.42/0.60 multiply(Y, inverse(Y))
% 0.42/0.60 = { by axiom 1 (single_axiom) R->L }
% 0.42/0.60 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(Y, inverse(Y)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.42/0.60 = { by axiom 1 (single_axiom) }
% 0.42/0.60 inverse(multiply(multiply(multiply(V, multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.42/0.60 = { by axiom 1 (single_axiom) R->L }
% 0.42/0.60 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), V)), Z), W), multiply(X, inverse(X)))), multiply(inverse(multiply(multiply(Z, W), V)), Z)), W), multiply(U, inverse(U))))
% 0.42/0.60 = { by axiom 1 (single_axiom) }
% 0.42/0.60 multiply(X, inverse(X))
% 0.42/0.60
% 0.42/0.60 Lemma 3: inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W)))) = inverse(multiply(Y, Z)).
% 0.42/0.60 Proof:
% 0.42/0.60 inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(X))), Y), Z), multiply(W, inverse(W))))
% 0.42/0.60 = { by lemma 2 }
% 0.42/0.60 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, Z), inverse(multiply(Y, Z)))), Y), Z), multiply(W, inverse(W))))
% 0.42/0.60 = { by axiom 1 (single_axiom) }
% 0.42/0.60 inverse(multiply(Y, Z))
% 0.42/0.60
% 0.42/0.60 Lemma 4: inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))) = inverse(multiply(Z, inverse(multiply(inverse(multiply(W, inverse(W))), Z)))).
% 0.42/0.60 Proof:
% 0.42/0.60 inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))))
% 0.42/0.60 = { by lemma 2 }
% 0.42/0.60 inverse(multiply(multiply(multiply(inverse(multiply(W, inverse(W))), Z), inverse(multiply(inverse(multiply(W, inverse(W))), Z))), multiply(Y, inverse(Y))))
% 0.42/0.60 = { by lemma 3 }
% 0.42/0.60 inverse(multiply(Z, inverse(multiply(inverse(multiply(W, inverse(W))), Z))))
% 0.42/0.60
% 0.42/0.60 Lemma 5: inverse(multiply(multiply(multiply(X, multiply(inverse(multiply(multiply(Y, Z), X)), Y)), Z), multiply(W, inverse(W)))) = multiply(V, inverse(V)).
% 0.42/0.60 Proof:
% 0.42/0.60 inverse(multiply(multiply(multiply(X, multiply(inverse(multiply(multiply(Y, Z), X)), Y)), Z), multiply(W, inverse(W))))
% 0.42/0.60 = { by axiom 1 (single_axiom) R->L }
% 0.42/0.60 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, Z), X)), Y), Z), multiply(V, inverse(V)))), multiply(inverse(multiply(multiply(Y, Z), X)), Y)), Z), multiply(W, inverse(W))))
% 0.42/0.60 = { by axiom 1 (single_axiom) }
% 0.42/0.60 multiply(V, inverse(V))
% 0.42/0.60
% 0.42/0.60 Lemma 6: inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y)) = multiply(W, inverse(W)).
% 0.42/0.60 Proof:
% 0.42/0.60 inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X), Y))
% 0.42/0.60 = { by lemma 3 R->L }
% 0.42/0.60 inverse(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(Z, inverse(Z))))), X)), Y), multiply(V, inverse(V))))
% 0.42/0.60 = { by lemma 5 }
% 0.42/0.60 multiply(W, inverse(W))
% 0.42/0.60
% 0.42/0.60 Lemma 7: inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y))) = multiply(Z, inverse(Z)).
% 0.42/0.60 Proof:
% 0.42/0.61 inverse(multiply(multiply(inverse(multiply(X, inverse(X))), Y), inverse(Y)))
% 0.42/0.61 = { by lemma 2 }
% 0.42/0.61 inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))), Y), inverse(Y)))
% 0.42/0.61 = { by lemma 6 }
% 0.42/0.61 multiply(Z, inverse(Z))
% 0.42/0.61
% 0.42/0.61 Lemma 8: inverse(multiply(X, inverse(multiply(inverse(multiply(Y, inverse(Y))), X)))) = multiply(Z, inverse(Z)).
% 0.42/0.61 Proof:
% 0.42/0.61 inverse(multiply(X, inverse(multiply(inverse(multiply(Y, inverse(Y))), X))))
% 0.42/0.61 = { by lemma 4 R->L }
% 0.42/0.61 inverse(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))), multiply(V, inverse(V))))
% 0.42/0.61 = { by lemma 7 R->L }
% 0.42/0.61 inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(W, inverse(W))), multiply(V, inverse(V))), inverse(multiply(V, inverse(V))))), inverse(multiply(W, inverse(W)))), multiply(V, inverse(V))))
% 0.42/0.61 = { by lemma 6 }
% 0.42/0.61 multiply(Z, inverse(Z))
% 0.42/0.61
% 0.42/0.61 Lemma 9: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z)))) = inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), Y)).
% 0.42/0.61 Proof:
% 0.42/0.61 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(Z, inverse(Z))))
% 0.42/0.61 = { by lemma 2 }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(multiply(W, inverse(W))), inverse(inverse(multiply(W, inverse(W))))), Y), multiply(Z, inverse(Z))))
% 0.42/0.61 = { by lemma 3 }
% 0.42/0.61 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), Y))
% 0.42/0.61
% 0.42/0.61 Lemma 10: inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), Y)) = inverse(Y).
% 0.42/0.61 Proof:
% 0.42/0.61 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), Y))
% 0.42/0.61 = { by lemma 9 R->L }
% 0.42/0.61 inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), Y), multiply(W, inverse(W))))
% 0.42/0.61 = { by lemma 7 R->L }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(Z, inverse(Z))), Y), inverse(Y))), inverse(multiply(Z, inverse(Z)))), Y), multiply(W, inverse(W))))
% 0.42/0.61 = { by axiom 1 (single_axiom) }
% 0.42/0.61 inverse(Y)
% 0.42/0.61
% 0.42/0.61 Lemma 11: inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, inverse(X)), Y)), Z), inverse(Z)), multiply(W, inverse(W)))) = Y.
% 0.42/0.61 Proof:
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, inverse(X)), Y)), Z), inverse(Z)), multiply(W, inverse(W))))
% 0.42/0.61 = { by lemma 2 }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), Y)), Z), inverse(Z)), multiply(W, inverse(W))))
% 0.42/0.61 = { by axiom 1 (single_axiom) }
% 0.42/0.61 Y
% 0.42/0.61
% 0.42/0.61 Lemma 12: inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), inverse(inverse(inverse(multiply(multiply(Y, inverse(Y)), Z)))))) = Z.
% 0.42/0.61 Proof:
% 0.42/0.61 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), inverse(inverse(inverse(multiply(multiply(Y, inverse(Y)), Z))))))
% 0.42/0.61 = { by lemma 9 R->L }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), Z)), inverse(inverse(multiply(multiply(Y, inverse(Y)), Z)))), inverse(inverse(inverse(multiply(multiply(Y, inverse(Y)), Z))))), multiply(W, inverse(W))))
% 0.42/0.61 = { by lemma 11 }
% 0.42/0.61 Z
% 0.42/0.61
% 0.42/0.61 Lemma 13: inverse(inverse(multiply(X, inverse(X)))) = multiply(Y, inverse(Y)).
% 0.42/0.61 Proof:
% 0.42/0.61 inverse(inverse(multiply(X, inverse(X))))
% 0.42/0.61 = { by lemma 8 R->L }
% 0.42/0.61 inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(multiply(W, inverse(W))), Z))))))
% 0.42/0.61 = { by lemma 4 R->L }
% 0.42/0.61 inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))))))
% 0.42/0.61 = { by lemma 10 R->L }
% 0.42/0.61 inverse(multiply(inverse(inverse(multiply(T, inverse(T)))), inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))))
% 0.42/0.61 = { by lemma 9 R->L }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), inverse(inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))))), inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), multiply(S, inverse(S))))
% 0.42/0.61 = { by lemma 10 R->L }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), inverse(multiply(inverse(inverse(multiply(X2, inverse(X2)))), inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))))))))), inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), multiply(S, inverse(S))))
% 0.42/0.61 = { by lemma 12 }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U))))), inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), multiply(S, inverse(S))))
% 0.42/0.61 = { by lemma 7 R->L }
% 0.42/0.61 inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), multiply(inverse(multiply(multiply(inverse(multiply(U, inverse(U))), inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), inverse(inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))))), inverse(multiply(U, inverse(U))))), inverse(inverse(multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))), multiply(S, inverse(S))))
% 0.42/0.61 = { by lemma 5 }
% 0.42/0.61 multiply(Y, inverse(Y))
% 0.42/0.61
% 0.42/0.61 Lemma 14: inverse(multiply(multiply(X, inverse(X)), Y)) = inverse(Y).
% 0.42/0.61 Proof:
% 0.42/0.61 inverse(multiply(multiply(X, inverse(X)), Y))
% 0.42/0.61 = { by lemma 13 R->L }
% 0.42/0.61 inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), Y))
% 0.42/0.61 = { by lemma 10 }
% 0.42/0.62 inverse(Y)
% 0.42/0.62
% 0.42/0.62 Lemma 15: inverse(inverse(inverse(inverse(X)))) = X.
% 0.42/0.62 Proof:
% 0.42/0.62 inverse(inverse(inverse(inverse(X))))
% 0.42/0.62 = { by lemma 10 R->L }
% 0.42/0.62 inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(X)))))
% 0.42/0.62 = { by lemma 14 R->L }
% 0.42/0.62 inverse(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(multiply(multiply(Z, inverse(Z)), X))))))
% 0.42/0.62 = { by lemma 12 }
% 0.42/0.62 X
% 0.42/0.62
% 0.42/0.62 Lemma 16: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.42/0.62 Proof:
% 0.42/0.62 multiply(multiply(X, inverse(X)), Y)
% 0.42/0.62 = { by lemma 13 R->L }
% 0.42/0.62 multiply(inverse(inverse(multiply(Z, inverse(Z)))), Y)
% 0.42/0.62 = { by lemma 15 R->L }
% 0.42/0.62 inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), Y)))))
% 0.42/0.62 = { by lemma 10 }
% 0.42/0.62 inverse(inverse(inverse(inverse(Y))))
% 0.42/0.62 = { by lemma 15 }
% 0.42/0.62 Y
% 0.42/0.62
% 0.42/0.62 Lemma 17: inverse(multiply(X, multiply(Y, inverse(Y)))) = inverse(X).
% 0.42/0.62 Proof:
% 0.42/0.62 inverse(multiply(X, multiply(Y, inverse(Y))))
% 0.42/0.62 = { by lemma 16 R->L }
% 0.42/0.62 inverse(multiply(multiply(multiply(Z, inverse(Z)), X), multiply(Y, inverse(Y))))
% 0.42/0.62 = { by lemma 9 }
% 0.42/0.62 inverse(multiply(inverse(inverse(multiply(W, inverse(W)))), X))
% 0.42/0.62 = { by lemma 10 }
% 0.42/0.62 inverse(X)
% 0.42/0.62
% 0.42/0.62 Lemma 18: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.42/0.62 Proof:
% 0.42/0.62 inverse(multiply(X, inverse(X)))
% 0.42/0.62 = { by lemma 2 }
% 0.42/0.62 inverse(multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(multiply(Z, inverse(Z))))), inverse(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(multiply(Z, inverse(Z))))))))
% 0.42/0.62 = { by lemma 13 R->L }
% 0.42/0.62 inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(multiply(Z, inverse(Z))))))))
% 0.42/0.62 = { by lemma 8 }
% 0.42/0.62 multiply(Y, inverse(Y))
% 0.42/0.62
% 0.42/0.62 Lemma 19: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.42/0.62 Proof:
% 0.42/0.62 multiply(inverse(X), X)
% 0.42/0.62 = { by lemma 15 R->L }
% 0.42/0.62 inverse(inverse(inverse(inverse(multiply(inverse(X), X)))))
% 0.42/0.62 = { by lemma 17 R->L }
% 0.42/0.62 inverse(inverse(inverse(inverse(multiply(inverse(multiply(X, multiply(Z, inverse(Z)))), X)))))
% 0.42/0.62 = { by lemma 17 R->L }
% 0.42/0.62 inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), multiply(W, inverse(W)))), X)))))
% 0.42/0.62 = { by lemma 18 R->L }
% 0.42/0.62 inverse(inverse(inverse(inverse(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), inverse(multiply(V, inverse(V))))), X)))))
% 0.42/0.62 = { by lemma 17 R->L }
% 0.42/0.62 inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(multiply(X, multiply(Z, inverse(Z))), inverse(multiply(V, inverse(V))))), X), multiply(Z, inverse(Z)))))))
% 0.42/0.62 = { by lemma 6 }
% 0.42/0.62 inverse(inverse(inverse(multiply(U, inverse(U)))))
% 0.42/0.62 = { by lemma 13 }
% 0.42/0.62 inverse(multiply(T, inverse(T)))
% 0.42/0.62 = { by lemma 18 }
% 0.42/0.62 multiply(Y, inverse(Y))
% 0.42/0.62
% 0.42/0.62 Lemma 20: inverse(inverse(X)) = X.
% 0.42/0.62 Proof:
% 0.42/0.62 inverse(inverse(X))
% 0.42/0.62 = { by lemma 14 R->L }
% 0.42/0.62 inverse(inverse(multiply(multiply(Y, inverse(Y)), X)))
% 0.42/0.62 = { by lemma 10 R->L }
% 0.42/0.62 inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(multiply(multiply(Y, inverse(Y)), X))))
% 0.42/0.62 = { by lemma 9 R->L }
% 0.42/0.62 inverse(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(multiply(Y, inverse(Y)), X))), multiply(V, inverse(V))))
% 0.42/0.62 = { by lemma 19 R->L }
% 0.42/0.62 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), X)), multiply(multiply(Y, inverse(Y)), X)), inverse(multiply(multiply(Y, inverse(Y)), X))), multiply(V, inverse(V))))
% 0.42/0.62 = { by lemma 11 }
% 0.42/0.62 X
% 0.42/0.62
% 0.42/0.63 Lemma 21: inverse(multiply(multiply(inverse(X), Y), inverse(Y))) = X.
% 0.42/0.63 Proof:
% 0.42/0.63 inverse(multiply(multiply(inverse(X), Y), inverse(Y)))
% 0.42/0.63 = { by lemma 14 R->L }
% 0.42/0.63 inverse(multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), X)), Y), inverse(Y)))
% 0.42/0.63 = { by lemma 17 R->L }
% 0.42/0.63 inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, inverse(Z)), X)), Y), inverse(Y)), multiply(W, inverse(W))))
% 0.42/0.63 = { by lemma 11 }
% 0.42/0.63 X
% 0.42/0.63
% 0.42/0.63 Lemma 22: inverse(multiply(multiply(X, Y), inverse(Y))) = inverse(X).
% 0.42/0.63 Proof:
% 0.42/0.63 inverse(multiply(multiply(X, Y), inverse(Y)))
% 0.42/0.63 = { by lemma 12 R->L }
% 0.42/0.63 inverse(multiply(multiply(inverse(multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X)))))), Y), inverse(Y)))
% 0.42/0.63 = { by lemma 21 }
% 0.42/0.63 multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X)))))
% 0.42/0.63 = { by lemma 13 }
% 0.42/0.63 multiply(multiply(V, inverse(V)), inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X)))))
% 0.42/0.63 = { by lemma 16 }
% 0.42/0.63 inverse(inverse(inverse(multiply(multiply(W, inverse(W)), X))))
% 0.42/0.63 = { by lemma 20 }
% 0.42/0.63 inverse(multiply(multiply(W, inverse(W)), X))
% 0.42/0.63 = { by lemma 14 }
% 0.42/0.63 inverse(X)
% 0.42/0.63
% 0.42/0.63 Lemma 23: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.42/0.63 Proof:
% 0.42/0.63 multiply(X, multiply(Y, inverse(Y)))
% 0.42/0.63 = { by lemma 15 R->L }
% 0.42/0.63 inverse(inverse(inverse(inverse(multiply(X, multiply(Y, inverse(Y)))))))
% 0.42/0.63 = { by lemma 17 }
% 0.42/0.63 inverse(inverse(inverse(inverse(X))))
% 0.42/0.63 = { by lemma 15 }
% 0.42/0.63 X
% 0.42/0.63
% 0.42/0.63 Lemma 24: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 0.42/0.63 Proof:
% 0.42/0.63 inverse(multiply(inverse(multiply(X, Y)), X))
% 0.42/0.63 = { by lemma 17 R->L }
% 0.42/0.63 inverse(multiply(multiply(inverse(multiply(X, Y)), X), multiply(Z, inverse(Z))))
% 0.42/0.63 = { by lemma 23 R->L }
% 0.42/0.63 inverse(multiply(multiply(inverse(multiply(multiply(X, multiply(W, inverse(W))), Y)), X), multiply(Z, inverse(Z))))
% 0.42/0.63 = { by lemma 23 R->L }
% 0.42/0.63 inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, multiply(W, inverse(W))), Y)), X), multiply(W, inverse(W))), multiply(Z, inverse(Z))))
% 0.42/0.63 = { by axiom 1 (single_axiom) }
% 0.42/0.63 Y
% 0.42/0.63
% 0.42/0.63 Lemma 25: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 0.42/0.63 Proof:
% 0.42/0.63 multiply(inverse(multiply(X, Y)), X)
% 0.42/0.63 = { by lemma 15 R->L }
% 0.42/0.63 inverse(inverse(inverse(inverse(multiply(inverse(multiply(X, Y)), X)))))
% 0.42/0.63 = { by lemma 24 }
% 0.42/0.63 inverse(inverse(inverse(Y)))
% 0.42/0.63 = { by lemma 20 }
% 0.42/0.63 inverse(Y)
% 0.42/0.63
% 0.42/0.63 Lemma 26: inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 0.42/0.63 Proof:
% 0.42/0.63 inverse(multiply(X, Y))
% 0.42/0.63 = { by lemma 15 R->L }
% 0.42/0.63 inverse(inverse(inverse(inverse(inverse(multiply(X, Y))))))
% 0.42/0.63 = { by lemma 22 R->L }
% 0.42/0.63 inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(X, Y)), X), inverse(X))))))
% 0.42/0.63 = { by lemma 15 }
% 0.42/0.63 multiply(multiply(inverse(multiply(X, Y)), X), inverse(X))
% 0.42/0.63 = { by lemma 25 }
% 0.42/0.63 multiply(inverse(Y), inverse(X))
% 0.42/0.63
% 0.42/0.63 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.42/0.63 Proof:
% 0.42/0.63 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.42/0.63 = { by lemma 19 }
% 0.42/0.63 tuple(multiply(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.42/0.63 = { by lemma 19 }
% 0.42/0.63 tuple(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3))
% 0.42/0.63 = { by lemma 16 }
% 0.42/0.63 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 0.42/0.63 = { by axiom 1 (single_axiom) R->L }
% 0.42/0.63 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V))))), c3))
% 0.42/0.63 = { by axiom 1 (single_axiom) R->L }
% 0.42/0.63 tuple(multiply(X, inverse(X)), a2, multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V))))), c3))
% 0.42/0.63 = { by lemma 26 R->L }
% 0.42/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))), c3))
% 0.42/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.42/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))), c3))), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(X2, inverse(X2)))))
% 0.42/0.64 = { by lemma 21 R->L }
% 0.42/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))), c3), inverse(c3))), multiply(inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))), c3))), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(X2, inverse(X2)))))
% 0.42/0.64 = { by lemma 25 }
% 0.42/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(multiply(inverse(inverse(inverse(c3))), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(X2, inverse(X2)))))
% 1.46/0.64 = { by lemma 20 }
% 1.46/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(X2, inverse(X2)))))
% 1.46/0.64 = { by axiom 1 (single_axiom) R->L }
% 1.46/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2, inverse(X2)), inverse(multiply(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(X2, inverse(X2)))))), X2), inverse(X2)), multiply(Y2, inverse(Y2)))))
% 1.46/0.64 = { by lemma 24 R->L }
% 1.46/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(X2, inverse(X2)))), multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), inverse(multiply(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(X2, inverse(X2)))))), X2), inverse(X2)), multiply(Y2, inverse(Y2)))))
% 1.46/0.64 = { by lemma 25 }
% 1.46/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), X2), inverse(X2)), multiply(Y2, inverse(Y2)))))
% 1.46/0.64 = { by lemma 26 }
% 1.46/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(Y2, inverse(Y2))), inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), X2), inverse(X2)))))
% 1.46/0.64 = { by lemma 26 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(multiply(inverse(inverse(Y2)), inverse(Y2)), inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), X2), inverse(X2)))))
% 1.46/0.65 = { by lemma 19 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(multiply(Z2, inverse(Z2)), inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), X2), inverse(X2)))))
% 1.46/0.65 = { by lemma 16 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), X2), inverse(X2))))
% 1.46/0.65 = { by lemma 26 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(X2)), inverse(multiply(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), X2))))
% 1.46/0.65 = { by lemma 26 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(X2)), multiply(inverse(X2), inverse(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))))))))
% 1.46/0.65 = { by lemma 20 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(X2)), multiply(inverse(X2), inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))))))
% 1.46/0.65 = { by lemma 22 R->L }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(inverse(X2), inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))), inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))))))), multiply(inverse(X2), inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))))))
% 1.46/0.65 = { by lemma 25 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, inverse(inverse(inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))))))
% 1.46/0.65 = { by lemma 20 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S))))))
% 1.46/0.65 = { by lemma 26 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), inverse(multiply(inverse(c3), multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))))))
% 1.46/0.65 = { by lemma 26 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), inverse(inverse(c3)))))
% 1.46/0.65 = { by lemma 20 }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(U, T), a3)), U), T), multiply(S, inverse(S)))), multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), c3)))
% 1.46/0.65 = { by axiom 1 (single_axiom) }
% 1.46/0.65 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), b3)), Z), W), multiply(V, inverse(V)))), c3)))
% 1.46/0.66 = { by axiom 1 (single_axiom) }
% 1.46/0.66 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 1.46/0.66 = { by lemma 19 R->L }
% 1.46/0.66 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 1.46/0.66 % SZS output end Proof
% 1.46/0.66
% 1.46/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
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