TSTP Solution File: GRP436-1 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP436-1 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 07:12:21 EDT 2024
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP436-1 : TPTP v8.2.0. Released v2.6.0.
% 0.11/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 10:18:23 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.50
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), X))))) = W.
% 0.19/0.54
% 0.19/0.54 Lemma 2: multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X))))) = W.
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 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)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 W
% 0.19/0.54
% 0.19/0.54 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))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(W))), multiply(W, multiply(V, X)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 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)))))
% 0.19/0.54 = { by lemma 2 }
% 0.19/0.54 multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y)))
% 0.19/0.54
% 0.19/0.54 Lemma 4: multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V))) = W.
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V)))
% 0.19/0.54 = { by lemma 3 R->L }
% 0.19/0.54 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)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 W
% 0.19/0.54
% 0.19/0.54 Lemma 5: multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), Z))) = W.
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), Z)))
% 0.19/0.54 = { by lemma 4 R->L }
% 0.19/0.54 multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(W, multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y))))))))), inverse(X))))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 W
% 0.19/0.54
% 0.19/0.54 Lemma 6: inverse(multiply(multiply(inverse(X), inverse(multiply(W, Z))), W)) = inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y)).
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(multiply(inverse(X), inverse(multiply(W, Z))), W))
% 0.19/0.54 = { by lemma 2 R->L }
% 0.19/0.54 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(W, Z))), W))))), inverse(S))), multiply(S, multiply(inverse(T), V)))))
% 0.19/0.54 = { by lemma 2 R->L }
% 0.19/0.54 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(W, multiply(X2, inverse(multiply(multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(Y2))), multiply(Y2, multiply(Y, X2)))))))), W))))), inverse(S))), multiply(S, multiply(inverse(T), V)))))
% 0.19/0.54 = { by lemma 3 }
% 0.19/0.54 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(W, multiply(T, multiply(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X)))))), W))))), inverse(S))), multiply(S, multiply(inverse(T), V)))))
% 0.19/0.54 = { by lemma 5 }
% 0.19/0.54 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(T), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))))), inverse(S))), multiply(S, multiply(inverse(T), V)))))
% 0.19/0.54 = { by lemma 2 }
% 0.19/0.54 inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))
% 0.19/0.54
% 0.19/0.54 Lemma 7: multiply(inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))), inverse(multiply(V, multiply(U, Z)))) = multiply(T, inverse(multiply(V, multiply(U, multiply(W, T))))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))), inverse(multiply(V, multiply(U, Z))))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 multiply(inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))), inverse(multiply(V, multiply(U, multiply(W, inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))))))))
% 0.19/0.54 = { by lemma 2 R->L }
% 0.19/0.54 multiply(T, inverse(multiply(multiply(S, multiply(multiply(inverse(S), inverse(multiply(W, multiply(inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))), inverse(multiply(V, multiply(U, multiply(W, inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))))))))))), inverse(U))), multiply(U, multiply(W, T)))))
% 0.19/0.54 = { by lemma 4 }
% 0.19/0.54 multiply(T, inverse(multiply(V, multiply(U, multiply(W, T)))))
% 0.19/0.54
% 0.19/0.54 Lemma 8: multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, Z))), inverse(W))) = multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, Z))), inverse(W)))
% 0.19/0.54 = { by lemma 2 R->L }
% 0.19/0.54 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)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 multiply(U, inverse(multiply(multiply(W, multiply(Y, inverse(T))), multiply(T, multiply(Z, U)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 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)))))
% 0.19/0.54 = { by lemma 2 }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W)))
% 0.19/0.54
% 0.19/0.54 Lemma 9: multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(Y), inverse(Z))), inverse(multiply(W, Y))), W))), inverse(multiply(inverse(V), inverse(Z))))) = V.
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(Y), inverse(Z))), inverse(multiply(W, Y))), W))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by lemma 6 }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(Y), inverse(Z))), inverse(multiply(multiply(inverse(U), inverse(multiply(Y, multiply(multiply(inverse(Y), inverse(Z)), multiply(T, inverse(U)))))), Y))), multiply(inverse(U), inverse(multiply(Y, multiply(multiply(inverse(Y), inverse(Z)), multiply(T, inverse(U))))))))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by lemma 5 }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(U), inverse(multiply(Y, multiply(multiply(inverse(Y), inverse(Z)), multiply(T, inverse(U))))))))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by lemma 7 R->L }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(multiply(S, multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), S))), T)))), inverse(multiply(Y, multiply(multiply(inverse(Y), inverse(Z)), inverse(Y2)))))))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(multiply(S, multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), S))), T)))), inverse(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), inverse(multiply(Z, W2))), Z2))))))), inverse(Y2)))))))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by lemma 8 }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(multiply(S, multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), S))), T)))), inverse(multiply(V, multiply(multiply(inverse(V), inverse(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), inverse(multiply(Z, W2))), Z2))))))), inverse(Y2)))))))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(multiply(S, multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(inverse(Y2), S))), T)))), inverse(multiply(V, multiply(multiply(inverse(V), inverse(Z)), inverse(Y2)))))))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by lemma 7 }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(T, multiply(inverse(U2), inverse(multiply(V, multiply(multiply(inverse(V), inverse(Z)), multiply(T, inverse(U2))))))))), inverse(multiply(inverse(V), inverse(Z)))))
% 0.19/0.54 = { by lemma 3 R->L }
% 0.19/0.54 multiply(T2, inverse(multiply(multiply(multiply(inverse(V), inverse(Z)), multiply(T, inverse(U2))), multiply(U2, multiply(multiply(inverse(U2), inverse(multiply(V, multiply(multiply(inverse(V), inverse(Z)), multiply(T, inverse(U2)))))), T2)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 V
% 0.19/0.54
% 0.19/0.54 Lemma 10: multiply(multiply(inverse(X), inverse(multiply(W, Z))), W) = multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(multiply(inverse(X), inverse(multiply(W, Z))), W)
% 0.19/0.54 = { by lemma 9 R->L }
% 0.19/0.54 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(multiply(inverse(U), inverse(T))), inverse(multiply(S, U))), S))), inverse(multiply(inverse(multiply(multiply(inverse(X), inverse(multiply(W, Z))), W)), inverse(T)))))
% 0.19/0.54 = { by lemma 6 }
% 0.19/0.54 multiply(V, multiply(multiply(inverse(V), inverse(multiply(multiply(inverse(multiply(inverse(U), inverse(T))), inverse(multiply(S, U))), S))), inverse(multiply(inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y)), inverse(T)))))
% 0.19/0.54 = { by lemma 9 }
% 0.19/0.54 multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y)
% 0.19/0.54
% 0.19/0.54 Lemma 11: multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), W))))) = X.
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), W)))))
% 0.19/0.54 = { by lemma 10 }
% 0.19/0.54 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(X, Y))), X)))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 X
% 0.19/0.54
% 0.19/0.54 Lemma 12: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(Y, inverse(Y))
% 0.19/0.54 = { by lemma 11 R->L }
% 0.19/0.54 multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))))
% 0.19/0.54 = { by lemma 11 R->L }
% 0.19/0.54 multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(S, U))), S))))), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))))
% 0.19/0.54 = { by lemma 8 }
% 0.19/0.54 multiply(X, multiply(multiply(inverse(X), inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), inverse(multiply(S, U))), S))))), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))))
% 0.19/0.54 = { by lemma 11 }
% 0.19/0.54 multiply(X, multiply(inverse(X), inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, Z))), V))))))
% 0.19/0.54 = { by lemma 11 }
% 0.19/0.54 multiply(X, inverse(X))
% 0.19/0.54
% 0.19/0.54 Lemma 13: multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, multiply(multiply(W, inverse(W)), inverse(Z)))))) = X.
% 0.19/0.54 Proof:
% 0.19/0.55 multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, multiply(multiply(W, inverse(W)), inverse(Z))))))
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(inverse(Z))), inverse(Z))))))
% 0.19/0.55 = { by lemma 11 R->L }
% 0.19/0.55 multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(Z), inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), inverse(multiply(T, V))), T))))))), inverse(Z))))))
% 0.19/0.55 = { by lemma 10 R->L }
% 0.19/0.55 multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(X, Y), inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), inverse(multiply(T, V))), T))))))), multiply(X, Y))))))
% 0.19/0.55 = { by lemma 11 }
% 0.19/0.55 multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(X, Y))), multiply(X, Y))))))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 X
% 0.19/0.55
% 0.19/0.55 Lemma 14: multiply(X, multiply(multiply(Y, inverse(Y)), inverse(X))) = multiply(Z, inverse(Z)).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(X, multiply(multiply(Y, inverse(Y)), inverse(X)))
% 0.19/0.55 = { by lemma 13 R->L }
% 0.19/0.55 multiply(multiply(multiply(X, multiply(multiply(Y, inverse(Y)), inverse(X))), multiply(X, multiply(multiply(Y, inverse(Y)), inverse(X)))), inverse(multiply(multiply(X, multiply(multiply(Y, inverse(Y)), inverse(X))), multiply(X, multiply(multiply(Y, inverse(Y)), inverse(X))))))
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 multiply(Z, inverse(Z))
% 0.19/0.55
% 0.19/0.55 Lemma 15: multiply(multiply(X, inverse(X)), inverse(Y)) = inverse(Y).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(multiply(X, inverse(X)), inverse(Y))
% 0.19/0.55 = { by lemma 2 R->L }
% 0.19/0.55 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(Y, multiply(multiply(X, inverse(X)), inverse(Y))))), inverse(V))), multiply(V, multiply(Y, Z)))))
% 0.19/0.55 = { by lemma 14 }
% 0.19/0.55 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(Y, inverse(Y)))), inverse(V))), multiply(V, multiply(Y, Z)))))
% 0.19/0.55 = { by lemma 2 }
% 0.19/0.55 inverse(Y)
% 0.19/0.55
% 0.19/0.55 Lemma 16: multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, inverse(Z))))) = X.
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(multiply(X, Y), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 0.19/0.55 = { by lemma 14 R->L }
% 0.19/0.55 multiply(multiply(X, Y), inverse(multiply(Y, multiply(W, multiply(multiply(V, inverse(V)), inverse(W))))))
% 0.19/0.55 = { by lemma 13 }
% 0.19/0.55 X
% 0.19/0.55
% 0.19/0.55 Lemma 17: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.55 = { by lemma 11 R->L }
% 0.19/0.55 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(Z), multiply(Y, inverse(Y))))), inverse(Z))))))
% 0.19/0.55 = { by lemma 15 R->L }
% 0.19/0.55 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, multiply(multiply(multiply(multiply(W, inverse(W)), inverse(Z)), inverse(multiply(inverse(Z), multiply(Y, inverse(Y))))), inverse(Z))))))
% 0.19/0.55 = { by lemma 16 }
% 0.19/0.55 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, multiply(multiply(W, inverse(W)), inverse(Z))))))
% 0.19/0.55 = { by lemma 15 }
% 0.19/0.55 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z)))))
% 0.19/0.55 = { by lemma 16 }
% 0.19/0.55 X
% 0.19/0.55
% 0.19/0.55 Lemma 18: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(X), X)
% 0.19/0.55 = { by lemma 13 R->L }
% 0.19/0.55 multiply(multiply(multiply(inverse(X), X), inverse(X)), inverse(multiply(inverse(X), multiply(Z, multiply(multiply(W, inverse(W)), inverse(Z))))))
% 0.19/0.55 = { by lemma 17 R->L }
% 0.19/0.55 multiply(multiply(multiply(inverse(X), X), inverse(multiply(X, multiply(V, inverse(V))))), inverse(multiply(inverse(X), multiply(Z, multiply(multiply(W, inverse(W)), inverse(Z))))))
% 0.19/0.55 = { by lemma 16 }
% 0.19/0.55 multiply(inverse(X), inverse(multiply(inverse(X), multiply(Z, multiply(multiply(W, inverse(W)), inverse(Z))))))
% 0.19/0.55 = { by lemma 14 }
% 0.19/0.55 multiply(inverse(X), inverse(multiply(inverse(X), multiply(U, inverse(U)))))
% 0.19/0.55 = { by lemma 17 }
% 0.19/0.55 multiply(inverse(X), inverse(inverse(X)))
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 multiply(Y, inverse(Y))
% 0.19/0.55
% 0.19/0.55 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(a1), a1)
% 0.19/0.55 = { by lemma 18 }
% 0.19/0.55 multiply(X, inverse(X))
% 0.19/0.55 = { by lemma 18 R->L }
% 0.19/0.55 multiply(inverse(b1), b1)
% 0.19/0.55 % SZS output end Proof
% 0.19/0.55
% 0.19/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
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