TSTP Solution File: GRP049-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP049-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n013.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 : Thu Aug 31 01:16:47 EDT 2023
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP049-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 02:17:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.55
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55
% 0.20/0.60 % SZS output start Proof
% 0.20/0.60 Take the following subset of the input axioms:
% 0.20/0.60 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)))).
% 0.20/0.60 fof(single_axiom, axiom, ![Z, Y, X]: multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, Y)), X)), inverse(multiply(Y, multiply(inverse(Y), Y))))))=X).
% 0.20/0.60
% 0.20/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.60 fresh(y, y, x1...xn) = u
% 0.20/0.60 C => fresh(s, t, x1...xn) = v
% 0.20/0.60 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.60 variables of u and v.
% 0.20/0.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.60 input problem has no model of domain size 1).
% 0.20/0.60
% 0.20/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.60
% 0.20/0.60 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(Y, multiply(inverse(Y), Y)))))) = Z.
% 0.20/0.60
% 0.20/0.60 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))) = multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y)))))).
% 0.20/0.60 Proof:
% 0.20/0.60 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 0.20/0.60 = { by axiom 1 (single_axiom) R->L }
% 1.58/0.60 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 1.58/0.60 = { by axiom 1 (single_axiom) }
% 1.58/0.60 multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 1.58/0.60
% 1.58/0.60 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z))))) = W.
% 1.58/0.60 Proof:
% 1.58/0.60 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 1.58/0.60 = { by lemma 2 }
% 1.58/0.60 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 1.58/0.60 = { by axiom 1 (single_axiom) }
% 1.58/0.60 W
% 1.58/0.60
% 1.58/0.60 Lemma 4: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y))))))) = Z.
% 1.58/0.60 Proof:
% 1.58/0.60 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 1.58/0.60 = { by lemma 2 R->L }
% 1.58/0.60 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), inverse(multiply(W, multiply(inverse(W), W))))))
% 1.58/0.60 = { by axiom 1 (single_axiom) }
% 1.58/0.60 Z
% 1.58/0.60
% 1.58/0.60 Lemma 5: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y)))) = Z.
% 1.58/0.60 Proof:
% 1.58/0.60 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))
% 1.58/0.61 = { by axiom 1 (single_axiom) R->L }
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 1.58/0.61 = { by lemma 3 R->L }
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 1.58/0.61 = { by lemma 3 R->L }
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 1.58/0.61 = { by lemma 3 }
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 1.58/0.61 = { by lemma 4 }
% 1.58/0.61 Z
% 1.58/0.61
% 1.58/0.61 Lemma 6: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W)) = multiply(inverse(multiply(V, Z)), multiply(V, W)).
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))
% 1.58/0.61 = { by lemma 4 R->L }
% 1.58/0.61 multiply(inverse(multiply(V, Z)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z)))))))
% 1.58/0.61 = { by lemma 3 }
% 1.58/0.61 multiply(inverse(multiply(V, Z)), multiply(V, W))
% 1.58/0.61
% 1.58/0.61 Lemma 7: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 1.58/0.61 = { by lemma 3 R->L }
% 1.58/0.61 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 1.58/0.61 = { by lemma 4 }
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))
% 1.58/0.61 = { by lemma 4 R->L }
% 1.58/0.61 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 1.58/0.61 = { by lemma 3 }
% 1.58/0.61 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 1.58/0.61
% 1.58/0.61 Lemma 8: multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W)) = multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W)).
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W))
% 1.58/0.61 = { by lemma 6 R->L }
% 1.58/0.61 multiply(V, multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 1.58/0.61 = { by lemma 3 R->L }
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), inverse(multiply(Z, multiply(inverse(Z), Z))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 1.58/0.61 = { by lemma 7 R->L }
% 1.58/0.61 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), inverse(multiply(Z, multiply(inverse(Z), Z))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 1.58/0.61 = { by lemma 3 }
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 1.58/0.61 = { by lemma 6 }
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W))
% 1.58/0.61
% 1.58/0.61 Lemma 9: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(inverse(Y), Y)
% 1.58/0.61 = { by lemma 5 R->L }
% 1.58/0.61 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Y)))), inverse(multiply(W, multiply(inverse(W), W)))))
% 1.58/0.61 = { by lemma 8 R->L }
% 1.58/0.61 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(X)))), inverse(multiply(W, multiply(inverse(W), W)))))
% 1.58/0.61 = { by lemma 5 }
% 1.58/0.61 multiply(inverse(X), X)
% 1.58/0.61
% 1.58/0.61 Lemma 10: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), inverse(multiply(W, multiply(inverse(W), W))))))) = multiply(inverse(multiply(Z, Y)), V).
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), inverse(multiply(W, multiply(inverse(W), W)))))))
% 1.58/0.61 = { by lemma 7 }
% 1.58/0.61 multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), V)), inverse(multiply(W, multiply(inverse(W), W)))))))
% 1.58/0.61 = { by axiom 1 (single_axiom) }
% 1.58/0.61 multiply(inverse(multiply(Z, Y)), V)
% 1.58/0.61
% 1.58/0.61 Lemma 11: multiply(X, multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(X, multiply(inverse(Z), Z))))) = multiply(inverse(W), W).
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(X, multiply(inverse(Z), Z)))))
% 1.58/0.61 = { by lemma 9 }
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(X, multiply(inverse(X), X)))))
% 1.58/0.61 = { by lemma 9 }
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(multiply(V, X)), multiply(V, X))), inverse(multiply(X, multiply(inverse(X), X)))))
% 1.58/0.61 = { by lemma 10 R->L }
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(multiply(V, U)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, X)), T)), inverse(multiply(X, multiply(inverse(X), X))))), inverse(multiply(T, multiply(inverse(T), T))))))))
% 1.58/0.61 = { by lemma 8 R->L }
% 1.58/0.61 multiply(inverse(W), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, inverse(W)))), multiply(inverse(multiply(V, U)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, X)), T)), inverse(multiply(X, multiply(inverse(X), X))))), inverse(multiply(T, multiply(inverse(T), T))))))))
% 1.58/0.61 = { by lemma 10 }
% 1.58/0.61 multiply(inverse(W), multiply(inverse(multiply(inverse(multiply(V, X)), multiply(V, inverse(W)))), inverse(multiply(X, multiply(inverse(X), X)))))
% 1.58/0.61 = { by lemma 5 R->L }
% 1.58/0.61 multiply(inverse(W), multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(V, X)), multiply(V, inverse(W)))), inverse(multiply(X, multiply(inverse(X), X)))))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))
% 1.58/0.61 = { by lemma 10 }
% 1.58/0.61 multiply(inverse(W), multiply(inverse(multiply(inverse(multiply(V, X2)), multiply(V, inverse(W)))), inverse(multiply(X2, multiply(inverse(X2), X2)))))
% 1.58/0.61 = { by lemma 5 }
% 1.58/0.61 multiply(inverse(W), W)
% 1.58/0.61
% 1.58/0.61 Lemma 12: inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Z), Z))))) = Y.
% 1.58/0.61 Proof:
% 1.58/0.61 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 1.58/0.61 = { by lemma 9 }
% 1.58/0.61 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 1.58/0.61 = { by lemma 9 }
% 1.58/0.61 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 1.58/0.61 = { by axiom 1 (single_axiom) R->L }
% 1.58/0.61 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(Y, multiply(inverse(Y), Y))))))), inverse(multiply(V, multiply(inverse(V), V))))))
% 1.58/0.61 = { by axiom 1 (single_axiom) }
% 1.58/0.61 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), inverse(multiply(V, multiply(inverse(V), V))))))
% 1.58/0.61 = { by axiom 1 (single_axiom) R->L }
% 1.58/0.61 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(U, multiply(inverse(U), U))))))), inverse(multiply(V, multiply(inverse(V), V))))))
% 1.58/0.61 = { by axiom 1 (single_axiom) }
% 1.58/0.61 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(U, multiply(inverse(U), U)))))
% 1.58/0.61 = { by lemma 3 }
% 1.58/0.61 Y
% 1.58/0.61
% 1.58/0.61 Lemma 13: multiply(X, multiply(inverse(multiply(inverse(Y), Y)), Z)) = multiply(multiply(inverse(W), W), multiply(X, Z)).
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(Y), Y)), Z))
% 1.58/0.61 = { by lemma 9 }
% 1.58/0.61 multiply(X, multiply(inverse(multiply(inverse(multiply(V, X)), multiply(V, X))), Z))
% 1.58/0.61 = { by lemma 8 }
% 1.58/0.61 multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), X)), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)))), Z))
% 1.58/0.61 = { by lemma 3 R->L }
% 1.58/0.61 multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), X)), multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), X)), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W))))))), inverse(multiply(X, multiply(inverse(X), X))))), Z))
% 1.58/0.61 = { by lemma 11 }
% 1.58/0.61 multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), inverse(multiply(X, multiply(inverse(X), X))))), Z))
% 1.58/0.61 = { by lemma 12 }
% 1.58/0.61 multiply(multiply(inverse(W), W), multiply(X, Z))
% 1.58/0.61
% 1.58/0.61 Lemma 14: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 1.58/0.61 Proof:
% 1.58/0.61 inverse(multiply(inverse(X), X))
% 1.58/0.61 = { by lemma 9 }
% 1.58/0.61 inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))
% 1.58/0.61 = { by lemma 9 }
% 1.58/0.61 inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 1.58/0.61 = { by lemma 4 R->L }
% 1.58/0.61 multiply(inverse(multiply(W, inverse(multiply(inverse(Z), Z)))), multiply(W, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))))))
% 1.58/0.61 = { by lemma 9 R->L }
% 1.58/0.61 multiply(inverse(multiply(W, inverse(multiply(inverse(Z), Z)))), multiply(W, inverse(multiply(inverse(Z), Z))))
% 1.58/0.61 = { by lemma 9 R->L }
% 1.58/0.61 multiply(inverse(Y), Y)
% 1.58/0.61
% 1.58/0.61 Lemma 15: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), inverse(multiply(multiply(Y, Z), multiply(inverse(multiply(V, Z)), multiply(V, Z))))))) = W.
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), inverse(multiply(multiply(Y, Z), multiply(inverse(multiply(V, Z)), multiply(V, Z)))))))
% 1.58/0.61 = { by lemma 7 }
% 1.58/0.61 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), inverse(multiply(multiply(Y, Z), multiply(inverse(multiply(Y, Z)), multiply(Y, Z)))))))
% 1.58/0.61 = { by axiom 1 (single_axiom) }
% 1.58/0.61 W
% 1.58/0.61
% 1.58/0.61 Lemma 16: multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), Z)), multiply(inverse(W), W)))) = Z.
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), Z)), multiply(inverse(W), W))))
% 1.58/0.61 = { by lemma 14 R->L }
% 1.58/0.61 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), Z)), inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, U))), multiply(inverse(multiply(V, U)), multiply(V, U)))))))
% 1.58/0.61 = { by lemma 14 }
% 1.58/0.61 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), Z)), inverse(multiply(multiply(inverse(U), U), multiply(inverse(multiply(V, U)), multiply(V, U)))))))
% 1.58/0.61 = { by lemma 14 R->L }
% 1.58/0.61 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))), Z)), inverse(multiply(multiply(inverse(U), U), multiply(inverse(multiply(V, U)), multiply(V, U)))))))
% 1.58/0.61 = { by lemma 14 }
% 1.58/0.61 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(X), X), multiply(inverse(U), U))), Z)), inverse(multiply(multiply(inverse(U), U), multiply(inverse(multiply(V, U)), multiply(V, U)))))))
% 1.58/0.61 = { by lemma 15 }
% 1.58/0.61 Z
% 1.58/0.61
% 1.58/0.61 Lemma 17: inverse(multiply(multiply(inverse(X), X), Y)) = inverse(Y).
% 1.58/0.61 Proof:
% 1.58/0.61 inverse(multiply(multiply(inverse(X), X), Y))
% 1.58/0.61 = { by lemma 12 R->L }
% 1.58/0.61 inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(W), W)))))
% 1.58/0.61 = { by lemma 14 }
% 1.58/0.61 inverse(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(W), W)))))
% 1.58/0.61 = { by lemma 16 }
% 1.58/0.61 inverse(Y)
% 1.58/0.61
% 1.58/0.61 Lemma 18: multiply(multiply(inverse(X), X), Y) = Y.
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(multiply(inverse(X), X), Y)
% 1.58/0.61 = { by lemma 4 R->L }
% 1.58/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(multiply(multiply(inverse(X), X), Y)), inverse(multiply(W, multiply(inverse(W), W)))))))
% 1.58/0.61 = { by lemma 17 }
% 1.58/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(Y), inverse(multiply(W, multiply(inverse(W), W)))))))
% 1.58/0.61 = { by lemma 4 }
% 1.58/0.61 Y
% 1.58/0.61
% 1.58/0.61 Lemma 19: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 1.58/0.61 Proof:
% 1.58/0.61 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 1.58/0.61 = { by lemma 17 R->L }
% 1.58/0.61 inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), X)), multiply(inverse(Y), Y)))
% 1.58/0.61 = { by lemma 18 R->L }
% 1.58/0.61 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), X)), multiply(inverse(Y), Y))))
% 1.58/0.61 = { by lemma 16 }
% 1.58/0.61 X
% 1.58/0.61
% 1.58/0.61 Lemma 20: multiply(X, multiply(inverse(X), Y)) = Y.
% 1.58/0.61 Proof:
% 1.58/0.61 multiply(X, multiply(inverse(X), Y))
% 1.58/0.61 = { by lemma 19 R->L }
% 1.58/0.61 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(Z), Z)))))
% 1.58/0.61 = { by lemma 14 R->L }
% 1.58/0.61 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)))))))
% 1.58/0.61 = { by lemma 17 R->L }
% 1.58/0.61 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W))))))))
% 1.58/0.61 = { by lemma 19 R->L }
% 1.58/0.61 multiply(inverse(multiply(inverse(X), multiply(inverse(W), W))), multiply(inverse(X), inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W))))))))
% 1.58/0.61 = { by lemma 4 }
% 1.58/0.62 Y
% 1.58/0.62
% 1.58/0.62 Lemma 21: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 1.58/0.62 Proof:
% 1.58/0.62 multiply(inverse(X), X)
% 1.58/0.62 = { by lemma 11 R->L }
% 1.58/0.62 multiply(Y, multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 1.58/0.62 = { by lemma 13 }
% 1.58/0.62 multiply(multiply(inverse(W), W), multiply(Y, inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 1.58/0.62 = { by lemma 20 }
% 1.58/0.62 multiply(multiply(inverse(W), W), multiply(Y, inverse(Y)))
% 1.58/0.62 = { by lemma 13 R->L }
% 1.58/0.62 multiply(Y, multiply(inverse(multiply(inverse(V), V)), inverse(Y)))
% 1.58/0.62 = { by lemma 14 }
% 1.58/0.62 multiply(Y, multiply(multiply(inverse(U), U), inverse(Y)))
% 1.58/0.62 = { by lemma 18 }
% 1.58/0.62 multiply(Y, inverse(Y))
% 1.58/0.62
% 1.58/0.62 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)).
% 1.58/0.62 Proof:
% 1.58/0.62 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.58/0.62 = { by lemma 18 }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.58/0.62 = { by lemma 21 }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 15 R->L }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), inverse(multiply(inverse(multiply(inverse(multiply(inverse(b3), multiply(inverse(Y), Y))), c3)), inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(multiply(Z, Y)), multiply(Z, Y)))))))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 19 }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), inverse(multiply(inverse(multiply(b3, c3)), inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(multiply(Z, Y)), multiply(Z, Y)))))))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 17 }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), inverse(multiply(inverse(multiply(b3, c3)), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, Y))))))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 14 }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), inverse(multiply(inverse(multiply(b3, c3)), multiply(inverse(W), W))))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 19 }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), multiply(b3, c3))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 18 R->L }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), multiply(multiply(inverse(V), V), multiply(b3, c3)))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 18 R->L }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(multiply(inverse(V), V), b3)), multiply(multiply(inverse(V), V), multiply(b3, c3)))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 7 R->L }
% 1.58/0.62 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(b3, c3)))), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 20 }
% 1.58/0.62 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 1.58/0.62 = { by lemma 21 R->L }
% 1.58/0.62 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 1.58/0.62 % SZS output end Proof
% 1.58/0.62
% 1.58/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------