TSTP Solution File: GRP055-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP055-1 : 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 : n024.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 01:16:48 EDT 2023
% Result : Unsatisfiable 0.22s 0.52s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP055-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 01:28:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.52 Command-line arguments: --no-flatten-goal
% 0.22/0.52
% 0.22/0.52 % SZS status Unsatisfiable
% 0.22/0.52
% 0.22/0.57 % SZS output start Proof
% 0.22/0.57 Take the following subset of the input axioms:
% 0.22/0.57 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)))).
% 0.22/0.57 fof(single_axiom, axiom, ![Z, X, Y]: inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), multiply(inverse(Y), inverse(multiply(inverse(Y), Y))))))), multiply(Z, Y)))=X).
% 0.22/0.57
% 0.22/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.57 fresh(y, y, x1...xn) = u
% 0.22/0.57 C => fresh(s, t, x1...xn) = v
% 0.22/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.57 variables of u and v.
% 0.22/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.57 input problem has no model of domain size 1).
% 0.22/0.57
% 0.22/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.57
% 0.22/0.58 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))) = Y.
% 0.22/0.58
% 0.22/0.58 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z)) = inverse(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V))).
% 0.22/0.58 Proof:
% 0.22/0.58 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))
% 0.22/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))), multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.22/0.58 = { by axiom 1 (single_axiom) }
% 0.22/0.58 inverse(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.22/0.58
% 0.22/0.58 Lemma 3: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.22/0.58 Proof:
% 0.22/0.58 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.22/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.22/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(W, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.22/0.58 = { by axiom 1 (single_axiom) }
% 0.22/0.58 inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.22/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.22/0.58 = { by axiom 1 (single_axiom) }
% 0.22/0.58 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.22/0.58 = { by axiom 1 (single_axiom) }
% 0.22/0.58 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.22/0.58
% 0.22/0.58 Lemma 4: multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z)))) = multiply(inverse(multiply(W, multiply(V, U))), multiply(W, multiply(V, U))).
% 0.22/0.58 Proof:
% 0.22/0.58 multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))
% 0.22/0.58 = { by lemma 2 R->L }
% 0.22/0.58 multiply(X, multiply(inverse(multiply(V, inverse(multiply(inverse(X), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.22/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.58 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(X), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U))), multiply(inverse(multiply(V, inverse(multiply(inverse(X), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.22/0.58 = { by lemma 3 R->L }
% 0.22/0.58 multiply(inverse(multiply(W, multiply(V, U))), multiply(W, multiply(V, U)))
% 0.22/0.58
% 0.22/0.58 Lemma 5: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.22/0.58 Proof:
% 0.22/0.58 multiply(inverse(Y), Y)
% 0.22/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.58 multiply(inverse(Y), inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(Y), multiply(inverse(X2), inverse(multiply(inverse(X2), X2))))))), multiply(S, X2))))
% 0.22/0.58 = { by lemma 4 }
% 0.22/0.58 multiply(inverse(multiply(V, multiply(U, T))), multiply(V, multiply(U, T)))
% 0.22/0.58 = { by lemma 4 R->L }
% 0.22/0.58 multiply(inverse(X), inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), multiply(inverse(W), inverse(multiply(inverse(W), W))))))), multiply(Z, W))))
% 0.22/0.58 = { by axiom 1 (single_axiom) }
% 0.22/0.58 multiply(inverse(X), X)
% 0.22/0.58
% 0.22/0.58 Lemma 6: multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))) = inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, X))).
% 0.22/0.58 Proof:
% 0.22/0.58 multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))
% 0.22/0.58 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))), multiply(inverse(X), inverse(multiply(inverse(X), X))))))), multiply(Z, X)))
% 0.22/0.58 = { by axiom 1 (single_axiom) }
% 0.22/0.58 inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, X)))
% 0.22/0.58
% 0.22/0.58 Lemma 7: inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))) = Y.
% 0.22/0.58 Proof:
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z)))))
% 0.22/0.58 = { by lemma 6 R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z)))))
% 0.22/0.58 = { by axiom 1 (single_axiom) }
% 0.22/0.58 Y
% 0.22/0.58
% 0.22/0.58 Lemma 8: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Z), Z))))) = Y.
% 0.22/0.58 Proof:
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))
% 0.22/0.58 = { by lemma 5 }
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))))
% 0.22/0.58 = { by lemma 5 }
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Y)))), multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))))
% 0.22/0.58 = { by lemma 7 }
% 0.22/0.58 Y
% 0.22/0.58
% 0.22/0.58 Lemma 9: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.22/0.58 Proof:
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y)))
% 0.22/0.58 = { by lemma 5 }
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.22/0.58 = { by lemma 8 }
% 0.22/0.58 inverse(multiply(inverse(Z), Z))
% 0.22/0.58
% 0.22/0.58 Lemma 10: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.22/0.58 Proof:
% 0.22/0.58 inverse(multiply(inverse(X), X))
% 0.22/0.58 = { by lemma 8 R->L }
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))
% 0.22/0.58 = { by lemma 9 R->L }
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))
% 0.22/0.58 = { by lemma 7 }
% 0.22/0.58 multiply(inverse(Y), Y)
% 0.22/0.58
% 0.22/0.58 Lemma 11: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 0.22/0.58 Proof:
% 0.22/0.58 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 0.22/0.58 = { by lemma 5 }
% 0.22/0.58 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 0.22/0.58 = { by lemma 3 R->L }
% 0.22/0.58 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.22/0.58
% 0.22/0.58 Lemma 12: inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Z), Z)))) = Y.
% 0.22/0.58 Proof:
% 0.22/0.58 inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Z), Z))))
% 0.22/0.58 = { by lemma 10 R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(W), W)))))
% 0.22/0.58 = { by lemma 11 R->L }
% 0.22/0.58 inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(Y), inverse(multiply(inverse(W), W)))))
% 0.22/0.58 = { by lemma 10 R->L }
% 0.22/0.58 inverse(multiply(inverse(inverse(multiply(inverse(U), U))), multiply(inverse(Y), inverse(multiply(inverse(W), W)))))
% 0.22/0.58 = { by lemma 8 }
% 0.22/0.58 Y
% 0.22/0.58
% 0.22/0.58 Lemma 13: multiply(Z, multiply(inverse(Z), Y)) = multiply(X, multiply(inverse(X), Y)).
% 0.22/0.58 Proof:
% 0.22/0.58 multiply(Z, multiply(inverse(Z), Y))
% 0.22/0.58 = { by lemma 12 R->L }
% 0.22/0.58 multiply(Z, multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(V), V))))), Y))
% 0.22/0.58 = { by lemma 7 R->L }
% 0.22/0.58 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V)))))), multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(V), V))))), Y))
% 0.22/0.58 = { by lemma 3 R->L }
% 0.22/0.58 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, X)), multiply(W, multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V)))))), multiply(inverse(inverse(multiply(inverse(multiply(W, X)), multiply(W, multiply(inverse(V), V))))), Y))
% 0.22/0.58 = { by lemma 7 }
% 0.22/0.58 multiply(X, multiply(inverse(inverse(multiply(inverse(multiply(W, X)), multiply(W, multiply(inverse(V), V))))), Y))
% 0.22/0.58 = { by lemma 12 }
% 0.22/0.59 multiply(X, multiply(inverse(X), Y))
% 0.22/0.59
% 0.22/0.59 Lemma 14: multiply(multiply(inverse(X), X), Y) = Y.
% 0.22/0.59 Proof:
% 0.22/0.59 multiply(multiply(inverse(X), X), Y)
% 0.22/0.59 = { by lemma 10 R->L }
% 0.22/0.59 multiply(inverse(multiply(inverse(Z), Z)), Y)
% 0.22/0.59 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.59 multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))))
% 0.22/0.59 = { by lemma 6 }
% 0.22/0.59 inverse(multiply(inverse(multiply(W, multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))))))))), multiply(W, multiply(inverse(Z), Z))))
% 0.22/0.59 = { by lemma 6 }
% 0.22/0.59 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))), multiply(W, multiply(inverse(Z), Z))))
% 0.22/0.59 = { by lemma 12 }
% 0.22/0.59 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))
% 0.22/0.59 = { by lemma 10 }
% 0.22/0.59 inverse(multiply(inverse(multiply(V, Y)), multiply(V, multiply(inverse(U), U))))
% 0.22/0.59 = { by lemma 12 }
% 0.22/0.59 Y
% 0.22/0.59
% 0.22/0.59 Lemma 15: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.22/0.59 Proof:
% 0.22/0.59 multiply(X, multiply(inverse(X), Y))
% 0.22/0.59 = { by lemma 13 }
% 0.22/0.59 multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(inverse(Z), Z)), Y))
% 0.22/0.59 = { by lemma 10 }
% 0.22/0.59 multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(W), W), Y))
% 0.22/0.59 = { by lemma 14 }
% 0.22/0.59 multiply(multiply(inverse(W), W), Y)
% 0.22/0.59 = { by lemma 14 }
% 0.22/0.59 Y
% 0.22/0.59
% 0.22/0.59 Lemma 16: multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z)) = multiply(W, multiply(inverse(W), Z)).
% 0.22/0.59 Proof:
% 0.22/0.59 multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z))
% 0.22/0.59 = { by lemma 11 R->L }
% 0.22/0.59 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.22/0.59 = { by lemma 10 }
% 0.22/0.59 multiply(multiply(inverse(U), U), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.22/0.59 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.59 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(S), inverse(multiply(inverse(S), S))))))), multiply(T, S))), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.22/0.59 = { by lemma 9 R->L }
% 0.22/0.59 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2))), multiply(inverse(S), inverse(multiply(inverse(S), S))))))), multiply(T, S))), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.22/0.59 = { by axiom 1 (single_axiom) }
% 0.22/0.59 multiply(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2)), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.22/0.59 = { by lemma 9 R->L }
% 0.22/0.59 multiply(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2)), multiply(inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(Y2), Y2))), Z))
% 0.22/0.59 = { by lemma 13 R->L }
% 0.22/0.59 multiply(W, multiply(inverse(W), Z))
% 0.22/0.59
% 0.22/0.59 Lemma 17: inverse(inverse(X)) = X.
% 0.22/0.59 Proof:
% 0.22/0.59 inverse(inverse(X))
% 0.22/0.59 = { by lemma 15 R->L }
% 0.22/0.59 inverse(inverse(multiply(Y, multiply(inverse(Y), X))))
% 0.22/0.59 = { by lemma 16 R->L }
% 0.22/0.59 inverse(inverse(multiply(inverse(multiply(Z, multiply(inverse(W), W))), multiply(Z, X))))
% 0.22/0.59 = { by lemma 10 R->L }
% 0.22/0.59 inverse(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(V), V)))), multiply(Z, X))))
% 0.22/0.59 = { by lemma 10 R->L }
% 0.22/0.59 inverse(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(inverse(X), X))))), multiply(Z, X))))
% 0.22/0.59 = { by lemma 15 R->L }
% 0.22/0.59 inverse(inverse(multiply(inverse(multiply(Z, inverse(multiply(X, multiply(inverse(X), inverse(multiply(inverse(X), X))))))), multiply(Z, X))))
% 0.22/0.59 = { by lemma 2 R->L }
% 0.22/0.59 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.22/0.59 = { by axiom 1 (single_axiom) }
% 0.22/0.59 X
% 0.22/0.59
% 0.22/0.59 Lemma 18: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.22/0.59 Proof:
% 0.22/0.59 multiply(inverse(X), X)
% 0.22/0.59 = { by lemma 5 }
% 0.22/0.59 multiply(inverse(multiply(Z, multiply(W, V))), multiply(Z, multiply(W, V)))
% 0.22/0.59 = { by lemma 4 R->L }
% 0.22/0.59 multiply(Y, inverse(multiply(inverse(multiply(U, inverse(multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Y), Y))))))), multiply(U, Y))))
% 0.22/0.59 = { by lemma 15 }
% 0.22/0.59 multiply(Y, inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(inverse(Y), Y))))), multiply(U, Y))))
% 0.22/0.59 = { by lemma 10 }
% 0.22/0.59 multiply(Y, inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(T), T)))), multiply(U, Y))))
% 0.22/0.59 = { by lemma 10 }
% 0.22/0.59 multiply(Y, inverse(multiply(inverse(multiply(U, multiply(inverse(S), S))), multiply(U, Y))))
% 0.22/0.59 = { by lemma 16 }
% 0.22/0.59 multiply(Y, inverse(multiply(X2, multiply(inverse(X2), Y))))
% 0.22/0.59 = { by lemma 15 }
% 0.22/0.59 multiply(Y, inverse(Y))
% 0.22/0.59
% 0.22/0.59 Lemma 19: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 0.22/0.59 Proof:
% 0.22/0.59 inverse(multiply(inverse(X), Y))
% 0.22/0.59 = { by lemma 15 R->L }
% 0.22/0.59 inverse(multiply(inverse(X), multiply(Y, multiply(inverse(Y), Y))))
% 0.22/0.59 = { by lemma 15 R->L }
% 0.22/0.59 inverse(multiply(inverse(multiply(Y, multiply(inverse(Y), X))), multiply(Y, multiply(inverse(Y), Y))))
% 0.22/0.59 = { by lemma 12 }
% 0.22/0.59 multiply(inverse(Y), X)
% 0.22/0.59
% 0.22/0.59 Lemma 20: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.22/0.59 Proof:
% 0.22/0.59 multiply(X, multiply(Y, inverse(Y)))
% 0.22/0.59 = { by lemma 18 R->L }
% 0.22/0.59 multiply(X, multiply(inverse(multiply(Z, multiply(W, V))), multiply(Z, multiply(W, V))))
% 0.22/0.59 = { by lemma 4 R->L }
% 0.22/0.59 multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))))
% 0.22/0.59 = { by lemma 13 R->L }
% 0.22/0.59 multiply(S, multiply(inverse(S), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))))
% 0.22/0.59 = { by lemma 15 }
% 0.22/0.59 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(X), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.22/0.59 = { by axiom 1 (single_axiom) }
% 0.22/0.59 X
% 0.22/0.59
% 0.22/0.59 Lemma 21: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 0.22/0.59 Proof:
% 0.22/0.59 inverse(multiply(inverse(multiply(X, Y)), X))
% 0.22/0.59 = { by lemma 19 }
% 0.22/0.59 multiply(inverse(X), multiply(X, Y))
% 0.22/0.59 = { by lemma 15 R->L }
% 0.22/0.59 multiply(inverse(multiply(X, multiply(inverse(X), X))), multiply(X, Y))
% 0.22/0.59 = { by lemma 16 }
% 0.22/0.59 multiply(Z, multiply(inverse(Z), Y))
% 0.22/0.59 = { by lemma 15 }
% 0.22/0.59 Y
% 0.22/0.59
% 0.22/0.59 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))).
% 0.22/0.59 Proof:
% 0.22/0.59 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.22/0.59 = { by lemma 14 }
% 0.22/0.59 tuple(multiply(inverse(a1), a1), a2, multiply(multiply(a3, b3), c3))
% 0.22/0.59 = { by lemma 18 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 0.22/0.59 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3)))))
% 0.22/0.59 = { by lemma 21 R->L }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))), inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))))), inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3)))))
% 0.22/0.59 = { by lemma 8 R->L }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(inverse(multiply(inverse(Y), Y))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))), inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))))), inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(a3, b3))))), inverse(multiply(inverse(Z), Z))))))
% 0.22/0.59 = { by lemma 21 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(inverse(multiply(inverse(Y), Y))), multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), inverse(multiply(inverse(Z), Z))))))
% 0.22/0.59 = { by lemma 19 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), inverse(multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), Y))))
% 0.22/0.59 = { by lemma 10 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(inverse(W), W))), inverse(multiply(inverse(Y), Y))))
% 0.22/0.59 = { by lemma 10 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(inverse(W), W))), multiply(inverse(V), V)))
% 0.22/0.59 = { by lemma 18 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(U, inverse(U)))), multiply(inverse(V), V)))
% 0.22/0.59 = { by lemma 18 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(U, inverse(U)))), multiply(T, inverse(T))))
% 0.22/0.59 = { by lemma 20 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(U, inverse(U)))))
% 0.22/0.59 = { by lemma 20 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, inverse(inverse(multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3)))))))))
% 0.22/0.59 = { by lemma 17 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3)))))))
% 0.22/0.59 = { by lemma 19 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(inverse(multiply(inverse(b3), inverse(multiply(inverse(b3), b3)))), c3)))
% 0.22/0.59 = { by lemma 19 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(inverse(inverse(multiply(inverse(b3), b3))), b3), c3)))
% 0.22/0.59 = { by lemma 17 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(multiply(multiply(inverse(b3), b3), b3), c3)))
% 0.22/0.59 = { by lemma 14 }
% 0.22/0.59 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 0.22/0.59 = { by lemma 18 R->L }
% 0.22/0.59 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.22/0.60 % SZS output end Proof
% 0.22/0.60
% 0.22/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------