TSTP Solution File: GRP052-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP052-1 : 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 : n007.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 0.19s 0.52s
% Output : Proof 1.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP052-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n007.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 19:30:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.52 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.52
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52
% 1.62/0.56 % SZS output start Proof
% 1.62/0.56 Take the following subset of the input axioms:
% 1.62/0.56 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)))).
% 1.62/0.56 fof(single_axiom, axiom, ![Z, Y, X]: multiply(Z, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(Z, inverse(Y))), X))), Y)))=X).
% 1.62/0.56
% 1.62/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.62/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.62/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.62/0.56 fresh(y, y, x1...xn) = u
% 1.62/0.56 C => fresh(s, t, x1...xn) = v
% 1.62/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 1.62/0.56 variables of u and v.
% 1.62/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.62/0.56 input problem has no model of domain size 1).
% 1.62/0.56
% 1.62/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 1.62/0.56
% 1.62/0.56 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(X, inverse(Y))), Z))), Y))) = Z.
% 1.62/0.56
% 1.62/0.56 Lemma 2: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X)) = multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z))).
% 1.62/0.56 Proof:
% 1.62/0.56 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))
% 1.62/0.56 = { by axiom 1 (single_axiom) R->L }
% 1.62/0.56 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))))), Z)))
% 1.62/0.56 = { by axiom 1 (single_axiom) }
% 1.62/0.56 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z)))
% 1.62/0.56
% 1.62/0.56 Lemma 3: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y)))) = Z.
% 1.62/0.56 Proof:
% 1.62/0.56 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y))))
% 1.62/0.56 = { by lemma 2 R->L }
% 1.62/0.56 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), inverse(W))), Z))), W)))
% 1.62/0.56 = { by axiom 1 (single_axiom) }
% 1.62/0.56 Z
% 1.62/0.56
% 1.62/0.56 Lemma 4: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X) = multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y)))).
% 1.62/0.56 Proof:
% 1.62/0.56 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X)
% 1.62/0.56 = { by lemma 3 R->L }
% 1.62/0.56 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X))), Y))))
% 1.62/0.56 = { by axiom 1 (single_axiom) }
% 1.62/0.56 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y))))
% 1.62/0.56
% 1.62/0.56 Lemma 5: multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X)))))) = Z.
% 1.62/0.56 Proof:
% 1.62/0.56 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X))))))
% 1.62/0.56 = { by lemma 4 R->L }
% 1.62/0.56 multiply(multiply(inverse(X), X), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(W))), Z))), W)))
% 1.62/0.56 = { by axiom 1 (single_axiom) }
% 1.62/0.56 Z
% 1.62/0.56
% 1.62/0.56 Lemma 6: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X)) = W.
% 1.62/0.56 Proof:
% 1.62/0.56 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X))
% 1.62/0.56 = { by lemma 2 }
% 1.62/0.56 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), W))), Z)))
% 1.62/0.56 = { by axiom 1 (single_axiom) }
% 1.62/0.56 W
% 1.62/0.56
% 1.62/0.56 Lemma 7: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W))))))) = multiply(inverse(multiply(multiply(inverse(W), W), inverse(Y))), V).
% 1.62/0.56 Proof:
% 1.62/0.56 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W)))))))
% 1.62/0.56 = { by lemma 4 R->L }
% 1.62/0.56 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(Y))), V))), Y))))
% 1.62/0.56 = { by lemma 3 }
% 1.62/0.56 multiply(inverse(multiply(multiply(inverse(W), W), inverse(Y))), V)
% 1.62/0.56
% 1.62/0.56 Lemma 8: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 1.62/0.56 Proof:
% 1.62/0.56 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 1.62/0.56 = { by lemma 6 R->L }
% 1.62/0.56 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 1.62/0.56 = { by lemma 6 R->L }
% 1.62/0.57 multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), Y)))), S)))), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 1.62/0.57 = { by axiom 1 (single_axiom) R->L }
% 1.62/0.57 multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), Y)))), S)))), multiply(W, inverse(multiply(inverse(multiply(U2, inverse(W2))), inverse(multiply(multiply(multiply(inverse(T2), T2), inverse(multiply(inverse(multiply(inverse(multiply(U2, inverse(W2))), inverse(T2))), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V)))), T2))))))
% 1.62/0.57 = { by lemma 2 }
% 1.62/0.57 multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), Y)))), S)))), multiply(W, inverse(multiply(inverse(multiply(U2, inverse(W2))), multiply(U2, inverse(multiply(multiply(multiply(inverse(W2), W2), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))), W2)))))))
% 1.62/0.57 = { by lemma 7 }
% 1.62/0.57 multiply(inverse(multiply(multiply(inverse(W2), W2), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), Y)))), S)))), multiply(multiply(inverse(W2), W2), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 1.62/0.57 = { by lemma 7 R->L }
% 1.62/0.57 multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), Y)))), S)))), multiply(X, inverse(multiply(inverse(multiply(Z2, inverse(W2))), multiply(Z2, inverse(multiply(multiply(multiply(inverse(W2), W2), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))), W2)))))))
% 1.62/0.57 = { by lemma 2 R->L }
% 1.62/0.57 multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), Y)))), S)))), multiply(X, inverse(multiply(inverse(multiply(Z2, inverse(W2))), inverse(multiply(multiply(multiply(inverse(V2), V2), inverse(multiply(inverse(multiply(inverse(multiply(Z2, inverse(W2))), inverse(V2))), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V)))), V2))))))
% 1.62/0.57 = { by axiom 1 (single_axiom) }
% 1.62/0.57 multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), Y)))), S)))), multiply(X, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 1.62/0.57 = { by lemma 6 }
% 1.75/0.57 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), Z)))), V))))
% 1.75/0.57 = { by lemma 6 }
% 1.75/0.57 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 1.75/0.57
% 1.75/0.57 Lemma 9: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(Z))))), X) = Z.
% 1.75/0.57 Proof:
% 1.75/0.57 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(Z))))), X)
% 1.75/0.57 = { by axiom 1 (single_axiom) R->L }
% 1.75/0.57 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(inverse(multiply(W, inverse(V))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(V))), inverse(U))), Z))), U)))))))), X)
% 1.75/0.57 = { by lemma 2 }
% 1.75/0.57 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(inverse(multiply(W, inverse(V))), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), inverse(Z)), V))))))))), X)
% 1.75/0.57 = { by lemma 7 }
% 1.75/0.57 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(X))), multiply(multiply(inverse(V), V), inverse(Z))))), X)
% 1.75/0.57 = { by lemma 4 }
% 1.75/0.57 multiply(inverse(multiply(T, inverse(V))), multiply(T, inverse(multiply(multiply(multiply(inverse(V), V), inverse(Z)), V))))
% 1.75/0.57 = { by lemma 3 }
% 1.75/0.57 Z
% 1.75/0.57
% 1.75/0.57 Lemma 10: multiply(multiply(inverse(X), X), inverse(Y)) = multiply(multiply(inverse(Z), Z), inverse(Y)).
% 1.75/0.57 Proof:
% 1.75/0.57 multiply(multiply(inverse(X), X), inverse(Y))
% 1.75/0.57 = { by lemma 5 R->L }
% 1.75/0.57 multiply(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))))), multiply(U, inverse(X))))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))))), multiply(U, inverse(X))))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))))), multiply(U, inverse(X))))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))))), multiply(T, inverse(multiply(multiply(multiply(inverse(X), X), inverse(Y)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))))), multiply(U, inverse(X))))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))))))))
% 1.75/0.57 = { by lemma 8 R->L }
% 1.75/0.57 multiply(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), multiply(V, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))))), multiply(U, inverse(X))))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))))), multiply(T, inverse(multiply(multiply(multiply(inverse(X), X), inverse(Y)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))))), multiply(U, inverse(X))))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))))))))
% 1.75/0.57 = { by lemma 9 }
% 1.75/0.57 multiply(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), multiply(V, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), inverse(multiply(inverse(multiply(T, inverse(X))), multiply(T, inverse(multiply(multiply(multiply(inverse(X), X), inverse(Y)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))), inverse(multiply(inverse(multiply(U, inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W))))), multiply(U, inverse(X))))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))))))))
% 1.75/0.57 = { by lemma 9 }
% 1.75/0.57 multiply(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), multiply(V, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), inverse(multiply(inverse(multiply(T, inverse(X))), multiply(T, inverse(multiply(multiply(multiply(inverse(X), X), inverse(Y)), X))))))
% 1.75/0.57 = { by axiom 1 (single_axiom) }
% 1.75/0.57 multiply(multiply(inverse(Z), multiply(V, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, inverse(W))), Z))), W)))), inverse(multiply(inverse(multiply(T, inverse(X))), multiply(T, inverse(multiply(multiply(multiply(inverse(X), X), inverse(Y)), X))))))
% 1.75/0.57 = { by axiom 1 (single_axiom) }
% 1.75/0.57 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(T, inverse(X))), multiply(T, inverse(multiply(multiply(multiply(inverse(X), X), inverse(Y)), X))))))
% 1.75/0.57 = { by lemma 2 R->L }
% 1.75/0.57 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(T, inverse(X))), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(X))), inverse(S))), Y))), S)))))
% 1.75/0.57 = { by axiom 1 (single_axiom) }
% 1.75/0.57 multiply(multiply(inverse(Z), Z), inverse(Y))
% 1.75/0.57
% 1.75/0.57 Lemma 11: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 1.75/0.57 Proof:
% 1.75/0.57 multiply(inverse(Y), Y)
% 1.75/0.57 = { by lemma 5 R->L }
% 1.75/0.58 multiply(multiply(inverse(inverse(Z)), inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(inverse(Z)))), multiply(W, inverse(multiply(multiply(inverse(Y), Y), inverse(Z)))))))
% 1.75/0.58 = { by lemma 10 R->L }
% 1.75/0.58 multiply(multiply(inverse(inverse(Z)), inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(inverse(Z)))), multiply(W, inverse(multiply(multiply(inverse(X), X), inverse(Z)))))))
% 1.75/0.58 = { by lemma 5 }
% 1.75/0.58 multiply(inverse(X), X)
% 1.75/0.58
% 1.75/0.58 Lemma 12: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z) = Z.
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z)
% 1.75/0.58 = { by lemma 10 R->L }
% 1.75/0.58 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Y), Y))), Z)
% 1.75/0.58 = { by lemma 11 }
% 1.75/0.58 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(W, inverse(Z))), multiply(W, inverse(Z))))), Z)
% 1.75/0.58 = { by lemma 9 }
% 1.75/0.58 Z
% 1.75/0.58
% 1.75/0.58 Lemma 13: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(Y), Z).
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 1.75/0.58 = { by lemma 8 }
% 1.75/0.58 multiply(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Y)), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 1.75/0.58 = { by lemma 12 }
% 1.75/0.58 multiply(inverse(Y), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 1.75/0.58 = { by lemma 12 }
% 1.75/0.58 multiply(inverse(Y), Z)
% 1.75/0.58
% 1.75/0.58 Lemma 14: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(Y), Z).
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 1.75/0.58 = { by lemma 11 }
% 1.75/0.58 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 1.75/0.58 = { by lemma 13 }
% 1.75/0.58 multiply(inverse(Y), Z)
% 1.75/0.58
% 1.75/0.58 Lemma 15: multiply(inverse(multiply(inverse(X), X)), Y) = Y.
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(multiply(inverse(X), X)), Y)
% 1.75/0.58 = { by axiom 1 (single_axiom) R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Z), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Z), inverse(W))), Y))), W))))
% 1.75/0.58 = { by lemma 14 }
% 1.75/0.58 multiply(inverse(Z), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Z), inverse(W))), Y))), W)))
% 1.75/0.58 = { by axiom 1 (single_axiom) }
% 1.75/0.58 Y
% 1.75/0.58
% 1.75/0.58 Lemma 16: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 1.75/0.58 = { by lemma 11 }
% 1.75/0.58 multiply(multiply(inverse(X), X), inverse(multiply(inverse(inverse(multiply(inverse(W), V))), inverse(multiply(inverse(W), V)))))
% 1.75/0.58 = { by lemma 13 R->L }
% 1.75/0.58 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(W), V)))), multiply(U, inverse(multiply(inverse(W), V))))))
% 1.75/0.58 = { by lemma 10 R->L }
% 1.75/0.58 multiply(multiply(inverse(multiply(inverse(W), V)), multiply(inverse(W), V)), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(W), V)))), multiply(U, inverse(multiply(inverse(W), V))))))
% 1.75/0.58 = { by lemma 14 R->L }
% 1.75/0.58 multiply(multiply(inverse(multiply(inverse(W), V)), multiply(inverse(W), V)), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(W), V)))), multiply(U, inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), V)))))))
% 1.75/0.58 = { by lemma 5 }
% 1.75/0.58 inverse(multiply(inverse(Z), Z))
% 1.75/0.58
% 1.75/0.58 Lemma 17: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 1.75/0.58 Proof:
% 1.75/0.58 inverse(multiply(inverse(X), X))
% 1.75/0.58 = { by lemma 16 R->L }
% 1.75/0.58 multiply(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z)))))))
% 1.75/0.58 = { by lemma 16 R->L }
% 1.75/0.58 multiply(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), multiply(W, inverse(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))))))))
% 1.75/0.58 = { by lemma 5 }
% 1.75/0.58 multiply(inverse(Y), Y)
% 1.75/0.58
% 1.75/0.58 Lemma 18: multiply(multiply(inverse(X), X), Y) = Y.
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(multiply(inverse(X), X), Y)
% 1.75/0.58 = { by lemma 17 R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(Z), Z)), Y)
% 1.75/0.58 = { by lemma 15 }
% 1.75/0.58 Y
% 1.75/0.58
% 1.75/0.58 Lemma 19: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), Z)), Y))) = Z.
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), Z)), Y)))
% 1.75/0.58 = { by lemma 18 R->L }
% 1.75/0.58 multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(X, inverse(Y))), Z))), Y)))
% 1.75/0.58 = { by axiom 1 (single_axiom) }
% 1.75/0.58 Z
% 1.75/0.58
% 1.75/0.58 Lemma 20: multiply(inverse(inverse(X)), multiply(inverse(Y), Y)) = X.
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 1.75/0.58 = { by lemma 17 R->L }
% 1.75/0.58 multiply(inverse(inverse(X)), inverse(multiply(inverse(Z), Z)))
% 1.75/0.58 = { by lemma 18 R->L }
% 1.75/0.58 multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(X))), inverse(multiply(inverse(Z), Z)))
% 1.75/0.58 = { by lemma 19 R->L }
% 1.75/0.58 multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(X))), inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(X))), inverse(Z))), X))), Z)))
% 1.75/0.58 = { by axiom 1 (single_axiom) }
% 1.75/0.58 X
% 1.75/0.58
% 1.75/0.58 Lemma 21: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 1.75/0.58 Proof:
% 1.75/0.58 inverse(multiply(inverse(X), Y))
% 1.75/0.58 = { by lemma 15 R->L }
% 1.75/0.58 inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(Y)), inverse(Y))), X)), Y))
% 1.75/0.58 = { by lemma 15 R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(Y)), inverse(Y))), X)), Y)))
% 1.75/0.58 = { by lemma 13 R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(inverse(Y)), multiply(inverse(Z), Z))), multiply(inverse(inverse(Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(Y)), inverse(Y))), X)), Y))))
% 1.75/0.58 = { by lemma 20 }
% 1.75/0.58 multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(Y)), inverse(Y))), X)), Y))))
% 1.75/0.58 = { by lemma 19 }
% 1.75/0.58 multiply(inverse(Y), X)
% 1.75/0.58
% 1.75/0.58 Lemma 22: multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(Z), Z)) = multiply(inverse(Y), X).
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(Z), Z))
% 1.75/0.58 = { by lemma 11 }
% 1.75/0.58 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(X), X))
% 1.75/0.58 = { by lemma 13 }
% 1.75/0.58 multiply(inverse(Y), X)
% 1.75/0.58
% 1.75/0.58 Lemma 23: multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(multiply(inverse(Y), X)), Z)) = Z.
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(multiply(inverse(Y), X)), Z))
% 1.75/0.58 = { by lemma 22 R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(multiply(inverse(Y), X)), multiply(inverse(W), W))), multiply(inverse(multiply(inverse(Y), X)), Z))
% 1.75/0.58 = { by lemma 13 }
% 1.75/0.58 multiply(inverse(multiply(inverse(W), W)), Z)
% 1.75/0.58 = { by lemma 15 }
% 1.75/0.58 Z
% 1.75/0.58
% 1.75/0.58 Lemma 24: multiply(X, multiply(inverse(X), Y)) = Y.
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(X, multiply(inverse(X), Y))
% 1.75/0.58 = { by axiom 1 (single_axiom) R->L }
% 1.75/0.58 multiply(X, multiply(inverse(multiply(inverse(Z), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Z), inverse(W))), X))), W)))), Y))
% 1.75/0.58 = { by axiom 1 (single_axiom) R->L }
% 1.75/0.58 multiply(multiply(inverse(Z), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Z), inverse(W))), X))), W))), multiply(inverse(multiply(inverse(Z), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Z), inverse(W))), X))), W)))), Y))
% 1.75/0.58 = { by lemma 21 R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Z), inverse(W))), X))), W))), Z)), multiply(inverse(multiply(inverse(Z), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Z), inverse(W))), X))), W)))), Y))
% 1.75/0.58 = { by lemma 23 }
% 1.75/0.58 Y
% 1.75/0.58
% 1.75/0.58 Lemma 25: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(X), multiply(inverse(Y), Y))
% 1.75/0.58 = { by lemma 20 R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(inverse(X)), multiply(inverse(Z), Z))), multiply(inverse(Y), Y))
% 1.75/0.58 = { by lemma 22 }
% 1.75/0.58 multiply(inverse(multiply(inverse(Z), Z)), inverse(X))
% 1.75/0.58 = { by lemma 15 }
% 1.75/0.58 inverse(X)
% 1.75/0.58
% 1.75/0.58 Lemma 26: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(X), X)
% 1.75/0.58 = { by lemma 24 R->L }
% 1.75/0.58 multiply(Y, multiply(inverse(Y), multiply(inverse(X), X)))
% 1.75/0.58 = { by lemma 25 }
% 1.75/0.58 multiply(Y, inverse(Y))
% 1.75/0.58
% 1.75/0.58 Lemma 27: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), W)) = multiply(inverse(Z), multiply(X, W)).
% 1.75/0.58 Proof:
% 1.75/0.58 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), W))
% 1.75/0.58 = { by lemma 13 R->L }
% 1.75/0.58 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), multiply(X, W)))
% 1.75/0.58 = { by lemma 13 }
% 1.75/0.58 multiply(inverse(Z), multiply(X, W))
% 1.75/0.58
% 1.75/0.58 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)).
% 1.75/0.58 Proof:
% 1.75/0.58 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.75/0.58 = { by lemma 18 }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.75/0.58 = { by lemma 26 }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 1.75/0.58 = { by lemma 23 R->L }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, Y)), b3)), multiply(inverse(multiply(inverse(b3), multiply(b3, Y))), c3))), multiply(X, inverse(X)))
% 1.75/0.58 = { by lemma 27 R->L }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, Y)), b3)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(b3, multiply(inverse(b3), b3))), b3)), multiply(inverse(multiply(inverse(b3), b3)), Y))), c3))), multiply(X, inverse(X)))
% 1.75/0.58 = { by lemma 15 }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, Y)), b3)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(b3, multiply(inverse(b3), b3))), b3)), Y)), c3))), multiply(X, inverse(X)))
% 1.75/0.58 = { by lemma 21 }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, Y)), b3)), multiply(multiply(inverse(Y), multiply(inverse(multiply(b3, multiply(inverse(b3), b3))), b3)), c3))), multiply(X, inverse(X)))
% 1.75/0.58 = { by lemma 24 }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, Y)), b3)), multiply(multiply(inverse(Y), multiply(inverse(b3), b3)), c3))), multiply(X, inverse(X)))
% 1.75/0.58 = { by lemma 25 }
% 1.75/0.58 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, Y)), b3)), multiply(inverse(Y), c3))), multiply(X, inverse(X)))
% 1.75/0.59 = { by lemma 27 }
% 1.75/0.59 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), multiply(b3, c3))), multiply(X, inverse(X)))
% 1.75/0.59 = { by lemma 13 R->L }
% 1.75/0.59 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(b3, c3)))), multiply(X, inverse(X)))
% 1.75/0.59 = { by lemma 24 }
% 1.75/0.59 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 1.75/0.59 = { by lemma 26 R->L }
% 1.75/0.59 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 1.75/0.59 % SZS output end Proof
% 1.75/0.59
% 1.75/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------