TSTP Solution File: GRP050-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP050-1 : 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 : n005.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 0.22s 0.58s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP050-1 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.14 % 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 : n005.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 : Mon Aug 28 23:47:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.58 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.58
% 0.22/0.58 % SZS status Unsatisfiable
% 0.22/0.58
% 0.22/0.64 % SZS output start Proof
% 0.22/0.64 Take the following subset of the input axioms:
% 0.22/0.64 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)))).
% 0.22/0.64 fof(single_axiom, axiom, ![Z, Y, X]: multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, Y)), X)), multiply(inverse(Y), multiply(inverse(Y), Y)))))=X).
% 0.22/0.64
% 0.22/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.64 fresh(y, y, x1...xn) = u
% 0.22/0.64 C => fresh(s, t, x1...xn) = v
% 0.22/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.64 variables of u and v.
% 0.22/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.64 input problem has no model of domain size 1).
% 0.22/0.64
% 0.22/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.64
% 0.22/0.64 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y))))) = Z.
% 0.22/0.64
% 0.22/0.64 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))) = multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y))))).
% 0.22/0.64 Proof:
% 0.22/0.64 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 0.22/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.64 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.22/0.64 = { by axiom 1 (single_axiom) }
% 0.22/0.64 multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.22/0.64
% 0.22/0.64 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z)))) = W.
% 0.22/0.64 Proof:
% 0.22/0.64 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 0.22/0.64 = { by lemma 2 }
% 0.22/0.64 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.22/0.64 = { by axiom 1 (single_axiom) }
% 0.22/0.64 W
% 0.22/0.64
% 0.22/0.64 Lemma 4: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y)))) = Z.
% 0.22/0.64 Proof:
% 0.22/0.64 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.22/0.64 = { by lemma 3 R->L }
% 0.22/0.64 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))), multiply(inverse(U), multiply(inverse(U), U)))), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.22/0.64 = { by lemma 3 R->L }
% 0.22/0.64 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), multiply(inverse(U), multiply(inverse(U), U)))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), multiply(inverse(U), multiply(inverse(U), U)))), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.22/0.64 = { by lemma 3 }
% 0.22/0.64 Z
% 0.22/0.64
% 0.22/0.64 Lemma 5: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y)))))) = Z.
% 0.22/0.64 Proof:
% 0.22/0.64 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.22/0.64 = { by lemma 2 R->L }
% 0.22/0.64 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.22/0.64 = { by axiom 1 (single_axiom) }
% 0.22/0.64 Z
% 0.22/0.64
% 0.22/0.64 Lemma 6: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(Y), multiply(inverse(Y), Y))) = Z.
% 0.22/0.64 Proof:
% 0.22/0.64 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(Y), multiply(inverse(Y), Y)))
% 0.22/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.64 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)))), multiply(inverse(Y), multiply(inverse(Y), Y)))), multiply(inverse(multiply(X, inverse(Z))), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z))))))))
% 0.22/0.64 = { by lemma 4 }
% 0.22/0.64 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), multiply(inverse(multiply(X, inverse(Z))), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z))))))))
% 0.22/0.64 = { by lemma 5 }
% 0.22/0.64 Z
% 0.22/0.64
% 0.22/0.64 Lemma 7: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W)) = multiply(inverse(multiply(V, Z)), multiply(V, W)).
% 0.22/0.64 Proof:
% 0.22/0.64 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))
% 0.22/0.64 = { by lemma 5 R->L }
% 0.22/0.64 multiply(inverse(multiply(V, Z)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
% 0.22/0.64 = { by lemma 3 }
% 0.22/0.64 multiply(inverse(multiply(V, Z)), multiply(V, W))
% 0.22/0.64
% 0.22/0.64 Lemma 8: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.22/0.64 Proof:
% 0.22/0.64 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.22/0.64 = { by lemma 3 R->L }
% 0.22/0.64 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.22/0.64 = { by lemma 5 }
% 0.22/0.64 multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))
% 0.22/0.64 = { by lemma 5 R->L }
% 0.22/0.64 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.22/0.64 = { by lemma 3 }
% 0.22/0.64 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.22/0.64
% 0.22/0.64 Lemma 9: 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)).
% 0.22/0.64 Proof:
% 0.22/0.64 multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W))
% 0.22/0.64 = { by lemma 7 R->L }
% 0.22/0.64 multiply(V, multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 0.22/0.64 = { by lemma 3 R->L }
% 0.22/0.64 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), multiply(inverse(Z), multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 0.22/0.64 = { by lemma 8 R->L }
% 0.22/0.64 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), multiply(inverse(Z), multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 0.22/0.64 = { by lemma 3 }
% 0.22/0.64 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 0.22/0.64 = { by lemma 7 }
% 0.22/0.64 multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W))
% 0.22/0.64
% 0.22/0.64 Lemma 10: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.22/0.64 Proof:
% 0.22/0.64 multiply(inverse(Y), Y)
% 0.22/0.64 = { by lemma 6 R->L }
% 0.22/0.64 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Y)))), multiply(inverse(W), multiply(inverse(W), W))))
% 0.22/0.64 = { by lemma 9 R->L }
% 0.22/0.64 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(X)))), multiply(inverse(W), multiply(inverse(W), W))))
% 0.22/0.64 = { by lemma 6 }
% 0.22/0.64 multiply(inverse(X), X)
% 0.22/0.64
% 0.22/0.64 Lemma 11: multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(Z), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, X)).
% 0.22/0.64 Proof:
% 0.22/0.64 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(Z), Z))
% 0.22/0.64 = { by lemma 10 }
% 0.22/0.64 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(X), X))
% 0.22/0.64 = { by lemma 8 R->L }
% 0.22/0.65 multiply(inverse(multiply(W, Y)), multiply(W, X))
% 0.22/0.65
% 0.22/0.65 Lemma 12: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 0.22/0.65 = { by lemma 10 }
% 0.22/0.65 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 0.22/0.65 = { by lemma 8 R->L }
% 0.22/0.65 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.22/0.65
% 0.22/0.65 Lemma 13: multiply(X, inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, multiply(inverse(W), W))))) = multiply(X, Z).
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, multiply(inverse(W), W)))))
% 0.22/0.65 = { by lemma 10 }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, multiply(inverse(Z), Z)))))
% 0.22/0.65 = { by lemma 12 R->L }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))), multiply(inverse(Z), multiply(inverse(Z), Z)))))
% 0.22/0.65 = { by lemma 2 R->L }
% 0.22/0.65 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Z)), V)), multiply(inverse(multiply(X, Z)), multiply(X, Z)))), multiply(inverse(V), multiply(inverse(V), V))))
% 0.22/0.65 = { by lemma 4 }
% 0.22/0.65 multiply(X, Z)
% 0.22/0.65
% 0.22/0.65 Lemma 14: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, W)), multiply(Z, multiply(inverse(Y), Y)))))) = multiply(inverse(Y), W).
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, W)), multiply(Z, multiply(inverse(Y), Y))))))
% 0.22/0.65 = { by lemma 8 }
% 0.22/0.65 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(Y), W)), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.22/0.65 = { by lemma 5 }
% 0.22/0.65 multiply(inverse(Y), W)
% 0.22/0.65
% 0.22/0.65 Lemma 15: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(Y), Z).
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.22/0.65 = { by lemma 13 R->L }
% 0.22/0.65 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(W, Z)), multiply(W, multiply(inverse(Y), Y))))))
% 0.22/0.65 = { by lemma 14 }
% 0.22/0.65 multiply(inverse(Y), Z)
% 0.22/0.65
% 0.22/0.65 Lemma 16: inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Y), Y)))) = Y.
% 0.22/0.65 Proof:
% 0.22/0.65 inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Y), Y))))
% 0.22/0.65 = { by lemma 8 }
% 0.22/0.65 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.22/0.65 = { by lemma 10 }
% 0.22/0.65 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), Y)), multiply(inverse(multiply(Z, W)), Y))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.22/0.65 = { by lemma 2 }
% 0.22/0.65 multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), Y)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.22/0.65 = { by axiom 1 (single_axiom) }
% 0.22/0.65 Y
% 0.22/0.65
% 0.22/0.65 Lemma 17: inverse(multiply(inverse(X), multiply(inverse(X), X))) = X.
% 0.22/0.65 Proof:
% 0.22/0.65 inverse(multiply(inverse(X), multiply(inverse(X), X)))
% 0.22/0.65 = { by lemma 15 R->L }
% 0.22/0.65 inverse(multiply(inverse(multiply(Y, X)), multiply(Y, multiply(inverse(X), X))))
% 0.22/0.65 = { by lemma 16 }
% 0.22/0.65 X
% 0.22/0.65
% 0.22/0.65 Lemma 18: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.22/0.65 Proof:
% 0.22/0.65 inverse(multiply(inverse(X), X))
% 0.22/0.65 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.65 multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(inverse(X), X)))), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.22/0.65 = { by lemma 10 }
% 0.22/0.65 multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(inverse(multiply(V, multiply(inverse(Y), Y))), multiply(V, multiply(inverse(Y), Y)))))), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.22/0.65 = { by lemma 13 }
% 0.22/0.65 multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(inverse(Y), Y))), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.22/0.65 = { by axiom 1 (single_axiom) }
% 0.22/0.65 multiply(inverse(Y), Y)
% 0.22/0.65
% 0.22/0.65 Lemma 19: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(V, Z)), multiply(V, Z)))))) = W.
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(V, Z)), multiply(V, Z))))))
% 0.22/0.65 = { by lemma 8 }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(Y, Z)), multiply(Y, Z))))))
% 0.22/0.65 = { by axiom 1 (single_axiom) }
% 0.22/0.65 W
% 0.22/0.65
% 0.22/0.65 Lemma 20: multiply(multiply(inverse(X), X), Y) = Y.
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(multiply(inverse(X), X), Y)
% 0.22/0.65 = { by lemma 13 R->L }
% 0.22/0.65 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), Y)), multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(W), W)))))
% 0.22/0.65 = { by lemma 15 R->L }
% 0.22/0.65 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), Y)), multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(V, W)), multiply(V, W))))))
% 0.22/0.65 = { by lemma 14 R->L }
% 0.22/0.65 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), inverse(multiply(inverse(multiply(U, W)), multiply(U, multiply(inverse(Z), Z))))))), Y)), multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(V, W)), multiply(V, W))))))
% 0.22/0.65 = { by lemma 18 }
% 0.22/0.65 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(X), X), multiply(inverse(Z), inverse(multiply(inverse(multiply(U, W)), multiply(U, multiply(inverse(Z), Z))))))), Y)), multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(V, W)), multiply(V, W))))))
% 0.22/0.65 = { by lemma 13 }
% 0.22/0.65 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(X), X), multiply(inverse(Z), W))), Y)), multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(V, W)), multiply(V, W))))))
% 0.22/0.65 = { by lemma 19 }
% 0.22/0.65 Y
% 0.22/0.65
% 0.22/0.65 Lemma 21: multiply(X, multiply(inverse(X), X)) = X.
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(X, multiply(inverse(X), X))
% 0.22/0.65 = { by lemma 17 R->L }
% 0.22/0.65 multiply(X, multiply(inverse(X), inverse(multiply(inverse(X), multiply(inverse(X), X)))))
% 0.22/0.65 = { by lemma 15 R->L }
% 0.22/0.65 multiply(X, multiply(inverse(X), inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))))))
% 0.22/0.65 = { by lemma 15 R->L }
% 0.22/0.65 multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, X)), multiply(Y, multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 0.22/0.65 = { by lemma 17 R->L }
% 0.22/0.65 multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), inverse(multiply(inverse(multiply(Y, X)), multiply(Y, multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 0.22/0.65 = { by lemma 14 }
% 0.22/0.65 multiply(inverse(multiply(inverse(X), X)), X)
% 0.22/0.65 = { by lemma 18 }
% 0.22/0.65 multiply(multiply(inverse(Z), Z), X)
% 0.22/0.65 = { by lemma 20 }
% 0.22/0.65 X
% 0.22/0.65
% 0.22/0.65 Lemma 22: multiply(X, inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X)))) = Z.
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))))
% 0.22/0.65 = { by lemma 11 R->L }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(X), Z)), multiply(inverse(X), X))))
% 0.22/0.65 = { by lemma 15 R->L }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(X), Z)), multiply(inverse(multiply(W, X)), multiply(W, X)))))
% 0.22/0.65 = { by lemma 15 R->L }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(X), Z)), multiply(inverse(multiply(V, multiply(W, X))), multiply(V, multiply(W, X))))))
% 0.22/0.65 = { by lemma 12 R->L }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(X), Z)), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(W, X)), multiply(W, X))))))
% 0.22/0.65 = { by lemma 21 R->L }
% 0.22/0.65 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(inverse(X), X))), Z)), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(W, X)), multiply(W, X))))))
% 0.22/0.65 = { by lemma 19 }
% 0.22/0.65 Z
% 0.22/0.65
% 0.22/0.65 Lemma 23: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(inverse(X), multiply(X, Y))
% 0.22/0.65 = { by lemma 13 R->L }
% 0.22/0.65 multiply(inverse(X), multiply(X, inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(X), X))))))
% 0.22/0.65 = { by lemma 20 R->L }
% 0.22/0.65 multiply(inverse(X), multiply(X, inverse(multiply(inverse(multiply(Z, Y)), multiply(multiply(inverse(Z), Z), multiply(Z, multiply(inverse(X), X)))))))
% 0.22/0.65 = { by lemma 16 R->L }
% 0.22/0.65 multiply(inverse(X), multiply(X, inverse(multiply(inverse(multiply(Z, Y)), multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(inverse(multiply(W, Z)), multiply(W, multiply(inverse(Z), Z)))), multiply(inverse(X), X)))))))
% 0.22/0.65 = { by lemma 9 R->L }
% 0.22/0.65 multiply(inverse(X), multiply(X, inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(multiply(inverse(multiply(V, Z)), multiply(V, Z))), multiply(inverse(X), X)))))))
% 0.22/0.65 = { by lemma 10 R->L }
% 0.22/0.65 multiply(inverse(X), multiply(X, inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 0.22/0.65 = { by lemma 21 R->L }
% 0.22/0.65 multiply(inverse(multiply(X, multiply(inverse(X), X))), multiply(X, inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 0.22/0.65 = { by lemma 14 }
% 0.22/0.65 multiply(inverse(multiply(inverse(X), X)), Y)
% 0.22/0.65 = { by lemma 18 }
% 0.22/0.65 multiply(multiply(inverse(U), U), Y)
% 0.22/0.65 = { by lemma 20 }
% 0.22/0.65 Y
% 0.22/0.65
% 0.22/0.65 Lemma 24: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(inverse(X), X)
% 0.22/0.65 = { by lemma 22 R->L }
% 0.22/0.65 multiply(Y, inverse(multiply(inverse(multiply(X, multiply(inverse(X), X))), multiply(X, Y))))
% 0.22/0.65 = { by lemma 21 }
% 0.22/0.65 multiply(Y, inverse(multiply(inverse(X), multiply(X, Y))))
% 0.22/0.65 = { by lemma 23 }
% 0.22/0.65 multiply(Y, inverse(Y))
% 0.22/0.65
% 0.22/0.65 Lemma 25: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 0.22/0.65 Proof:
% 0.22/0.65 inverse(multiply(inverse(multiply(X, Y)), X))
% 0.22/0.65 = { by lemma 21 R->L }
% 0.22/0.65 inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(X), X))))
% 0.22/0.65 = { by lemma 23 R->L }
% 0.22/0.65 multiply(inverse(Z), multiply(Z, inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(X), X))))))
% 0.22/0.65 = { by lemma 13 }
% 0.22/0.65 multiply(inverse(Z), multiply(Z, Y))
% 0.22/0.65 = { by lemma 23 }
% 0.22/0.65 Y
% 0.22/0.65
% 0.22/0.65 Lemma 26: multiply(X, multiply(inverse(Y), Y)) = X.
% 0.22/0.65 Proof:
% 0.22/0.65 multiply(X, multiply(inverse(Y), Y))
% 0.22/0.65 = { by lemma 25 R->L }
% 0.22/0.65 multiply(inverse(multiply(inverse(multiply(Z, X)), Z)), multiply(inverse(Y), Y))
% 0.22/0.65 = { by lemma 11 }
% 0.22/0.65 multiply(inverse(multiply(W, Z)), multiply(W, multiply(Z, X)))
% 0.22/0.65 = { by lemma 15 }
% 0.22/0.65 multiply(inverse(Z), multiply(Z, X))
% 0.22/0.65 = { by lemma 23 }
% 0.22/0.65 X
% 0.22/0.65
% 0.22/0.65 Lemma 27: inverse(multiply(inverse(X), inverse(Y))) = multiply(Y, X).
% 0.22/0.65 Proof:
% 0.22/0.65 inverse(multiply(inverse(X), inverse(Y)))
% 0.22/0.65 = { by lemma 26 R->L }
% 0.22/0.65 inverse(multiply(inverse(X), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.22/0.65 = { by lemma 23 R->L }
% 0.22/0.65 multiply(inverse(Z), multiply(Z, inverse(multiply(inverse(X), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.22/0.65 = { by lemma 15 R->L }
% 0.22/0.65 multiply(inverse(multiply(inverse(multiply(Z, Y)), Z)), multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(multiply(inverse(X), multiply(inverse(Y), multiply(inverse(Y), Y)))))))
% 0.22/0.65 = { by lemma 25 }
% 0.22/0.65 multiply(Y, multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(multiply(inverse(X), multiply(inverse(Y), multiply(inverse(Y), Y)))))))
% 0.22/0.65 = { by lemma 5 }
% 0.22/0.65 multiply(Y, X)
% 0.22/0.65
% 0.22/0.65 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)).
% 0.22/0.65 Proof:
% 0.22/0.65 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.22/0.66 = { by lemma 20 }
% 0.22/0.66 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.22/0.66 = { by lemma 24 }
% 0.22/0.66 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 27 R->L }
% 0.22/0.66 tuple(a2, inverse(multiply(inverse(c3), inverse(multiply(a3, b3)))), multiply(X, inverse(X)))
% 0.22/0.66 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.66 tuple(a2, multiply(a3, inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), inverse(multiply(inverse(c3), inverse(multiply(a3, b3)))))), multiply(inverse(b3), multiply(inverse(b3), b3))))), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 25 R->L }
% 0.22/0.66 tuple(a2, multiply(a3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(c3, inverse(multiply(a3, b3)))), c3)), inverse(multiply(inverse(c3), inverse(multiply(a3, b3)))))), multiply(inverse(b3), multiply(inverse(b3), b3))))), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 21 R->L }
% 0.22/0.66 tuple(a2, multiply(a3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(c3, inverse(multiply(a3, b3)))), multiply(c3, multiply(inverse(c3), c3)))), inverse(multiply(inverse(c3), inverse(multiply(a3, b3)))))), multiply(inverse(b3), multiply(inverse(b3), b3))))), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 14 R->L }
% 0.22/0.66 tuple(a2, multiply(a3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(c3, inverse(multiply(a3, b3)))), multiply(c3, multiply(inverse(c3), c3)))), inverse(multiply(inverse(multiply(Y, c3)), multiply(Y, inverse(multiply(inverse(multiply(c3, inverse(multiply(a3, b3)))), multiply(c3, multiply(inverse(c3), c3))))))))), multiply(inverse(b3), multiply(inverse(b3), b3))))), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 22 }
% 0.22/0.66 tuple(a2, multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), multiply(inverse(b3), b3))))), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 26 }
% 0.22/0.66 tuple(a2, multiply(a3, inverse(multiply(inverse(c3), inverse(b3)))), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 27 }
% 0.22/0.66 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 0.22/0.66 = { by lemma 24 R->L }
% 0.22/0.66 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 0.22/0.66 % SZS output end Proof
% 0.22/0.66
% 0.22/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------