TSTP Solution File: GRP057-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP057-1 : 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 01:16:48 EDT 2023
% Result : Unsatisfiable 0.20s 0.56s
% Output : Proof 1.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP057-1 : 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
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 00:29:31 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --no-flatten-goal
% 0.20/0.56
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56
% 1.69/0.63 % SZS output start Proof
% 1.69/0.63 Take the following subset of the input axioms:
% 1.69/0.63 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)))).
% 1.69/0.63 fof(single_axiom, axiom, ![X, Y, Z, U]: multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(inverse(X), Z))), U), inverse(multiply(Y, U)))))=Z).
% 1.69/0.63
% 1.69/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.69/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.69/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.69/0.63 fresh(y, y, x1...xn) = u
% 1.69/0.63 C => fresh(s, t, x1...xn) = v
% 1.69/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 1.69/0.63 variables of u and v.
% 1.69/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.69/0.63 input problem has no model of domain size 1).
% 1.69/0.63
% 1.69/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 1.69/0.63
% 1.69/0.63 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(inverse(X), Z))), W), inverse(multiply(Y, W))))) = Z.
% 1.69/0.63
% 1.69/0.63 Lemma 2: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W)))) = multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), Z)), U), inverse(multiply(V, U))))).
% 1.69/0.63 Proof:
% 1.69/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W))))
% 1.69/0.63 = { by axiom 1 (single_axiom) R->L }
% 1.69/0.63 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(Y), inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W))))))), U), inverse(multiply(V, U)))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), Z)), U), inverse(multiply(V, U)))))
% 1.69/0.63
% 1.69/0.63 Lemma 3: multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), W), inverse(multiply(Y, W)))))) = Z.
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), W), inverse(multiply(Y, W))))))
% 1.69/0.63 = { by lemma 2 R->L }
% 1.69/0.63 multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 Z
% 1.69/0.63
% 1.69/0.63 Lemma 4: multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(W, Z)))))) = multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U))))).
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(W, Z))))))
% 1.69/0.63 = { by lemma 3 R->L }
% 1.69/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U))))))), Z), inverse(multiply(W, Z))))))
% 1.69/0.63 = { by lemma 3 }
% 1.69/0.63 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U)))))
% 1.69/0.63
% 1.69/0.63 Lemma 5: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Z), W)), V), inverse(multiply(Z, V))))))) = multiply(inverse(inverse(Y)), W).
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Z), W)), V), inverse(multiply(Z, V)))))))
% 1.69/0.63 = { by lemma 2 R->L }
% 1.69/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(U), multiply(inverse(inverse(Y)), W))), T), inverse(multiply(U, T))))))
% 1.69/0.63 = { by lemma 4 }
% 1.69/0.63 multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), multiply(inverse(U), multiply(inverse(inverse(Y)), W)))), X2), inverse(multiply(S, X2)))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 multiply(inverse(inverse(Y)), W)
% 1.69/0.63
% 1.69/0.63 Lemma 6: multiply(inverse(inverse(X)), multiply(inverse(X), Y)) = multiply(inverse(Z), multiply(Z, Y)).
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(inverse(inverse(X)), multiply(inverse(X), Y))
% 1.69/0.63 = { by lemma 5 R->L }
% 1.69/0.63 multiply(inverse(Z), multiply(Z, multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), Y))), V), inverse(multiply(W, V)))))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 multiply(inverse(Z), multiply(Z, Y))
% 1.69/0.63
% 1.69/0.63 Lemma 7: multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(X), Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V)))).
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(X), Z)))))
% 1.69/0.63 = { by lemma 3 R->L }
% 1.69/0.63 multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)), multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))))), Z), inverse(multiply(inverse(X), Z)))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))
% 1.69/0.63
% 1.69/0.63 Lemma 8: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), multiply(Y, Z)))), W), inverse(multiply(X, W)))) = Z.
% 1.69/0.63 Proof:
% 1.69/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), multiply(Y, Z)))), W), inverse(multiply(X, W))))
% 1.69/0.63 = { by lemma 7 R->L }
% 1.69/0.63 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(Y, Z))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.63 = { by lemma 6 R->L }
% 1.69/0.63 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(inverse(V)), multiply(inverse(V), Z))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 Z
% 1.69/0.63
% 1.69/0.63 Lemma 9: multiply(inverse(Z), multiply(Z, Y)) = multiply(inverse(X), multiply(X, Y)).
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(inverse(Z), multiply(Z, Y))
% 1.69/0.63 = { by lemma 3 R->L }
% 1.69/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(Z), multiply(Z, Y)))), V), inverse(multiply(W, V))))))
% 1.69/0.63 = { by lemma 8 }
% 1.69/0.63 multiply(inverse(X), multiply(X, Y))
% 1.69/0.63
% 1.69/0.63 Lemma 10: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W)))) = multiply(inverse(V), multiply(V, inverse(multiply(multiply(inverse(Z), U), inverse(multiply(Y, U)))))).
% 1.69/0.63 Proof:
% 1.69/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W))))
% 1.69/0.63 = { by lemma 3 R->L }
% 1.69/0.63 multiply(inverse(V), multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W)))))), U), inverse(multiply(Y, U))))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 multiply(inverse(V), multiply(V, inverse(multiply(multiply(inverse(Z), U), inverse(multiply(Y, U))))))
% 1.69/0.63
% 1.69/0.63 Lemma 11: multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(Z), W), inverse(multiply(X, W))))))) = Z.
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(Z), W), inverse(multiply(X, W)))))))
% 1.69/0.63 = { by lemma 10 R->L }
% 1.69/0.63 multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 Z
% 1.69/0.63
% 1.69/0.63 Lemma 12: multiply(multiply(inverse(X), W), inverse(multiply(Z, W))) = multiply(multiply(inverse(X), Y), inverse(multiply(Z, Y))).
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(multiply(inverse(X), W), inverse(multiply(Z, W)))
% 1.69/0.63 = { by lemma 3 R->L }
% 1.69/0.63 multiply(multiply(inverse(multiply(inverse(T2), multiply(T2, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), W), inverse(multiply(Z, W)))
% 1.69/0.63 = { by lemma 9 }
% 1.69/0.63 multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), W), inverse(multiply(Z, W)))
% 1.69/0.63 = { by lemma 11 R->L }
% 1.69/0.63 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), W), inverse(multiply(Z, W)))), X2), inverse(multiply(T, X2)))))))
% 1.69/0.63 = { by axiom 1 (single_axiom) R->L }
% 1.69/0.63 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(Y2)), inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(inverse(inverse(inverse(Y2))), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U)))))))), W2), inverse(multiply(Z2, W2))))))), W), inverse(multiply(Z, W)))), X2), inverse(multiply(T, X2)))))))
% 1.69/0.63 = { by lemma 2 }
% 1.69/0.63 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(V2), inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(inverse(inverse(inverse(Y2))), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U)))))))), W2), inverse(multiply(Z2, W2)))))), U2), inverse(multiply(V2, U2))))), X2), inverse(multiply(T, X2)))))))
% 1.69/0.63 = { by lemma 2 R->L }
% 1.69/0.63 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(Y2)), inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(inverse(inverse(inverse(Y2))), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U)))))))), W2), inverse(multiply(Z2, W2))))))), Y), inverse(multiply(Z, Y)))), X2), inverse(multiply(T, X2)))))))
% 1.69/0.63 = { by axiom 1 (single_axiom) }
% 1.69/0.63 multiply(inverse(T), multiply(inverse(S), multiply(S, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), Y), inverse(multiply(Z, Y)))), X2), inverse(multiply(T, X2)))))))
% 1.69/0.63 = { by lemma 11 }
% 1.69/0.63 multiply(multiply(inverse(multiply(inverse(Z), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(V), X)), U), inverse(multiply(V, U))))))), Y), inverse(multiply(Z, Y)))
% 1.69/0.63 = { by lemma 3 }
% 1.69/0.63 multiply(multiply(inverse(X), Y), inverse(multiply(Z, Y)))
% 1.69/0.63
% 1.69/0.63 Lemma 13: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 1.69/0.63 Proof:
% 1.69/0.63 multiply(Y, inverse(Y))
% 1.69/0.63 = { by axiom 1 (single_axiom) R->L }
% 1.69/0.63 multiply(multiply(S, inverse(multiply(multiply(inverse(multiply(inverse(Y2), multiply(inverse(S), Y))), Z2), inverse(multiply(Y2, Z2))))), inverse(Y))
% 1.69/0.64 = { by lemma 4 R->L }
% 1.69/0.64 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2)))))), inverse(Y))
% 1.69/0.64 = { by lemma 3 R->L }
% 1.69/0.64 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2)))))), inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2))))))))
% 1.69/0.64 = { by lemma 12 R->L }
% 1.69/0.64 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T)))))), inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T))))))))
% 1.69/0.64 = { by lemma 3 }
% 1.69/0.64 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T)))))), inverse(X))
% 1.69/0.64 = { by lemma 4 }
% 1.69/0.64 multiply(multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(Z), X))), V), inverse(multiply(W, V))))), inverse(X))
% 1.69/0.64 = { by axiom 1 (single_axiom) }
% 1.69/0.64 multiply(X, inverse(X))
% 1.69/0.64
% 1.69/0.64 Lemma 14: multiply(inverse(Z), multiply(Z, inverse(X))) = multiply(inverse(X), multiply(Y, inverse(Y))).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(Z), multiply(Z, inverse(X)))
% 1.69/0.64 = { by lemma 9 }
% 1.69/0.64 multiply(inverse(X), multiply(X, inverse(X)))
% 1.69/0.64 = { by lemma 13 R->L }
% 1.69/0.64 multiply(inverse(X), multiply(Y, inverse(Y)))
% 1.69/0.64
% 1.69/0.64 Lemma 15: multiply(inverse(X), multiply(X, Y)) = multiply(Y, multiply(Z, inverse(Z))).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(X), multiply(X, Y))
% 1.69/0.64 = { by axiom 1 (single_axiom) R->L }
% 1.69/0.64 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(W), multiply(inverse(X), multiply(X, Y))))), U), inverse(multiply(V, U)))))
% 1.69/0.64 = { by lemma 4 R->L }
% 1.69/0.64 multiply(inverse(T), multiply(T, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), S), inverse(multiply(W, S))))))
% 1.69/0.64 = { by lemma 14 }
% 1.69/0.64 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), S), inverse(multiply(W, S)))), multiply(Z, inverse(Z)))
% 1.69/0.64 = { by lemma 8 }
% 1.69/0.64 multiply(Y, multiply(Z, inverse(Z)))
% 1.69/0.64
% 1.69/0.64 Lemma 16: inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))) = multiply(Y, inverse(multiply(W, inverse(W)))).
% 1.69/0.64 Proof:
% 1.69/0.64 inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))))
% 1.69/0.64 = { by lemma 7 R->L }
% 1.69/0.64 multiply(Y, inverse(multiply(multiply(inverse(Y), V), inverse(multiply(inverse(Y), V)))))
% 1.69/0.64 = { by lemma 13 R->L }
% 1.69/0.64 multiply(Y, inverse(multiply(W, inverse(W))))
% 1.69/0.64
% 1.69/0.64 Lemma 17: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z)))))) = Y.
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z))))))
% 1.69/0.64 = { by lemma 15 }
% 1.69/0.64 multiply(multiply(Y, inverse(multiply(Z, inverse(Z)))), multiply(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))), inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))))
% 1.69/0.64 = { by lemma 16 R->L }
% 1.69/0.64 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V)))), multiply(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))), inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))))
% 1.69/0.64 = { by lemma 4 }
% 1.69/0.64 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(U), multiply(inverse(W), Y))), T), inverse(multiply(U, T)))))
% 1.69/0.64 = { by axiom 1 (single_axiom) }
% 1.69/0.64 Y
% 1.69/0.64
% 1.69/0.64 Lemma 18: multiply(inverse(X), multiply(X, multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(X), multiply(X, multiply(Y, inverse(Y))))
% 1.69/0.64 = { by lemma 13 }
% 1.69/0.64 multiply(inverse(X), multiply(X, multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z))))))
% 1.69/0.64 = { by lemma 17 }
% 1.69/0.64 multiply(Z, inverse(Z))
% 1.69/0.64
% 1.69/0.64 Lemma 19: multiply(inverse(X), multiply(X, inverse(multiply(Y, inverse(Y))))) = multiply(Z, inverse(Z)).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(X), multiply(X, inverse(multiply(Y, inverse(Y)))))
% 1.69/0.64 = { by lemma 14 }
% 1.69/0.64 multiply(inverse(multiply(Y, inverse(Y))), multiply(W, inverse(W)))
% 1.69/0.64 = { by lemma 18 R->L }
% 1.69/0.64 multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(V), multiply(V, multiply(Y, inverse(Y)))))
% 1.69/0.64 = { by lemma 15 }
% 1.69/0.64 multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(Y, inverse(Y)), multiply(U, inverse(U))))
% 1.69/0.64 = { by lemma 18 }
% 1.69/0.64 multiply(Z, inverse(Z))
% 1.69/0.64
% 1.69/0.64 Lemma 20: multiply(inverse(X), multiply(X, inverse(inverse(Y)))) = Y.
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(X), multiply(X, inverse(inverse(Y))))
% 1.69/0.64 = { by lemma 14 }
% 1.69/0.64 multiply(inverse(inverse(Y)), multiply(Z, inverse(Z)))
% 1.69/0.64 = { by lemma 19 R->L }
% 1.69/0.64 multiply(inverse(inverse(Y)), multiply(inverse(W), multiply(W, inverse(multiply(V, inverse(V))))))
% 1.69/0.64 = { by lemma 5 R->L }
% 1.69/0.64 multiply(inverse(U), multiply(U, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(W), multiply(W, inverse(multiply(V, inverse(V))))))), S), inverse(multiply(T, S)))))))
% 1.69/0.64 = { by lemma 8 }
% 1.69/0.64 multiply(inverse(U), multiply(U, multiply(Y, inverse(multiply(V, inverse(V))))))
% 1.69/0.64 = { by lemma 17 }
% 1.69/0.64 Y
% 1.69/0.64
% 1.69/0.64 Lemma 21: multiply(inverse(inverse(inverse(X))), X) = multiply(Y, inverse(Y)).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(inverse(inverse(X))), X)
% 1.69/0.64 = { by lemma 20 R->L }
% 1.69/0.64 multiply(inverse(inverse(inverse(X))), multiply(inverse(inverse(X)), multiply(inverse(X), inverse(inverse(X)))))
% 1.69/0.64 = { by lemma 18 }
% 1.69/0.64 multiply(Y, inverse(Y))
% 1.69/0.64
% 1.69/0.64 Lemma 22: multiply(inverse(X), multiply(X, Y)) = inverse(inverse(Y)).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(X), multiply(X, Y))
% 1.69/0.64 = { by lemma 6 R->L }
% 1.69/0.64 multiply(inverse(inverse(inverse(inverse(Y)))), multiply(inverse(inverse(inverse(Y))), Y))
% 1.69/0.64 = { by lemma 21 }
% 1.69/0.64 multiply(inverse(inverse(inverse(inverse(Y)))), multiply(inverse(inverse(inverse(Y))), inverse(inverse(inverse(inverse(Y))))))
% 1.69/0.64 = { by lemma 20 }
% 1.69/0.64 inverse(inverse(Y))
% 1.69/0.64
% 1.69/0.64 Lemma 23: inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))) = inverse(inverse(Y)).
% 1.69/0.64 Proof:
% 1.69/0.64 inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))))
% 1.69/0.64 = { by lemma 20 R->L }
% 1.69/0.64 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(W), multiply(W, inverse(inverse(Y)))))), Z), inverse(multiply(X, Z))))
% 1.69/0.64 = { by lemma 8 }
% 1.69/0.64 inverse(inverse(Y))
% 1.69/0.64
% 1.69/0.64 Lemma 24: inverse(inverse(inverse(inverse(X)))) = X.
% 1.69/0.64 Proof:
% 1.69/0.64 inverse(inverse(inverse(inverse(X))))
% 1.69/0.64 = { by lemma 23 R->L }
% 1.69/0.64 inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))
% 1.69/0.64 = { by lemma 20 R->L }
% 1.69/0.64 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z)))))))), multiply(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))), inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))))))
% 1.69/0.64 = { by lemma 21 R->L }
% 1.69/0.64 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z)))))))), multiply(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))), inverse(multiply(multiply(inverse(multiply(inverse(Y), X)), Z), inverse(multiply(Y, Z))))))
% 1.69/0.64 = { by lemma 3 }
% 1.69/0.64 X
% 1.69/0.64
% 1.69/0.64 Lemma 25: multiply(multiply(X, W), inverse(multiply(Z, W))) = multiply(multiply(X, Y), inverse(multiply(Z, Y))).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(multiply(X, W), inverse(multiply(Z, W)))
% 1.69/0.64 = { by lemma 8 R->L }
% 1.69/0.64 multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), W), inverse(multiply(Z, W)))
% 1.69/0.64 = { by lemma 12 }
% 1.69/0.64 multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), Y), inverse(multiply(Z, Y)))
% 1.69/0.64 = { by lemma 8 }
% 1.69/0.64 multiply(multiply(X, Y), inverse(multiply(Z, Y)))
% 1.69/0.64
% 1.69/0.64 Lemma 26: multiply(X, multiply(multiply(inverse(X), Y), inverse(multiply(Z, inverse(Z))))) = Y.
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(X, multiply(multiply(inverse(X), Y), inverse(multiply(Z, inverse(Z)))))
% 1.69/0.64 = { by lemma 16 R->L }
% 1.69/0.64 multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), Y))), V), inverse(multiply(W, V)))))
% 1.69/0.64 = { by lemma 4 R->L }
% 1.69/0.64 multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), T), inverse(multiply(X, T))))))
% 1.69/0.64 = { by lemma 16 }
% 1.69/0.64 multiply(inverse(U), multiply(U, multiply(Y, inverse(multiply(S, inverse(S))))))
% 1.69/0.64 = { by lemma 17 }
% 1.69/0.64 Y
% 1.69/0.64
% 1.69/0.64 Lemma 27: multiply(inverse(multiply(X, Y)), X) = inverse(inverse(inverse(Y))).
% 1.69/0.64 Proof:
% 1.69/0.64 multiply(inverse(multiply(X, Y)), X)
% 1.69/0.64 = { by lemma 24 R->L }
% 1.69/0.64 inverse(inverse(inverse(inverse(multiply(inverse(multiply(X, Y)), X)))))
% 1.69/0.64 = { by lemma 23 R->L }
% 1.69/0.64 inverse(multiply(multiply(inverse(multiply(inverse(Z), inverse(inverse(multiply(inverse(multiply(X, Y)), X))))), W), inverse(multiply(Z, W))))
% 1.69/0.64 = { by lemma 7 R->L }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(X, Y)), X)))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 23 R->L }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(multiply(X, Y)), X))), S), inverse(multiply(T, S))))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 24 R->L }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(inverse(inverse(inverse(inverse(multiply(X, Y)))))), X))), S), inverse(multiply(T, S))))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 2 }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(X, Y)))), inverse(multiply(multiply(inverse(multiply(inverse(X2), X)), Y2), inverse(multiply(X2, Y2)))))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 23 }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(multiply(X, Y)))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 22 R->L }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), Y), inverse(multiply(X, Y)))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 25 R->L }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(inverse(X)))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 26 R->L }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Y)), multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X))))), inverse(multiply(Z2, multiply(multiply(inverse(Z2), inverse(X)), inverse(multiply(X, inverse(X)))))))), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 23 }
% 1.69/0.64 multiply(V, inverse(multiply(multiply(inverse(inverse(Y)), U), inverse(multiply(inverse(V), U)))))
% 1.69/0.64 = { by lemma 7 }
% 1.69/0.65 inverse(multiply(multiply(inverse(multiply(inverse(W2), inverse(Y))), V2), inverse(multiply(W2, V2))))
% 1.69/0.65 = { by lemma 23 }
% 1.69/0.65 inverse(inverse(inverse(Y)))
% 1.69/0.65
% 1.69/0.65 Lemma 28: inverse(inverse(X)) = X.
% 1.69/0.65 Proof:
% 1.69/0.65 inverse(inverse(X))
% 1.69/0.65 = { by lemma 22 R->L }
% 1.69/0.65 multiply(inverse(Y), multiply(Y, X))
% 1.69/0.65 = { by axiom 1 (single_axiom) R->L }
% 1.69/0.65 multiply(inverse(multiply(multiply(Y, X), inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(multiply(Y, X)), Y))), W), inverse(multiply(Z, W)))))), multiply(Y, X))
% 1.69/0.65 = { by lemma 27 }
% 1.69/0.65 multiply(inverse(multiply(multiply(Y, X), inverse(multiply(multiply(inverse(multiply(inverse(Z), inverse(inverse(inverse(X))))), W), inverse(multiply(Z, W)))))), multiply(Y, X))
% 1.69/0.65 = { by lemma 23 }
% 1.69/0.65 multiply(inverse(multiply(multiply(Y, X), inverse(inverse(inverse(inverse(inverse(X))))))), multiply(Y, X))
% 1.69/0.65 = { by lemma 24 }
% 1.69/0.65 multiply(inverse(multiply(multiply(Y, X), inverse(X))), multiply(Y, X))
% 1.69/0.65 = { by lemma 27 }
% 1.69/0.65 inverse(inverse(inverse(inverse(X))))
% 1.69/0.65 = { by lemma 24 }
% 1.69/0.65 X
% 1.69/0.65
% 1.69/0.65 Lemma 29: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 1.69/0.65 Proof:
% 1.69/0.65 multiply(inverse(X), X)
% 1.69/0.65 = { by lemma 28 R->L }
% 1.69/0.65 multiply(inverse(X), inverse(inverse(X)))
% 1.69/0.65 = { by lemma 13 R->L }
% 1.69/0.65 multiply(Y, inverse(Y))
% 1.69/0.65
% 1.69/0.65 Lemma 30: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 1.69/0.65 Proof:
% 1.69/0.65 inverse(multiply(inverse(X), Y))
% 1.69/0.65 = { by lemma 28 R->L }
% 1.69/0.65 inverse(inverse(inverse(multiply(inverse(X), Y))))
% 1.69/0.65 = { by lemma 23 R->L }
% 1.69/0.65 inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(X), Y))), W), inverse(multiply(Z, W)))))
% 1.69/0.65 = { by lemma 16 }
% 1.69/0.65 inverse(multiply(multiply(inverse(X), Y), inverse(multiply(V, inverse(V)))))
% 1.69/0.65 = { by lemma 28 R->L }
% 1.69/0.65 inverse(inverse(inverse(multiply(multiply(inverse(X), Y), inverse(multiply(V, inverse(V)))))))
% 1.69/0.65 = { by lemma 27 R->L }
% 1.69/0.65 multiply(inverse(multiply(X, multiply(multiply(inverse(X), Y), inverse(multiply(V, inverse(V)))))), X)
% 1.69/0.65 = { by lemma 26 }
% 1.69/0.65 multiply(inverse(Y), X)
% 1.69/0.65
% 1.69/0.65 Lemma 31: multiply(multiply(X, inverse(X)), Y) = Y.
% 1.69/0.65 Proof:
% 1.69/0.65 multiply(multiply(X, inverse(X)), Y)
% 1.69/0.65 = { by lemma 13 }
% 1.69/0.65 multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), Y)
% 1.69/0.65 = { by lemma 16 R->L }
% 1.69/0.65 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(Z, inverse(Z)))), V), inverse(multiply(W, V)))), Y)
% 1.69/0.65 = { by lemma 19 R->L }
% 1.69/0.65 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(U), multiply(U, inverse(multiply(Y, inverse(Y))))))), V), inverse(multiply(W, V)))), Y)
% 1.69/0.65 = { by lemma 8 }
% 1.69/0.65 multiply(inverse(multiply(Y, inverse(Y))), Y)
% 1.69/0.65 = { by lemma 27 }
% 1.69/0.65 inverse(inverse(inverse(inverse(Y))))
% 1.69/0.65 = { by lemma 24 }
% 1.69/0.65 Y
% 1.69/0.65
% 1.69/0.65 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)).
% 1.69/0.65 Proof:
% 1.69/0.65 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.69/0.65 = { by lemma 29 }
% 1.69/0.65 tuple(multiply(multiply(X, inverse(X)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.69/0.65 = { by lemma 31 }
% 1.69/0.65 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.69/0.65 = { by lemma 29 }
% 1.69/0.65 tuple(a2, multiply(multiply(a3, b3), c3), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by axiom 1 (single_axiom) R->L }
% 1.69/0.65 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(b3)), c3))), W), inverse(multiply(Z, W)))))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 30 R->L }
% 1.69/0.65 tuple(a2, multiply(multiply(a3, b3), inverse(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(b3)), c3))), W), inverse(multiply(Z, W))))), b3))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 25 }
% 1.69/0.65 tuple(a2, multiply(multiply(a3, inverse(a3)), inverse(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(b3)), c3))), W), inverse(multiply(Z, W))))), inverse(a3)))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 30 }
% 1.69/0.65 tuple(a2, multiply(multiply(a3, inverse(a3)), multiply(inverse(inverse(a3)), inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(b3)), c3))), W), inverse(multiply(Z, W)))))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 31 }
% 1.69/0.65 tuple(a2, multiply(inverse(inverse(a3)), inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(b3)), c3))), W), inverse(multiply(Z, W))))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 28 }
% 1.69/0.65 tuple(a2, multiply(a3, inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(inverse(b3)), c3))), W), inverse(multiply(Z, W))))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 10 }
% 1.69/0.65 tuple(a2, multiply(a3, multiply(inverse(V), multiply(V, inverse(multiply(multiply(inverse(c3), U), inverse(multiply(b3, U))))))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 4 }
% 1.69/0.65 tuple(a2, multiply(a3, multiply(b3, inverse(multiply(multiply(inverse(multiply(inverse(T), c3)), S), inverse(multiply(T, S)))))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 23 }
% 1.69/0.65 tuple(a2, multiply(a3, multiply(b3, inverse(inverse(c3)))), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 28 }
% 1.69/0.65 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(Y, inverse(Y)))
% 1.69/0.65 = { by lemma 29 R->L }
% 1.69/0.65 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 1.69/0.65 % SZS output end Proof
% 1.69/0.65
% 1.69/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------