TSTP Solution File: GRP056-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP056-1 : 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 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP056-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 22:55:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.46 Command-line arguments: --no-flatten-goal
% 0.20/0.46
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46
% 0.20/0.54 % SZS output start Proof
% 0.20/0.54 Take the following subset of the input axioms:
% 0.20/0.54 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)))).
% 0.20/0.54 fof(single_axiom, axiom, ![Z, X, Y]: multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), Y)))), multiply(Z, inverse(Y)))), inverse(multiply(inverse(Y), Y)))=X).
% 0.20/0.54
% 0.20/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.54 fresh(y, y, x1...xn) = u
% 0.20/0.54 C => fresh(s, t, x1...xn) = v
% 0.20/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.54 variables of u and v.
% 0.20/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.54 input problem has no model of domain size 1).
% 0.20/0.54
% 0.20/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.54
% 0.20/0.54 Axiom 1 (single_axiom): multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Z)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z))) = Y.
% 0.20/0.54
% 0.20/0.54 Lemma 2: multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))) = multiply(inverse(multiply(W, inverse(multiply(inverse(Y), Z)))), multiply(W, inverse(Z))).
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.54 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), Z)))), multiply(W, inverse(Z)))), inverse(multiply(inverse(Z), Z)))))), multiply(X, inverse(inverse(multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.54 = { by axiom 1 (single_axiom) }
% 0.20/0.54 multiply(inverse(multiply(W, inverse(multiply(inverse(Y), Z)))), multiply(W, inverse(Z)))
% 0.20/0.54
% 0.20/0.54 Lemma 3: multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))
% 0.20/0.54 = { by lemma 2 R->L }
% 0.20/0.54 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.54 = { by axiom 1 (single_axiom) }
% 0.20/0.54 Y
% 0.20/0.54
% 0.20/0.54 Lemma 4: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z))) = Y.
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z)))
% 0.20/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.54 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z)))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.20/0.54 = { by lemma 3 }
% 0.20/0.54 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z)))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.20/0.54 = { by axiom 1 (single_axiom) }
% 0.20/0.54 Y
% 0.20/0.54
% 0.20/0.54 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(Z))) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z))).
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(Z)))
% 0.20/0.54 = { by lemma 4 R->L }
% 0.20/0.54 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.20/0.54 = { by lemma 3 R->L }
% 0.20/0.54 multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z)))
% 0.20/0.55
% 0.20/0.55 Lemma 6: multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W))) = multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(W))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W)))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W)))
% 0.20/0.55 = { by lemma 5 R->L }
% 0.20/0.55 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(W)))
% 0.20/0.55
% 0.20/0.55 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(Y), Y)
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(Y), W)))), multiply(U, inverse(W)))), inverse(multiply(inverse(W), W))))
% 0.20/0.55 = { by lemma 6 }
% 0.20/0.55 multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(multiply(inverse(W), W))))
% 0.20/0.55 = { by lemma 6 R->L }
% 0.20/0.55 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), W)))), multiply(Z, inverse(W)))), inverse(multiply(inverse(W), W))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(inverse(X), X)
% 0.20/0.55
% 0.20/0.55 Lemma 8: multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(W), W))) = Z.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(W), W)))
% 0.20/0.55 = { by lemma 7 }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))
% 0.20/0.55 = { by lemma 7 }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Z), Z)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 Z
% 0.20/0.55
% 0.20/0.55 Lemma 9: multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(X), Z)))), multiply(W, inverse(Z)))), inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.55 = { by lemma 6 }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.55 = { by lemma 8 }
% 0.20/0.55 multiply(inverse(Z), Z)
% 0.20/0.55
% 0.20/0.55 Lemma 10: multiply(inverse(multiply(inverse(X), X)), Y) = Y.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(multiply(inverse(X), X)), Y)
% 0.20/0.55 = { by lemma 9 R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(Y))), multiply(Z, inverse(Y)))), inverse(multiply(inverse(Y), Y)))), Y)
% 0.20/0.55 = { by lemma 8 R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(W), W)))), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(Y))), multiply(Z, inverse(Y)))), inverse(multiply(inverse(Y), Y)))), Y))))), inverse(multiply(inverse(V), V)))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(W), W)))), multiply(Z, inverse(Y)))), inverse(multiply(inverse(V), V)))
% 0.20/0.55 = { by lemma 8 }
% 0.20/0.55 Y
% 0.20/0.55
% 0.20/0.55 Lemma 11: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(inverse(X), X))
% 0.20/0.55 = { by lemma 10 R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(X), X)))
% 0.20/0.55 = { by lemma 9 }
% 0.20/0.55 multiply(inverse(Y), Y)
% 0.20/0.55
% 0.20/0.55 Lemma 12: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z))) = multiply(inverse(inverse(Y)), inverse(Z)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z)))
% 0.20/0.55 = { by lemma 5 }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(Y))), multiply(inverse(multiply(inverse(W), W)), inverse(Z)))
% 0.20/0.55 = { by lemma 10 }
% 0.20/0.55 multiply(inverse(inverse(Y)), multiply(inverse(multiply(inverse(W), W)), inverse(Z)))
% 0.20/0.55 = { by lemma 10 }
% 0.20/0.55 multiply(inverse(inverse(Y)), inverse(Z))
% 0.20/0.55
% 0.20/0.55 Lemma 13: multiply(inverse(inverse(X)), multiply(inverse(Y), Y)) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 0.20/0.55 = { by lemma 10 R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(X))), multiply(inverse(Y), Y))
% 0.20/0.55 = { by lemma 11 R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(X))), multiply(inverse(Y), Y))
% 0.20/0.55 = { by lemma 11 R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(X))), inverse(multiply(inverse(V), V)))
% 0.20/0.55 = { by lemma 12 R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(W), W)))), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))
% 0.20/0.55 = { by lemma 8 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 14: inverse(inverse(X)) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(inverse(X))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(inverse(X))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 10 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(X)))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 11 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(X)))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 12 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 8 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X)))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 13 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(T), T))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 11 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), inverse(multiply(inverse(U), U)))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 12 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X)))))), multiply(S, inverse(multiply(inverse(U), U))))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 13 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(U), U))))), multiply(S, inverse(multiply(inverse(U), U))))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 6 }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))), multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))), multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))))), inverse(X))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 11 }
% 0.20/0.56 multiply(inverse(multiply(inverse(multiply(inverse(Y2), Y2)), inverse(X))), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 multiply(inverse(inverse(X)), inverse(multiply(inverse(X), X)))
% 0.20/0.56 = { by lemma 7 R->L }
% 0.20/0.56 multiply(inverse(inverse(X)), inverse(multiply(inverse(Z2), Z2)))
% 0.20/0.56 = { by lemma 11 }
% 0.20/0.56 multiply(inverse(inverse(X)), multiply(inverse(W2), W2))
% 0.20/0.56 = { by lemma 13 }
% 0.20/0.56 X
% 0.20/0.56
% 0.20/0.56 Lemma 15: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(inverse(X), X)
% 0.20/0.56 = { by lemma 7 }
% 0.20/0.56 multiply(inverse(inverse(Y)), inverse(Y))
% 0.20/0.56 = { by lemma 14 }
% 0.20/0.56 multiply(Y, inverse(Y))
% 0.20/0.56
% 0.20/0.56 Lemma 16: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(X, multiply(Y, inverse(Y)))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 multiply(X, multiply(inverse(Z), Z))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(inverse(inverse(X)), multiply(inverse(Z), Z))
% 0.20/0.56 = { by lemma 13 }
% 0.20/0.56 X
% 0.20/0.56
% 0.20/0.56 Lemma 17: multiply(multiply(inverse(X), X), Y) = Y.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(inverse(X), X), Y)
% 0.20/0.56 = { by lemma 11 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(Z), Z)), Y)
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 Y
% 0.20/0.56
% 0.20/0.56 Lemma 18: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 0.20/0.56 Proof:
% 0.20/0.56 inverse(multiply(X, inverse(Y)))
% 0.20/0.56 = { by lemma 16 R->L }
% 0.20/0.56 multiply(inverse(multiply(X, inverse(Y))), multiply(Z, inverse(Z)))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(inverse(multiply(X, inverse(Y))), inverse(inverse(multiply(Z, inverse(Z)))))
% 0.20/0.56 = { by lemma 17 R->L }
% 0.20/0.56 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(inverse(W), W), inverse(multiply(Z, inverse(Z))))))
% 0.20/0.56 = { by lemma 15 }
% 0.20/0.56 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(V, inverse(V)), inverse(multiply(Z, inverse(Z))))))
% 0.20/0.56 = { by lemma 16 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(U, inverse(U)))), inverse(multiply(multiply(V, inverse(V)), inverse(multiply(Z, inverse(Z))))))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(U, inverse(U)))), inverse(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(U, inverse(U)))), inverse(multiply(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(inverse(multiply(multiply(X, inverse(Y)), inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(Y)))), inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.20/0.57 = { by lemma 12 R->L }
% 0.20/0.57 multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(X, inverse(Y))))), multiply(S, inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.20/0.57 = { by lemma 2 }
% 0.20/0.57 multiply(inverse(multiply(X2, inverse(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))), multiply(X2, inverse(multiply(X, inverse(inverse(multiply(inverse(T), T)))))))
% 0.20/0.57 = { by lemma 12 }
% 0.20/0.57 multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.20/0.57 = { by lemma 5 R->L }
% 0.20/0.57 multiply(multiply(inverse(multiply(Y2, inverse(Y))), multiply(Y2, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.20/0.57 = { by lemma 12 }
% 0.20/0.57 multiply(multiply(inverse(inverse(Y)), inverse(inverse(multiply(inverse(T), T)))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 multiply(multiply(Y, inverse(inverse(multiply(inverse(T), T)))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 multiply(multiply(Y, multiply(inverse(T), T)), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 multiply(multiply(Y, multiply(inverse(T), T)), inverse(multiply(X, multiply(inverse(T), T))))
% 0.20/0.57 = { by lemma 15 }
% 0.20/0.57 multiply(multiply(Y, multiply(Z2, inverse(Z2))), inverse(multiply(X, multiply(inverse(T), T))))
% 0.20/0.57 = { by lemma 15 }
% 0.20/0.57 multiply(multiply(Y, multiply(Z2, inverse(Z2))), inverse(multiply(X, multiply(W2, inverse(W2)))))
% 0.20/0.57 = { by lemma 16 }
% 0.20/0.57 multiply(Y, inverse(multiply(X, multiply(W2, inverse(W2)))))
% 0.20/0.57 = { by lemma 16 }
% 0.20/0.57 multiply(Y, inverse(X))
% 0.20/0.57
% 0.20/0.57 Lemma 19: multiply(inverse(X), inverse(Y)) = inverse(multiply(Y, X)).
% 0.20/0.57 Proof:
% 0.20/0.57 multiply(inverse(X), inverse(Y))
% 0.20/0.57 = { by lemma 18 R->L }
% 0.20/0.57 inverse(multiply(Y, inverse(inverse(X))))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 inverse(multiply(Y, X))
% 0.20/0.57
% 0.20/0.57 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)).
% 0.20/0.57 Proof:
% 0.20/0.57 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.20/0.57 = { by lemma 17 }
% 0.20/0.57 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.20/0.57 = { by lemma 15 }
% 0.20/0.57 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 tuple(a2, multiply(multiply(a3, inverse(inverse(b3))), c3), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 18 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), c3), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 16 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(c3, multiply(Y, inverse(Y)))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 15 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(c3, multiply(inverse(inverse(b3)), inverse(b3)))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(c3, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(inverse(c3)), inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 12 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(multiply(Z, inverse(c3))), multiply(Z, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3))))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 14 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(inverse(multiply(inverse(multiply(Z, inverse(c3))), multiply(Z, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3))))))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 17 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(multiply(inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))), inverse(multiply(inverse(inverse(b3)), inverse(b3)))), inverse(inverse(multiply(inverse(multiply(Z, inverse(c3))), multiply(Z, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))))))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 18 R->L }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(c3))), multiply(Z, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))), inverse(multiply(inverse(inverse(b3)), inverse(b3)))))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 2 }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(c3), inverse(b3))))), multiply(W, inverse(inverse(b3)))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 12 }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(multiply(inverse(inverse(multiply(inverse(c3), inverse(b3)))), inverse(inverse(b3))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 18 }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(b3), inverse(inverse(inverse(multiply(inverse(c3), inverse(b3))))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(b3), inverse(multiply(inverse(c3), inverse(b3))))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 12 }
% 0.20/0.57 tuple(a2, multiply(inverse(inverse(a3)), inverse(multiply(inverse(c3), inverse(b3)))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 19 }
% 0.20/0.57 tuple(a2, inverse(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 18 }
% 0.20/0.57 tuple(a2, multiply(a3, inverse(multiply(inverse(c3), inverse(b3)))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 19 R->L }
% 0.20/0.57 tuple(a2, multiply(a3, multiply(inverse(inverse(b3)), inverse(inverse(c3)))), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 tuple(a2, multiply(a3, multiply(inverse(inverse(b3)), c3)), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 14 }
% 0.20/0.57 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 0.20/0.57 = { by lemma 15 R->L }
% 0.20/0.57 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57
% 0.20/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------