TSTP Solution File: GRP051-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP051-1 : 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 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP051-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 22:28:38 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.49 Command-line arguments: --no-flatten-goal
% 0.21/0.49
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49
% 0.21/0.55 % SZS output start Proof
% 0.21/0.55 Take the following subset of the input axioms:
% 0.21/0.55 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)))).
% 0.21/0.55 fof(single_axiom, axiom, ![Z, X, Y]: multiply(multiply(inverse(multiply(Z, inverse(multiply(X, Y)))), multiply(Z, inverse(Y))), inverse(multiply(inverse(Y), Y)))=X).
% 0.21/0.55
% 0.21/0.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.55 fresh(y, y, x1...xn) = u
% 0.21/0.55 C => fresh(s, t, x1...xn) = v
% 0.21/0.55 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.55 variables of u and v.
% 0.21/0.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.55 input problem has no model of domain size 1).
% 0.21/0.55
% 0.21/0.55 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.55
% 0.21/0.55 Axiom 1 (single_axiom): multiply(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))) = Y.
% 0.21/0.55
% 0.21/0.55 Lemma 2: multiply(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(Y, Z)))), multiply(W, inverse(Z))).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(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)))))
% 0.21/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.55 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(W, inverse(multiply(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)))))
% 0.21/0.55 = { by axiom 1 (single_axiom) }
% 0.21/0.55 multiply(inverse(multiply(W, inverse(multiply(Y, Z)))), multiply(W, inverse(Z)))
% 0.21/0.55
% 0.21/0.55 Lemma 3: multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))
% 0.21/0.55 = { by lemma 2 R->L }
% 0.21/0.55 multiply(multiply(inverse(multiply(W, inverse(multiply(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)))))
% 0.21/0.55 = { by axiom 1 (single_axiom) }
% 0.21/0.55 Y
% 0.21/0.55
% 0.21/0.55 Lemma 4: inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))) = Y.
% 0.21/0.55 Proof:
% 0.21/0.55 inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))
% 0.21/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.55 multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(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)))))
% 0.21/0.55 = { by lemma 3 }
% 0.21/0.55 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.21/0.55 = { by axiom 1 (single_axiom) }
% 0.21/0.56 Y
% 0.21/0.56
% 0.21/0.56 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z)) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)).
% 0.21/0.56 Proof:
% 0.21/0.56 multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z))
% 0.21/0.56 = { by lemma 4 R->L }
% 0.21/0.56 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.21/0.56 = { by lemma 3 R->L }
% 0.21/0.56 multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.21/0.56 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.56 multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.21/0.56 = { by axiom 1 (single_axiom) }
% 0.21/0.56 multiply(multiply(inverse(multiply(T, inverse(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.21/0.56 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.56 multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.21/0.56 = { by axiom 1 (single_axiom) }
% 0.21/0.56 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.21/0.56 = { by lemma 3 }
% 0.21/0.56 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.21/0.56 = { by lemma 4 }
% 0.21/0.56 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 0.21/0.56
% 0.21/0.56 Lemma 6: multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W)) = multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W)).
% 0.21/0.56 Proof:
% 0.21/0.56 multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.21/0.56 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.56 multiply(inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z)))), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.21/0.56 = { by lemma 5 R->L }
% 0.21/0.56 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W))
% 0.21/0.56
% 0.21/0.56 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.21/0.56 Proof:
% 0.21/0.56 multiply(inverse(Y), Y)
% 0.21/0.56 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.56 multiply(inverse(Y), multiply(multiply(inverse(multiply(U, inverse(multiply(Y, W)))), multiply(U, inverse(W))), inverse(multiply(inverse(W), W))))
% 0.21/0.56 = { by lemma 6 }
% 0.21/0.56 multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(multiply(inverse(W), W))))
% 0.21/0.56 = { by lemma 6 R->L }
% 0.21/0.56 multiply(inverse(X), multiply(multiply(inverse(multiply(Z, inverse(multiply(X, W)))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W))))
% 0.21/0.56 = { by axiom 1 (single_axiom) }
% 0.21/0.56 multiply(inverse(X), X)
% 0.21/0.56
% 0.21/0.56 Lemma 8: multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(W), W))) = inverse(Z).
% 0.21/0.56 Proof:
% 0.21/0.56 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(W), W)))
% 0.21/0.56 = { by lemma 7 }
% 0.21/0.56 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 0.21/0.56 = { by lemma 7 }
% 0.21/0.56 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Z), Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 0.21/0.56 = { by axiom 1 (single_axiom) }
% 0.21/0.56 inverse(Z)
% 0.21/0.56
% 0.21/0.56 Lemma 9: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.21/0.56 Proof:
% 0.21/0.56 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.21/0.56 = { by lemma 7 }
% 0.21/0.56 multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(Z), Z)))), multiply(W, inverse(multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), Y)))
% 0.21/0.56 = { by lemma 8 }
% 0.21/0.56 inverse(multiply(inverse(Z), Z))
% 0.21/0.56
% 0.21/0.56 Lemma 10: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)) = multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z)).
% 0.21/0.56 Proof:
% 0.21/0.56 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z))
% 0.21/0.56 = { by lemma 7 }
% 0.21/0.56 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(inverse(U), U))), inverse(multiply(inverse(U), U)))))), multiply(X, Z))
% 0.21/0.56 = { by lemma 6 R->L }
% 0.21/0.56 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(U), U)))))), multiply(T, inverse(inverse(multiply(inverse(U), U))))), Z))
% 0.21/0.56 = { by lemma 9 }
% 0.21/0.56 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(T, inverse(inverse(multiply(inverse(U), U))))), multiply(T, inverse(inverse(multiply(inverse(U), U))))), Z))
% 0.21/0.56 = { by lemma 7 R->L }
% 0.21/0.56 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z))
% 0.21/0.56
% 0.21/0.56 Lemma 11: multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)), inverse(multiply(inverse(W), W))) = Z.
% 0.21/0.56 Proof:
% 0.21/0.56 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)), inverse(multiply(inverse(W), W)))
% 0.21/0.56 = { by lemma 4 R->L }
% 0.21/0.56 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(W), W)))
% 0.21/0.56 = { by lemma 8 }
% 0.21/0.56 inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))
% 0.21/0.56 = { by lemma 4 }
% 0.21/0.56 Z
% 0.21/0.57
% 0.21/0.57 Lemma 12: multiply(multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(Y), Y), Z)), inverse(multiply(inverse(W), W))) = Z.
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(Y), Y), Z)), inverse(multiply(inverse(W), W)))
% 0.21/0.57 = { by lemma 10 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(V, inverse(multiply(inverse(U), U)))), multiply(V, Z)), inverse(multiply(inverse(W), W)))
% 0.21/0.57 = { by lemma 11 }
% 0.21/0.57 Z
% 0.21/0.57
% 0.21/0.57 Lemma 13: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.21/0.57 = { by lemma 7 }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.21/0.57 = { by lemma 7 }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(V), V)))), multiply(W, inverse(multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.21/0.57 = { by lemma 10 }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(multiply(inverse(U), U), inverse(multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.21/0.57 = { by lemma 9 }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(T), T)))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.21/0.57 = { by lemma 10 }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(S), S)), multiply(multiply(inverse(X2), X2), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.21/0.57 = { by lemma 12 }
% 0.21/0.57 multiply(inverse(Z), Z)
% 0.21/0.57
% 0.21/0.57 Lemma 14: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.21/0.57 Proof:
% 0.21/0.57 inverse(multiply(inverse(X), X))
% 0.21/0.57 = { by lemma 9 R->L }
% 0.21/0.57 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W)))
% 0.21/0.57 = { by lemma 13 }
% 0.21/0.57 multiply(inverse(Y), Y)
% 0.21/0.57
% 0.21/0.57 Lemma 15: multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W)))) = Z.
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W))))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, inverse(multiply(inverse(V), V)))))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(inverse(multiply(inverse(U), U)), multiply(multiply(inverse(Y), Y), multiply(Z, inverse(multiply(inverse(V), V)))))
% 0.21/0.57 = { by lemma 10 R->L }
% 0.21/0.57 multiply(inverse(multiply(T, inverse(multiply(inverse(S), S)))), multiply(T, multiply(Z, inverse(multiply(inverse(V), V)))))
% 0.21/0.57 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(X2, inverse(multiply(multiply(inverse(multiply(T, inverse(multiply(inverse(S), S)))), multiply(T, multiply(Z, inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(V), V)))))), multiply(X2, inverse(inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))
% 0.21/0.57 = { by lemma 11 }
% 0.21/0.57 multiply(multiply(inverse(multiply(X2, inverse(multiply(Z, inverse(multiply(inverse(V), V)))))), multiply(X2, inverse(inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))
% 0.21/0.57 = { by lemma 2 }
% 0.21/0.57 multiply(inverse(multiply(Y2, inverse(multiply(multiply(Z, inverse(multiply(inverse(V), V))), V)))), multiply(Y2, inverse(V)))
% 0.21/0.57 = { by lemma 3 }
% 0.21/0.57 Z
% 0.21/0.57
% 0.21/0.57 Lemma 16: inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W)))) = inverse(multiply(X, inverse(W))).
% 0.21/0.57 Proof:
% 0.21/0.57 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W))))
% 0.21/0.57 = { by lemma 7 }
% 0.21/0.57 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(W), W))), W))))
% 0.21/0.57 = { by lemma 7 }
% 0.21/0.57 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(W))), multiply(X, inverse(W))), inverse(multiply(inverse(W), W))), W))))
% 0.21/0.57 = { by lemma 4 }
% 0.21/0.57 inverse(multiply(X, inverse(W)))
% 0.21/0.57
% 0.21/0.57 Lemma 17: inverse(multiply(X, inverse(multiply(multiply(inverse(Y), Y), Z)))) = inverse(multiply(X, inverse(Z))).
% 0.21/0.57 Proof:
% 0.21/0.57 inverse(multiply(X, inverse(multiply(multiply(inverse(Y), Y), Z))))
% 0.21/0.57 = { by lemma 13 R->L }
% 0.21/0.57 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))))
% 0.21/0.57 = { by lemma 16 }
% 0.21/0.57 inverse(multiply(X, inverse(Z)))
% 0.21/0.57
% 0.21/0.57 Lemma 18: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.21/0.57 = { by lemma 4 R->L }
% 0.21/0.57 multiply(inverse(multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Y, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), multiply(W, Z))
% 0.21/0.57 = { by lemma 5 }
% 0.21/0.57 multiply(inverse(multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Y, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), multiply(X, Z))
% 0.21/0.57 = { by lemma 4 }
% 0.21/0.57 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.21/0.57
% 0.21/0.57 Lemma 19: multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), multiply(inverse(W), W)) = Y.
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, multiply(inverse(U), U)))))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, inverse(multiply(inverse(T), T))))))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, inverse(inverse(multiply(inverse(S), S)))))))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(X2), X2)))), multiply(V, inverse(inverse(multiply(inverse(S), S)))))))
% 0.21/0.57 = { by lemma 10 }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(Y2), Y2)), multiply(multiply(inverse(Z2), Z2), inverse(inverse(multiply(inverse(S), S)))))))
% 0.21/0.57 = { by lemma 14 }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(multiply(inverse(Z2), Z2), inverse(inverse(multiply(inverse(S), S)))))))
% 0.21/0.57 = { by lemma 14 }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(multiply(inverse(Z2), Z2), inverse(multiply(inverse(V2), V2))))))
% 0.21/0.57 = { by lemma 13 }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 15 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(T2), T2), multiply(multiply(inverse(S2), S2), multiply(Y, multiply(inverse(U2), U2))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 17 }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(S2), S2), multiply(Y, multiply(inverse(U2), U2)))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 17 }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(X, inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(X, inverse(multiply(inverse(X3), X3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 18 }
% 0.21/0.57 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(multiply(inverse(Y3), Y3), inverse(multiply(inverse(X3), X3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 9 }
% 0.21/0.57 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), inverse(multiply(inverse(Z3), Z3))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), inverse(multiply(inverse(Z3), Z3))), inverse(multiply(inverse(multiply(inverse(U2), U2)), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by lemma 9 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(multiply(inverse(Y3), Y3), inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(multiply(inverse(Y3), Y3), inverse(multiply(inverse(U2), U2)))), inverse(multiply(inverse(multiply(inverse(U2), U2)), multiply(inverse(U2), U2))))
% 0.21/0.57 = { by axiom 1 (single_axiom) }
% 0.21/0.57 Y
% 0.21/0.57
% 0.21/0.57 Lemma 20: multiply(multiply(inverse(X), X), Y) = Y.
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(multiply(inverse(X), X), Y)
% 0.21/0.57 = { by lemma 13 R->L }
% 0.21/0.57 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W))), Y)
% 0.21/0.57 = { by lemma 19 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W))), Y)))), multiply(V, multiply(inverse(U), U))), multiply(inverse(T), T))
% 0.21/0.57 = { by lemma 16 }
% 0.21/0.57 multiply(multiply(inverse(multiply(V, inverse(Y))), multiply(V, multiply(inverse(U), U))), multiply(inverse(T), T))
% 0.21/0.57 = { by lemma 19 }
% 0.21/0.57 Y
% 0.21/0.57
% 0.21/0.57 Lemma 21: multiply(X, multiply(inverse(Y), Y)) = X.
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(X, multiply(inverse(Y), Y))
% 0.21/0.57 = { by lemma 20 R->L }
% 0.21/0.57 multiply(multiply(inverse(Z), Z), multiply(X, multiply(inverse(Y), Y)))
% 0.21/0.57 = { by lemma 12 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), multiply(multiply(inverse(Z), Z), multiply(X, multiply(inverse(Y), Y))))), inverse(multiply(inverse(U), U)))
% 0.21/0.57 = { by lemma 15 }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(W), W)), X), inverse(multiply(inverse(U), U)))
% 0.21/0.57 = { by lemma 20 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(T), T), X)), inverse(multiply(inverse(U), U)))
% 0.21/0.57 = { by lemma 12 }
% 0.21/0.57 X
% 0.21/0.57
% 0.21/0.57 Lemma 22: multiply(inverse(X), multiply(X, Y)) = inverse(inverse(Y)).
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(inverse(X), multiply(X, Y))
% 0.21/0.57 = { by lemma 21 R->L }
% 0.21/0.57 multiply(inverse(multiply(X, multiply(inverse(Z), Z))), multiply(X, Y))
% 0.21/0.57 = { by lemma 18 }
% 0.21/0.57 multiply(inverse(multiply(inverse(Y), multiply(inverse(Z), Z))), multiply(inverse(Y), Y))
% 0.21/0.57 = { by lemma 7 R->L }
% 0.21/0.57 multiply(inverse(multiply(inverse(Y), multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 0.21/0.57 = { by lemma 21 }
% 0.21/0.57 multiply(inverse(inverse(Y)), multiply(inverse(W), W))
% 0.21/0.57 = { by lemma 21 }
% 0.21/0.57 inverse(inverse(Y))
% 0.21/0.57
% 0.21/0.57 Lemma 23: inverse(inverse(X)) = X.
% 0.21/0.57 Proof:
% 0.21/0.57 inverse(inverse(X))
% 0.21/0.57 = { by lemma 21 R->L }
% 0.21/0.57 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 0.21/0.57 = { by lemma 14 R->L }
% 0.21/0.57 multiply(inverse(inverse(X)), inverse(multiply(inverse(Z), Z)))
% 0.21/0.57 = { by lemma 22 R->L }
% 0.21/0.57 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(W), W), X)), inverse(multiply(inverse(Z), Z)))
% 0.21/0.57 = { by lemma 12 }
% 0.21/0.57 X
% 0.21/0.57
% 0.21/0.57 Lemma 24: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(inverse(X), X)
% 0.21/0.57 = { by lemma 7 }
% 0.21/0.57 multiply(inverse(inverse(Y)), inverse(Y))
% 0.21/0.57 = { by lemma 23 }
% 0.21/0.57 multiply(Y, inverse(Y))
% 0.21/0.57
% 0.21/0.57 Lemma 25: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, Z)).
% 0.21/0.57 Proof:
% 0.21/0.57 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 0.21/0.57 = { by lemma 7 }
% 0.21/0.57 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 0.21/0.57 = { by lemma 18 R->L }
% 0.21/0.58 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.21/0.58
% 0.21/0.58 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1)).
% 0.21/0.58 Proof:
% 0.21/0.58 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.21/0.58 = { by lemma 20 }
% 0.21/0.58 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.21/0.58 = { by lemma 24 }
% 0.21/0.58 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 23 R->L }
% 0.21/0.58 tuple(a2, multiply(inverse(inverse(multiply(a3, b3))), c3), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 19 R->L }
% 0.21/0.58 tuple(a2, multiply(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(a3, b3))), c3)))), multiply(Y, multiply(inverse(Z), Z))), multiply(inverse(W), W)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 16 R->L }
% 0.21/0.58 tuple(a2, multiply(multiply(inverse(multiply(Y, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(U), U))), multiply(inverse(inverse(multiply(a3, b3))), c3))))), multiply(Y, multiply(inverse(Z), Z))), multiply(inverse(W), W)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 9 }
% 0.21/0.58 tuple(a2, multiply(multiply(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(T), T)), multiply(inverse(inverse(multiply(a3, b3))), c3))))), multiply(Y, multiply(inverse(Z), Z))), multiply(inverse(W), W)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 25 }
% 0.21/0.58 tuple(a2, multiply(multiply(inverse(multiply(Y, inverse(multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, c3))))), multiply(Y, multiply(inverse(Z), Z))), multiply(inverse(W), W)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 19 }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 20 R->L }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, multiply(multiply(inverse(S), S), inverse(multiply(a3, b3))))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 14 R->L }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(X2), X2)), inverse(multiply(a3, b3))))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 21 R->L }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(X2), X2)), multiply(inverse(multiply(a3, b3)), multiply(inverse(Y2), Y2))))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 25 }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(a3), multiply(a3, b3))), multiply(inverse(a3), multiply(inverse(Y2), Y2))))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 21 }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, multiply(inverse(multiply(inverse(a3), multiply(a3, b3))), inverse(a3)))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 22 }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, multiply(inverse(inverse(inverse(b3))), inverse(a3)))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 23 }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(b3, multiply(inverse(b3), inverse(a3)))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 23 R->L }
% 0.21/0.58 tuple(a2, multiply(inverse(multiply(inverse(inverse(b3)), multiply(inverse(b3), inverse(a3)))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 22 }
% 0.21/0.58 tuple(a2, multiply(inverse(inverse(inverse(inverse(a3)))), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 23 }
% 0.21/0.58 tuple(a2, multiply(inverse(inverse(a3)), multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 23 }
% 0.21/0.58 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 0.21/0.58 = { by lemma 24 R->L }
% 0.21/0.58 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58
% 0.21/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------