TSTP Solution File: GRP071-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP071-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 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 : n019.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 01:16:52 EDT 2023
% Result : Unsatisfiable 5.64s 1.08s
% Output : Proof 6.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP071-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.00/0.13 % 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 : n019.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 23:03:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.64/1.08 Command-line arguments: --no-flatten-goal
% 5.64/1.08
% 5.64/1.08 % SZS status Unsatisfiable
% 5.64/1.08
% 5.97/1.20 % SZS output start Proof
% 5.97/1.20 Take the following subset of the input axioms:
% 5.97/1.20 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=divide(X, inverse(Y))).
% 5.97/1.20 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)))).
% 5.97/1.20 fof(single_axiom, axiom, ![Z, U, X2, Y2]: divide(inverse(divide(X2, divide(Y2, divide(Z, U)))), divide(divide(U, Z), X2))=Y2).
% 5.97/1.20
% 5.97/1.20 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.97/1.20 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.97/1.20 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.97/1.20 fresh(y, y, x1...xn) = u
% 5.97/1.20 C => fresh(s, t, x1...xn) = v
% 5.97/1.20 where fresh is a fresh function symbol and x1..xn are the free
% 5.97/1.20 variables of u and v.
% 5.97/1.20 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.97/1.20 input problem has no model of domain size 1).
% 5.97/1.20
% 5.97/1.20 The encoding turns the above axioms into the following unit equations and goals:
% 5.97/1.20
% 5.97/1.20 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 5.97/1.20 Axiom 2 (single_axiom): divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)) = Y.
% 5.97/1.20
% 5.97/1.20 Lemma 3: divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, divide(W, V))))) = divide(V, W).
% 5.97/1.20 Proof:
% 5.97/1.20 divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, divide(W, V)))))
% 5.97/1.20 = { by axiom 1 (multiply) }
% 5.97/1.20 divide(inverse(X), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, divide(W, V))))))
% 5.97/1.20 = { by axiom 2 (single_axiom) R->L }
% 5.97/1.20 divide(inverse(divide(inverse(divide(divide(Z, Y), divide(X, divide(W, V)))), divide(divide(V, W), divide(Z, Y)))), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, divide(W, V))))))
% 5.97/1.20 = { by axiom 2 (single_axiom) }
% 5.97/1.20 divide(V, W)
% 5.97/1.20
% 5.97/1.20 Lemma 4: multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(W, V)))), Z) = divide(W, V).
% 5.97/1.20 Proof:
% 5.97/1.20 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(W, V)))), Z)
% 5.97/1.20 = { by axiom 1 (multiply) }
% 5.97/1.20 divide(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(W, V)))), inverse(Z))
% 5.97/1.20 = { by lemma 3 R->L }
% 5.97/1.20 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, divide(inverse(Z), multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(W, V)))))))))
% 5.97/1.20 = { by lemma 3 }
% 5.97/1.20 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, divide(V, W)))))
% 5.97/1.20 = { by lemma 3 }
% 5.97/1.20 divide(W, V)
% 5.97/1.20
% 5.97/1.20 Lemma 5: multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), Z) = W.
% 5.97/1.20 Proof:
% 5.97/1.20 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), Z)
% 5.97/1.20 = { by axiom 2 (single_axiom) R->L }
% 5.97/1.20 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))))), Z)
% 5.97/1.20 = { by lemma 4 }
% 5.97/1.20 divide(inverse(divide(V, divide(W, divide(U, T)))), divide(divide(T, U), V))
% 5.97/1.20 = { by axiom 2 (single_axiom) }
% 5.97/1.20 W
% 5.97/1.20
% 5.97/1.20 Lemma 6: multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), inverse(V)) = multiply(divide(U, T), divide(divide(T, U), divide(V, divide(W, Z)))).
% 5.97/1.20 Proof:
% 5.97/1.20 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), inverse(V))
% 5.97/1.20 = { by lemma 3 R->L }
% 5.97/1.20 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(W, Z))))))), inverse(V))
% 5.97/1.20 = { by lemma 5 }
% 5.97/1.21 multiply(divide(U, T), divide(divide(T, U), divide(V, divide(W, Z))))
% 5.97/1.21
% 5.97/1.21 Lemma 7: multiply(divide(X, Y), divide(divide(Y, X), divide(Z, multiply(W, Z)))) = W.
% 5.97/1.21 Proof:
% 5.97/1.21 multiply(divide(X, Y), divide(divide(Y, X), divide(Z, multiply(W, Z))))
% 5.97/1.21 = { by axiom 1 (multiply) }
% 5.97/1.21 multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(W, inverse(Z)))))
% 5.97/1.21 = { by lemma 6 R->L }
% 5.97/1.21 multiply(multiply(divide(V, U), divide(divide(U, V), divide(inverse(Z), W))), inverse(Z))
% 5.97/1.21 = { by lemma 5 }
% 5.97/1.21 W
% 5.97/1.21
% 6.58/1.21 Lemma 8: multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(multiply(W, V), V)))) = multiply(W, inverse(Z)).
% 6.58/1.21 Proof:
% 6.58/1.21 multiply(divide(X, Y), divide(divide(Y, X), divide(Z, divide(multiply(W, V), V))))
% 6.58/1.21 = { by lemma 6 R->L }
% 6.58/1.21 multiply(multiply(divide(U, T), divide(divide(T, U), divide(V, multiply(W, V)))), inverse(Z))
% 6.58/1.21 = { by lemma 7 }
% 6.58/1.21 multiply(W, inverse(Z))
% 6.58/1.21
% 6.58/1.21 Lemma 9: multiply(multiply(X, inverse(Y)), Y) = divide(multiply(X, Z), Z).
% 6.58/1.21 Proof:
% 6.58/1.21 multiply(multiply(X, inverse(Y)), Y)
% 6.58/1.21 = { by lemma 8 R->L }
% 6.58/1.21 multiply(multiply(divide(W, V), divide(divide(V, W), divide(Y, divide(multiply(X, Z), Z)))), Y)
% 6.58/1.21 = { by lemma 4 }
% 6.58/1.21 divide(multiply(X, Z), Z)
% 6.58/1.21
% 6.58/1.21 Lemma 10: divide(multiply(X, Z), Z) = divide(multiply(X, Y), Y).
% 6.58/1.21 Proof:
% 6.58/1.21 divide(multiply(X, Z), Z)
% 6.58/1.21 = { by lemma 4 R->L }
% 6.58/1.21 multiply(multiply(divide(T, S), divide(divide(S, T), divide(U, divide(multiply(X, Z), Z)))), U)
% 6.58/1.21 = { by lemma 8 }
% 6.58/1.21 multiply(multiply(X, inverse(U)), U)
% 6.58/1.21 = { by lemma 8 R->L }
% 6.58/1.21 multiply(multiply(divide(W, V), divide(divide(V, W), divide(U, divide(multiply(X, Y), Y)))), U)
% 6.58/1.21 = { by lemma 4 }
% 6.58/1.21 divide(multiply(X, Y), Y)
% 6.58/1.21
% 6.58/1.21 Lemma 11: divide(Z, multiply(Y, Z)) = divide(X, multiply(Y, X)).
% 6.58/1.21 Proof:
% 6.58/1.21 divide(Z, multiply(Y, Z))
% 6.58/1.21 = { by lemma 3 R->L }
% 6.58/1.21 divide(inverse(W), multiply(divide(V, U), divide(divide(U, V), divide(W, divide(multiply(Y, Z), Z)))))
% 6.58/1.21 = { by lemma 10 }
% 6.58/1.21 divide(inverse(W), multiply(divide(V, U), divide(divide(U, V), divide(W, divide(multiply(Y, X), X)))))
% 6.58/1.21 = { by lemma 3 }
% 6.58/1.21 divide(X, multiply(Y, X))
% 6.58/1.21
% 6.58/1.21 Lemma 12: divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, W)))) = multiply(divide(divide(V, U), T), divide(T, divide(W, divide(U, V)))).
% 6.58/1.21 Proof:
% 6.58/1.21 divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, W))))
% 6.58/1.21 = { by axiom 2 (single_axiom) R->L }
% 6.58/1.21 divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, divide(inverse(divide(T, divide(W, divide(U, V)))), divide(divide(V, U), T))))))
% 6.58/1.21 = { by lemma 3 }
% 6.58/1.21 divide(divide(divide(V, U), T), inverse(divide(T, divide(W, divide(U, V)))))
% 6.58/1.21 = { by axiom 1 (multiply) R->L }
% 6.58/1.21 multiply(divide(divide(V, U), T), divide(T, divide(W, divide(U, V))))
% 6.58/1.21
% 6.58/1.21 Lemma 13: divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, multiply(W, V))))) = divide(inverse(V), W).
% 6.58/1.21 Proof:
% 6.58/1.21 divide(inverse(X), multiply(divide(Y, Z), divide(divide(Z, Y), divide(X, multiply(W, V)))))
% 6.58/1.21 = { by axiom 1 (multiply) }
% 6.58/1.21 divide(inverse(X), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, multiply(W, V))))))
% 6.58/1.21 = { by axiom 2 (single_axiom) R->L }
% 6.58/1.21 divide(inverse(divide(inverse(divide(divide(Z, Y), divide(X, divide(W, inverse(V))))), divide(divide(inverse(V), W), divide(Z, Y)))), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, multiply(W, V))))))
% 6.58/1.21 = { by axiom 1 (multiply) R->L }
% 6.58/1.21 divide(inverse(divide(inverse(divide(divide(Z, Y), divide(X, multiply(W, V)))), divide(divide(inverse(V), W), divide(Z, Y)))), divide(divide(Y, Z), inverse(divide(divide(Z, Y), divide(X, multiply(W, V))))))
% 6.58/1.21 = { by axiom 2 (single_axiom) }
% 6.58/1.21 divide(inverse(V), W)
% 6.58/1.21
% 6.58/1.21 Lemma 14: multiply(multiply(divide(X, Y), divide(divide(Y, X), multiply(Z, W))), Z) = inverse(W).
% 6.58/1.21 Proof:
% 6.58/1.21 multiply(multiply(divide(X, Y), divide(divide(Y, X), multiply(Z, W))), Z)
% 6.58/1.21 = { by axiom 1 (multiply) }
% 6.58/1.21 multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, inverse(W)))), Z)
% 6.58/1.21 = { by lemma 5 }
% 6.58/1.21 inverse(W)
% 6.58/1.21
% 6.58/1.21 Lemma 15: multiply(multiply(divide(X, Y), divide(divide(Y, X), Z)), divide(W, V)) = inverse(divide(divide(V, W), divide(U, multiply(Z, U)))).
% 6.58/1.21 Proof:
% 6.58/1.21 multiply(multiply(divide(X, Y), divide(divide(Y, X), Z)), divide(W, V))
% 6.58/1.21 = { by lemma 7 R->L }
% 6.58/1.21 multiply(multiply(divide(X, Y), divide(divide(Y, X), multiply(divide(W, V), divide(divide(V, W), divide(U, multiply(Z, U)))))), divide(W, V))
% 6.58/1.21 = { by lemma 14 }
% 6.58/1.21 inverse(divide(divide(V, W), divide(U, multiply(Z, U))))
% 6.58/1.21
% 6.58/1.21 Lemma 16: multiply(multiply(divide(X, Y), Z), multiply(divide(W, V), divide(divide(V, W), Z))) = inverse(divide(Y, X)).
% 6.58/1.21 Proof:
% 6.58/1.21 multiply(multiply(divide(X, Y), Z), multiply(divide(W, V), divide(divide(V, W), Z)))
% 6.58/1.21 = { by lemma 7 R->L }
% 6.58/1.21 multiply(multiply(divide(X, Y), multiply(divide(Y, X), divide(divide(X, Y), divide(U, multiply(Z, U))))), multiply(divide(W, V), divide(divide(V, W), Z)))
% 6.58/1.21 = { by axiom 1 (multiply) }
% 6.58/1.21 multiply(multiply(divide(X, Y), divide(divide(Y, X), inverse(divide(divide(X, Y), divide(U, multiply(Z, U)))))), multiply(divide(W, V), divide(divide(V, W), Z)))
% 6.58/1.21 = { by lemma 15 R->L }
% 6.58/1.21 multiply(multiply(divide(X, Y), divide(divide(Y, X), multiply(multiply(divide(W, V), divide(divide(V, W), Z)), divide(Y, X)))), multiply(divide(W, V), divide(divide(V, W), Z)))
% 6.58/1.21 = { by lemma 14 }
% 6.58/1.21 inverse(divide(Y, X))
% 6.58/1.21
% 6.58/1.21 Lemma 17: multiply(divide(divide(X, Y), Z), divide(Z, divide(W, divide(Y, X)))) = divide(divide(V, multiply(multiply(divide(U, T), W), V)), divide(T, U)).
% 6.58/1.21 Proof:
% 6.58/1.21 multiply(divide(divide(X, Y), Z), divide(Z, divide(W, divide(Y, X))))
% 6.58/1.21 = { by lemma 12 R->L }
% 6.58/1.21 divide(inverse(S), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(S, W))))
% 6.58/1.21 = { by lemma 7 R->L }
% 6.58/1.21 divide(inverse(S), multiply(divide(X2, Y2), divide(divide(Y2, X2), divide(S, multiply(divide(T, U), divide(divide(U, T), divide(Z2, multiply(W, Z2))))))))
% 6.58/1.21 = { by lemma 13 }
% 6.58/1.21 divide(inverse(divide(divide(U, T), divide(Z2, multiply(W, Z2)))), divide(T, U))
% 6.58/1.21 = { by lemma 15 R->L }
% 6.58/1.21 divide(multiply(multiply(divide(W2, V2), divide(divide(V2, W2), W)), divide(T, U)), divide(T, U))
% 6.58/1.21 = { by axiom 1 (multiply) }
% 6.58/1.21 divide(divide(multiply(divide(W2, V2), divide(divide(V2, W2), W)), inverse(divide(T, U))), divide(T, U))
% 6.58/1.21 = { by lemma 16 R->L }
% 6.58/1.21 divide(divide(multiply(divide(W2, V2), divide(divide(V2, W2), W)), multiply(multiply(divide(U, T), W), multiply(divide(W2, V2), divide(divide(V2, W2), W)))), divide(T, U))
% 6.58/1.21 = { by lemma 11 R->L }
% 6.58/1.21 divide(divide(V, multiply(multiply(divide(U, T), W), V)), divide(T, U))
% 6.58/1.21
% 6.58/1.21 Lemma 18: divide(divide(X, Y), divide(Z, multiply(multiply(divide(Y, X), W), Z))) = W.
% 6.58/1.21 Proof:
% 6.58/1.21 divide(divide(X, Y), divide(Z, multiply(multiply(divide(Y, X), W), Z)))
% 6.58/1.21 = { by lemma 3 R->L }
% 6.58/1.21 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(Z, multiply(multiply(divide(Y, X), W), Z)), divide(X, Y))))))
% 6.58/1.21 = { by lemma 17 R->L }
% 6.58/1.21 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, multiply(divide(divide(S, X2), Y2), divide(Y2, divide(W, divide(X2, S))))))))
% 6.58/1.21 = { by lemma 13 }
% 6.58/1.21 divide(inverse(divide(Y2, divide(W, divide(X2, S)))), divide(divide(S, X2), Y2))
% 6.58/1.21 = { by axiom 2 (single_axiom) }
% 6.58/1.21 W
% 6.58/1.21
% 6.58/1.21 Lemma 19: divide(divide(X, Y), divide(Z, divide(multiply(divide(Y, X), W), W))) = inverse(Z).
% 6.58/1.21 Proof:
% 6.58/1.21 divide(divide(X, Y), divide(Z, divide(multiply(divide(Y, X), W), W)))
% 6.58/1.21 = { by lemma 9 R->L }
% 6.58/1.21 divide(divide(X, Y), divide(Z, multiply(multiply(divide(Y, X), inverse(Z)), Z)))
% 6.58/1.21 = { by lemma 11 R->L }
% 6.58/1.21 divide(divide(X, Y), divide(V, multiply(multiply(divide(Y, X), inverse(Z)), V)))
% 6.58/1.21 = { by lemma 18 }
% 6.58/1.21 inverse(Z)
% 6.58/1.21
% 6.58/1.21 Lemma 20: divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X)) = inverse(divide(Z, divide(Y, divide(V, W)))).
% 6.58/1.21 Proof:
% 6.58/1.21 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X))
% 6.58/1.21 = { by axiom 2 (single_axiom) R->L }
% 6.58/1.21 divide(inverse(divide(X, divide(inverse(divide(Z, divide(Y, divide(V, W)))), divide(divide(W, V), Z)))), divide(divide(Z, divide(W, V)), X))
% 6.58/1.21 = { by axiom 2 (single_axiom) }
% 6.58/1.21 inverse(divide(Z, divide(Y, divide(V, W))))
% 6.58/1.21
% 6.58/1.21 Lemma 21: inverse(inverse(divide(X, divide(Y, divide(inverse(divide(divide(Z, W), Y)), divide(W, Z)))))) = X.
% 6.58/1.21 Proof:
% 6.58/1.21 inverse(inverse(divide(X, divide(Y, divide(inverse(divide(divide(Z, W), Y)), divide(W, Z))))))
% 6.58/1.21 = { by lemma 20 R->L }
% 6.58/1.21 inverse(divide(inverse(divide(divide(Z, W), Y)), divide(divide(X, divide(divide(W, Z), inverse(divide(divide(Z, W), Y)))), divide(Z, W))))
% 6.58/1.21 = { by lemma 20 R->L }
% 6.58/1.21 divide(inverse(divide(V, divide(X, divide(divide(W, Z), inverse(divide(divide(Z, W), Y)))))), divide(divide(inverse(divide(divide(Z, W), Y)), divide(W, Z)), V))
% 6.58/1.21 = { by axiom 2 (single_axiom) }
% 6.58/1.21 X
% 6.58/1.21
% 6.58/1.21 Lemma 22: divide(inverse(divide(divide(W, V), Z)), divide(V, W)) = divide(inverse(divide(divide(X, Y), Z)), divide(Y, X)).
% 6.58/1.21 Proof:
% 6.58/1.21 divide(inverse(divide(divide(W, V), Z)), divide(V, W))
% 6.58/1.21 = { by lemma 13 R->L }
% 6.58/1.21 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, multiply(divide(V, W), divide(divide(W, V), Z))))))
% 6.58/1.21 = { by axiom 2 (single_axiom) R->L }
% 6.58/1.21 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, multiply(divide(V, W), divide(divide(W, V), divide(inverse(divide(X2, divide(Z, divide(Y2, Z2)))), divide(divide(Z2, Y2), X2))))))))
% 6.58/1.21 = { by lemma 5 R->L }
% 6.58/1.21 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, multiply(multiply(divide(W2, V2), divide(divide(V2, W2), divide(inverse(inverse(divide(X2, divide(Z, divide(Y2, Z2))))), multiply(divide(V, W), divide(divide(W, V), divide(inverse(divide(X2, divide(Z, divide(Y2, Z2)))), divide(divide(Z2, Y2), X2))))))), inverse(inverse(divide(X2, divide(Z, divide(Y2, Z2))))))))))
% 6.58/1.21 = { by lemma 3 }
% 6.58/1.21 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, multiply(multiply(divide(W2, V2), divide(divide(V2, W2), divide(X2, divide(Z2, Y2)))), inverse(inverse(divide(X2, divide(Z, divide(Y2, Z2))))))))))
% 6.58/1.21 = { by lemma 3 R->L }
% 6.58/1.21 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, multiply(multiply(divide(W2, V2), divide(divide(V2, W2), divide(inverse(inverse(divide(X2, divide(Z, divide(Y2, Z2))))), multiply(divide(Y, X), divide(divide(X, Y), divide(inverse(divide(X2, divide(Z, divide(Y2, Z2)))), divide(divide(Z2, Y2), X2))))))), inverse(inverse(divide(X2, divide(Z, divide(Y2, Z2))))))))))
% 6.58/1.21 = { by lemma 5 }
% 6.58/1.21 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, multiply(divide(Y, X), divide(divide(X, Y), divide(inverse(divide(X2, divide(Z, divide(Y2, Z2)))), divide(divide(Z2, Y2), X2))))))))
% 6.58/1.21 = { by axiom 2 (single_axiom) }
% 6.58/1.21 divide(inverse(U), multiply(divide(T, S), divide(divide(S, T), divide(U, multiply(divide(Y, X), divide(divide(X, Y), Z))))))
% 6.58/1.21 = { by lemma 13 }
% 6.58/1.21 divide(inverse(divide(divide(X, Y), Z)), divide(Y, X))
% 6.58/1.21
% 6.58/1.21 Lemma 23: divide(X, multiply(multiply(divide(Y, Z), divide(divide(Z, Y), W)), X)) = W.
% 6.58/1.21 Proof:
% 6.58/1.21 divide(X, multiply(multiply(divide(Y, Z), divide(divide(Z, Y), W)), X))
% 6.58/1.21 = { by lemma 11 }
% 6.58/1.21 divide(divide(V, U), multiply(multiply(divide(Y, Z), divide(divide(Z, Y), W)), divide(V, U)))
% 6.58/1.21 = { by lemma 15 }
% 6.58/1.21 divide(divide(V, U), inverse(divide(divide(U, V), divide(T, multiply(W, T)))))
% 6.58/1.21 = { by axiom 1 (multiply) R->L }
% 6.58/1.21 multiply(divide(V, U), divide(divide(U, V), divide(T, multiply(W, T))))
% 6.58/1.21 = { by lemma 7 }
% 6.58/1.21 W
% 6.58/1.21
% 6.58/1.21 Lemma 24: divide(X, multiply(Y, divide(Z, multiply(Y, Z)))) = X.
% 6.58/1.21 Proof:
% 6.58/1.21 divide(X, multiply(Y, divide(Z, multiply(Y, Z))))
% 6.58/1.21 = { by lemma 21 R->L }
% 6.58/1.21 divide(X, multiply(Y, inverse(inverse(divide(divide(Z, multiply(Y, Z)), divide(W, divide(inverse(divide(divide(V, U), W)), divide(U, V))))))))
% 6.58/1.21 = { by lemma 8 R->L }
% 6.58/1.21 divide(X, multiply(divide(T, S), divide(divide(S, T), divide(inverse(divide(divide(Z, multiply(Y, Z)), divide(W, divide(inverse(divide(divide(V, U), W)), divide(U, V))))), divide(multiply(Y, Z), Z)))))
% 6.58/1.21 = { by lemma 22 R->L }
% 6.58/1.21 divide(X, multiply(divide(T, S), divide(divide(S, T), divide(inverse(divide(divide(X2, multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), X2)), divide(W, divide(inverse(divide(divide(V, U), W)), divide(U, V))))), divide(multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), X2), X2)))))
% 6.58/1.21 = { by lemma 8 }
% 6.58/1.21 divide(X, multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), inverse(inverse(divide(divide(X2, multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), X2)), divide(W, divide(inverse(divide(divide(V, U), W)), divide(U, V))))))))
% 6.58/1.21 = { by lemma 21 }
% 6.58/1.21 divide(X, multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), divide(X2, multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), X2))))
% 6.58/1.21 = { by lemma 23 }
% 6.58/1.21 divide(X, multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), X))
% 6.58/1.21 = { by lemma 11 R->L }
% 6.58/1.21 divide(W2, multiply(multiply(divide(Y2, Z2), divide(divide(Z2, Y2), X)), W2))
% 6.58/1.21 = { by lemma 23 }
% 6.58/1.21 X
% 6.58/1.21
% 6.58/1.21 Lemma 25: multiply(divide(X, W), divide(W, Z)) = multiply(divide(X, Y), divide(Y, Z)).
% 6.58/1.21 Proof:
% 6.58/1.21 multiply(divide(X, W), divide(W, Z))
% 6.58/1.21 = { by axiom 1 (multiply) }
% 6.58/1.21 divide(divide(X, W), inverse(divide(W, Z)))
% 6.58/1.21 = { by lemma 3 R->L }
% 6.58/1.21 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(inverse(divide(W, Z)), divide(X, W))))))
% 6.58/1.21 = { by lemma 18 R->L }
% 6.58/1.21 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(multiply(divide(X2, S), divide(inverse(divide(W, Z)), divide(X, W))), Y2)))))))
% 6.58/1.21 = { by axiom 1 (multiply) }
% 6.58/1.21 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), inverse(divide(inverse(divide(W, Z)), divide(X, W)))), Y2)))))))
% 6.58/1.22 = { by axiom 2 (single_axiom) R->L }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), inverse(divide(inverse(divide(W, Z)), divide(X, divide(inverse(divide(T2, divide(W, divide(S2, X3)))), divide(divide(X3, S2), T2)))))), Y2)))))))
% 6.58/1.22 = { by axiom 2 (single_axiom) R->L }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), inverse(divide(inverse(divide(divide(inverse(divide(T2, divide(W, divide(S2, X3)))), divide(divide(X3, S2), T2)), Z)), divide(X, divide(inverse(divide(T2, divide(W, divide(S2, X3)))), divide(divide(X3, S2), T2)))))), Y2)))))))
% 6.58/1.22 = { by lemma 20 R->L }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), divide(inverse(divide(U2, X)), divide(divide(inverse(divide(divide(inverse(divide(T2, divide(W, divide(S2, X3)))), divide(divide(X3, S2), T2)), Z)), divide(divide(divide(X3, S2), T2), inverse(divide(T2, divide(W, divide(S2, X3)))))), U2))), Y2)))))))
% 6.58/1.22 = { by lemma 22 R->L }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), divide(inverse(divide(U2, X)), divide(divide(inverse(divide(divide(inverse(divide(Z2, divide(Y, divide(W2, V2)))), divide(divide(V2, W2), Z2)), Z)), divide(divide(divide(V2, W2), Z2), inverse(divide(Z2, divide(Y, divide(W2, V2)))))), U2))), Y2)))))))
% 6.58/1.22 = { by lemma 20 }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), inverse(divide(inverse(divide(divide(inverse(divide(Z2, divide(Y, divide(W2, V2)))), divide(divide(V2, W2), Z2)), Z)), divide(X, divide(inverse(divide(Z2, divide(Y, divide(W2, V2)))), divide(divide(V2, W2), Z2)))))), Y2)))))))
% 6.58/1.22 = { by axiom 2 (single_axiom) }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), inverse(divide(inverse(divide(Y, Z)), divide(X, divide(inverse(divide(Z2, divide(Y, divide(W2, V2)))), divide(divide(V2, W2), Z2)))))), Y2)))))))
% 6.58/1.22 = { by axiom 2 (single_axiom) }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(divide(divide(X2, S), inverse(divide(inverse(divide(Y, Z)), divide(X, Y)))), Y2)))))))
% 6.58/1.22 = { by axiom 1 (multiply) R->L }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(divide(S, X2), divide(Y2, multiply(multiply(divide(X2, S), divide(inverse(divide(Y, Z)), divide(X, Y))), Y2)))))))
% 6.58/1.22 = { by lemma 18 }
% 6.58/1.22 divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(inverse(divide(Y, Z)), divide(X, Y))))))
% 6.58/1.22 = { by lemma 3 }
% 6.58/1.22 divide(divide(X, Y), inverse(divide(Y, Z)))
% 6.58/1.22 = { by axiom 1 (multiply) R->L }
% 6.58/1.22 multiply(divide(X, Y), divide(Y, Z))
% 6.58/1.22
% 6.58/1.22 Lemma 26: multiply(divide(X, Z), Z) = multiply(divide(X, Y), Y).
% 6.58/1.22 Proof:
% 6.58/1.22 multiply(divide(X, Z), Z)
% 6.58/1.22 = { by lemma 24 R->L }
% 6.58/1.22 multiply(divide(X, Z), divide(Z, multiply(W, divide(V, multiply(W, V)))))
% 6.58/1.22 = { by lemma 25 }
% 6.58/1.22 multiply(divide(X, Y), divide(Y, multiply(W, divide(V, multiply(W, V)))))
% 6.58/1.22 = { by lemma 24 }
% 6.58/1.22 multiply(divide(X, Y), Y)
% 6.58/1.22
% 6.58/1.22 Lemma 27: multiply(divide(X, Y), Y) = divide(multiply(X, Z), Z).
% 6.58/1.22 Proof:
% 6.58/1.22 multiply(divide(X, Y), Y)
% 6.58/1.22 = { by lemma 24 R->L }
% 6.58/1.22 divide(multiply(divide(X, Y), Y), multiply(W, divide(V, multiply(W, V))))
% 6.58/1.22 = { by lemma 26 }
% 6.58/1.22 divide(multiply(divide(X, multiply(W, divide(V, multiply(W, V)))), multiply(W, divide(V, multiply(W, V)))), multiply(W, divide(V, multiply(W, V))))
% 6.58/1.22 = { by lemma 10 R->L }
% 6.58/1.22 divide(multiply(divide(X, multiply(W, divide(V, multiply(W, V)))), Z), Z)
% 6.58/1.22 = { by lemma 24 }
% 6.58/1.22 divide(multiply(X, Z), Z)
% 6.58/1.22
% 6.58/1.22 Lemma 28: inverse(divide(divide(X, Y), divide(Z, multiply(divide(divide(Y, X), W), Z)))) = W.
% 6.58/1.22 Proof:
% 6.58/1.22 inverse(divide(divide(X, Y), divide(Z, multiply(divide(divide(Y, X), W), Z))))
% 6.58/1.22 = { by lemma 15 R->L }
% 6.58/1.22 multiply(multiply(divide(V, U), divide(divide(U, V), divide(divide(Y, X), W))), divide(Y, X))
% 6.58/1.22 = { by lemma 5 }
% 6.58/1.22 W
% 6.58/1.22
% 6.58/1.22 Lemma 29: inverse(inverse(X)) = X.
% 6.58/1.22 Proof:
% 6.58/1.22 inverse(inverse(X))
% 6.58/1.22 = { by lemma 19 R->L }
% 6.58/1.22 inverse(divide(divide(Y, Z), divide(X, divide(multiply(divide(Z, Y), W), W))))
% 6.58/1.22 = { by lemma 27 R->L }
% 6.58/1.22 inverse(divide(divide(Y, Z), divide(X, multiply(divide(divide(Z, Y), X), X))))
% 6.58/1.22 = { by lemma 11 R->L }
% 6.58/1.22 inverse(divide(divide(Y, Z), divide(V, multiply(divide(divide(Z, Y), X), V))))
% 6.58/1.22 = { by lemma 28 }
% 6.58/1.22 X
% 6.58/1.22
% 6.58/1.22 Lemma 30: multiply(X, inverse(Y)) = divide(X, Y).
% 6.58/1.22 Proof:
% 6.58/1.22 multiply(X, inverse(Y))
% 6.58/1.22 = { by lemma 19 R->L }
% 6.58/1.22 multiply(X, divide(divide(Z, W), divide(Y, divide(multiply(divide(W, Z), V), V))))
% 6.58/1.22 = { by lemma 27 R->L }
% 6.58/1.22 multiply(X, divide(divide(Z, W), divide(Y, multiply(divide(divide(W, Z), Y), Y))))
% 6.58/1.22 = { by axiom 1 (multiply) }
% 6.58/1.22 divide(X, inverse(divide(divide(Z, W), divide(Y, multiply(divide(divide(W, Z), Y), Y)))))
% 6.58/1.22 = { by lemma 28 }
% 6.58/1.22 divide(X, Y)
% 6.58/1.22
% 6.58/1.22 Lemma 31: divide(inverse(divide(X, Y)), divide(divide(Z, multiply(W, V)), X)) = inverse(divide(Z, divide(Y, divide(inverse(V), W)))).
% 6.58/1.22 Proof:
% 6.58/1.22 divide(inverse(divide(X, Y)), divide(divide(Z, multiply(W, V)), X))
% 6.58/1.22 = { by axiom 1 (multiply) }
% 6.58/1.22 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, inverse(V))), X))
% 6.58/1.22 = { by lemma 20 }
% 6.58/1.22 inverse(divide(Z, divide(Y, divide(inverse(V), W))))
% 6.58/1.22
% 6.58/1.22 Lemma 32: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 6.58/1.22 Proof:
% 6.58/1.22 multiply(Y, inverse(Y))
% 6.58/1.22 = { by axiom 1 (multiply) }
% 6.58/1.22 divide(Y, inverse(inverse(Y)))
% 6.58/1.22 = { by lemma 19 R->L }
% 6.58/1.22 divide(Y, divide(divide(Z, W), divide(inverse(Y), divide(multiply(divide(W, Z), V), V))))
% 6.58/1.22 = { by lemma 18 R->L }
% 6.58/1.22 divide(divide(U, T), divide(S, multiply(multiply(divide(T, U), divide(Y, divide(divide(Z, W), divide(inverse(Y), divide(multiply(divide(W, Z), V), V))))), S)))
% 6.58/1.22 = { by axiom 1 (multiply) }
% 6.58/1.22 divide(divide(U, T), divide(S, multiply(divide(divide(T, U), inverse(divide(Y, divide(divide(Z, W), divide(inverse(Y), divide(multiply(divide(W, Z), V), V)))))), S)))
% 6.58/1.22 = { by lemma 31 R->L }
% 6.58/1.22 divide(divide(U, T), divide(S, multiply(divide(divide(T, U), divide(inverse(divide(X2, divide(Z, W))), divide(divide(Y, multiply(divide(multiply(divide(W, Z), V), V), Y)), X2))), S)))
% 6.58/1.22 = { by lemma 11 }
% 6.58/1.22 divide(divide(U, T), divide(S, multiply(divide(divide(T, U), divide(inverse(divide(X2, divide(Z, W))), divide(divide(X, multiply(divide(multiply(divide(W, Z), V), V), X)), X2))), S)))
% 6.58/1.22 = { by lemma 31 }
% 6.58/1.22 divide(divide(U, T), divide(S, multiply(divide(divide(T, U), inverse(divide(X, divide(divide(Z, W), divide(inverse(X), divide(multiply(divide(W, Z), V), V)))))), S)))
% 6.58/1.22 = { by axiom 1 (multiply) R->L }
% 6.58/1.22 divide(divide(U, T), divide(S, multiply(multiply(divide(T, U), divide(X, divide(divide(Z, W), divide(inverse(X), divide(multiply(divide(W, Z), V), V))))), S)))
% 6.58/1.22 = { by lemma 18 }
% 6.58/1.22 divide(X, divide(divide(Z, W), divide(inverse(X), divide(multiply(divide(W, Z), V), V))))
% 6.58/1.22 = { by lemma 19 }
% 6.58/1.22 divide(X, inverse(inverse(X)))
% 6.58/1.22 = { by axiom 1 (multiply) R->L }
% 6.58/1.22 multiply(X, inverse(X))
% 6.58/1.22
% 6.58/1.22 Lemma 33: divide(X, multiply(multiply(divide(Y, Z), multiply(divide(Z, Y), W)), X)) = inverse(W).
% 6.58/1.22 Proof:
% 6.58/1.22 divide(X, multiply(multiply(divide(Y, Z), multiply(divide(Z, Y), W)), X))
% 6.58/1.22 = { by axiom 1 (multiply) }
% 6.58/1.22 divide(X, multiply(multiply(divide(Y, Z), divide(divide(Z, Y), inverse(W))), X))
% 6.58/1.22 = { by lemma 23 }
% 6.58/1.22 inverse(W)
% 6.58/1.22
% 6.58/1.22 Lemma 34: divide(multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), V), V) = divide(W, Z).
% 6.58/1.22 Proof:
% 6.58/1.22 divide(multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), V), V)
% 6.58/1.22 = { by lemma 9 R->L }
% 6.58/1.22 multiply(multiply(multiply(divide(X, Y), divide(divide(Y, X), divide(Z, W))), inverse(U)), U)
% 6.58/1.22 = { by lemma 6 }
% 6.58/1.22 multiply(multiply(divide(T, S), divide(divide(S, T), divide(U, divide(W, Z)))), U)
% 6.58/1.22 = { by lemma 5 }
% 6.58/1.22 divide(W, Z)
% 6.58/1.22
% 6.58/1.22 Lemma 35: multiply(divide(multiply(X, Y), Y), Z) = divide(multiply(multiply(X, Z), W), W).
% 6.58/1.22 Proof:
% 6.58/1.22 multiply(divide(multiply(X, Y), Y), Z)
% 6.58/1.22 = { by lemma 10 }
% 6.58/1.22 multiply(divide(multiply(X, Z), Z), Z)
% 6.58/1.22 = { by lemma 26 R->L }
% 6.58/1.22 multiply(divide(multiply(X, Z), V), V)
% 6.58/1.22 = { by lemma 27 }
% 6.58/1.22 divide(multiply(multiply(X, Z), W), W)
% 6.58/1.22
% 6.58/1.22 Lemma 36: multiply(inverse(X), X) = divide(Y, Y).
% 6.58/1.22 Proof:
% 6.58/1.22 multiply(inverse(X), X)
% 6.58/1.22 = { by axiom 1 (multiply) }
% 6.58/1.22 divide(inverse(X), inverse(X))
% 6.58/1.22 = { by lemma 33 R->L }
% 6.58/1.22 divide(inverse(X), divide(Z, multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z)))
% 6.58/1.22 = { by lemma 33 R->L }
% 6.58/1.22 divide(divide(Z, multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z)), divide(Z, multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z)))
% 6.58/1.22 = { by lemma 34 R->L }
% 6.58/1.22 divide(divide(Z, multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z)), divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), S), S))
% 6.58/1.22 = { by lemma 34 R->L }
% 6.58/1.22 divide(divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), X2), X2), divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), S), S))
% 6.58/1.22 = { by lemma 9 R->L }
% 6.58/1.22 divide(multiply(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), inverse(divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), S), S))), divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), S), S)), divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), S), S))
% 6.58/1.22 = { by lemma 35 R->L }
% 6.58/1.22 multiply(divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), S), S), inverse(divide(multiply(multiply(divide(U, T), divide(divide(T, U), divide(multiply(multiply(divide(W, V), multiply(divide(V, W), X)), Z), Z))), S), S)))
% 6.58/1.22 = { by lemma 32 R->L }
% 6.58/1.22 multiply(Y, inverse(Y))
% 6.58/1.22 = { by lemma 30 }
% 6.58/1.22 divide(Y, Y)
% 6.58/1.22
% 6.58/1.22 Lemma 37: multiply(divide(X, X), Y) = divide(multiply(Y, Z), Z).
% 6.58/1.22 Proof:
% 6.58/1.22 multiply(divide(X, X), Y)
% 6.58/1.22 = { by lemma 30 R->L }
% 6.58/1.22 multiply(multiply(X, inverse(X)), Y)
% 6.58/1.22 = { by lemma 32 }
% 6.58/1.22 multiply(multiply(Y, inverse(Y)), Y)
% 6.58/1.22 = { by lemma 9 }
% 6.58/1.22 divide(multiply(Y, Z), Z)
% 6.58/1.22
% 6.58/1.22 Lemma 38: divide(inverse(X), multiply(Y, inverse(Y))) = divide(Z, multiply(X, Z)).
% 6.58/1.22 Proof:
% 6.58/1.22 divide(inverse(X), multiply(Y, inverse(Y)))
% 6.58/1.22 = { by lemma 32 }
% 6.58/1.22 divide(inverse(X), multiply(X, inverse(X)))
% 6.58/1.22 = { by lemma 11 R->L }
% 6.58/1.22 divide(Z, multiply(X, Z))
% 6.58/1.22
% 6.58/1.22 Lemma 39: divide(X, divide(Y, Y)) = X.
% 6.58/1.22 Proof:
% 6.58/1.22 divide(X, divide(Y, Y))
% 6.58/1.22 = { by lemma 23 R->L }
% 6.58/1.22 divide(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)), divide(Y, Y))
% 6.58/1.22 = { by lemma 7 R->L }
% 6.58/1.22 divide(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)), multiply(divide(U, T), divide(divide(T, U), divide(Y, multiply(divide(Y, Y), Y)))))
% 6.58/1.22 = { by lemma 27 }
% 6.58/1.22 divide(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)), multiply(divide(U, T), divide(divide(T, U), divide(Y, divide(multiply(Y, S), S)))))
% 6.58/1.22 = { by lemma 29 R->L }
% 6.58/1.22 divide(inverse(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)))), multiply(divide(U, T), divide(divide(T, U), divide(Y, divide(multiply(Y, S), S)))))
% 6.58/1.22 = { by lemma 37 R->L }
% 6.58/1.22 divide(inverse(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)))), multiply(divide(U, T), divide(divide(T, U), divide(Y, multiply(divide(X2, X2), Y)))))
% 6.58/1.22 = { by lemma 24 R->L }
% 6.58/1.22 divide(inverse(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)))), multiply(divide(U, T), divide(divide(T, U), divide(Y, multiply(divide(divide(X2, X2), multiply(Y2, divide(Z2, multiply(Y2, Z2)))), Y)))))
% 6.58/1.23 = { by lemma 38 R->L }
% 6.58/1.23 divide(inverse(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)))), multiply(divide(U, T), divide(divide(T, U), divide(inverse(divide(divide(X2, X2), multiply(Y2, divide(Z2, multiply(Y2, Z2))))), multiply(X2, inverse(X2))))))
% 6.58/1.23 = { by lemma 30 }
% 6.58/1.23 divide(inverse(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)))), multiply(divide(U, T), divide(divide(T, U), divide(inverse(divide(divide(X2, X2), multiply(Y2, divide(Z2, multiply(Y2, Z2))))), divide(X2, X2)))))
% 6.58/1.23 = { by lemma 22 }
% 6.58/1.23 divide(inverse(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)))), multiply(divide(U, T), divide(divide(T, U), divide(inverse(divide(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)), multiply(Y2, divide(Z2, multiply(Y2, Z2))))), divide(multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z), Z)))))
% 6.58/1.23 = { by lemma 24 }
% 6.58/1.23 divide(inverse(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z)))), multiply(divide(U, T), divide(divide(T, U), divide(inverse(divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z))), divide(multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z), Z)))))
% 6.58/1.23 = { by lemma 3 }
% 6.58/1.23 divide(Z, multiply(multiply(divide(W, V), divide(divide(V, W), X)), Z))
% 6.58/1.23 = { by lemma 23 }
% 6.58/1.23 X
% 6.58/1.23
% 6.58/1.23 Lemma 40: divide(X, divide(divide(Y, Z), divide(W, multiply(X, W)))) = divide(multiply(divide(Z, Y), V), V).
% 6.58/1.23 Proof:
% 6.58/1.23 divide(X, divide(divide(Y, Z), divide(W, multiply(X, W))))
% 6.58/1.23 = { by lemma 7 R->L }
% 6.58/1.23 divide(multiply(divide(Z, Y), divide(divide(Y, Z), divide(W, multiply(X, W)))), divide(divide(Y, Z), divide(W, multiply(X, W))))
% 6.58/1.23 = { by lemma 10 R->L }
% 6.58/1.23 divide(multiply(divide(Z, Y), V), V)
% 6.58/1.23
% 6.58/1.23 Lemma 41: divide(multiply(X, Y), Y) = X.
% 6.58/1.23 Proof:
% 6.58/1.23 divide(multiply(X, Y), Y)
% 6.58/1.23 = { by lemma 10 }
% 6.58/1.23 divide(multiply(X, divide(divide(Z, W), divide(Z, W))), divide(divide(Z, W), divide(Z, W)))
% 6.58/1.23 = { by lemma 39 }
% 6.58/1.23 multiply(X, divide(divide(Z, W), divide(Z, W)))
% 6.58/1.23 = { by axiom 1 (multiply) }
% 6.58/1.23 divide(X, inverse(divide(divide(Z, W), divide(Z, W))))
% 6.58/1.23 = { by lemma 39 R->L }
% 6.58/1.23 divide(X, inverse(divide(divide(divide(Z, W), divide(inverse(divide(Z, W)), inverse(divide(Z, W)))), divide(Z, W))))
% 6.58/1.23 = { by lemma 30 R->L }
% 6.58/1.23 divide(X, inverse(divide(divide(divide(Z, W), multiply(inverse(divide(Z, W)), inverse(inverse(divide(Z, W))))), divide(Z, W))))
% 6.58/1.23 = { by lemma 29 R->L }
% 6.58/1.23 divide(X, inverse(divide(divide(inverse(inverse(divide(Z, W))), multiply(inverse(divide(Z, W)), inverse(inverse(divide(Z, W))))), divide(Z, W))))
% 6.58/1.23 = { by lemma 39 R->L }
% 6.58/1.23 divide(X, inverse(divide(divide(divide(inverse(inverse(divide(Z, W))), multiply(inverse(divide(Z, W)), inverse(inverse(divide(Z, W))))), divide(Z, W)), divide(V, V))))
% 6.58/1.23 = { by lemma 16 R->L }
% 6.58/1.23 divide(X, inverse(divide(divide(divide(inverse(inverse(divide(Z, W))), multiply(multiply(multiply(divide(W, Z), divide(divide(Z, W), divide(U, multiply(divide(W, Z), U)))), multiply(divide(Z, W), divide(divide(W, Z), divide(divide(Z, W), divide(U, multiply(divide(W, Z), U)))))), inverse(inverse(divide(Z, W))))), divide(Z, W)), divide(V, V))))
% 6.58/1.23 = { by lemma 40 }
% 6.58/1.23 divide(X, inverse(divide(divide(divide(inverse(inverse(divide(Z, W))), multiply(multiply(multiply(divide(W, Z), divide(divide(Z, W), divide(U, multiply(divide(W, Z), U)))), multiply(divide(Z, W), divide(multiply(divide(W, Z), T), T))), inverse(inverse(divide(Z, W))))), divide(Z, W)), divide(V, V))))
% 6.58/1.23 = { by lemma 7 }
% 6.58/1.23 divide(X, inverse(divide(divide(divide(inverse(inverse(divide(Z, W))), multiply(multiply(divide(W, Z), multiply(divide(Z, W), divide(multiply(divide(W, Z), T), T))), inverse(inverse(divide(Z, W))))), divide(Z, W)), divide(V, V))))
% 6.58/1.23 = { by lemma 17 R->L }
% 6.58/1.23 divide(X, inverse(divide(multiply(divide(divide(S, X2), Y2), divide(Y2, divide(multiply(divide(Z, W), divide(multiply(divide(W, Z), T), T)), divide(X2, S)))), divide(V, V))))
% 6.58/1.23 = { by lemma 12 R->L }
% 6.58/1.23 divide(X, inverse(divide(divide(inverse(Z2), multiply(divide(W2, V2), divide(divide(V2, W2), divide(Z2, multiply(divide(Z, W), divide(multiply(divide(W, Z), T), T)))))), divide(V, V))))
% 6.58/1.23 = { by lemma 13 }
% 6.58/1.23 divide(X, inverse(divide(divide(inverse(divide(multiply(divide(W, Z), T), T)), divide(Z, W)), divide(V, V))))
% 6.58/1.23 = { by lemma 40 R->L }
% 6.58/1.23 divide(X, inverse(divide(divide(inverse(divide(divide(W, Z), divide(divide(Z, W), divide(U2, multiply(divide(W, Z), U2))))), divide(Z, W)), divide(V, V))))
% 6.58/1.23 = { by lemma 21 R->L }
% 6.58/1.23 divide(X, inverse(inverse(divide(inverse(divide(divide(inverse(divide(divide(W, Z), divide(divide(Z, W), divide(U2, multiply(divide(W, Z), U2))))), divide(Z, W)), divide(V, V))), divide(divide(divide(Z, W), divide(U2, multiply(divide(W, Z), U2))), divide(inverse(divide(divide(W, Z), divide(divide(Z, W), divide(U2, multiply(divide(W, Z), U2))))), divide(Z, W)))))))
% 6.58/1.23 = { by lemma 20 }
% 6.58/1.23 divide(X, inverse(inverse(inverse(divide(divide(Z, W), divide(divide(V, V), divide(multiply(divide(W, Z), U2), U2)))))))
% 6.58/1.23 = { by lemma 19 }
% 6.58/1.23 divide(X, inverse(inverse(inverse(inverse(divide(V, V))))))
% 6.58/1.23 = { by lemma 29 }
% 6.58/1.23 divide(X, inverse(inverse(divide(V, V))))
% 6.58/1.23 = { by lemma 29 }
% 6.58/1.23 divide(X, divide(V, V))
% 6.58/1.23 = { by lemma 39 }
% 6.58/1.23 X
% 6.58/1.23
% 6.58/1.23 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 6.58/1.23 Proof:
% 6.58/1.23 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 6.58/1.23 = { by lemma 36 }
% 6.58/1.23 tuple(divide(X, X), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 6.58/1.23 = { by lemma 36 }
% 6.58/1.23 tuple(divide(X, X), multiply(divide(Y, Y), a2), multiply(multiply(a3, b3), c3))
% 6.58/1.23 = { by lemma 37 }
% 6.58/1.23 tuple(divide(X, X), divide(multiply(a2, Z), Z), multiply(multiply(a3, b3), c3))
% 6.58/1.23 = { by lemma 41 }
% 6.58/1.23 tuple(divide(X, X), a2, multiply(multiply(a3, b3), c3))
% 6.58/1.23 = { by lemma 29 R->L }
% 6.58/1.23 tuple(divide(X, X), a2, multiply(inverse(inverse(multiply(a3, b3))), c3))
% 6.58/1.23 = { by lemma 41 R->L }
% 6.58/1.23 tuple(divide(X, X), a2, divide(multiply(multiply(inverse(inverse(multiply(a3, b3))), c3), W), W))
% 6.58/1.23 = { by lemma 3 R->L }
% 6.58/1.23 tuple(divide(X, X), a2, divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(W, multiply(multiply(inverse(inverse(multiply(a3, b3))), c3), W)))))))
% 6.58/1.23 = { by lemma 38 R->L }
% 6.58/1.23 tuple(divide(X, X), a2, divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(inverse(multiply(inverse(inverse(multiply(a3, b3))), c3)), multiply(multiply(a3, b3), inverse(multiply(a3, b3)))))))))
% 6.58/1.23 = { by axiom 1 (multiply) }
% 6.58/1.23 tuple(divide(X, X), a2, divide(inverse(V), multiply(divide(U, T), divide(divide(T, U), divide(V, divide(inverse(multiply(inverse(inverse(multiply(a3, b3))), c3)), divide(multiply(a3, b3), inverse(inverse(multiply(a3, b3))))))))))
% 6.58/1.23 = { by lemma 3 }
% 6.58/1.23 tuple(divide(X, X), a2, divide(divide(multiply(a3, b3), inverse(inverse(multiply(a3, b3)))), inverse(multiply(inverse(inverse(multiply(a3, b3))), c3))))
% 6.58/1.23 = { by axiom 1 (multiply) R->L }
% 6.58/1.23 tuple(divide(X, X), a2, multiply(divide(multiply(a3, b3), inverse(inverse(multiply(a3, b3)))), multiply(inverse(inverse(multiply(a3, b3))), c3)))
% 6.58/1.23 = { by axiom 1 (multiply) }
% 6.58/1.23 tuple(divide(X, X), a2, multiply(divide(multiply(a3, b3), inverse(inverse(multiply(a3, b3)))), divide(inverse(inverse(multiply(a3, b3))), inverse(c3))))
% 6.58/1.23 = { by lemma 25 }
% 6.58/1.23 tuple(divide(X, X), a2, multiply(divide(multiply(a3, b3), b3), divide(b3, inverse(c3))))
% 6.58/1.23 = { by axiom 1 (multiply) R->L }
% 6.58/1.23 tuple(divide(X, X), a2, multiply(divide(multiply(a3, b3), b3), multiply(b3, c3)))
% 6.58/1.23 = { by lemma 35 }
% 6.58/1.23 tuple(divide(X, X), a2, divide(multiply(multiply(a3, multiply(b3, c3)), S), S))
% 6.58/1.23 = { by lemma 41 }
% 6.58/1.23 tuple(divide(X, X), a2, multiply(a3, multiply(b3, c3)))
% 6.58/1.23 = { by lemma 36 R->L }
% 6.58/1.23 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 6.58/1.23 % SZS output end Proof
% 6.58/1.23
% 6.58/1.23 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------