TSTP Solution File: GRP072-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP072-1 : 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 : n029.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 11.68s 1.90s
% Output : Proof 13.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP072-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.12/0.13 % 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 : n029.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 21:32:26 EDT 2023
% 0.14/0.34 % CPUTime :
% 11.68/1.90 Command-line arguments: --no-flatten-goal
% 11.68/1.90
% 11.68/1.90 % SZS status Unsatisfiable
% 11.68/1.90
% 13.04/2.04 % SZS output start Proof
% 13.04/2.04 Take the following subset of the input axioms:
% 13.04/2.04 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=divide(X, inverse(Y))).
% 13.04/2.04 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)))).
% 13.04/2.04 fof(single_axiom, axiom, ![Z, U, X2, Y2]: divide(divide(inverse(divide(X2, Y2)), divide(divide(Z, U), X2)), divide(U, Z))=Y2).
% 13.04/2.04
% 13.04/2.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.04/2.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.04/2.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.04/2.04 fresh(y, y, x1...xn) = u
% 13.04/2.04 C => fresh(s, t, x1...xn) = v
% 13.04/2.04 where fresh is a fresh function symbol and x1..xn are the free
% 13.04/2.04 variables of u and v.
% 13.04/2.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.04/2.04 input problem has no model of domain size 1).
% 13.04/2.04
% 13.04/2.04 The encoding turns the above axioms into the following unit equations and goals:
% 13.04/2.04
% 13.04/2.04 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 13.04/2.04 Axiom 2 (single_axiom): divide(divide(inverse(divide(X, Y)), divide(divide(Z, W), X)), divide(W, Z)) = Y.
% 13.04/2.04
% 13.04/2.04 Lemma 3: divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W))) = Z.
% 13.04/2.04 Proof:
% 13.04/2.04 divide(divide(inverse(divide(divide(X, Y), Z)), W), multiply(divide(divide(Y, X), V), divide(V, W)))
% 13.04/2.04 = { by axiom 1 (multiply) }
% 13.04/2.04 divide(divide(inverse(divide(divide(X, Y), Z)), W), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 13.04/2.04 = { by axiom 2 (single_axiom) R->L }
% 13.04/2.04 divide(divide(inverse(divide(divide(X, Y), Z)), divide(divide(inverse(divide(V, W)), divide(divide(Y, X), V)), divide(X, Y))), divide(divide(divide(Y, X), V), inverse(divide(V, W))))
% 13.04/2.04 = { by axiom 2 (single_axiom) }
% 13.04/2.04 Z
% 13.04/2.04
% 13.04/2.04 Lemma 4: divide(divide(inverse(X), Y), multiply(divide(multiply(Z, divide(divide(W, V), X)), U), divide(U, Y))) = multiply(divide(divide(V, W), T), divide(T, Z)).
% 13.04/2.04 Proof:
% 13.04/2.04 divide(divide(inverse(X), Y), multiply(divide(multiply(Z, divide(divide(W, V), X)), U), divide(U, Y)))
% 13.04/2.04 = { by axiom 1 (multiply) }
% 13.04/2.04 divide(divide(inverse(X), Y), multiply(divide(divide(Z, inverse(divide(divide(W, V), X))), U), divide(U, Y)))
% 13.04/2.04 = { by lemma 3 R->L }
% 13.04/2.04 divide(divide(inverse(divide(divide(inverse(divide(divide(W, V), X)), Z), multiply(divide(divide(V, W), T), divide(T, Z)))), Y), multiply(divide(divide(Z, inverse(divide(divide(W, V), X))), U), divide(U, Y)))
% 13.04/2.04 = { by lemma 3 }
% 13.04/2.04 multiply(divide(divide(V, W), T), divide(T, Z))
% 13.04/2.04
% 13.04/2.04 Lemma 5: multiply(divide(divide(X, Y), V), divide(V, W)) = multiply(divide(divide(X, Y), Z), divide(Z, W)).
% 13.04/2.04 Proof:
% 13.04/2.04 multiply(divide(divide(X, Y), V), divide(V, W))
% 13.04/2.04 = { by lemma 3 R->L }
% 13.04/2.04 divide(divide(inverse(divide(divide(inverse(divide(divide(Y, X), U)), W), multiply(divide(divide(X, Y), V), divide(V, W)))), T), multiply(divide(divide(W, inverse(divide(divide(Y, X), U))), S), divide(S, T)))
% 13.04/2.04 = { by lemma 3 }
% 13.04/2.04 divide(divide(inverse(U), T), multiply(divide(divide(W, inverse(divide(divide(Y, X), U))), S), divide(S, T)))
% 13.04/2.04 = { by lemma 3 R->L }
% 13.04/2.04 divide(divide(inverse(divide(divide(inverse(divide(divide(Y, X), U)), W), multiply(divide(divide(X, Y), Z), divide(Z, W)))), T), multiply(divide(divide(W, inverse(divide(divide(Y, X), U))), S), divide(S, T)))
% 13.04/2.04 = { by lemma 3 }
% 13.04/2.04 multiply(divide(divide(X, Y), Z), divide(Z, W))
% 13.04/2.04
% 13.04/2.04 Lemma 6: divide(divide(inverse(divide(X, Y)), divide(multiply(Z, W), X)), divide(inverse(W), Z)) = Y.
% 13.04/2.04 Proof:
% 13.04/2.04 divide(divide(inverse(divide(X, Y)), divide(multiply(Z, W), X)), divide(inverse(W), Z))
% 13.04/2.04 = { by axiom 1 (multiply) }
% 13.04/2.04 divide(divide(inverse(divide(X, Y)), divide(divide(Z, inverse(W)), X)), divide(inverse(W), Z))
% 13.04/2.04 = { by axiom 2 (single_axiom) }
% 13.04/2.04 Y
% 13.04/2.04
% 13.04/2.04 Lemma 7: multiply(divide(divide(inverse(divide(X, Y)), divide(multiply(Z, W), X)), V), divide(V, U)) = multiply(Y, divide(divide(inverse(W), Z), U)).
% 13.04/2.04 Proof:
% 13.04/2.04 multiply(divide(divide(inverse(divide(X, Y)), divide(multiply(Z, W), X)), V), divide(V, U))
% 13.04/2.04 = { by lemma 5 }
% 13.04/2.04 multiply(divide(divide(inverse(divide(X, Y)), divide(multiply(Z, W), X)), divide(inverse(W), Z)), divide(divide(inverse(W), Z), U))
% 13.04/2.04 = { by lemma 6 }
% 13.04/2.04 multiply(Y, divide(divide(inverse(W), Z), U))
% 13.04/2.04
% 13.04/2.04 Lemma 8: divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(W, V), U), divide(U, Z))) = multiply(divide(multiply(divide(divide(Y, X), T), divide(T, V)), S), divide(S, W)).
% 13.04/2.04 Proof:
% 13.04/2.04 divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(W, V), U), divide(U, Z)))
% 13.04/2.04 = { by axiom 2 (single_axiom) R->L }
% 13.04/2.04 divide(divide(inverse(divide(X, Y)), Z), multiply(divide(multiply(W, divide(divide(inverse(divide(T, V)), divide(divide(Y, X), T)), divide(X, Y))), U), divide(U, Z)))
% 13.04/2.04 = { by lemma 4 }
% 13.04/2.04 multiply(divide(divide(divide(divide(Y, X), T), inverse(divide(T, V))), S), divide(S, W))
% 13.04/2.04 = { by axiom 1 (multiply) R->L }
% 13.04/2.04 multiply(divide(multiply(divide(divide(Y, X), T), divide(T, V)), S), divide(S, W))
% 13.04/2.04
% 13.04/2.04 Lemma 9: divide(divide(inverse(divide(divide(inverse(X), Y), Z)), W), multiply(divide(multiply(Y, X), V), divide(V, W))) = Z.
% 13.04/2.04 Proof:
% 13.04/2.04 divide(divide(inverse(divide(divide(inverse(X), Y), Z)), W), multiply(divide(multiply(Y, X), V), divide(V, W)))
% 13.04/2.04 = { by axiom 1 (multiply) }
% 13.04/2.04 divide(divide(inverse(divide(divide(inverse(X), Y), Z)), W), divide(divide(multiply(Y, X), V), inverse(divide(V, W))))
% 13.04/2.04 = { by lemma 6 R->L }
% 13.04/2.04 divide(divide(inverse(divide(divide(inverse(X), Y), Z)), divide(divide(inverse(divide(V, W)), divide(multiply(Y, X), V)), divide(inverse(X), Y))), divide(divide(multiply(Y, X), V), inverse(divide(V, W))))
% 13.04/2.04 = { by axiom 2 (single_axiom) }
% 13.04/2.04 Z
% 13.04/2.04
% 13.04/2.04 Lemma 10: multiply(divide(multiply(divide(divide(X, divide(inverse(Y), Z)), W), divide(W, Y)), V), divide(V, Z)) = X.
% 13.04/2.04 Proof:
% 13.04/2.04 multiply(divide(multiply(divide(divide(X, divide(inverse(Y), Z)), W), divide(W, Y)), V), divide(V, Z))
% 13.04/2.04 = { by lemma 8 R->L }
% 13.04/2.04 divide(divide(inverse(divide(divide(inverse(Y), Z), X)), U), multiply(divide(multiply(Z, Y), T), divide(T, U)))
% 13.04/2.04 = { by lemma 9 }
% 13.04/2.04 X
% 13.04/2.04
% 13.04/2.04 Lemma 11: multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V)) = divide(inverse(divide(U, X)), divide(multiply(V, Z), U)).
% 13.04/2.04 Proof:
% 13.04/2.04 multiply(divide(multiply(divide(X, Y), divide(Y, Z)), W), divide(W, V))
% 13.04/2.04 = { by axiom 2 (single_axiom) R->L }
% 13.04/2.04 multiply(divide(multiply(divide(divide(divide(inverse(divide(U, X)), divide(divide(V, inverse(Z)), U)), divide(inverse(Z), V)), Y), divide(Y, Z)), W), divide(W, V))
% 13.04/2.05 = { by lemma 10 }
% 13.04/2.05 divide(inverse(divide(U, X)), divide(divide(V, inverse(Z)), U))
% 13.04/2.05 = { by axiom 1 (multiply) R->L }
% 13.04/2.05 divide(inverse(divide(U, X)), divide(multiply(V, Z), U))
% 13.04/2.05
% 13.04/2.05 Lemma 12: divide(divide(inverse(X), Y), divide(inverse(divide(Z, divide(W, V))), divide(multiply(Y, X), Z))) = divide(V, W).
% 13.04/2.05 Proof:
% 13.04/2.05 divide(divide(inverse(X), Y), divide(inverse(divide(Z, divide(W, V))), divide(multiply(Y, X), Z)))
% 13.04/2.05 = { by lemma 11 R->L }
% 13.04/2.05 divide(divide(inverse(X), Y), multiply(divide(multiply(divide(divide(W, V), U), divide(U, X)), T), divide(T, Y)))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 divide(divide(inverse(X), Y), multiply(divide(divide(divide(divide(W, V), U), inverse(divide(U, X))), T), divide(T, Y)))
% 13.04/2.05 = { by axiom 2 (single_axiom) R->L }
% 13.04/2.05 divide(divide(inverse(divide(divide(inverse(divide(U, X)), divide(divide(W, V), U)), divide(V, W))), Y), multiply(divide(divide(divide(divide(W, V), U), inverse(divide(U, X))), T), divide(T, Y)))
% 13.04/2.05 = { by lemma 3 }
% 13.04/2.05 divide(V, W)
% 13.04/2.05
% 13.04/2.05 Lemma 13: multiply(divide(X, W), divide(W, Z)) = multiply(divide(X, Y), divide(Y, Z)).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(divide(X, W), divide(W, Z))
% 13.04/2.05 = { by axiom 2 (single_axiom) R->L }
% 13.04/2.05 multiply(divide(divide(divide(inverse(divide(V, X)), divide(divide(U, T), V)), divide(T, U)), W), divide(W, Z))
% 13.04/2.05 = { by lemma 5 }
% 13.04/2.05 multiply(divide(divide(divide(inverse(divide(V, X)), divide(divide(U, T), V)), divide(T, U)), Y), divide(Y, Z))
% 13.04/2.05 = { by axiom 2 (single_axiom) }
% 13.04/2.05 multiply(divide(X, Y), divide(Y, Z))
% 13.04/2.05
% 13.04/2.05 Lemma 14: multiply(divide(X, divide(inverse(divide(Y, Z)), divide(multiply(W, V), Y))), Z) = multiply(divide(X, U), divide(U, divide(inverse(V), W))).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(divide(X, divide(inverse(divide(Y, Z)), divide(multiply(W, V), Y))), Z)
% 13.04/2.05 = { by lemma 6 R->L }
% 13.04/2.05 multiply(divide(X, divide(inverse(divide(Y, Z)), divide(multiply(W, V), Y))), divide(divide(inverse(divide(Y, Z)), divide(multiply(W, V), Y)), divide(inverse(V), W)))
% 13.04/2.05 = { by lemma 13 R->L }
% 13.04/2.05 multiply(divide(X, U), divide(U, divide(inverse(V), W)))
% 13.04/2.05
% 13.04/2.05 Lemma 15: multiply(divide(Z, W), divide(W, Z)) = multiply(divide(X, Y), divide(Y, X)).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(divide(Z, W), divide(W, Z))
% 13.04/2.05 = { by lemma 12 R->L }
% 13.04/2.05 multiply(divide(divide(inverse(V), U), divide(inverse(divide(X2, divide(W, Z))), divide(multiply(U, V), X2))), divide(W, Z))
% 13.04/2.05 = { by lemma 14 }
% 13.04/2.05 multiply(divide(divide(inverse(V), U), S), divide(S, divide(inverse(V), U)))
% 13.04/2.05 = { by lemma 14 R->L }
% 13.04/2.05 multiply(divide(divide(inverse(V), U), divide(inverse(divide(T, divide(Y, X))), divide(multiply(U, V), T))), divide(Y, X))
% 13.04/2.05 = { by lemma 12 }
% 13.04/2.05 multiply(divide(X, Y), divide(Y, X))
% 13.04/2.05
% 13.04/2.05 Lemma 16: multiply(multiply(X, Y), divide(inverse(Y), Z)) = multiply(divide(X, W), divide(W, Z)).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(multiply(X, Y), divide(inverse(Y), Z))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 multiply(divide(X, inverse(Y)), divide(inverse(Y), Z))
% 13.04/2.05 = { by lemma 13 R->L }
% 13.04/2.05 multiply(divide(X, W), divide(W, Z))
% 13.04/2.05
% 13.04/2.05 Lemma 17: multiply(multiply(divide(X, Y), divide(Y, X)), divide(inverse(multiply(Z, W)), V)) = multiply(divide(divide(inverse(W), Z), U), divide(U, V)).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(multiply(divide(X, Y), divide(Y, X)), divide(inverse(multiply(Z, W)), V))
% 13.04/2.05 = { by lemma 15 }
% 13.04/2.05 multiply(multiply(divide(inverse(W), Z), divide(Z, inverse(W))), divide(inverse(multiply(Z, W)), V))
% 13.04/2.05 = { by axiom 1 (multiply) R->L }
% 13.04/2.05 multiply(multiply(divide(inverse(W), Z), multiply(Z, W)), divide(inverse(multiply(Z, W)), V))
% 13.04/2.05 = { by lemma 16 }
% 13.04/2.05 multiply(divide(divide(inverse(W), Z), U), divide(U, V))
% 13.04/2.05
% 13.04/2.05 Lemma 18: divide(divide(inverse(multiply(X, Y)), divide(divide(Z, W), X)), divide(W, Z)) = inverse(Y).
% 13.04/2.05 Proof:
% 13.04/2.05 divide(divide(inverse(multiply(X, Y)), divide(divide(Z, W), X)), divide(W, Z))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 divide(divide(inverse(divide(X, inverse(Y))), divide(divide(Z, W), X)), divide(W, Z))
% 13.04/2.05 = { by axiom 2 (single_axiom) }
% 13.04/2.05 inverse(Y)
% 13.04/2.05
% 13.04/2.05 Lemma 19: multiply(X, divide(divide(inverse(divide(Y, Z)), divide(Z, Y)), divide(W, V))) = multiply(X, divide(V, W)).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(X, divide(divide(inverse(divide(Y, Z)), divide(Z, Y)), divide(W, V)))
% 13.04/2.05 = { by lemma 7 R->L }
% 13.04/2.05 multiply(divide(divide(inverse(divide(U, X)), divide(multiply(divide(Z, Y), divide(Y, Z)), U)), T), divide(T, divide(W, V)))
% 13.04/2.05 = { by lemma 15 }
% 13.04/2.05 multiply(divide(divide(inverse(divide(U, X)), divide(multiply(divide(divide(V, W), S), divide(S, divide(V, W))), U)), T), divide(T, divide(W, V)))
% 13.04/2.05 = { by lemma 7 }
% 13.04/2.05 multiply(X, divide(divide(inverse(divide(S, divide(V, W))), divide(divide(V, W), S)), divide(W, V)))
% 13.04/2.05 = { by axiom 2 (single_axiom) }
% 13.04/2.05 multiply(X, divide(V, W))
% 13.04/2.05
% 13.04/2.05 Lemma 20: inverse(divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Z, W))) = inverse(divide(W, Z)).
% 13.04/2.05 Proof:
% 13.04/2.05 inverse(divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Z, W)))
% 13.04/2.05 = { by lemma 18 R->L }
% 13.04/2.05 divide(divide(inverse(multiply(V, divide(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Z, W)))), divide(divide(U, T), V)), divide(T, U))
% 13.04/2.05 = { by lemma 19 }
% 13.04/2.05 divide(divide(inverse(multiply(V, divide(W, Z))), divide(divide(U, T), V)), divide(T, U))
% 13.04/2.05 = { by lemma 18 }
% 13.04/2.05 inverse(divide(W, Z))
% 13.04/2.05
% 13.04/2.05 Lemma 21: divide(inverse(divide(W, V)), divide(multiply(Z, V), W)) = divide(inverse(divide(X, Y)), divide(multiply(Z, Y), X)).
% 13.04/2.05 Proof:
% 13.04/2.05 divide(inverse(divide(W, V)), divide(multiply(Z, V), W))
% 13.04/2.05 = { by lemma 11 R->L }
% 13.04/2.05 multiply(divide(multiply(divide(V, S), divide(S, V)), T), divide(T, Z))
% 13.04/2.05 = { by lemma 15 }
% 13.04/2.05 multiply(divide(multiply(divide(Y, U), divide(U, Y)), T), divide(T, Z))
% 13.04/2.05 = { by lemma 11 }
% 13.04/2.05 divide(inverse(divide(X, Y)), divide(multiply(Z, Y), X))
% 13.04/2.05
% 13.04/2.05 Lemma 22: multiply(divide(multiply(X, W), V), divide(V, W)) = multiply(divide(multiply(X, Y), Z), divide(Z, Y)).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(divide(multiply(X, W), V), divide(V, W))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 divide(divide(multiply(X, W), V), inverse(divide(V, W)))
% 13.04/2.05 = { by lemma 12 R->L }
% 13.04/2.05 divide(divide(inverse(U), T), divide(inverse(divide(S, divide(inverse(divide(V, W)), divide(multiply(X, W), V)))), divide(multiply(T, U), S)))
% 13.04/2.05 = { by lemma 21 }
% 13.04/2.05 divide(divide(inverse(U), T), divide(inverse(divide(S, divide(inverse(divide(Z, Y)), divide(multiply(X, Y), Z)))), divide(multiply(T, U), S)))
% 13.04/2.05 = { by lemma 12 }
% 13.04/2.05 divide(divide(multiply(X, Y), Z), inverse(divide(Z, Y)))
% 13.04/2.05 = { by axiom 1 (multiply) R->L }
% 13.04/2.05 multiply(divide(multiply(X, Y), Z), divide(Z, Y))
% 13.04/2.05
% 13.04/2.05 Lemma 23: divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), W), X)) = multiply(divide(multiply(divide(Y, Z), V), U), divide(U, V)).
% 13.04/2.05 Proof:
% 13.04/2.05 divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), W), X))
% 13.04/2.05 = { by lemma 11 R->L }
% 13.04/2.05 multiply(divide(multiply(divide(Y, Z), divide(Z, W)), T), divide(T, divide(Z, W)))
% 13.04/2.05 = { by lemma 22 R->L }
% 13.04/2.05 multiply(divide(multiply(divide(Y, Z), V), U), divide(U, V))
% 13.04/2.05
% 13.04/2.05 Lemma 24: inverse(divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), Y), X))) = inverse(divide(W, Z)).
% 13.04/2.05 Proof:
% 13.04/2.05 inverse(divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), Y), X)))
% 13.04/2.05 = { by lemma 11 R->L }
% 13.04/2.05 inverse(multiply(divide(multiply(divide(Y, V), divide(V, Y)), U), divide(U, divide(Z, W))))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 inverse(divide(divide(multiply(divide(Y, V), divide(V, Y)), U), inverse(divide(U, divide(Z, W)))))
% 13.04/2.05 = { by lemma 20 R->L }
% 13.04/2.05 inverse(divide(divide(inverse(divide(V, Y)), divide(Y, V)), divide(inverse(divide(U, divide(Z, W))), divide(multiply(divide(Y, V), divide(V, Y)), U))))
% 13.04/2.05 = { by lemma 12 }
% 13.04/2.05 inverse(divide(W, Z))
% 13.04/2.05
% 13.04/2.05 Lemma 25: multiply(multiply(divide(X, Y), divide(Y, X)), divide(inverse(divide(Z, W)), V)) = multiply(divide(divide(W, Z), U), divide(U, V)).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(multiply(divide(X, Y), divide(Y, X)), divide(inverse(divide(Z, W)), V))
% 13.04/2.05 = { by lemma 15 }
% 13.04/2.05 multiply(multiply(divide(W, Z), divide(Z, W)), divide(inverse(divide(Z, W)), V))
% 13.04/2.05 = { by lemma 16 }
% 13.04/2.05 multiply(divide(divide(W, Z), U), divide(U, V))
% 13.04/2.05
% 13.04/2.05 Lemma 26: multiply(divide(multiply(divide(X, Y), Y), Z), divide(Z, W)) = divide(X, W).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(divide(multiply(divide(X, Y), Y), Z), divide(Z, W))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 multiply(divide(divide(divide(X, Y), inverse(Y)), Z), divide(Z, W))
% 13.04/2.05 = { by lemma 4 R->L }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(W, divide(divide(inverse(Y), divide(X, Y)), V)), T), divide(T, U)))
% 13.04/2.05 = { by lemma 7 R->L }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(divide(divide(inverse(divide(S, W)), divide(multiply(divide(X, Y), Y), S)), X2), divide(X2, V)), T), divide(T, U)))
% 13.04/2.05 = { by lemma 17 R->L }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), divide(inverse(multiply(divide(multiply(divide(X, Y), Y), S), divide(S, W))), V)), T), divide(T, U)))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), divide(inverse(divide(divide(multiply(divide(X, Y), Y), S), inverse(divide(S, W)))), V)), T), divide(T, U)))
% 13.04/2.05 = { by lemma 20 R->L }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), divide(inverse(divide(divide(inverse(divide(W2, divide(inverse(divide(V2, U2)), divide(multiply(divide(W, X), U2), V2)))), divide(divide(inverse(divide(V2, U2)), divide(multiply(divide(W, X), U2), V2)), W2)), divide(inverse(divide(S, W)), divide(multiply(divide(X, Y), Y), S)))), V)), T), divide(T, U)))
% 13.04/2.05 = { by lemma 23 }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), divide(inverse(divide(divide(inverse(divide(W2, divide(inverse(divide(V2, U2)), divide(multiply(divide(W, X), U2), V2)))), divide(divide(inverse(divide(V2, U2)), divide(multiply(divide(W, X), U2), V2)), W2)), multiply(divide(multiply(divide(W, X), U2), V2), divide(V2, U2)))), V)), T), divide(T, U)))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), divide(inverse(divide(divide(inverse(divide(W2, divide(inverse(divide(V2, U2)), divide(multiply(divide(W, X), U2), V2)))), divide(divide(inverse(divide(V2, U2)), divide(multiply(divide(W, X), U2), V2)), W2)), divide(divide(multiply(divide(W, X), U2), V2), inverse(divide(V2, U2))))), V)), T), divide(T, U)))
% 13.04/2.05 = { by axiom 2 (single_axiom) }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), divide(inverse(divide(inverse(divide(V2, U2)), divide(multiply(divide(W, X), U2), V2))), V)), T), divide(T, U)))
% 13.04/2.05 = { by lemma 24 }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(multiply(divide(Y2, Z2), divide(Z2, Y2)), divide(inverse(divide(X, W)), V)), T), divide(T, U)))
% 13.04/2.05 = { by lemma 25 }
% 13.04/2.05 divide(divide(inverse(V), U), multiply(divide(multiply(divide(divide(W, X), T2), divide(T2, V)), T), divide(T, U)))
% 13.04/2.05 = { by lemma 11 }
% 13.04/2.05 divide(divide(inverse(V), U), divide(inverse(divide(S2, divide(W, X))), divide(multiply(U, V), S2)))
% 13.04/2.05 = { by lemma 12 }
% 13.04/2.05 divide(X, W)
% 13.04/2.05
% 13.04/2.05 Lemma 27: divide(divide(inverse(divide(inverse(X), Y)), multiply(divide(Z, W), X)), divide(W, Z)) = Y.
% 13.04/2.05 Proof:
% 13.04/2.05 divide(divide(inverse(divide(inverse(X), Y)), multiply(divide(Z, W), X)), divide(W, Z))
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 divide(divide(inverse(divide(inverse(X), Y)), divide(divide(Z, W), inverse(X))), divide(W, Z))
% 13.04/2.05 = { by axiom 2 (single_axiom) }
% 13.04/2.05 Y
% 13.04/2.05
% 13.04/2.05 Lemma 28: divide(divide(inverse(divide(X, Y)), multiply(divide(Z, W), divide(W, Z))), divide(V, U)) = divide(multiply(divide(Y, X), U), V).
% 13.04/2.05 Proof:
% 13.04/2.05 divide(divide(inverse(divide(X, Y)), multiply(divide(Z, W), divide(W, Z))), divide(V, U))
% 13.04/2.05 = { by lemma 24 R->L }
% 13.04/2.05 divide(divide(inverse(divide(inverse(divide(V, U)), divide(multiply(divide(Y, X), U), V))), multiply(divide(Z, W), divide(W, Z))), divide(V, U))
% 13.04/2.05 = { by lemma 15 }
% 13.04/2.05 divide(divide(inverse(divide(inverse(divide(V, U)), divide(multiply(divide(Y, X), U), V))), multiply(divide(U, V), divide(V, U))), divide(V, U))
% 13.04/2.05 = { by lemma 27 }
% 13.04/2.05 divide(multiply(divide(Y, X), U), V)
% 13.04/2.05
% 13.04/2.05 Lemma 29: divide(multiply(multiply(X, divide(Y, Z)), Z), Y) = X.
% 13.04/2.05 Proof:
% 13.04/2.05 divide(multiply(multiply(X, divide(Y, Z)), Z), Y)
% 13.04/2.05 = { by axiom 1 (multiply) }
% 13.04/2.05 divide(multiply(divide(X, inverse(divide(Y, Z))), Z), Y)
% 13.04/2.05 = { by lemma 28 R->L }
% 13.04/2.05 divide(divide(inverse(divide(inverse(divide(Y, Z)), X)), multiply(divide(Z, Y), divide(Y, Z))), divide(Y, Z))
% 13.04/2.05 = { by lemma 27 }
% 13.04/2.05 X
% 13.04/2.05
% 13.04/2.05 Lemma 30: multiply(divide(X, Z), Z) = multiply(divide(X, Y), Y).
% 13.04/2.05 Proof:
% 13.04/2.05 multiply(divide(X, Z), Z)
% 13.04/2.05 = { by lemma 26 R->L }
% 13.04/2.05 multiply(multiply(divide(multiply(divide(X, Y), Y), S), divide(S, Z)), Z)
% 13.04/2.06 = { by lemma 3 R->L }
% 13.04/2.06 divide(divide(inverse(divide(divide(W, V), multiply(multiply(divide(multiply(divide(X, Y), Y), S), divide(S, Z)), Z))), U), multiply(divide(divide(V, W), T), divide(T, U)))
% 13.04/2.06 = { by lemma 29 R->L }
% 13.04/2.06 divide(divide(inverse(divide(multiply(multiply(divide(divide(W, V), multiply(multiply(divide(multiply(divide(X, Y), Y), S), divide(S, Z)), Z)), divide(multiply(divide(X, Y), Y), S)), S), multiply(divide(X, Y), Y))), U), multiply(divide(divide(V, W), T), divide(T, U)))
% 13.04/2.06 = { by lemma 29 R->L }
% 13.04/2.06 divide(divide(inverse(divide(multiply(multiply(divide(divide(W, V), multiply(multiply(divide(multiply(divide(X, Y), Y), S), divide(S, Z)), Z)), divide(multiply(multiply(divide(multiply(divide(X, Y), Y), S), divide(S, Z)), Z), S)), S), multiply(divide(X, Y), Y))), U), multiply(divide(divide(V, W), T), divide(T, U)))
% 13.04/2.06 = { by lemma 13 R->L }
% 13.04/2.06 divide(divide(inverse(divide(multiply(multiply(divide(divide(W, V), multiply(divide(X, Y), Y)), divide(multiply(divide(X, Y), Y), S)), S), multiply(divide(X, Y), Y))), U), multiply(divide(divide(V, W), T), divide(T, U)))
% 13.04/2.06 = { by lemma 29 }
% 13.04/2.06 divide(divide(inverse(divide(divide(W, V), multiply(divide(X, Y), Y))), U), multiply(divide(divide(V, W), T), divide(T, U)))
% 13.04/2.06 = { by lemma 3 }
% 13.04/2.06 multiply(divide(X, Y), Y)
% 13.04/2.06
% 13.04/2.06 Lemma 31: divide(multiply(divide(Z, W), W), Z) = divide(multiply(divide(X, Y), Y), X).
% 13.04/2.06 Proof:
% 13.04/2.06 divide(multiply(divide(Z, W), W), Z)
% 13.04/2.06 = { by lemma 12 R->L }
% 13.04/2.06 divide(divide(inverse(V), U), divide(inverse(divide(T, divide(Z, multiply(divide(Z, W), W)))), divide(multiply(U, V), T)))
% 13.04/2.06 = { by lemma 26 R->L }
% 13.04/2.06 divide(divide(inverse(V), U), divide(inverse(divide(T, multiply(divide(multiply(divide(Z, W), W), X2), divide(X2, multiply(divide(Z, W), W))))), divide(multiply(U, V), T)))
% 13.04/2.06 = { by lemma 15 R->L }
% 13.04/2.06 divide(divide(inverse(V), U), divide(inverse(divide(T, multiply(divide(multiply(divide(X, Y), Y), S), divide(S, multiply(divide(X, Y), Y))))), divide(multiply(U, V), T)))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 divide(divide(inverse(V), U), divide(inverse(divide(T, divide(X, multiply(divide(X, Y), Y)))), divide(multiply(U, V), T)))
% 13.04/2.06 = { by lemma 12 }
% 13.04/2.06 divide(multiply(divide(X, Y), Y), X)
% 13.04/2.06
% 13.04/2.06 Lemma 32: multiply(divide(multiply(divide(X, Y), Y), X), Z) = Z.
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(divide(multiply(divide(X, Y), Y), X), Z)
% 13.04/2.06 = { by lemma 31 }
% 13.04/2.06 multiply(divide(multiply(divide(divide(inverse(divide(W, Z)), divide(divide(V, U), W)), T), T), divide(inverse(divide(W, Z)), divide(divide(V, U), W))), Z)
% 13.04/2.06 = { by axiom 2 (single_axiom) R->L }
% 13.04/2.06 multiply(divide(multiply(divide(divide(inverse(divide(W, Z)), divide(divide(V, U), W)), T), T), divide(inverse(divide(W, Z)), divide(divide(V, U), W))), divide(divide(inverse(divide(W, Z)), divide(divide(V, U), W)), divide(U, V)))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 divide(divide(inverse(divide(W, Z)), divide(divide(V, U), W)), divide(U, V))
% 13.04/2.06 = { by axiom 2 (single_axiom) }
% 13.04/2.06 Z
% 13.04/2.06
% 13.04/2.06 Lemma 33: multiply(divide(X, Y), divide(Y, X)) = divide(Z, multiply(divide(Z, W), W)).
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(divide(X, Y), divide(Y, X))
% 13.04/2.06 = { by lemma 15 }
% 13.04/2.06 multiply(divide(multiply(divide(Z, W), W), V), divide(V, multiply(divide(Z, W), W)))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 divide(Z, multiply(divide(Z, W), W))
% 13.04/2.06
% 13.04/2.06 Lemma 34: divide(multiply(divide(X, Y), Y), X) = divide(Z, multiply(divide(Z, W), W)).
% 13.04/2.06 Proof:
% 13.04/2.06 divide(multiply(divide(X, Y), Y), X)
% 13.04/2.06 = { by lemma 26 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(multiply(divide(X, Y), Y), X), X), V), divide(V, X))
% 13.04/2.06 = { by lemma 32 }
% 13.04/2.06 multiply(divide(X, V), divide(V, X))
% 13.04/2.06 = { by lemma 33 }
% 13.04/2.06 divide(Z, multiply(divide(Z, W), W))
% 13.04/2.06
% 13.04/2.06 Lemma 35: multiply(multiply(divide(inverse(X), Y), Y), X) = divide(Z, multiply(divide(Z, W), W)).
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(multiply(divide(inverse(X), Y), Y), X)
% 13.04/2.06 = { by axiom 1 (multiply) }
% 13.04/2.06 divide(multiply(divide(inverse(X), Y), Y), inverse(X))
% 13.04/2.06 = { by lemma 31 R->L }
% 13.04/2.06 divide(multiply(divide(V, U), U), V)
% 13.04/2.06 = { by lemma 34 }
% 13.04/2.06 divide(Z, multiply(divide(Z, W), W))
% 13.04/2.06
% 13.04/2.06 Lemma 36: divide(inverse(divide(X, divide(Y, divide(inverse(Z), W)))), divide(multiply(W, Z), X)) = Y.
% 13.04/2.06 Proof:
% 13.04/2.06 divide(inverse(divide(X, divide(Y, divide(inverse(Z), W)))), divide(multiply(W, Z), X))
% 13.04/2.06 = { by lemma 11 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(divide(Y, divide(inverse(Z), W)), V), divide(V, Z)), U), divide(U, W))
% 13.04/2.06 = { by lemma 10 }
% 13.04/2.06 Y
% 13.04/2.06
% 13.04/2.06 Lemma 37: multiply(divide(X, multiply(divide(X, Y), Y)), Z) = Z.
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(divide(X, multiply(divide(X, Y), Y)), Z)
% 13.04/2.06 = { by lemma 35 R->L }
% 13.04/2.06 multiply(multiply(multiply(divide(inverse(divide(W, divide(Z, divide(inverse(V), U)))), T), T), divide(W, divide(Z, divide(inverse(V), U)))), Z)
% 13.04/2.06 = { by axiom 1 (multiply) }
% 13.04/2.06 multiply(divide(multiply(divide(inverse(divide(W, divide(Z, divide(inverse(V), U)))), T), T), inverse(divide(W, divide(Z, divide(inverse(V), U))))), Z)
% 13.04/2.06 = { by lemma 36 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(inverse(divide(W, divide(Z, divide(inverse(V), U)))), T), T), inverse(divide(W, divide(Z, divide(inverse(V), U))))), divide(inverse(divide(W, divide(Z, divide(inverse(V), U)))), divide(multiply(U, V), W)))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 divide(inverse(divide(W, divide(Z, divide(inverse(V), U)))), divide(multiply(U, V), W))
% 13.04/2.06 = { by lemma 36 }
% 13.04/2.06 Z
% 13.04/2.06
% 13.04/2.06 Lemma 38: divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), Y), X)) = multiply(divide(multiply(divide(W, Z), V), U), divide(U, V)).
% 13.04/2.06 Proof:
% 13.04/2.06 divide(inverse(divide(X, Y)), divide(multiply(divide(Z, W), Y), X))
% 13.04/2.06 = { by lemma 21 }
% 13.04/2.06 divide(inverse(divide(T, divide(S, X2))), divide(multiply(divide(Z, W), divide(S, X2)), T))
% 13.04/2.06 = { by lemma 11 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(divide(S, X2), Y2), divide(Y2, divide(S, X2))), Z2), divide(Z2, divide(Z, W)))
% 13.04/2.06 = { by lemma 8 R->L }
% 13.04/2.06 divide(divide(inverse(divide(X2, S)), W2), multiply(divide(multiply(divide(Z, W), divide(S, X2)), V2), divide(V2, W2)))
% 13.04/2.06 = { by lemma 19 R->L }
% 13.04/2.06 divide(divide(inverse(divide(X2, S)), W2), multiply(divide(multiply(divide(Z, W), divide(divide(inverse(divide(Z, W)), divide(W, Z)), divide(X2, S))), V2), divide(V2, W2)))
% 13.04/2.06 = { by lemma 7 R->L }
% 13.04/2.06 divide(divide(inverse(divide(X2, S)), W2), multiply(divide(multiply(divide(divide(inverse(divide(U2, divide(Z, W))), divide(multiply(divide(W, Z), divide(Z, W)), U2)), T2), divide(T2, divide(X2, S))), V2), divide(V2, W2)))
% 13.04/2.06 = { by lemma 21 R->L }
% 13.04/2.06 divide(divide(inverse(divide(X2, S)), W2), multiply(divide(multiply(divide(divide(inverse(divide(S2, V)), divide(multiply(divide(W, Z), V), S2)), T2), divide(T2, divide(X2, S))), V2), divide(V2, W2)))
% 13.04/2.06 = { by lemma 7 }
% 13.04/2.06 divide(divide(inverse(divide(X2, S)), W2), multiply(divide(multiply(V, divide(divide(inverse(V), divide(W, Z)), divide(X2, S))), V2), divide(V2, W2)))
% 13.04/2.06 = { by lemma 4 }
% 13.04/2.06 multiply(divide(divide(divide(W, Z), inverse(V)), U), divide(U, V))
% 13.04/2.06 = { by axiom 1 (multiply) R->L }
% 13.04/2.06 multiply(divide(multiply(divide(W, Z), V), U), divide(U, V))
% 13.04/2.06
% 13.04/2.06 Lemma 39: inverse(multiply(divide(multiply(divide(X, Y), Z), W), divide(W, Z))) = inverse(divide(X, Y)).
% 13.04/2.06 Proof:
% 13.04/2.06 inverse(multiply(divide(multiply(divide(X, Y), Z), W), divide(W, Z)))
% 13.04/2.06 = { by lemma 38 R->L }
% 13.04/2.06 inverse(divide(inverse(divide(V, U)), divide(multiply(divide(Y, X), U), V)))
% 13.04/2.06 = { by lemma 24 }
% 13.04/2.06 inverse(divide(X, Y))
% 13.04/2.06
% 13.04/2.06 Lemma 40: multiply(X, divide(divide(inverse(X), divide(Y, Z)), W)) = multiply(divide(divide(Z, Y), V), divide(V, W)).
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(X, divide(divide(inverse(X), divide(Y, Z)), W))
% 13.04/2.06 = { by lemma 7 R->L }
% 13.04/2.06 multiply(divide(divide(inverse(divide(U, X)), divide(multiply(divide(Y, Z), X), U)), T), divide(T, W))
% 13.04/2.06 = { by lemma 17 R->L }
% 13.04/2.06 multiply(multiply(divide(S, X2), divide(X2, S)), divide(inverse(multiply(divide(multiply(divide(Y, Z), X), U), divide(U, X))), W))
% 13.04/2.06 = { by lemma 39 }
% 13.04/2.06 multiply(multiply(divide(S, X2), divide(X2, S)), divide(inverse(divide(Y, Z)), W))
% 13.04/2.06 = { by lemma 25 }
% 13.04/2.06 multiply(divide(divide(Z, Y), V), divide(V, W))
% 13.04/2.06
% 13.04/2.06 Lemma 41: multiply(divide(multiply(divide(X, Y), Z), W), divide(W, Z)) = divide(X, Y).
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(divide(multiply(divide(X, Y), Z), W), divide(W, Z))
% 13.04/2.06 = { by axiom 1 (multiply) }
% 13.04/2.06 multiply(divide(divide(divide(X, Y), inverse(Z)), W), divide(W, Z))
% 13.04/2.06 = { by lemma 4 R->L }
% 13.04/2.06 divide(divide(inverse(V), U), multiply(divide(multiply(Z, divide(divide(inverse(Z), divide(X, Y)), V)), T), divide(T, U)))
% 13.04/2.06 = { by lemma 40 }
% 13.04/2.06 divide(divide(inverse(V), U), multiply(divide(multiply(divide(divide(Y, X), S), divide(S, V)), T), divide(T, U)))
% 13.04/2.06 = { by lemma 11 }
% 13.04/2.06 divide(divide(inverse(V), U), divide(inverse(divide(X2, divide(Y, X))), divide(multiply(U, V), X2)))
% 13.04/2.06 = { by lemma 12 }
% 13.04/2.06 divide(X, Y)
% 13.04/2.06
% 13.04/2.06 Lemma 42: multiply(divide(X, multiply(divide(X, Y), Y)), divide(Z, W)) = multiply(divide(divide(Z, W), V), V).
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(divide(X, multiply(divide(X, Y), Y)), divide(Z, W))
% 13.04/2.06 = { by lemma 34 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(Z, W), W), Z), divide(Z, W))
% 13.04/2.06 = { by lemma 28 R->L }
% 13.04/2.06 multiply(divide(divide(inverse(divide(W, Z)), multiply(divide(W, U), divide(U, W))), divide(Z, W)), divide(Z, W))
% 13.04/2.06 = { by lemma 32 R->L }
% 13.04/2.06 multiply(divide(divide(inverse(divide(W, Z)), multiply(divide(multiply(divide(multiply(divide(W, Z), Z), W), W), U), divide(U, W))), divide(Z, W)), divide(Z, W))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 multiply(divide(divide(inverse(divide(W, Z)), divide(multiply(divide(W, Z), Z), W)), divide(Z, W)), divide(Z, W))
% 13.04/2.06 = { by lemma 38 }
% 13.04/2.06 multiply(divide(multiply(divide(multiply(divide(Z, W), T), S), divide(S, T)), divide(Z, W)), divide(Z, W))
% 13.04/2.06 = { by lemma 41 }
% 13.04/2.06 multiply(divide(divide(Z, W), divide(Z, W)), divide(Z, W))
% 13.04/2.06 = { by lemma 30 R->L }
% 13.04/2.06 multiply(divide(divide(Z, W), V), V)
% 13.04/2.06
% 13.04/2.06 Lemma 43: divide(inverse(divide(X, Y)), Z) = divide(divide(Y, X), Z).
% 13.04/2.06 Proof:
% 13.04/2.06 divide(inverse(divide(X, Y)), Z)
% 13.04/2.06 = { by lemma 26 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(inverse(divide(X, Y)), divide(Y, X)), divide(Y, X)), W), divide(W, Z))
% 13.04/2.06 = { by lemma 37 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(inverse(divide(X, Y)), divide(multiply(divide(V, multiply(divide(V, U), U)), Y), X)), divide(Y, X)), W), divide(W, Z))
% 13.04/2.06 = { by lemma 35 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(inverse(divide(X, Y)), divide(multiply(multiply(multiply(divide(inverse(divide(X, Y)), T), T), divide(X, Y)), Y), X)), divide(Y, X)), W), divide(W, Z))
% 13.04/2.06 = { by lemma 29 }
% 13.04/2.06 multiply(divide(multiply(divide(inverse(divide(X, Y)), multiply(divide(inverse(divide(X, Y)), T), T)), divide(Y, X)), W), divide(W, Z))
% 13.04/2.06 = { by lemma 42 }
% 13.04/2.06 multiply(divide(multiply(divide(divide(Y, X), S), S), W), divide(W, Z))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 divide(divide(Y, X), Z)
% 13.04/2.06
% 13.04/2.06 Lemma 44: multiply(X, divide(Y, Z)) = divide(X, divide(Z, Y)).
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(X, divide(Y, Z))
% 13.04/2.06 = { by axiom 1 (multiply) }
% 13.04/2.06 divide(X, inverse(divide(Y, Z)))
% 13.04/2.06 = { by lemma 12 R->L }
% 13.04/2.06 divide(divide(inverse(W), V), divide(inverse(divide(U, divide(inverse(divide(Y, Z)), X))), divide(multiply(V, W), U)))
% 13.04/2.06 = { by lemma 43 }
% 13.04/2.06 divide(divide(inverse(W), V), divide(inverse(divide(U, divide(divide(Z, Y), X))), divide(multiply(V, W), U)))
% 13.04/2.06 = { by lemma 12 }
% 13.04/2.06 divide(X, divide(Z, Y))
% 13.04/2.06
% 13.04/2.06 Lemma 45: multiply(divide(multiply(X, Y), Z), divide(Z, W)) = divide(multiply(divide(X, divide(V, Y)), V), W).
% 13.04/2.06 Proof:
% 13.04/2.06 multiply(divide(multiply(X, Y), Z), divide(Z, W))
% 13.04/2.06 = { by lemma 29 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(multiply(multiply(X, divide(Y, V)), V), Y), Y), Z), divide(Z, W))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 divide(multiply(multiply(X, divide(Y, V)), V), W)
% 13.04/2.06 = { by lemma 44 }
% 13.04/2.06 divide(multiply(divide(X, divide(V, Y)), V), W)
% 13.04/2.06
% 13.04/2.06 Lemma 46: divide(multiply(divide(divide(X, Y), divide(Z, W)), Z), W) = divide(X, Y).
% 13.04/2.06 Proof:
% 13.04/2.06 divide(multiply(divide(divide(X, Y), divide(Z, W)), Z), W)
% 13.04/2.06 = { by lemma 45 R->L }
% 13.04/2.06 multiply(divide(multiply(divide(X, Y), W), V), divide(V, W))
% 13.04/2.06 = { by lemma 22 }
% 13.04/2.06 multiply(divide(multiply(divide(X, Y), Y), U), divide(U, Y))
% 13.04/2.06 = { by lemma 26 }
% 13.04/2.06 divide(X, Y)
% 13.04/2.06
% 13.04/2.06 Lemma 47: divide(divide(inverse(X), divide(Y, Z)), divide(Z, Y)) = inverse(X).
% 13.04/2.06 Proof:
% 13.04/2.06 divide(divide(inverse(X), divide(Y, Z)), divide(Z, Y))
% 13.04/2.06 = { by lemma 37 R->L }
% 13.04/2.06 divide(divide(inverse(multiply(divide(W, multiply(divide(W, V), V)), X)), divide(Y, Z)), divide(Z, Y))
% 13.04/2.06 = { by lemma 32 R->L }
% 13.04/2.06 divide(divide(inverse(multiply(divide(W, multiply(divide(W, V), V)), X)), divide(multiply(divide(multiply(divide(Y, Z), Z), Y), Y), Z)), divide(Z, Y))
% 13.04/2.06 = { by lemma 28 R->L }
% 13.04/2.06 divide(divide(inverse(multiply(divide(W, multiply(divide(W, V), V)), X)), divide(multiply(divide(divide(inverse(divide(Z, Y)), multiply(divide(U, T), divide(T, U))), divide(Y, Z)), Y), Z)), divide(Z, Y))
% 13.04/2.06 = { by lemma 46 }
% 13.04/2.06 divide(divide(inverse(multiply(divide(W, multiply(divide(W, V), V)), X)), divide(inverse(divide(Z, Y)), multiply(divide(U, T), divide(T, U)))), divide(Z, Y))
% 13.04/2.06 = { by lemma 43 }
% 13.04/2.06 divide(divide(inverse(multiply(divide(W, multiply(divide(W, V), V)), X)), divide(divide(Y, Z), multiply(divide(U, T), divide(T, U)))), divide(Z, Y))
% 13.04/2.06 = { by lemma 33 }
% 13.04/2.06 divide(divide(inverse(multiply(divide(W, multiply(divide(W, V), V)), X)), divide(divide(Y, Z), divide(W, multiply(divide(W, V), V)))), divide(Z, Y))
% 13.04/2.06 = { by lemma 18 }
% 13.04/2.06 inverse(X)
% 13.04/2.06
% 13.04/2.06 Lemma 48: divide(multiply(inverse(X), Y), Z) = divide(inverse(X), divide(Z, Y)).
% 13.04/2.06 Proof:
% 13.04/2.06 divide(multiply(inverse(X), Y), Z)
% 13.04/2.06 = { by lemma 47 R->L }
% 13.04/2.06 divide(multiply(divide(divide(inverse(X), divide(Z, Y)), divide(Y, Z)), Y), Z)
% 13.04/2.06 = { by lemma 46 }
% 13.04/2.06 divide(inverse(X), divide(Z, Y))
% 13.04/2.06
% 13.04/2.06 Lemma 49: divide(multiply(divide(X, divide(Y, Z)), Y), Z) = X.
% 13.04/2.06 Proof:
% 13.04/2.06 divide(multiply(divide(X, divide(Y, Z)), Y), Z)
% 13.04/2.06 = { by axiom 2 (single_axiom) R->L }
% 13.04/2.07 divide(multiply(divide(divide(divide(inverse(divide(W, X)), divide(divide(V, U), W)), divide(U, V)), divide(Y, Z)), Y), Z)
% 13.04/2.07 = { by lemma 46 }
% 13.04/2.07 divide(divide(inverse(divide(W, X)), divide(divide(V, U), W)), divide(U, V))
% 13.04/2.07 = { by axiom 2 (single_axiom) }
% 13.04/2.07 X
% 13.04/2.07
% 13.04/2.07 Lemma 50: multiply(divide(inverse(X), Y), Y) = inverse(X).
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(divide(inverse(X), Y), Y)
% 13.04/2.07 = { by lemma 30 }
% 13.04/2.07 multiply(divide(inverse(X), divide(Z, W)), divide(Z, W))
% 13.04/2.07 = { by lemma 48 R->L }
% 13.04/2.07 multiply(divide(multiply(inverse(X), W), Z), divide(Z, W))
% 13.04/2.07 = { by lemma 45 }
% 13.04/2.07 divide(multiply(divide(inverse(X), divide(V, W)), V), W)
% 13.04/2.07 = { by lemma 49 }
% 13.04/2.07 inverse(X)
% 13.04/2.07
% 13.04/2.07 Lemma 51: divide(X, multiply(divide(X, Y), Y)) = multiply(Z, inverse(Z)).
% 13.04/2.07 Proof:
% 13.04/2.07 divide(X, multiply(divide(X, Y), Y))
% 13.04/2.07 = { by lemma 33 R->L }
% 13.04/2.07 multiply(divide(divide(W, V), U), divide(U, divide(W, V)))
% 13.04/2.07 = { by lemma 40 R->L }
% 13.04/2.07 multiply(Z, divide(divide(inverse(Z), divide(V, W)), divide(W, V)))
% 13.04/2.07 = { by lemma 47 }
% 13.04/2.07 multiply(Z, inverse(Z))
% 13.04/2.07
% 13.04/2.07 Lemma 52: divide(inverse(inverse(X)), X) = multiply(Y, inverse(Y)).
% 13.04/2.07 Proof:
% 13.04/2.07 divide(inverse(inverse(X)), X)
% 13.04/2.07 = { by lemma 18 R->L }
% 13.04/2.07 divide(divide(divide(inverse(multiply(X, inverse(X))), divide(divide(Z, W), X)), divide(W, Z)), X)
% 13.04/2.07 = { by lemma 51 R->L }
% 13.04/2.07 divide(divide(divide(inverse(divide(X, multiply(divide(X, V), V))), divide(divide(Z, W), X)), divide(W, Z)), X)
% 13.04/2.07 = { by axiom 2 (single_axiom) }
% 13.04/2.07 divide(multiply(divide(X, V), V), X)
% 13.04/2.07 = { by lemma 34 }
% 13.04/2.07 divide(U, multiply(divide(U, T), T))
% 13.04/2.07 = { by lemma 51 }
% 13.04/2.07 multiply(Y, inverse(Y))
% 13.04/2.07
% 13.04/2.07 Lemma 53: multiply(multiply(X, inverse(X)), Y) = Y.
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(multiply(X, inverse(X)), Y)
% 13.04/2.07 = { by lemma 51 R->L }
% 13.04/2.07 multiply(divide(Z, multiply(divide(Z, W), W)), Y)
% 13.04/2.07 = { by lemma 37 }
% 13.04/2.07 Y
% 13.04/2.07
% 13.04/2.07 Lemma 54: inverse(inverse(X)) = X.
% 13.04/2.07 Proof:
% 13.04/2.07 inverse(inverse(X))
% 13.04/2.07 = { by lemma 50 R->L }
% 13.04/2.07 multiply(divide(inverse(inverse(X)), X), X)
% 13.04/2.07 = { by lemma 52 }
% 13.04/2.07 multiply(multiply(Y, inverse(Y)), X)
% 13.04/2.07 = { by lemma 53 }
% 13.04/2.07 X
% 13.04/2.07
% 13.04/2.07 Lemma 55: inverse(divide(X, Y)) = divide(Y, X).
% 13.04/2.07 Proof:
% 13.04/2.07 inverse(divide(X, Y))
% 13.04/2.07 = { by lemma 10 R->L }
% 13.04/2.07 multiply(divide(multiply(divide(divide(inverse(divide(X, Y)), divide(inverse(Z), W)), V), divide(V, Z)), U), divide(U, W))
% 13.04/2.07 = { by lemma 43 }
% 13.04/2.07 multiply(divide(multiply(divide(divide(divide(Y, X), divide(inverse(Z), W)), V), divide(V, Z)), U), divide(U, W))
% 13.04/2.07 = { by lemma 10 }
% 13.04/2.07 divide(Y, X)
% 13.04/2.07
% 13.04/2.07 Lemma 56: divide(inverse(X), Y) = inverse(multiply(Y, X)).
% 13.04/2.07 Proof:
% 13.04/2.07 divide(inverse(X), Y)
% 13.04/2.07 = { by lemma 55 R->L }
% 13.04/2.07 inverse(divide(Y, inverse(X)))
% 13.04/2.07 = { by axiom 1 (multiply) R->L }
% 13.04/2.07 inverse(multiply(Y, X))
% 13.04/2.07
% 13.04/2.07 Lemma 57: multiply(X, inverse(Y)) = divide(X, Y).
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(X, inverse(Y))
% 13.04/2.07 = { by axiom 1 (multiply) }
% 13.04/2.07 divide(X, inverse(inverse(Y)))
% 13.04/2.07 = { by lemma 54 }
% 13.04/2.07 divide(X, Y)
% 13.04/2.07
% 13.04/2.07 Lemma 58: multiply(divide(X, X), Y) = Y.
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(divide(X, X), Y)
% 13.04/2.07 = { by lemma 57 R->L }
% 13.04/2.07 multiply(multiply(X, inverse(X)), Y)
% 13.04/2.07 = { by lemma 53 }
% 13.04/2.07 Y
% 13.04/2.07
% 13.04/2.07 Lemma 59: multiply(inverse(inverse(inverse(X))), X) = divide(Y, Y).
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(inverse(inverse(inverse(X))), X)
% 13.04/2.07 = { by lemma 58 R->L }
% 13.04/2.07 multiply(divide(Z, Z), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 41 R->L }
% 13.04/2.07 multiply(multiply(divide(multiply(divide(Z, Z), W), V), divide(V, W)), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 37 R->L }
% 13.04/2.07 multiply(multiply(divide(U, multiply(divide(U, T), T)), multiply(divide(multiply(divide(Z, Z), W), V), divide(V, W))), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by axiom 1 (multiply) }
% 13.04/2.07 multiply(divide(divide(U, multiply(divide(U, T), T)), inverse(multiply(divide(multiply(divide(Z, Z), W), V), divide(V, W)))), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 39 }
% 13.04/2.07 multiply(divide(divide(U, multiply(divide(U, T), T)), inverse(divide(Z, Z))), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by axiom 1 (multiply) R->L }
% 13.04/2.07 multiply(multiply(divide(U, multiply(divide(U, T), T)), divide(Z, Z)), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 42 }
% 13.04/2.07 multiply(multiply(divide(divide(Z, Z), S), S), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 55 R->L }
% 13.04/2.07 multiply(multiply(divide(inverse(divide(Z, Z)), S), S), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 57 R->L }
% 13.04/2.07 multiply(multiply(divide(inverse(multiply(Z, inverse(Z))), S), S), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 52 R->L }
% 13.04/2.07 multiply(multiply(divide(inverse(divide(inverse(inverse(inverse(X))), inverse(X))), S), S), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 47 R->L }
% 13.04/2.07 multiply(multiply(divide(inverse(divide(inverse(divide(divide(inverse(inverse(X)), divide(X2, Y2)), divide(Y2, X2))), inverse(X))), S), S), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by axiom 1 (multiply) R->L }
% 13.04/2.07 multiply(multiply(divide(inverse(multiply(inverse(divide(divide(inverse(inverse(X)), divide(X2, Y2)), divide(Y2, X2))), X)), S), S), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 47 }
% 13.04/2.07 multiply(multiply(divide(inverse(multiply(inverse(inverse(inverse(X))), X)), S), S), multiply(inverse(inverse(inverse(X))), X))
% 13.04/2.07 = { by lemma 35 }
% 13.04/2.07 divide(Z2, multiply(divide(Z2, W2), W2))
% 13.04/2.07 = { by lemma 51 }
% 13.04/2.07 multiply(Y, inverse(Y))
% 13.04/2.07 = { by lemma 57 }
% 13.04/2.07 divide(Y, Y)
% 13.04/2.07
% 13.04/2.07 Lemma 60: multiply(inverse(X), X) = divide(Y, Y).
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(inverse(X), X)
% 13.04/2.07 = { by lemma 54 R->L }
% 13.04/2.07 multiply(inverse(inverse(inverse(X))), X)
% 13.04/2.07 = { by lemma 59 }
% 13.04/2.07 divide(Y, Y)
% 13.04/2.07
% 13.04/2.07 Lemma 61: multiply(divide(X, Y), Y) = X.
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(divide(X, Y), Y)
% 13.04/2.07 = { by lemma 54 R->L }
% 13.04/2.07 multiply(divide(inverse(inverse(X)), Y), Y)
% 13.04/2.07 = { by lemma 50 }
% 13.04/2.07 inverse(inverse(X))
% 13.04/2.07 = { by lemma 54 }
% 13.04/2.07 X
% 13.04/2.07
% 13.04/2.07 Lemma 62: divide(X, multiply(Y, X)) = inverse(Y).
% 13.04/2.07 Proof:
% 13.04/2.07 divide(X, multiply(Y, X))
% 13.04/2.07 = { by lemma 57 R->L }
% 13.04/2.07 multiply(X, inverse(multiply(Y, X)))
% 13.04/2.07 = { by lemma 58 R->L }
% 13.04/2.07 multiply(multiply(divide(Z, Z), X), inverse(multiply(Y, X)))
% 13.04/2.07 = { by lemma 59 R->L }
% 13.04/2.07 multiply(multiply(multiply(inverse(inverse(inverse(Y))), Y), X), inverse(multiply(Y, X)))
% 13.04/2.07 = { by axiom 1 (multiply) }
% 13.04/2.07 multiply(divide(multiply(inverse(inverse(inverse(Y))), Y), inverse(X)), inverse(multiply(Y, X)))
% 13.04/2.07 = { by lemma 26 R->L }
% 13.04/2.07 multiply(multiply(divide(multiply(divide(multiply(inverse(inverse(inverse(Y))), Y), W), W), Y), divide(Y, inverse(X))), inverse(multiply(Y, X)))
% 13.04/2.07 = { by axiom 1 (multiply) R->L }
% 13.04/2.07 multiply(multiply(divide(multiply(divide(multiply(inverse(inverse(inverse(Y))), Y), W), W), Y), multiply(Y, X)), inverse(multiply(Y, X)))
% 13.04/2.07 = { by lemma 48 }
% 13.04/2.07 multiply(multiply(divide(multiply(divide(inverse(inverse(inverse(Y))), divide(W, Y)), W), Y), multiply(Y, X)), inverse(multiply(Y, X)))
% 13.04/2.07 = { by lemma 49 }
% 13.04/2.07 multiply(multiply(inverse(inverse(inverse(Y))), multiply(Y, X)), inverse(multiply(Y, X)))
% 13.04/2.07 = { by lemma 54 }
% 13.04/2.07 multiply(multiply(inverse(Y), multiply(Y, X)), inverse(multiply(Y, X)))
% 13.04/2.07 = { by axiom 1 (multiply) }
% 13.04/2.07 multiply(divide(inverse(Y), inverse(multiply(Y, X))), inverse(multiply(Y, X)))
% 13.04/2.07 = { by lemma 61 }
% 13.04/2.07 inverse(Y)
% 13.04/2.07
% 13.04/2.07 Lemma 63: divide(divide(X, Y), Z) = divide(X, multiply(Z, Y)).
% 13.04/2.07 Proof:
% 13.04/2.07 divide(divide(X, Y), Z)
% 13.04/2.07 = { by lemma 9 R->L }
% 13.04/2.07 divide(divide(divide(inverse(divide(divide(inverse(W), multiply(Y, inverse(W))), divide(X, Y))), V), multiply(divide(multiply(multiply(Y, inverse(W)), W), U), divide(U, V))), Z)
% 13.04/2.07 = { by lemma 62 }
% 13.04/2.07 divide(divide(divide(inverse(divide(inverse(Y), divide(X, Y))), V), multiply(divide(multiply(multiply(Y, inverse(W)), W), U), divide(U, V))), Z)
% 13.04/2.07 = { by lemma 8 }
% 13.04/2.07 divide(multiply(divide(multiply(divide(divide(divide(X, Y), inverse(Y)), T), divide(T, W)), S), divide(S, multiply(Y, inverse(W)))), Z)
% 13.04/2.07 = { by lemma 11 }
% 13.04/2.07 divide(divide(inverse(divide(X2, divide(divide(X, Y), inverse(Y)))), divide(multiply(multiply(Y, inverse(W)), W), X2)), Z)
% 13.04/2.07 = { by axiom 1 (multiply) R->L }
% 13.04/2.07 divide(divide(inverse(divide(X2, multiply(divide(X, Y), Y))), divide(multiply(multiply(Y, inverse(W)), W), X2)), Z)
% 13.04/2.07 = { by lemma 57 }
% 13.04/2.07 divide(divide(inverse(divide(X2, multiply(divide(X, Y), Y))), divide(multiply(divide(Y, W), W), X2)), Z)
% 13.04/2.07 = { by lemma 23 }
% 13.04/2.07 divide(multiply(divide(multiply(divide(multiply(divide(X, Y), Y), Y), Y), Y2), divide(Y2, Y)), Z)
% 13.04/2.07 = { by lemma 26 }
% 13.04/2.07 divide(divide(multiply(divide(X, Y), Y), Y), Z)
% 13.04/2.07 = { by lemma 57 R->L }
% 13.04/2.07 multiply(divide(multiply(divide(X, Y), Y), Y), inverse(Z))
% 13.04/2.07 = { by lemma 62 R->L }
% 13.04/2.07 multiply(divide(multiply(divide(X, Y), Y), Y), divide(Y, multiply(Z, Y)))
% 13.04/2.07 = { by lemma 26 }
% 13.04/2.07 divide(X, multiply(Z, Y))
% 13.04/2.07
% 13.04/2.07 Lemma 64: multiply(divide(X, Y), multiply(Y, Z)) = multiply(X, Z).
% 13.04/2.07 Proof:
% 13.04/2.07 multiply(divide(X, Y), multiply(Y, Z))
% 13.68/2.07 = { by axiom 1 (multiply) }
% 13.68/2.07 multiply(divide(X, Y), divide(Y, inverse(Z)))
% 13.68/2.07 = { by lemma 13 }
% 13.68/2.07 multiply(divide(X, W), divide(W, inverse(Z)))
% 13.68/2.07 = { by lemma 44 }
% 13.68/2.07 divide(divide(X, W), divide(inverse(Z), W))
% 13.68/2.07 = { by lemma 63 }
% 13.68/2.07 divide(X, multiply(divide(inverse(Z), W), W))
% 13.68/2.07 = { by lemma 61 }
% 13.68/2.07 divide(X, inverse(Z))
% 13.68/2.07 = { by axiom 1 (multiply) R->L }
% 13.68/2.07 multiply(X, Z)
% 13.68/2.07
% 13.68/2.07 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))).
% 13.68/2.07 Proof:
% 13.68/2.07 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 13.68/2.07 = { by lemma 60 }
% 13.68/2.07 tuple(divide(X, X), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 13.68/2.07 = { by lemma 60 }
% 13.68/2.07 tuple(divide(X, X), multiply(divide(Y, Y), a2), multiply(multiply(a3, b3), c3))
% 13.68/2.07 = { by lemma 58 }
% 13.68/2.07 tuple(divide(X, X), a2, multiply(multiply(a3, b3), c3))
% 13.68/2.07 = { by lemma 64 R->L }
% 13.68/2.07 tuple(divide(X, X), a2, multiply(multiply(divide(a3, Z), multiply(Z, b3)), c3))
% 13.68/2.07 = { by lemma 64 R->L }
% 13.68/2.07 tuple(divide(X, X), a2, multiply(divide(multiply(divide(a3, Z), multiply(Z, b3)), W), multiply(W, c3)))
% 13.68/2.07 = { by axiom 1 (multiply) }
% 13.68/2.07 tuple(divide(X, X), a2, multiply(divide(multiply(divide(a3, Z), multiply(Z, b3)), W), divide(W, inverse(c3))))
% 13.68/2.07 = { by axiom 1 (multiply) }
% 13.68/2.07 tuple(divide(X, X), a2, multiply(divide(multiply(divide(a3, Z), divide(Z, inverse(b3))), W), divide(W, inverse(c3))))
% 13.68/2.07 = { by lemma 11 }
% 13.68/2.07 tuple(divide(X, X), a2, divide(inverse(divide(V, a3)), divide(multiply(inverse(c3), inverse(b3)), V)))
% 13.68/2.07 = { by lemma 56 }
% 13.68/2.07 tuple(divide(X, X), a2, inverse(multiply(divide(multiply(inverse(c3), inverse(b3)), V), divide(V, a3))))
% 13.68/2.07 = { by lemma 44 }
% 13.68/2.07 tuple(divide(X, X), a2, inverse(divide(divide(multiply(inverse(c3), inverse(b3)), V), divide(a3, V))))
% 13.68/2.07 = { by lemma 55 }
% 13.68/2.07 tuple(divide(X, X), a2, divide(divide(a3, V), divide(multiply(inverse(c3), inverse(b3)), V)))
% 13.68/2.07 = { by lemma 63 }
% 13.68/2.07 tuple(divide(X, X), a2, divide(a3, multiply(divide(multiply(inverse(c3), inverse(b3)), V), V)))
% 13.68/2.07 = { by lemma 61 }
% 13.68/2.07 tuple(divide(X, X), a2, divide(a3, multiply(inverse(c3), inverse(b3))))
% 13.68/2.07 = { by lemma 57 }
% 13.68/2.07 tuple(divide(X, X), a2, divide(a3, divide(inverse(c3), b3)))
% 13.68/2.07 = { by lemma 56 }
% 13.68/2.07 tuple(divide(X, X), a2, divide(a3, inverse(multiply(b3, c3))))
% 13.68/2.07 = { by axiom 1 (multiply) R->L }
% 13.68/2.07 tuple(divide(X, X), a2, multiply(a3, multiply(b3, c3)))
% 13.68/2.07 = { by lemma 60 R->L }
% 13.68/2.07 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 13.68/2.07 % SZS output end Proof
% 13.68/2.07
% 13.68/2.07 RESULT: Unsatisfiable (the axioms are contradictory).
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