TSTP Solution File: GRP083-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP083-1 : 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 : n017.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 01:16:55 EDT 2023
% Result : Unsatisfiable 0.19s 0.58s
% Output : Proof 2.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP083-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n017.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 23:51:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 Command-line arguments: --no-flatten-goal
% 0.19/0.58
% 0.19/0.58 % SZS status Unsatisfiable
% 0.19/0.58
% 2.56/0.69 % SZS output start Proof
% 2.56/0.69 Take the following subset of the input axioms:
% 2.56/0.69 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=inverse(double_divide(Y, X))).
% 2.56/0.69 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)))).
% 2.56/0.69 fof(single_axiom, axiom, ![Z, U, X2, Y2]: double_divide(double_divide(X2, inverse(double_divide(Y2, Z))), double_divide(inverse(Y2), inverse(double_divide(U, double_divide(X2, U)))))=Z).
% 2.56/0.69
% 2.56/0.69 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.56/0.69 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.56/0.69 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.56/0.69 fresh(y, y, x1...xn) = u
% 2.56/0.69 C => fresh(s, t, x1...xn) = v
% 2.56/0.69 where fresh is a fresh function symbol and x1..xn are the free
% 2.56/0.69 variables of u and v.
% 2.56/0.69 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.56/0.69 input problem has no model of domain size 1).
% 2.56/0.69
% 2.56/0.69 The encoding turns the above axioms into the following unit equations and goals:
% 2.56/0.69
% 2.56/0.69 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 2.56/0.69 Axiom 2 (single_axiom): double_divide(double_divide(X, inverse(double_divide(Y, Z))), double_divide(inverse(Y), inverse(double_divide(W, double_divide(X, W))))) = Z.
% 2.56/0.69
% 2.56/0.69 Lemma 3: double_divide(double_divide(X, multiply(Y, Z)), double_divide(inverse(Z), multiply(double_divide(X, W), W))) = Y.
% 2.56/0.69 Proof:
% 2.56/0.69 double_divide(double_divide(X, multiply(Y, Z)), double_divide(inverse(Z), multiply(double_divide(X, W), W)))
% 2.56/0.69 = { by axiom 1 (multiply) }
% 2.56/0.69 double_divide(double_divide(X, multiply(Y, Z)), double_divide(inverse(Z), inverse(double_divide(W, double_divide(X, W)))))
% 2.56/0.69 = { by axiom 1 (multiply) }
% 2.56/0.69 double_divide(double_divide(X, inverse(double_divide(Z, Y))), double_divide(inverse(Z), inverse(double_divide(W, double_divide(X, W)))))
% 2.56/0.69 = { by axiom 2 (single_axiom) }
% 2.56/0.69 Y
% 2.56/0.69
% 2.56/0.69 Lemma 4: double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), double_divide(multiply(W, Z), multiply(double_divide(X, V), V))) = Y.
% 2.56/0.69 Proof:
% 2.56/0.69 double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), double_divide(multiply(W, Z), multiply(double_divide(X, V), V)))
% 2.56/0.69 = { by axiom 1 (multiply) }
% 2.56/0.69 double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), double_divide(inverse(double_divide(Z, W)), multiply(double_divide(X, V), V)))
% 2.56/0.69 = { by lemma 3 }
% 2.56/0.69 Y
% 2.56/0.69
% 2.56/0.69 Lemma 5: multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(W, X))) = inverse(W).
% 2.56/0.69 Proof:
% 2.56/0.69 multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(W, X)))
% 2.56/0.69 = { by axiom 1 (multiply) }
% 2.56/0.69 inverse(double_divide(double_divide(Y, multiply(W, X)), double_divide(inverse(X), multiply(double_divide(Y, Z), Z))))
% 2.56/0.69 = { by lemma 3 }
% 2.56/0.69 inverse(W)
% 2.56/0.69
% 2.56/0.69 Lemma 6: double_divide(inverse(X), multiply(double_divide(Y, W), W)) = double_divide(inverse(X), multiply(double_divide(Y, Z), Z)).
% 2.56/0.69 Proof:
% 2.56/0.69 double_divide(inverse(X), multiply(double_divide(Y, W), W))
% 2.56/0.69 = { by lemma 3 R->L }
% 2.56/0.69 double_divide(double_divide(V, multiply(double_divide(inverse(X), multiply(double_divide(Y, W), W)), double_divide(Y, multiply(U, X)))), double_divide(inverse(double_divide(Y, multiply(U, X))), multiply(double_divide(V, T), T)))
% 2.56/0.69 = { by lemma 5 }
% 2.56/0.69 double_divide(double_divide(V, inverse(U)), double_divide(inverse(double_divide(Y, multiply(U, X))), multiply(double_divide(V, T), T)))
% 2.56/0.69 = { by lemma 5 R->L }
% 2.56/0.70 double_divide(double_divide(V, multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(U, X)))), double_divide(inverse(double_divide(Y, multiply(U, X))), multiply(double_divide(V, T), T)))
% 2.56/0.70 = { by lemma 3 }
% 2.56/0.70 double_divide(inverse(X), multiply(double_divide(Y, Z), Z))
% 2.56/0.70
% 2.56/0.70 Lemma 7: double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(inverse(W), multiply(double_divide(inverse(X), V), V))) = double_divide(Y, W).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(inverse(W), multiply(double_divide(inverse(X), V), V)))
% 2.56/0.70 = { by lemma 6 }
% 2.56/0.70 double_divide(double_divide(inverse(X), multiply(double_divide(Y, W), W)), double_divide(inverse(W), multiply(double_divide(inverse(X), V), V)))
% 2.56/0.70 = { by lemma 3 }
% 2.56/0.70 double_divide(Y, W)
% 2.56/0.70
% 2.56/0.70 Lemma 8: multiply(double_divide(X, Z), Z) = multiply(double_divide(X, Y), Y).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(X, Z), Z)
% 2.56/0.70 = { by lemma 3 R->L }
% 2.56/0.70 double_divide(double_divide(W, multiply(multiply(double_divide(X, Z), Z), inverse(V))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 2.56/0.70 = { by axiom 1 (multiply) }
% 2.56/0.70 double_divide(double_divide(W, inverse(double_divide(inverse(V), multiply(double_divide(X, Z), Z)))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 2.56/0.70 = { by lemma 6 }
% 2.56/0.70 double_divide(double_divide(W, inverse(double_divide(inverse(V), multiply(double_divide(X, Y), Y)))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 2.56/0.70 = { by axiom 1 (multiply) R->L }
% 2.56/0.70 double_divide(double_divide(W, multiply(multiply(double_divide(X, Y), Y), inverse(V))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 2.56/0.70 = { by lemma 3 }
% 2.56/0.70 multiply(double_divide(X, Y), Y)
% 2.56/0.70
% 2.56/0.70 Lemma 9: multiply(X, double_divide(inverse(Y), multiply(double_divide(Z, W), W))) = multiply(double_divide(double_divide(Z, multiply(X, Y)), V), V).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(X, double_divide(inverse(Y), multiply(double_divide(Z, W), W)))
% 2.56/0.70 = { by lemma 3 R->L }
% 2.56/0.70 multiply(double_divide(double_divide(Z, multiply(X, Y)), double_divide(inverse(Y), multiply(double_divide(Z, W), W))), double_divide(inverse(Y), multiply(double_divide(Z, W), W)))
% 2.56/0.70 = { by lemma 8 R->L }
% 2.56/0.70 multiply(double_divide(double_divide(Z, multiply(X, Y)), V), V)
% 2.56/0.70
% 2.56/0.70 Lemma 10: multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), V), V) = multiply(Y, X).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), V), V)
% 2.56/0.70 = { by lemma 9 R->L }
% 2.56/0.70 multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), double_divide(inverse(Z), multiply(double_divide(X, Y), Y)))
% 2.56/0.70 = { by lemma 5 }
% 2.56/0.70 inverse(double_divide(X, Y))
% 2.56/0.70 = { by axiom 1 (multiply) R->L }
% 2.56/0.70 multiply(Y, X)
% 2.56/0.70
% 2.56/0.70 Lemma 11: double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), X) = Y.
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), X)
% 2.56/0.70 = { by lemma 7 R->L }
% 2.56/0.70 double_divide(double_divide(inverse(V), multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), U), U)), double_divide(inverse(X), multiply(double_divide(inverse(V), T), T)))
% 2.56/0.70 = { by lemma 10 }
% 2.56/0.70 double_divide(double_divide(inverse(V), multiply(Y, X)), double_divide(inverse(X), multiply(double_divide(inverse(V), T), T)))
% 2.56/0.70 = { by lemma 3 }
% 2.56/0.70 Y
% 2.56/0.70
% 2.56/0.70 Lemma 12: multiply(double_divide(multiply(X, Y), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(V, double_divide(Y, X)))) = inverse(V).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(multiply(X, Y), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(V, double_divide(Y, X))))
% 2.56/0.70 = { by axiom 1 (multiply) }
% 2.56/0.70 multiply(double_divide(inverse(double_divide(Y, X)), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(V, double_divide(Y, X))))
% 2.56/0.70 = { by lemma 5 }
% 2.56/0.70 inverse(V)
% 2.56/0.70
% 2.56/0.70 Lemma 13: multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(double_divide(W, V), V))) = multiply(X, W).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(double_divide(W, V), V)))
% 2.56/0.70 = { by lemma 8 }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(double_divide(W, X), X)))
% 2.56/0.70 = { by lemma 5 }
% 2.56/0.70 inverse(double_divide(W, X))
% 2.56/0.70 = { by axiom 1 (multiply) R->L }
% 2.56/0.70 multiply(X, W)
% 2.56/0.70
% 2.56/0.70 Lemma 14: multiply(double_divide(inverse(X), multiply(Y, multiply(double_divide(Z, W), W))), Y) = multiply(X, Z).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(Y, multiply(double_divide(Z, W), W))), Y)
% 2.56/0.70 = { by lemma 10 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(V), U), U)), V)), T), T)), Y)
% 2.56/0.70 = { by lemma 11 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(V), U), U)), V)), T), T)), double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(V), U), U)), V)), multiply(double_divide(Z, W), W)))
% 2.56/0.70 = { by lemma 13 }
% 2.56/0.70 multiply(X, Z)
% 2.56/0.70
% 2.56/0.70 Lemma 15: multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y) = inverse(Z).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y)
% 2.56/0.70 = { by lemma 10 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(Z, X), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), U), U)), Y)
% 2.56/0.70 = { by lemma 11 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(Z, X), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), U), U)), double_divide(double_divide(multiply(Z, X), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), multiply(Z, X)))
% 2.56/0.70 = { by lemma 5 }
% 2.56/0.70 inverse(Z)
% 2.56/0.70
% 2.56/0.70 Lemma 16: multiply(double_divide(inverse(X), multiply(Y, multiply(Z, W))), Y) = multiply(multiply(X, multiply(double_divide(W, V), V)), inverse(Z)).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(Y, multiply(Z, W))), Y)
% 2.56/0.70 = { by lemma 14 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(Y, multiply(double_divide(inverse(Z), multiply(X, multiply(double_divide(W, V), V))), X))), Y)
% 2.56/0.70 = { by lemma 15 }
% 2.56/0.70 inverse(double_divide(inverse(Z), multiply(X, multiply(double_divide(W, V), V))))
% 2.56/0.70 = { by axiom 1 (multiply) R->L }
% 2.56/0.70 multiply(multiply(X, multiply(double_divide(W, V), V)), inverse(Z))
% 2.56/0.70
% 2.56/0.70 Lemma 17: multiply(multiply(X, multiply(double_divide(Y, Z), Z)), multiply(Y, W)) = multiply(X, W).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(multiply(X, multiply(double_divide(Y, Z), Z)), multiply(Y, W))
% 2.56/0.70 = { by axiom 1 (multiply) }
% 2.56/0.70 multiply(multiply(X, multiply(double_divide(Y, Z), Z)), inverse(double_divide(W, Y)))
% 2.56/0.70 = { by lemma 16 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(V, multiply(double_divide(W, Y), Y))), V)
% 2.56/0.70 = { by lemma 8 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(V, multiply(double_divide(W, U), U))), V)
% 2.56/0.70 = { by lemma 14 }
% 2.56/0.70 multiply(X, W)
% 2.56/0.70
% 2.56/0.70 Lemma 18: double_divide(X, double_divide(inverse(Y), multiply(X, multiply(Z, Y)))) = Z.
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(X, double_divide(inverse(Y), multiply(X, multiply(Z, Y))))
% 2.56/0.70 = { by lemma 10 R->L }
% 2.56/0.70 double_divide(X, double_divide(inverse(Y), multiply(double_divide(double_divide(multiply(Z, Y), multiply(double_divide(inverse(X), multiply(double_divide(inverse(W), V), V)), W)), U), U)))
% 2.56/0.70 = { by lemma 11 R->L }
% 2.56/0.70 double_divide(double_divide(double_divide(multiply(Z, Y), multiply(double_divide(inverse(X), multiply(double_divide(inverse(W), V), V)), W)), multiply(Z, Y)), double_divide(inverse(Y), multiply(double_divide(double_divide(multiply(Z, Y), multiply(double_divide(inverse(X), multiply(double_divide(inverse(W), V), V)), W)), U), U)))
% 2.56/0.70 = { by lemma 3 }
% 2.56/0.70 Z
% 2.56/0.70
% 2.56/0.70 Lemma 19: double_divide(inverse(W), multiply(Y, multiply(Z, W))) = double_divide(inverse(X), multiply(Y, multiply(Z, X))).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(inverse(W), multiply(Y, multiply(Z, W)))
% 2.56/0.70 = { by lemma 18 R->L }
% 2.56/0.70 double_divide(V, double_divide(inverse(Y), multiply(V, multiply(double_divide(inverse(W), multiply(Y, multiply(Z, W))), Y))))
% 2.56/0.70 = { by lemma 15 }
% 2.56/0.70 double_divide(V, double_divide(inverse(Y), multiply(V, inverse(Z))))
% 2.56/0.70 = { by lemma 15 R->L }
% 2.56/0.70 double_divide(V, double_divide(inverse(Y), multiply(V, multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y))))
% 2.56/0.70 = { by lemma 18 }
% 2.56/0.70 double_divide(inverse(X), multiply(Y, multiply(Z, X)))
% 2.56/0.70
% 2.56/0.70 Lemma 20: double_divide(inverse(Z), multiply(Y, Z)) = double_divide(inverse(X), multiply(Y, X)).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(inverse(Z), multiply(Y, Z))
% 2.56/0.70 = { by lemma 17 R->L }
% 2.56/0.70 double_divide(inverse(Z), multiply(multiply(Y, multiply(double_divide(W, V), V)), multiply(W, Z)))
% 2.56/0.70 = { by lemma 19 }
% 2.56/0.70 double_divide(inverse(X), multiply(multiply(Y, multiply(double_divide(W, V), V)), multiply(W, X)))
% 2.56/0.70 = { by lemma 17 }
% 2.56/0.70 double_divide(inverse(X), multiply(Y, X))
% 2.56/0.70
% 2.56/0.70 Lemma 21: multiply(multiply(X, multiply(double_divide(X, Y), Y)), inverse(Z)) = inverse(Z).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(multiply(X, multiply(double_divide(X, Y), Y)), inverse(Z))
% 2.56/0.70 = { by lemma 16 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(double_divide(W, multiply(Z, X)), multiply(Z, X))), double_divide(W, multiply(Z, X)))
% 2.56/0.70 = { by lemma 5 }
% 2.56/0.70 inverse(Z)
% 2.56/0.70
% 2.56/0.70 Lemma 22: double_divide(inverse(X), multiply(Y, X)) = multiply(double_divide(Y, Z), Z).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(inverse(X), multiply(Y, X))
% 2.56/0.70 = { by lemma 20 }
% 2.56/0.70 double_divide(inverse(multiply(double_divide(Y, Z), Z)), multiply(Y, multiply(double_divide(Y, Z), Z)))
% 2.56/0.70 = { by lemma 18 R->L }
% 2.56/0.70 double_divide(inverse(multiply(double_divide(Y, Z), Z)), double_divide(W, double_divide(inverse(inverse(V)), multiply(W, multiply(multiply(Y, multiply(double_divide(Y, Z), Z)), inverse(V))))))
% 2.56/0.70 = { by lemma 21 }
% 2.56/0.70 double_divide(inverse(multiply(double_divide(Y, Z), Z)), double_divide(W, double_divide(inverse(inverse(V)), multiply(W, inverse(V)))))
% 2.56/0.70 = { by lemma 21 R->L }
% 2.56/0.70 double_divide(inverse(multiply(double_divide(Y, Z), Z)), double_divide(W, double_divide(inverse(inverse(V)), multiply(W, multiply(multiply(U, multiply(double_divide(U, T), T)), inverse(V))))))
% 2.56/0.70 = { by lemma 18 }
% 2.56/0.70 double_divide(inverse(multiply(double_divide(Y, Z), Z)), multiply(U, multiply(double_divide(U, T), T)))
% 2.56/0.70 = { by lemma 18 R->L }
% 2.56/0.70 double_divide(S, double_divide(inverse(U), multiply(S, multiply(double_divide(inverse(multiply(double_divide(Y, Z), Z)), multiply(U, multiply(double_divide(U, T), T))), U))))
% 2.56/0.70 = { by lemma 14 }
% 2.56/0.70 double_divide(S, double_divide(inverse(U), multiply(S, multiply(multiply(double_divide(Y, Z), Z), U))))
% 2.56/0.70 = { by lemma 18 }
% 2.56/0.70 multiply(double_divide(Y, Z), Z)
% 2.56/0.70
% 2.56/0.70 Lemma 23: double_divide(inverse(X), multiply(double_divide(Y, Z), Z)) = multiply(double_divide(double_divide(Y, X), W), W).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(inverse(X), multiply(double_divide(Y, Z), Z))
% 2.56/0.70 = { by lemma 6 }
% 2.56/0.70 double_divide(inverse(X), multiply(double_divide(Y, X), X))
% 2.56/0.70 = { by lemma 20 R->L }
% 2.56/0.70 double_divide(inverse(V), multiply(double_divide(Y, X), V))
% 2.56/0.70 = { by lemma 22 }
% 2.56/0.70 multiply(double_divide(double_divide(Y, X), W), W)
% 2.56/0.70
% 2.56/0.70 Lemma 24: double_divide(double_divide(X, inverse(Y)), double_divide(multiply(multiply(Y, Z), W), multiply(double_divide(X, V), V))) = double_divide(inverse(Z), multiply(double_divide(W, U), U)).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(double_divide(X, inverse(Y)), double_divide(multiply(multiply(Y, Z), W), multiply(double_divide(X, V), V)))
% 2.56/0.70 = { by axiom 1 (multiply) }
% 2.56/0.70 double_divide(double_divide(X, inverse(Y)), double_divide(inverse(double_divide(W, multiply(Y, Z))), multiply(double_divide(X, V), V)))
% 2.56/0.70 = { by lemma 5 R->L }
% 2.56/0.70 double_divide(double_divide(X, multiply(double_divide(inverse(Z), multiply(double_divide(W, U), U)), double_divide(W, multiply(Y, Z)))), double_divide(inverse(double_divide(W, multiply(Y, Z))), multiply(double_divide(X, V), V)))
% 2.56/0.70 = { by lemma 3 }
% 2.56/0.70 double_divide(inverse(Z), multiply(double_divide(W, U), U))
% 2.56/0.70
% 2.56/0.70 Lemma 25: multiply(double_divide(inverse(X), multiply(Y, inverse(Z))), Y) = multiply(multiply(X, multiply(Z, W)), inverse(W)).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(Y, inverse(Z))), Y)
% 2.56/0.70 = { by lemma 15 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), multiply(Y, multiply(double_divide(inverse(W), multiply(X, multiply(Z, W))), X))), Y)
% 2.56/0.70 = { by lemma 15 }
% 2.56/0.70 inverse(double_divide(inverse(W), multiply(X, multiply(Z, W))))
% 2.56/0.70 = { by axiom 1 (multiply) R->L }
% 2.56/0.70 multiply(multiply(X, multiply(Z, W)), inverse(W))
% 2.56/0.70
% 2.56/0.70 Lemma 26: multiply(double_divide(multiply(X, Y), multiply(Z, multiply(W, double_divide(Y, X)))), Z) = inverse(W).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(multiply(X, Y), multiply(Z, multiply(W, double_divide(Y, X)))), Z)
% 2.56/0.70 = { by lemma 10 R->L }
% 2.56/0.70 multiply(double_divide(multiply(X, Y), multiply(double_divide(double_divide(multiply(W, double_divide(Y, X)), multiply(double_divide(inverse(Z), multiply(double_divide(inverse(V), U), U)), V)), T), T)), Z)
% 2.56/0.70 = { by lemma 11 R->L }
% 2.56/0.70 multiply(double_divide(multiply(X, Y), multiply(double_divide(double_divide(multiply(W, double_divide(Y, X)), multiply(double_divide(inverse(Z), multiply(double_divide(inverse(V), U), U)), V)), T), T)), double_divide(double_divide(multiply(W, double_divide(Y, X)), multiply(double_divide(inverse(Z), multiply(double_divide(inverse(V), U), U)), V)), multiply(W, double_divide(Y, X))))
% 2.56/0.70 = { by lemma 12 }
% 2.56/0.70 inverse(W)
% 2.56/0.70
% 2.56/0.70 Lemma 27: double_divide(X, double_divide(inverse(Y), multiply(X, inverse(Z)))) = double_divide(inverse(W), multiply(Y, multiply(Z, W))).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(X, double_divide(inverse(Y), multiply(X, inverse(Z))))
% 2.56/0.70 = { by lemma 15 R->L }
% 2.56/0.70 double_divide(X, double_divide(inverse(Y), multiply(X, multiply(double_divide(inverse(W), multiply(Y, multiply(Z, W))), Y))))
% 2.56/0.70 = { by lemma 18 }
% 2.56/0.70 double_divide(inverse(W), multiply(Y, multiply(Z, W)))
% 2.56/0.70
% 2.56/0.70 Lemma 28: double_divide(inverse(X), multiply(inverse(Y), multiply(Y, X))) = multiply(Z, multiply(double_divide(Z, W), W)).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(inverse(X), multiply(inverse(Y), multiply(Y, X)))
% 2.56/0.70 = { by lemma 27 R->L }
% 2.56/0.70 double_divide(V, double_divide(inverse(inverse(Y)), multiply(V, inverse(Y))))
% 2.56/0.70 = { by lemma 21 R->L }
% 2.56/0.70 double_divide(V, double_divide(inverse(inverse(Y)), multiply(V, multiply(multiply(Z, multiply(double_divide(Z, W), W)), inverse(Y)))))
% 2.56/0.70 = { by lemma 18 }
% 2.56/0.70 multiply(Z, multiply(double_divide(Z, W), W))
% 2.56/0.70
% 2.56/0.70 Lemma 29: multiply(X, multiply(double_divide(X, Y), Y)) = double_divide(Z, multiply(double_divide(Z, W), W)).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(X, multiply(double_divide(X, Y), Y))
% 2.56/0.70 = { by lemma 28 R->L }
% 2.56/0.70 double_divide(inverse(V), multiply(inverse(U), multiply(U, V)))
% 2.56/0.70 = { by lemma 27 R->L }
% 2.56/0.70 double_divide(Z, double_divide(inverse(inverse(U)), multiply(Z, inverse(U))))
% 2.56/0.70 = { by lemma 22 }
% 2.56/0.70 double_divide(Z, multiply(double_divide(Z, W), W))
% 2.56/0.70
% 2.56/0.70 Lemma 30: multiply(double_divide(multiply(double_divide(X, Y), Y), Z), Z) = multiply(double_divide(inverse(X), W), W).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(multiply(double_divide(X, Y), Y), Z), Z)
% 2.56/0.70 = { by lemma 22 R->L }
% 2.56/0.70 multiply(double_divide(double_divide(inverse(V), multiply(X, V)), Z), Z)
% 2.56/0.70 = { by lemma 23 R->L }
% 2.56/0.70 double_divide(inverse(multiply(X, V)), multiply(double_divide(inverse(V), U), U))
% 2.56/0.70 = { by lemma 24 R->L }
% 2.56/0.70 double_divide(double_divide(T, inverse(S)), double_divide(multiply(multiply(S, multiply(X, V)), inverse(V)), multiply(double_divide(T, X2), X2)))
% 2.56/0.70 = { by lemma 25 R->L }
% 2.56/0.70 double_divide(double_divide(T, inverse(S)), double_divide(multiply(double_divide(inverse(S), multiply(Y2, inverse(X))), Y2), multiply(double_divide(T, X2), X2)))
% 2.56/0.70 = { by lemma 26 R->L }
% 2.56/0.70 double_divide(double_divide(T, inverse(S)), double_divide(multiply(double_divide(inverse(S), multiply(Y2, multiply(double_divide(multiply(Z2, W2), multiply(S, multiply(X, double_divide(W2, Z2)))), S))), Y2), multiply(double_divide(T, X2), X2)))
% 2.56/0.70 = { by lemma 15 }
% 2.56/0.70 double_divide(double_divide(T, inverse(S)), double_divide(inverse(double_divide(multiply(Z2, W2), multiply(S, multiply(X, double_divide(W2, Z2))))), multiply(double_divide(T, X2), X2)))
% 2.56/0.70 = { by axiom 1 (multiply) R->L }
% 2.56/0.70 double_divide(double_divide(T, inverse(S)), double_divide(multiply(multiply(S, multiply(X, double_divide(W2, Z2))), multiply(Z2, W2)), multiply(double_divide(T, X2), X2)))
% 2.56/0.70 = { by lemma 24 }
% 2.56/0.70 double_divide(inverse(multiply(X, double_divide(W2, Z2))), multiply(double_divide(multiply(Z2, W2), V2), V2))
% 2.56/0.70 = { by lemma 23 }
% 2.56/0.70 multiply(double_divide(double_divide(multiply(Z2, W2), multiply(X, double_divide(W2, Z2))), double_divide(multiply(Z2, W2), multiply(double_divide(multiply(Z2, W2), U2), U2))), double_divide(multiply(Z2, W2), multiply(double_divide(multiply(Z2, W2), U2), U2)))
% 2.56/0.70 = { by lemma 4 }
% 2.56/0.70 multiply(X, double_divide(multiply(Z2, W2), multiply(double_divide(multiply(Z2, W2), U2), U2)))
% 2.56/0.70 = { by lemma 29 R->L }
% 2.56/0.70 multiply(X, multiply(T2, multiply(double_divide(T2, S2), S2)))
% 2.56/0.70 = { by lemma 28 R->L }
% 2.56/0.70 multiply(X, double_divide(inverse(X3), multiply(inverse(X), multiply(X, X3))))
% 2.56/0.70 = { by lemma 18 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), double_divide(inverse(X3), multiply(inverse(X), multiply(X, X3)))), double_divide(inverse(X3), multiply(inverse(X), multiply(X, X3))))
% 2.56/0.70 = { by lemma 8 R->L }
% 2.56/0.70 multiply(double_divide(inverse(X), W), W)
% 2.56/0.70
% 2.56/0.70 Lemma 31: double_divide(multiply(double_divide(X, Y), Y), Z) = double_divide(inverse(X), Z).
% 2.56/0.70 Proof:
% 2.56/0.70 double_divide(multiply(double_divide(X, Y), Y), Z)
% 2.56/0.70 = { by lemma 7 R->L }
% 2.56/0.70 double_divide(double_divide(inverse(W), multiply(double_divide(multiply(double_divide(X, Y), Y), V), V)), double_divide(inverse(Z), multiply(double_divide(inverse(W), U), U)))
% 2.56/0.70 = { by lemma 30 }
% 2.56/0.70 double_divide(double_divide(inverse(W), multiply(double_divide(inverse(X), T), T)), double_divide(inverse(Z), multiply(double_divide(inverse(W), U), U)))
% 2.56/0.70 = { by lemma 7 }
% 2.56/0.70 double_divide(inverse(X), Z)
% 2.56/0.70
% 2.56/0.70 Lemma 32: multiply(double_divide(X, double_divide(Y, X)), Z) = multiply(Y, Z).
% 2.56/0.70 Proof:
% 2.56/0.70 multiply(double_divide(X, double_divide(Y, X)), Z)
% 2.56/0.70 = { by axiom 1 (multiply) }
% 2.56/0.70 inverse(double_divide(Z, double_divide(X, double_divide(Y, X))))
% 2.56/0.70 = { by lemma 12 R->L }
% 2.56/0.70 multiply(double_divide(multiply(double_divide(Y, X), X), multiply(double_divide(inverse(W), V), V)), double_divide(inverse(W), multiply(double_divide(Z, double_divide(X, double_divide(Y, X))), double_divide(X, double_divide(Y, X)))))
% 2.56/0.70 = { by lemma 9 }
% 2.56/0.70 multiply(double_divide(double_divide(Z, multiply(double_divide(multiply(double_divide(Y, X), X), multiply(double_divide(inverse(W), V), V)), W)), U), U)
% 2.56/0.70 = { by lemma 31 }
% 2.56/0.70 multiply(double_divide(double_divide(Z, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), U), U)
% 2.56/0.70 = { by lemma 10 }
% 2.56/0.71 multiply(Y, Z)
% 2.56/0.71
% 2.56/0.71 Lemma 33: double_divide(X, double_divide(Y, X)) = Y.
% 2.56/0.71 Proof:
% 2.56/0.71 double_divide(X, double_divide(Y, X))
% 2.56/0.71 = { by lemma 3 R->L }
% 2.56/0.71 double_divide(double_divide(Z, multiply(double_divide(X, double_divide(Y, X)), W)), double_divide(inverse(W), multiply(double_divide(Z, V), V)))
% 2.56/0.71 = { by lemma 32 }
% 2.56/0.71 double_divide(double_divide(Z, multiply(Y, W)), double_divide(inverse(W), multiply(double_divide(Z, V), V)))
% 2.56/0.71 = { by lemma 3 }
% 2.56/0.71 Y
% 2.56/0.71
% 2.56/0.71 Lemma 34: multiply(double_divide(X, Y), Y) = inverse(X).
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(double_divide(X, Y), Y)
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 inverse(double_divide(Y, double_divide(X, Y)))
% 2.56/0.71 = { by lemma 33 }
% 2.56/0.71 inverse(X)
% 2.56/0.71
% 2.56/0.71 Lemma 35: double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(multiply(W, V), multiply(double_divide(inverse(X), U), U))) = double_divide(Y, double_divide(V, W)).
% 2.56/0.71 Proof:
% 2.56/0.71 double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(multiply(W, V), multiply(double_divide(inverse(X), U), U)))
% 2.56/0.71 = { by lemma 6 }
% 2.56/0.71 double_divide(double_divide(inverse(X), multiply(double_divide(Y, double_divide(V, W)), double_divide(V, W))), double_divide(multiply(W, V), multiply(double_divide(inverse(X), U), U)))
% 2.56/0.71 = { by lemma 4 }
% 2.56/0.71 double_divide(Y, double_divide(V, W))
% 2.56/0.71
% 2.56/0.71 Lemma 36: multiply(X, double_divide(X, Y)) = inverse(Y).
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(X, double_divide(X, Y))
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 inverse(double_divide(double_divide(X, Y), X))
% 2.56/0.71 = { by lemma 7 R->L }
% 2.56/0.71 inverse(double_divide(double_divide(inverse(Z), multiply(double_divide(double_divide(X, Y), W), W)), double_divide(inverse(X), multiply(double_divide(inverse(Z), V), V))))
% 2.56/0.71 = { by lemma 31 R->L }
% 2.56/0.71 inverse(double_divide(double_divide(inverse(Z), multiply(double_divide(double_divide(X, Y), W), W)), double_divide(multiply(double_divide(X, Y), Y), multiply(double_divide(inverse(Z), V), V))))
% 2.56/0.71 = { by lemma 35 }
% 2.56/0.71 inverse(double_divide(double_divide(X, Y), double_divide(Y, double_divide(X, Y))))
% 2.56/0.71 = { by lemma 5 R->L }
% 2.56/0.71 multiply(double_divide(inverse(U), multiply(double_divide(T, S), S)), double_divide(T, multiply(double_divide(double_divide(X, Y), double_divide(Y, double_divide(X, Y))), U)))
% 2.56/0.71 = { by lemma 32 }
% 2.56/0.71 multiply(double_divide(inverse(U), multiply(double_divide(T, S), S)), double_divide(T, multiply(Y, U)))
% 2.56/0.71 = { by lemma 5 }
% 2.56/0.71 inverse(Y)
% 2.56/0.71
% 2.56/0.71 Lemma 37: multiply(multiply(X, Z), inverse(Z)) = multiply(multiply(X, Y), inverse(Y)).
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(multiply(X, Z), inverse(Z))
% 2.56/0.71 = { by lemma 17 R->L }
% 2.56/0.71 multiply(multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, Z)), inverse(Z))
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 inverse(double_divide(inverse(Z), multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, Z))))
% 2.56/0.71 = { by lemma 19 }
% 2.56/0.71 inverse(double_divide(inverse(Y), multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, Y))))
% 2.56/0.71 = { by axiom 1 (multiply) R->L }
% 2.56/0.71 multiply(multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, Y)), inverse(Y))
% 2.56/0.71 = { by lemma 17 }
% 2.56/0.71 multiply(multiply(X, Y), inverse(Y))
% 2.56/0.71
% 2.56/0.71 Lemma 38: multiply(inverse(X), X) = double_divide(inverse(Y), Y).
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(inverse(X), X)
% 2.56/0.71 = { by lemma 34 R->L }
% 2.56/0.71 multiply(multiply(double_divide(X, Z), Z), X)
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 inverse(double_divide(X, multiply(double_divide(X, Z), Z)))
% 2.56/0.71 = { by lemma 34 R->L }
% 2.56/0.71 multiply(double_divide(double_divide(X, multiply(double_divide(X, Z), Z)), W), W)
% 2.56/0.71 = { by lemma 23 R->L }
% 2.56/0.71 double_divide(inverse(multiply(double_divide(X, Z), Z)), multiply(double_divide(X, Z), Z))
% 2.56/0.71 = { by lemma 33 R->L }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(multiply(double_divide(X, Z), Z)), multiply(double_divide(X, Z), Z)), V))
% 2.56/0.71 = { by lemma 7 R->L }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(U), multiply(double_divide(double_divide(inverse(multiply(double_divide(X, Z), Z)), multiply(double_divide(X, Z), Z)), T), T)), double_divide(inverse(V), multiply(double_divide(inverse(U), S), S))))
% 2.56/0.71 = { by lemma 23 R->L }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(U), double_divide(inverse(multiply(double_divide(X, Z), Z)), multiply(double_divide(inverse(multiply(double_divide(X, Z), Z)), X2), X2))), double_divide(inverse(V), multiply(double_divide(inverse(U), S), S))))
% 2.56/0.71 = { by lemma 24 R->L }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(U), double_divide(double_divide(Y2, inverse(Z2)), double_divide(multiply(multiply(Z2, multiply(double_divide(X, Z), Z)), inverse(multiply(double_divide(X, Z), Z))), multiply(double_divide(Y2, W2), W2)))), double_divide(inverse(V), multiply(double_divide(inverse(U), S), S))))
% 2.56/0.71 = { by lemma 37 R->L }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(U), double_divide(double_divide(Y2, inverse(Z2)), double_divide(multiply(multiply(Z2, Y), inverse(Y)), multiply(double_divide(Y2, W2), W2)))), double_divide(inverse(V), multiply(double_divide(inverse(U), S), S))))
% 2.56/0.71 = { by lemma 24 }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(U), double_divide(inverse(Y), multiply(double_divide(inverse(Y), V2), V2))), double_divide(inverse(V), multiply(double_divide(inverse(U), S), S))))
% 2.56/0.71 = { by lemma 23 }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(U), multiply(double_divide(double_divide(inverse(Y), Y), U2), U2)), double_divide(inverse(V), multiply(double_divide(inverse(U), S), S))))
% 2.56/0.71 = { by lemma 7 }
% 2.56/0.71 double_divide(V, double_divide(double_divide(inverse(Y), Y), V))
% 2.56/0.71 = { by lemma 33 }
% 2.56/0.71 double_divide(inverse(Y), Y)
% 2.56/0.71
% 2.56/0.71 Lemma 39: double_divide(inverse(X), X) = double_divide(Y, inverse(Y)).
% 2.56/0.71 Proof:
% 2.56/0.71 double_divide(inverse(X), X)
% 2.56/0.71 = { by lemma 38 R->L }
% 2.56/0.71 multiply(inverse(Z), Z)
% 2.56/0.71 = { by lemma 34 R->L }
% 2.56/0.71 multiply(multiply(double_divide(Z, W), W), Z)
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 inverse(double_divide(Z, multiply(double_divide(Z, W), W)))
% 2.56/0.71 = { by lemma 29 R->L }
% 2.56/0.71 inverse(multiply(V, multiply(double_divide(V, U), U)))
% 2.56/0.71 = { by lemma 21 R->L }
% 2.56/0.71 multiply(multiply(V, multiply(double_divide(V, U), U)), inverse(multiply(V, multiply(double_divide(V, U), U))))
% 2.56/0.71 = { by lemma 34 R->L }
% 2.56/0.71 multiply(multiply(V, multiply(double_divide(V, U), U)), multiply(double_divide(multiply(V, multiply(double_divide(V, U), U)), T), T))
% 2.56/0.71 = { by lemma 29 }
% 2.56/0.71 double_divide(Y, multiply(double_divide(Y, S), S))
% 2.56/0.71 = { by lemma 34 }
% 2.56/0.71 double_divide(Y, inverse(Y))
% 2.56/0.71
% 2.56/0.71 Lemma 40: inverse(inverse(X)) = X.
% 2.56/0.71 Proof:
% 2.56/0.71 inverse(inverse(X))
% 2.56/0.71 = { by lemma 4 R->L }
% 2.56/0.71 double_divide(double_divide(double_divide(multiply(inverse(inverse(X)), double_divide(Y, Z)), multiply(double_divide(inverse(W), multiply(double_divide(inverse(V), U), U)), V)), multiply(inverse(inverse(X)), double_divide(Y, Z))), double_divide(multiply(Z, Y), multiply(double_divide(double_divide(multiply(inverse(inverse(X)), double_divide(Y, Z)), multiply(double_divide(inverse(W), multiply(double_divide(inverse(V), U), U)), V)), T), T)))
% 2.56/0.71 = { by lemma 11 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(double_divide(double_divide(multiply(inverse(inverse(X)), double_divide(Y, Z)), multiply(double_divide(inverse(W), multiply(double_divide(inverse(V), U), U)), V)), T), T)))
% 2.56/0.71 = { by lemma 10 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, multiply(inverse(inverse(X)), double_divide(Y, Z)))))
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, inverse(double_divide(double_divide(Y, Z), inverse(inverse(X)))))))
% 2.56/0.71 = { by lemma 34 R->L }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, multiply(double_divide(double_divide(double_divide(Y, Z), inverse(inverse(X))), S), S))))
% 2.56/0.71 = { by lemma 23 R->L }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(inverse(inverse(inverse(X))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 36 R->L }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(inverse(multiply(X, double_divide(X, inverse(X)))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 39 R->L }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(inverse(multiply(X, double_divide(inverse(X2), X2))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(inverse(inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 33 R->L }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(double_divide(double_divide(inverse(Y2), multiply(inverse(inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(inverse(double_divide(double_divide(inverse(X2), X2), X)), Y2))), double_divide(inverse(inverse(double_divide(double_divide(inverse(X2), X2), X))), double_divide(inverse(Y2), multiply(inverse(inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(inverse(double_divide(double_divide(inverse(X2), X2), X)), Y2))))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 18 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(double_divide(double_divide(inverse(Y2), multiply(inverse(inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(inverse(double_divide(double_divide(inverse(X2), X2), X)), Y2))), inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 28 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(double_divide(multiply(Z2, multiply(double_divide(Z2, W2), W2)), inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 29 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(double_divide(double_divide(inverse(X2), multiply(double_divide(inverse(X2), V2), V2)), inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 23 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(double_divide(multiply(double_divide(double_divide(inverse(X2), X2), X), X), inverse(double_divide(double_divide(inverse(X2), X2), X))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 36 R->L }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(double_divide(multiply(double_divide(double_divide(inverse(X2), X2), X), X), multiply(X, double_divide(X, double_divide(double_divide(inverse(X2), X2), X)))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(double_divide(inverse(double_divide(X, double_divide(double_divide(inverse(X2), X2), X))), multiply(X, double_divide(X, double_divide(double_divide(inverse(X2), X2), X)))), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 22 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(multiply(double_divide(X, U2), U2), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 34 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, double_divide(inverse(X), multiply(double_divide(double_divide(Y, Z), X), X)))))
% 2.56/0.71 = { by lemma 22 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, multiply(double_divide(double_divide(double_divide(Y, Z), X), T2), T2))))
% 2.56/0.71 = { by lemma 34 }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, inverse(double_divide(double_divide(Y, Z), X)))))
% 2.56/0.71 = { by axiom 1 (multiply) R->L }
% 2.56/0.71 double_divide(W, double_divide(multiply(Z, Y), multiply(W, multiply(X, double_divide(Y, Z)))))
% 2.56/0.71 = { by lemma 18 R->L }
% 2.56/0.71 double_divide(W, double_divide(S2, double_divide(inverse(W), multiply(S2, multiply(double_divide(multiply(Z, Y), multiply(W, multiply(X, double_divide(Y, Z)))), W)))))
% 2.56/0.71 = { by lemma 26 }
% 2.56/0.71 double_divide(W, double_divide(S2, double_divide(inverse(W), multiply(S2, inverse(X)))))
% 2.56/0.71 = { by lemma 27 }
% 2.56/0.71 double_divide(W, double_divide(inverse(X3), multiply(W, multiply(X, X3))))
% 2.56/0.71 = { by lemma 18 }
% 2.56/0.71 X
% 2.56/0.71
% 2.56/0.71 Lemma 41: multiply(double_divide(W, double_divide(Y, W)), Z) = multiply(double_divide(X, double_divide(Y, X)), Z).
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(double_divide(W, double_divide(Y, W)), Z)
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 inverse(double_divide(Z, double_divide(W, double_divide(Y, W))))
% 2.56/0.71 = { by lemma 35 R->L }
% 2.56/0.71 inverse(double_divide(double_divide(inverse(V), multiply(double_divide(Z, U), U)), double_divide(multiply(double_divide(Y, W), W), multiply(double_divide(inverse(V), T), T))))
% 2.56/0.71 = { by lemma 8 }
% 2.56/0.71 inverse(double_divide(double_divide(inverse(V), multiply(double_divide(Z, U), U)), double_divide(multiply(double_divide(Y, X), X), multiply(double_divide(inverse(V), T), T))))
% 2.56/0.71 = { by lemma 35 }
% 2.56/0.71 inverse(double_divide(Z, double_divide(X, double_divide(Y, X))))
% 2.56/0.71 = { by axiom 1 (multiply) R->L }
% 2.56/0.71 multiply(double_divide(X, double_divide(Y, X)), Z)
% 2.56/0.71
% 2.56/0.71 Lemma 42: double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), W) = double_divide(V, double_divide(double_divide(Y, multiply(W, X)), V)).
% 2.56/0.71 Proof:
% 2.56/0.71 double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), W)
% 2.56/0.71 = { by lemma 3 R->L }
% 2.56/0.71 double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(double_divide(Y, multiply(W, X)), double_divide(inverse(X), multiply(double_divide(Y, Z), Z))))
% 2.56/0.71 = { by lemma 3 R->L }
% 2.56/0.71 double_divide(double_divide(U, multiply(double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(double_divide(Y, multiply(W, X)), double_divide(inverse(X), multiply(double_divide(Y, Z), Z)))), T)), double_divide(inverse(T), multiply(double_divide(U, S), S)))
% 2.56/0.71 = { by lemma 41 R->L }
% 2.56/0.71 double_divide(double_divide(U, multiply(double_divide(V, double_divide(double_divide(Y, multiply(W, X)), V)), T)), double_divide(inverse(T), multiply(double_divide(U, S), S)))
% 2.56/0.71 = { by lemma 3 }
% 2.56/0.71 double_divide(V, double_divide(double_divide(Y, multiply(W, X)), V))
% 2.56/0.71
% 2.56/0.71 Lemma 43: multiply(multiply(X, Y), inverse(Y)) = inverse(multiply(double_divide(X, Z), Z)).
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(multiply(X, Y), inverse(Y))
% 2.56/0.71 = { by lemma 37 }
% 2.56/0.71 multiply(multiply(X, multiply(double_divide(X, Z), Z)), inverse(multiply(double_divide(X, Z), Z)))
% 2.56/0.71 = { by lemma 21 }
% 2.56/0.71 inverse(multiply(double_divide(X, Z), Z))
% 2.56/0.71
% 2.56/0.71 Lemma 44: multiply(inverse(X), multiply(X, Y)) = Y.
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(inverse(X), multiply(X, Y))
% 2.56/0.71 = { by lemma 36 R->L }
% 2.56/0.71 multiply(multiply(Y, double_divide(Y, X)), multiply(X, Y))
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 multiply(multiply(Y, double_divide(Y, X)), inverse(double_divide(Y, X)))
% 2.56/0.71 = { by lemma 43 }
% 2.56/0.71 inverse(multiply(double_divide(Y, Z), Z))
% 2.56/0.71 = { by lemma 34 }
% 2.56/0.71 inverse(inverse(Y))
% 2.56/0.71 = { by lemma 40 }
% 2.56/0.71 Y
% 2.56/0.71
% 2.56/0.71 Lemma 45: multiply(X, inverse(Y)) = double_divide(inverse(X), Y).
% 2.56/0.71 Proof:
% 2.56/0.71 multiply(X, inverse(Y))
% 2.56/0.71 = { by axiom 1 (multiply) }
% 2.56/0.71 inverse(double_divide(inverse(Y), X))
% 2.56/0.71 = { by lemma 34 R->L }
% 2.56/0.71 multiply(double_divide(double_divide(inverse(Y), X), Z), Z)
% 2.56/0.71 = { by lemma 23 R->L }
% 2.56/0.71 double_divide(inverse(X), multiply(double_divide(inverse(Y), W), W))
% 2.56/0.71 = { by lemma 34 }
% 2.56/0.71 double_divide(inverse(X), inverse(inverse(Y)))
% 2.56/0.71 = { by lemma 31 R->L }
% 2.56/0.71 double_divide(multiply(double_divide(X, V), V), inverse(inverse(Y)))
% 2.56/0.71 = { by lemma 34 R->L }
% 2.56/0.71 double_divide(multiply(double_divide(X, V), V), multiply(double_divide(inverse(Y), multiply(U, T)), multiply(U, T)))
% 2.56/0.71 = { by lemma 33 R->L }
% 2.56/0.71 double_divide(S, double_divide(double_divide(multiply(double_divide(X, V), V), multiply(double_divide(inverse(Y), multiply(U, T)), multiply(U, T))), S))
% 2.56/0.71 = { by lemma 42 R->L }
% 2.56/0.71 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(U, T)))
% 2.56/0.71 = { by lemma 44 R->L }
% 2.56/0.71 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(multiply(inverse(Y2), multiply(Y2, U)), T)))
% 2.56/0.71 = { by lemma 11 R->L }
% 2.56/0.71 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(inverse(multiply(inverse(Y2), multiply(Y2, U))), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.71 = { by lemma 15 R->L }
% 2.56/0.71 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(multiply(double_divide(inverse(inverse(U)), multiply(U2, multiply(multiply(inverse(Y2), multiply(Y2, U)), inverse(U)))), U2), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.71 = { by lemma 25 R->L }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(multiply(double_divide(inverse(inverse(U)), multiply(U2, multiply(double_divide(inverse(inverse(Y2)), multiply(T2, inverse(Y2))), T2))), U2), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.72 = { by lemma 21 R->L }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(multiply(double_divide(inverse(inverse(U)), multiply(U2, multiply(double_divide(inverse(inverse(Y2)), multiply(T2, multiply(multiply(S2, multiply(double_divide(S2, X3), X3)), inverse(Y2)))), T2))), U2), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.72 = { by lemma 15 }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(multiply(double_divide(inverse(inverse(U)), multiply(U2, inverse(multiply(S2, multiply(double_divide(S2, X3), X3))))), U2), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.72 = { by lemma 29 }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(multiply(double_divide(inverse(inverse(U)), multiply(U2, inverse(double_divide(Y3, multiply(double_divide(Y3, Z3), Z3))))), U2), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.72 = { by axiom 1 (multiply) R->L }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(multiply(double_divide(inverse(inverse(U)), multiply(U2, multiply(multiply(double_divide(Y3, Z3), Z3), Y3))), U2), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.72 = { by lemma 16 }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(multiply(multiply(inverse(U), multiply(double_divide(Y3, Z3), Z3)), inverse(multiply(double_divide(Y3, Z3), Z3))), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.72 = { by lemma 43 }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(double_divide(Z2, multiply(double_divide(inverse(multiply(double_divide(inverse(U), W3), W3)), multiply(double_divide(inverse(W2), V2), V2)), W2)), Z2), T)))
% 2.56/0.72 = { by lemma 11 }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(multiply(double_divide(inverse(U), W3), W3), T)))
% 2.56/0.72 = { by lemma 22 R->L }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(inverse(multiply(U, T)), multiply(inverse(U), multiply(U, T))), T)))
% 2.56/0.72 = { by lemma 44 }
% 2.56/0.72 double_divide(double_divide(inverse(multiply(U, T)), multiply(double_divide(multiply(double_divide(X, V), V), X2), X2)), double_divide(inverse(Y), multiply(double_divide(inverse(multiply(U, T)), T), T)))
% 2.56/0.72 = { by lemma 7 }
% 2.56/0.72 double_divide(multiply(double_divide(X, V), V), Y)
% 2.56/0.72 = { by lemma 31 }
% 2.56/0.72 double_divide(inverse(X), Y)
% 2.56/0.72
% 2.56/0.72 Lemma 46: multiply(inverse(X), Y) = double_divide(X, inverse(Y)).
% 2.56/0.72 Proof:
% 2.56/0.72 multiply(inverse(X), Y)
% 2.56/0.72 = { by axiom 1 (multiply) }
% 2.56/0.72 inverse(double_divide(Y, inverse(X)))
% 2.56/0.72 = { by lemma 34 R->L }
% 2.56/0.72 multiply(double_divide(double_divide(Y, inverse(X)), Z), Z)
% 2.56/0.72 = { by lemma 23 R->L }
% 2.56/0.72 double_divide(inverse(inverse(X)), multiply(double_divide(Y, W), W))
% 2.56/0.72 = { by lemma 40 }
% 2.56/0.72 double_divide(X, multiply(double_divide(Y, W), W))
% 2.56/0.72 = { by lemma 34 }
% 2.56/0.72 double_divide(X, inverse(Y))
% 2.56/0.72
% 2.56/0.72 Lemma 47: multiply(X, multiply(double_divide(Y, Z), Z)) = multiply(X, inverse(Y)).
% 2.56/0.72 Proof:
% 2.56/0.72 multiply(X, multiply(double_divide(Y, Z), Z))
% 2.56/0.72 = { by lemma 13 R->L }
% 2.56/0.72 multiply(double_divide(inverse(X), multiply(double_divide(W, V), V)), double_divide(W, multiply(double_divide(multiply(double_divide(Y, Z), Z), U), U)))
% 2.56/0.72 = { by lemma 30 }
% 2.56/0.72 multiply(double_divide(inverse(X), multiply(double_divide(W, V), V)), double_divide(W, multiply(double_divide(inverse(Y), T), T)))
% 2.56/0.72 = { by lemma 13 }
% 2.56/0.72 multiply(X, inverse(Y))
% 2.56/0.72
% 2.56/0.72 Lemma 48: multiply(double_divide(inverse(X), Y), multiply(Y, Z)) = multiply(X, Z).
% 2.56/0.72 Proof:
% 2.56/0.72 multiply(double_divide(inverse(X), Y), multiply(Y, Z))
% 2.56/0.72 = { by lemma 45 R->L }
% 2.56/0.72 multiply(multiply(X, inverse(Y)), multiply(Y, Z))
% 2.56/0.72 = { by lemma 47 R->L }
% 2.56/0.72 multiply(multiply(X, multiply(double_divide(Y, W), W)), multiply(Y, Z))
% 2.56/0.72 = { by lemma 17 }
% 2.56/0.72 multiply(X, Z)
% 2.56/0.72
% 2.56/0.72 Lemma 49: double_divide(double_divide(inverse(X), Y), Z) = multiply(Y, double_divide(X, Z)).
% 2.56/0.72 Proof:
% 2.56/0.72 double_divide(double_divide(inverse(X), Y), Z)
% 2.56/0.72 = { by lemma 45 R->L }
% 2.56/0.72 double_divide(multiply(X, inverse(Y)), Z)
% 2.56/0.72 = { by lemma 32 R->L }
% 2.56/0.72 double_divide(multiply(double_divide(W, double_divide(X, W)), inverse(Y)), Z)
% 2.56/0.72 = { by axiom 1 (multiply) }
% 2.56/0.72 double_divide(inverse(double_divide(inverse(Y), double_divide(W, double_divide(X, W)))), Z)
% 2.56/0.72 = { by lemma 45 R->L }
% 2.56/0.72 multiply(double_divide(inverse(Y), double_divide(W, double_divide(X, W))), inverse(Z))
% 2.56/0.72 = { by lemma 47 R->L }
% 2.56/0.72 multiply(double_divide(inverse(Y), double_divide(W, double_divide(X, W))), multiply(double_divide(Z, double_divide(X, Z)), double_divide(X, Z)))
% 2.56/0.72 = { by lemma 41 R->L }
% 2.56/0.72 multiply(double_divide(inverse(Y), double_divide(W, double_divide(X, W))), multiply(double_divide(W, double_divide(X, W)), double_divide(X, Z)))
% 2.56/0.72 = { by lemma 48 }
% 2.56/0.72 multiply(Y, double_divide(X, Z))
% 2.56/0.72
% 2.56/0.72 Lemma 50: double_divide(multiply(X, Y), Z) = double_divide(Y, multiply(Z, X)).
% 2.56/0.72 Proof:
% 2.56/0.72 double_divide(multiply(X, Y), Z)
% 2.56/0.72 = { by axiom 1 (multiply) }
% 2.56/0.72 double_divide(inverse(double_divide(Y, X)), Z)
% 2.56/0.72 = { by lemma 31 R->L }
% 2.56/0.72 double_divide(multiply(double_divide(double_divide(Y, X), W), W), Z)
% 2.56/0.72 = { by lemma 23 R->L }
% 2.56/0.72 double_divide(double_divide(inverse(X), multiply(double_divide(Y, V), V)), Z)
% 2.56/0.72 = { by lemma 49 }
% 2.56/0.72 multiply(multiply(double_divide(Y, V), V), double_divide(X, Z))
% 2.56/0.72 = { by lemma 34 }
% 2.56/0.72 multiply(inverse(Y), double_divide(X, Z))
% 2.56/0.72 = { by lemma 46 }
% 2.56/0.72 double_divide(Y, inverse(double_divide(X, Z)))
% 2.56/0.72 = { by axiom 1 (multiply) R->L }
% 2.56/0.72 double_divide(Y, multiply(Z, X))
% 2.56/0.72
% 2.56/0.72 Lemma 51: multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 2.56/0.72 Proof:
% 2.56/0.72 multiply(multiply(X, Y), Z)
% 2.56/0.72 = { by axiom 1 (multiply) }
% 2.56/0.72 inverse(double_divide(Z, multiply(X, Y)))
% 2.56/0.72 = { by lemma 50 R->L }
% 2.56/0.72 inverse(double_divide(multiply(Y, Z), X))
% 2.56/0.72 = { by axiom 1 (multiply) R->L }
% 2.56/0.72 multiply(X, multiply(Y, Z))
% 2.56/0.72
% 2.56/0.72 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))).
% 2.56/0.72 Proof:
% 2.56/0.72 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 2.56/0.72 = { by lemma 38 }
% 2.56/0.72 tuple(double_divide(inverse(X), X), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 2.56/0.72 = { by lemma 38 }
% 2.56/0.72 tuple(double_divide(inverse(X), X), multiply(double_divide(inverse(Y), Y), a2), multiply(multiply(a3, b3), c3))
% 2.56/0.72 = { by lemma 39 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(inverse(Y), Y), a2), multiply(multiply(a3, b3), c3))
% 2.56/0.72 = { by lemma 39 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(W, inverse(W)), a2), multiply(multiply(a3, b3), c3))
% 2.56/0.72 = { by lemma 51 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(W, inverse(W)), a2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 39 R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(inverse(V), V), a2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by axiom 1 (multiply) }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), inverse(double_divide(a2, double_divide(inverse(V), V))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 12 R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(multiply(V, inverse(V)), multiply(double_divide(double_divide(inverse(U), T), S), S)), double_divide(double_divide(inverse(U), T), multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V)))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 49 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(multiply(V, inverse(V)), multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(T, double_divide(U, multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V))))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 17 R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(multiply(double_divide(multiply(V, inverse(V)), multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(double_divide(inverse(U), T), multiply(T, double_divide(U, multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V)))))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 51 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(multiply(V, inverse(V)), multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), multiply(double_divide(inverse(U), T), multiply(T, double_divide(U, multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V))))))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 50 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), multiply(double_divide(inverse(U), T), multiply(T, double_divide(U, multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V))))))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 48 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), multiply(U, double_divide(U, multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V)))))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 36 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), inverse(multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V))))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 45 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), double_divide(inverse(multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(double_divide(a2, double_divide(inverse(V), V)), double_divide(inverse(V), V)))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 9 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(double_divide(a2, multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), multiply(double_divide(double_divide(inverse(U), T), S), S))), X2), X2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 34 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), inverse(double_divide(a2, multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), multiply(double_divide(double_divide(inverse(U), T), S), S)))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by axiom 1 (multiply) R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), multiply(double_divide(double_divide(inverse(U), T), S), S)), a2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 51 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), a2)), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 32 R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(Y2, double_divide(double_divide(inverse(V), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), V)), Y2)), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), a2)), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 42 R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(double_divide(inverse(V), multiply(double_divide(inverse(V), Z2), Z2)), multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(multiply(double_divide(double_divide(inverse(U), T), S), S), a2)), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 51 R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(multiply(double_divide(double_divide(inverse(V), multiply(double_divide(inverse(V), Z2), Z2)), multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(double_divide(double_divide(inverse(U), T), S), S)), a2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 32 R->L }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(W2, double_divide(multiply(double_divide(double_divide(inverse(V), multiply(double_divide(inverse(V), Z2), Z2)), multiply(double_divide(double_divide(inverse(U), T), S), S)), multiply(double_divide(double_divide(inverse(U), T), S), S)), W2)), a2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 31 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(double_divide(W2, double_divide(inverse(double_divide(inverse(V), multiply(double_divide(inverse(V), Z2), Z2))), W2)), a2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 32 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), multiply(inverse(double_divide(inverse(V), multiply(double_divide(inverse(V), Z2), Z2))), a2), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 46 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), double_divide(double_divide(inverse(V), multiply(double_divide(inverse(V), Z2), Z2)), inverse(a2)), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 42 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), double_divide(V2, double_divide(double_divide(inverse(V), multiply(inverse(a2), V)), V2)), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 33 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), double_divide(inverse(V), multiply(inverse(a2), V)), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 46 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), double_divide(inverse(V), double_divide(a2, inverse(V))), multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 33 }
% 2.56/0.72 tuple(double_divide(Z, inverse(Z)), a2, multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 39 R->L }
% 2.56/0.72 tuple(double_divide(inverse(U2), U2), a2, multiply(a3, multiply(b3, c3)))
% 2.56/0.72 = { by lemma 38 R->L }
% 2.56/0.72 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 2.56/0.72 % SZS output end Proof
% 2.56/0.72
% 2.56/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
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