%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : BOO014-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : Wed Aug 30 18:11:23 EDT 2023

% Result   : Unsatisfiable 169.78s 22.02s
% Output   : Proof 174.08s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : BOO014-10 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 07:49:56 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 169.78/22.02  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 169.78/22.02  
% 169.78/22.02  % SZS status Unsatisfiable
% 169.78/22.02  
% 172.90/22.44  % SZS output start Proof
% 172.90/22.44  Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 172.90/22.44  Axiom 2 (x_plus_y): sum(x, y, x_plus_y) = true.
% 172.90/22.44  Axiom 3 (additive_identity1): sum(additive_identity, X, X) = true.
% 172.90/22.44  Axiom 4 (multiplicative_identity2): product(X, multiplicative_identity, X) = true.
% 172.90/22.44  Axiom 5 (multiplicative_identity1): product(multiplicative_identity, X, X) = true.
% 172.90/22.44  Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 172.90/22.44  Axiom 7 (additive_inverse2): sum(X, inverse(X), multiplicative_identity) = true.
% 172.90/22.44  Axiom 8 (additive_inverse1): sum(inverse(X), X, multiplicative_identity) = true.
% 172.90/22.44  Axiom 9 (multiplicative_inverse2): product(X, inverse(X), additive_identity) = true.
% 172.90/22.44  Axiom 10 (multiplicative_inverse1): product(inverse(X), X, additive_identity) = true.
% 172.90/22.44  Axiom 11 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 172.90/22.44  Axiom 12 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 172.90/22.44  Axiom 13 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 172.90/22.44  Axiom 14 (x_inverse_times_y_inverse): product(inverse(x), inverse(y), x_inverse_times_y_inverse) = true.
% 172.90/22.44  Axiom 15 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 172.90/22.44  Axiom 16 (commutativity_of_multiplication): ifeq(product(X, Y, Z), true, product(Y, X, Z), true) = true.
% 172.90/22.44  Axiom 17 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 172.90/22.44  Axiom 18 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 172.90/22.44  Axiom 19 (distributivity2): ifeq(product(X, Y, Z), true, ifeq(product(X, W, V), true, ifeq(sum(V, Z, U), true, ifeq(sum(W, Y, T), true, product(X, T, U), true), true), true), true) = true.
% 172.90/22.44  Axiom 20 (distributivity4): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(sum(V, Z, U), true, ifeq(sum(W, X, T), true, product(T, Y, U), true), true), true), true) = true.
% 172.90/22.44  Axiom 21 (distributivity8): ifeq(product(X, Y, Z), true, ifeq(product(W, V, U), true, ifeq(sum(V, T, Y), true, ifeq(sum(W, T, X), true, sum(U, T, Z), true), true), true), true) = true.
% 172.90/22.44  
% 172.90/22.44  Lemma 22: ifeq2(sum(X, Y, Z), true, add(X, Y), Z) = Z.
% 172.90/22.44  Proof:
% 172.90/22.44    ifeq2(sum(X, Y, Z), true, add(X, Y), Z)
% 172.90/22.44  = { by axiom 6 (ifeq_axiom) R->L }
% 172.90/22.44    ifeq2(sum(X, Y, Z), true, ifeq2(true, true, add(X, Y), Z), Z)
% 172.90/22.44  = { by axiom 12 (closure_of_addition) R->L }
% 172.90/22.44    ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, add(X, Y)), true, add(X, Y), Z), Z)
% 172.90/22.44  = { by axiom 17 (addition_is_well_defined) }
% 172.90/22.44    Z
% 172.90/22.44  
% 172.90/22.44  Lemma 23: add(X, Y) = add(Y, X).
% 172.90/22.44  Proof:
% 172.90/22.44    add(X, Y)
% 172.90/22.44  = { by lemma 22 R->L }
% 172.90/22.44    ifeq2(sum(Y, X, add(X, Y)), true, add(Y, X), add(X, Y))
% 172.90/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 172.90/22.44    ifeq2(ifeq(true, true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 172.90/22.44  = { by axiom 12 (closure_of_addition) R->L }
% 172.90/22.44    ifeq2(ifeq(sum(X, Y, add(X, Y)), true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 172.90/22.44  = { by axiom 15 (commutativity_of_addition) }
% 172.90/22.44    ifeq2(true, true, add(Y, X), add(X, Y))
% 172.90/22.44  = { by axiom 6 (ifeq_axiom) }
% 172.90/22.44    add(Y, X)
% 172.90/22.44  
% 172.90/22.44  Lemma 24: ifeq2(product(X, Y, Z), true, multiply(X, Y), Z) = Z.
% 172.90/22.44  Proof:
% 172.90/22.44    ifeq2(product(X, Y, Z), true, multiply(X, Y), Z)
% 172.90/22.44  = { by axiom 6 (ifeq_axiom) R->L }
% 172.90/22.44    ifeq2(product(X, Y, Z), true, ifeq2(true, true, multiply(X, Y), Z), Z)
% 172.90/22.44  = { by axiom 13 (closure_of_multiplication) R->L }
% 172.90/22.44    ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, multiply(X, Y)), true, multiply(X, Y), Z), Z)
% 172.90/22.44  = { by axiom 18 (multiplication_is_well_defined) }
% 172.90/22.44    Z
% 172.90/22.44  
% 172.90/22.44  Lemma 25: product(X, Y, multiply(Y, X)) = true.
% 172.90/22.44  Proof:
% 172.90/22.44    product(X, Y, multiply(Y, X))
% 172.90/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 172.90/22.44    ifeq(true, true, product(X, Y, multiply(Y, X)), true)
% 172.90/22.44  = { by axiom 13 (closure_of_multiplication) R->L }
% 172.90/22.44    ifeq(product(Y, X, multiply(Y, X)), true, product(X, Y, multiply(Y, X)), true)
% 172.90/22.44  = { by axiom 16 (commutativity_of_multiplication) }
% 172.90/22.44    true
% 172.90/22.44  
% 172.90/22.44  Lemma 26: multiply(X, Y) = multiply(Y, X).
% 172.90/22.44  Proof:
% 172.90/22.44    multiply(X, Y)
% 172.90/22.44  = { by lemma 24 R->L }
% 172.90/22.44    ifeq2(product(Y, X, multiply(X, Y)), true, multiply(Y, X), multiply(X, Y))
% 172.90/22.44  = { by lemma 25 }
% 172.90/22.44    ifeq2(true, true, multiply(Y, X), multiply(X, Y))
% 172.90/22.44  = { by axiom 6 (ifeq_axiom) }
% 172.90/22.44    multiply(Y, X)
% 172.90/22.44  
% 172.90/22.44  Lemma 27: ifeq2(product(X, multiplicative_identity, Y), true, Y, X) = X.
% 172.90/22.44  Proof:
% 172.90/22.44    ifeq2(product(X, multiplicative_identity, Y), true, Y, X)
% 172.90/22.44  = { by axiom 6 (ifeq_axiom) R->L }
% 172.90/22.44    ifeq2(true, true, ifeq2(product(X, multiplicative_identity, Y), true, Y, X), X)
% 172.90/22.44  = { by axiom 4 (multiplicative_identity2) R->L }
% 172.90/22.44    ifeq2(product(X, multiplicative_identity, X), true, ifeq2(product(X, multiplicative_identity, Y), true, Y, X), X)
% 172.90/22.44  = { by axiom 18 (multiplication_is_well_defined) }
% 172.90/22.44    X
% 172.90/22.44  
% 172.90/22.44  Lemma 28: ifeq(product(X, Y, additive_identity), true, ifeq(product(X, Z, W), true, ifeq(sum(Z, Y, V), true, product(X, V, W), true), true), true) = true.
% 172.90/22.44  Proof:
% 172.90/22.44    ifeq(product(X, Y, additive_identity), true, ifeq(product(X, Z, W), true, ifeq(sum(Z, Y, V), true, product(X, V, W), true), true), true)
% 172.90/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 172.90/22.44    ifeq(product(X, Y, additive_identity), true, ifeq(product(X, Z, W), true, ifeq(true, true, ifeq(sum(Z, Y, V), true, product(X, V, W), true), true), true), true)
% 172.90/22.44  = { by axiom 1 (additive_identity2) R->L }
% 172.90/22.44    ifeq(product(X, Y, additive_identity), true, ifeq(product(X, Z, W), true, ifeq(sum(W, additive_identity, W), true, ifeq(sum(Z, Y, V), true, product(X, V, W), true), true), true), true)
% 172.90/22.44  = { by axiom 19 (distributivity2) }
% 172.90/22.44    true
% 172.90/22.44  
% 172.90/22.44  Lemma 29: ifeq(product(X, inverse(Y), additive_identity), true, ifeq(product(X, Y, Z), true, product(X, multiplicative_identity, Z), true), true) = true.
% 172.90/22.44  Proof:
% 172.90/22.44    ifeq(product(X, inverse(Y), additive_identity), true, ifeq(product(X, Y, Z), true, product(X, multiplicative_identity, Z), true), true)
% 172.90/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 172.90/22.44    ifeq(product(X, inverse(Y), additive_identity), true, ifeq(product(X, Y, Z), true, ifeq(true, true, product(X, multiplicative_identity, Z), true), true), true)
% 172.90/22.44  = { by axiom 7 (additive_inverse2) R->L }
% 172.90/22.44    ifeq(product(X, inverse(Y), additive_identity), true, ifeq(product(X, Y, Z), true, ifeq(sum(Y, inverse(Y), multiplicative_identity), true, product(X, multiplicative_identity, Z), true), true), true)
% 172.90/22.44  = { by lemma 28 }
% 172.90/22.44    true
% 172.90/22.44  
% 172.90/22.44  Lemma 30: inverse(inverse(X)) = X.
% 172.90/22.44  Proof:
% 172.90/22.44    inverse(inverse(X))
% 172.90/22.44  = { by lemma 27 R->L }
% 172.90/22.44    ifeq2(product(inverse(inverse(X)), multiplicative_identity, X), true, X, inverse(inverse(X)))
% 172.90/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 172.90/22.44    ifeq2(ifeq(true, true, product(inverse(inverse(X)), multiplicative_identity, X), true), true, X, inverse(inverse(X)))
% 172.90/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 172.90/22.44    ifeq2(ifeq(true, true, ifeq(true, true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 172.90/22.44  = { by axiom 10 (multiplicative_inverse1) R->L }
% 172.90/22.44    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(true, true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 172.90/22.44  = { by axiom 16 (commutativity_of_multiplication) R->L }
% 172.90/22.44    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), X), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 172.90/22.44  = { by lemma 27 R->L }
% 172.90/22.44    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(product(X, multiplicative_identity, multiply(X, inverse(inverse(X)))), true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 172.90/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 172.90/22.44    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(ifeq(true, true, product(X, multiplicative_identity, multiply(X, inverse(inverse(X)))), true), true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 172.90/22.44  = { by axiom 13 (closure_of_multiplication) R->L }
% 172.90/22.44    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(ifeq(product(X, inverse(inverse(X)), multiply(X, inverse(inverse(X)))), true, product(X, multiplicative_identity, multiply(X, inverse(inverse(X)))), true), true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.44  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.44    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(ifeq(true, true, ifeq(product(X, inverse(inverse(X)), multiply(X, inverse(inverse(X)))), true, product(X, multiplicative_identity, multiply(X, inverse(inverse(X)))), true), true), true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.44  = { by axiom 9 (multiplicative_inverse2) R->L }
% 173.28/22.45    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, inverse(inverse(X)), multiply(X, inverse(inverse(X)))), true, product(X, multiplicative_identity, multiply(X, inverse(inverse(X)))), true), true), true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, inverse(inverse(X)), multiply(X, inverse(inverse(X)))), true, ifeq(true, true, product(X, multiplicative_identity, multiply(X, inverse(inverse(X)))), true), true), true), true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.45  = { by axiom 8 (additive_inverse1) R->L }
% 173.28/22.45    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, inverse(inverse(X)), multiply(X, inverse(inverse(X)))), true, ifeq(sum(inverse(inverse(X)), inverse(X), multiplicative_identity), true, product(X, multiplicative_identity, multiply(X, inverse(inverse(X)))), true), true), true), true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.45  = { by lemma 28 }
% 173.28/22.45    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), ifeq2(true, true, multiply(X, inverse(inverse(X))), X)), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.45    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(product(X, inverse(inverse(X)), multiply(X, inverse(inverse(X)))), true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.45  = { by axiom 13 (closure_of_multiplication) }
% 173.28/22.45    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(ifeq(true, true, product(inverse(inverse(X)), X, X), true), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.45    ifeq2(ifeq(product(inverse(inverse(X)), inverse(X), additive_identity), true, ifeq(product(inverse(inverse(X)), X, X), true, product(inverse(inverse(X)), multiplicative_identity, X), true), true), true, X, inverse(inverse(X)))
% 173.28/22.45  = { by lemma 29 }
% 173.28/22.45    ifeq2(true, true, X, inverse(inverse(X)))
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.45    X
% 173.28/22.45  
% 173.28/22.45  Lemma 31: sum(y, x, x_plus_y) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    sum(y, x, x_plus_y)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(true, true, sum(y, x, x_plus_y), true)
% 173.28/22.45  = { by axiom 2 (x_plus_y) R->L }
% 173.28/22.45    ifeq(sum(x, y, x_plus_y), true, sum(y, x, x_plus_y), true)
% 173.28/22.45  = { by axiom 15 (commutativity_of_addition) }
% 173.28/22.45    true
% 173.28/22.45  
% 173.28/22.45  Lemma 32: multiply(X, inverse(X)) = additive_identity.
% 173.28/22.45  Proof:
% 173.28/22.45    multiply(X, inverse(X))
% 173.28/22.45  = { by axiom 18 (multiplication_is_well_defined) R->L }
% 173.28/22.45    ifeq2(product(X, inverse(X), multiply(X, inverse(X))), true, ifeq2(product(X, inverse(X), additive_identity), true, additive_identity, multiply(X, inverse(X))), multiply(X, inverse(X)))
% 173.28/22.45  = { by axiom 9 (multiplicative_inverse2) }
% 173.28/22.45    ifeq2(product(X, inverse(X), multiply(X, inverse(X))), true, ifeq2(true, true, additive_identity, multiply(X, inverse(X))), multiply(X, inverse(X)))
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.45    ifeq2(product(X, inverse(X), multiply(X, inverse(X))), true, additive_identity, multiply(X, inverse(X)))
% 173.28/22.45  = { by axiom 13 (closure_of_multiplication) }
% 173.28/22.45    ifeq2(true, true, additive_identity, multiply(X, inverse(X)))
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.45    additive_identity
% 173.28/22.45  
% 173.28/22.45  Lemma 33: ifeq(product(X, Y, Z), true, product(X, add(Y, inverse(X)), Z), true) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq(product(X, Y, Z), true, product(X, add(Y, inverse(X)), Z), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(product(X, Y, Z), true, ifeq(true, true, product(X, add(Y, inverse(X)), Z), true), true)
% 173.28/22.45  = { by axiom 12 (closure_of_addition) R->L }
% 173.28/22.45    ifeq(product(X, Y, Z), true, ifeq(sum(Y, inverse(X), add(Y, inverse(X))), true, product(X, add(Y, inverse(X)), Z), true), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(true, true, ifeq(product(X, Y, Z), true, ifeq(sum(Y, inverse(X), add(Y, inverse(X))), true, product(X, add(Y, inverse(X)), Z), true), true), true)
% 173.28/22.45  = { by axiom 9 (multiplicative_inverse2) R->L }
% 173.28/22.45    ifeq(product(X, inverse(X), additive_identity), true, ifeq(product(X, Y, Z), true, ifeq(sum(Y, inverse(X), add(Y, inverse(X))), true, product(X, add(Y, inverse(X)), Z), true), true), true)
% 173.28/22.45  = { by lemma 28 }
% 173.28/22.45    true
% 173.28/22.45  
% 173.28/22.45  Lemma 34: ifeq2(product(X, Y, Z), true, multiply(Y, X), Z) = Z.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq2(product(X, Y, Z), true, multiply(Y, X), Z)
% 173.28/22.45  = { by lemma 26 R->L }
% 173.28/22.45    ifeq2(product(X, Y, Z), true, multiply(X, Y), Z)
% 173.28/22.45  = { by lemma 24 }
% 173.28/22.45    Z
% 173.28/22.45  
% 173.28/22.45  Lemma 35: multiply(X, add(Y, inverse(X))) = multiply(X, Y).
% 173.28/22.45  Proof:
% 173.28/22.45    multiply(X, add(Y, inverse(X)))
% 173.28/22.45  = { by lemma 26 R->L }
% 173.28/22.45    multiply(add(Y, inverse(X)), X)
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.45    ifeq2(true, true, multiply(add(Y, inverse(X)), X), multiply(X, Y))
% 173.28/22.45  = { by lemma 33 R->L }
% 173.28/22.45    ifeq2(ifeq(product(X, Y, multiply(X, Y)), true, product(X, add(Y, inverse(X)), multiply(X, Y)), true), true, multiply(add(Y, inverse(X)), X), multiply(X, Y))
% 173.28/22.45  = { by axiom 13 (closure_of_multiplication) }
% 173.28/22.45    ifeq2(ifeq(true, true, product(X, add(Y, inverse(X)), multiply(X, Y)), true), true, multiply(add(Y, inverse(X)), X), multiply(X, Y))
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.45    ifeq2(product(X, add(Y, inverse(X)), multiply(X, Y)), true, multiply(add(Y, inverse(X)), X), multiply(X, Y))
% 173.28/22.45  = { by lemma 34 }
% 173.28/22.45    multiply(X, Y)
% 173.28/22.45  
% 173.28/22.45  Lemma 36: multiply(inverse(X), add(X, Y)) = multiply(Y, inverse(X)).
% 173.28/22.45  Proof:
% 173.28/22.45    multiply(inverse(X), add(X, Y))
% 173.28/22.45  = { by lemma 23 R->L }
% 173.28/22.45    multiply(inverse(X), add(Y, X))
% 173.28/22.45  = { by lemma 30 R->L }
% 173.28/22.45    multiply(inverse(X), add(Y, inverse(inverse(X))))
% 173.28/22.45  = { by lemma 35 }
% 173.28/22.45    multiply(inverse(X), Y)
% 173.28/22.45  = { by lemma 26 }
% 173.28/22.45    multiply(Y, inverse(X))
% 173.28/22.45  
% 173.28/22.45  Lemma 37: ifeq2(sum(additive_identity, X, Y), true, Y, X) = X.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq2(sum(additive_identity, X, Y), true, Y, X)
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.45    ifeq2(true, true, ifeq2(sum(additive_identity, X, Y), true, Y, X), X)
% 173.28/22.45  = { by axiom 3 (additive_identity1) R->L }
% 173.28/22.45    ifeq2(sum(additive_identity, X, X), true, ifeq2(sum(additive_identity, X, Y), true, Y, X), X)
% 173.28/22.45  = { by axiom 17 (addition_is_well_defined) }
% 173.28/22.45    X
% 173.28/22.45  
% 173.28/22.45  Lemma 38: ifeq2(product(multiplicative_identity, X, Y), true, Y, X) = X.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq2(product(multiplicative_identity, X, Y), true, Y, X)
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.45    ifeq2(true, true, ifeq2(product(multiplicative_identity, X, Y), true, Y, X), X)
% 173.28/22.45  = { by axiom 5 (multiplicative_identity1) R->L }
% 173.28/22.45    ifeq2(product(multiplicative_identity, X, X), true, ifeq2(product(multiplicative_identity, X, Y), true, Y, X), X)
% 173.28/22.45  = { by axiom 18 (multiplication_is_well_defined) }
% 173.28/22.45    X
% 173.28/22.45  
% 173.28/22.45  Lemma 39: ifeq2(sum(X, inverse(X), Y), true, multiplicative_identity, Y) = Y.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq2(sum(X, inverse(X), Y), true, multiplicative_identity, Y)
% 173.28/22.45  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.45    ifeq2(sum(X, inverse(X), Y), true, ifeq2(true, true, multiplicative_identity, Y), Y)
% 173.28/22.45  = { by axiom 7 (additive_inverse2) R->L }
% 173.28/22.45    ifeq2(sum(X, inverse(X), Y), true, ifeq2(sum(X, inverse(X), multiplicative_identity), true, multiplicative_identity, Y), Y)
% 173.28/22.45  = { by axiom 17 (addition_is_well_defined) }
% 173.28/22.45    Y
% 173.28/22.45  
% 173.28/22.45  Lemma 40: ifeq(product(X, Y, Z), true, ifeq(sum(Y, W, multiplicative_identity), true, ifeq(sum(X, W, V), true, sum(Z, W, V), true), true), true) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq(product(X, Y, Z), true, ifeq(sum(Y, W, multiplicative_identity), true, ifeq(sum(X, W, V), true, sum(Z, W, V), true), true), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(true, true, ifeq(product(X, Y, Z), true, ifeq(sum(Y, W, multiplicative_identity), true, ifeq(sum(X, W, V), true, sum(Z, W, V), true), true), true), true)
% 173.28/22.45  = { by axiom 4 (multiplicative_identity2) R->L }
% 173.28/22.45    ifeq(product(V, multiplicative_identity, V), true, ifeq(product(X, Y, Z), true, ifeq(sum(Y, W, multiplicative_identity), true, ifeq(sum(X, W, V), true, sum(Z, W, V), true), true), true), true)
% 173.28/22.45  = { by axiom 21 (distributivity8) }
% 173.28/22.45    true
% 173.28/22.45  
% 173.28/22.45  Lemma 41: sum(multiply(X, inverse(Y)), Y, add(X, Y)) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    sum(multiply(X, inverse(Y)), Y, add(X, Y))
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(true, true, sum(multiply(X, inverse(Y)), Y, add(X, Y)), true)
% 173.28/22.45  = { by axiom 12 (closure_of_addition) R->L }
% 173.28/22.45    ifeq(sum(X, Y, add(X, Y)), true, sum(multiply(X, inverse(Y)), Y, add(X, Y)), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(true, true, ifeq(sum(X, Y, add(X, Y)), true, sum(multiply(X, inverse(Y)), Y, add(X, Y)), true), true)
% 173.28/22.45  = { by axiom 13 (closure_of_multiplication) R->L }
% 173.28/22.45    ifeq(product(X, inverse(Y), multiply(X, inverse(Y))), true, ifeq(sum(X, Y, add(X, Y)), true, sum(multiply(X, inverse(Y)), Y, add(X, Y)), true), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(product(X, inverse(Y), multiply(X, inverse(Y))), true, ifeq(true, true, ifeq(sum(X, Y, add(X, Y)), true, sum(multiply(X, inverse(Y)), Y, add(X, Y)), true), true), true)
% 173.28/22.45  = { by axiom 8 (additive_inverse1) R->L }
% 173.28/22.45    ifeq(product(X, inverse(Y), multiply(X, inverse(Y))), true, ifeq(sum(inverse(Y), Y, multiplicative_identity), true, ifeq(sum(X, Y, add(X, Y)), true, sum(multiply(X, inverse(Y)), Y, add(X, Y)), true), true), true)
% 173.28/22.45  = { by lemma 40 }
% 173.28/22.45    true
% 173.28/22.45  
% 173.28/22.45  Lemma 42: ifeq2(sum(X, Y, Z), true, add(Y, X), Z) = Z.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq2(sum(X, Y, Z), true, add(Y, X), Z)
% 173.28/22.45  = { by lemma 23 R->L }
% 173.28/22.45    ifeq2(sum(X, Y, Z), true, add(X, Y), Z)
% 173.28/22.45  = { by lemma 22 }
% 173.28/22.45    Z
% 173.28/22.45  
% 173.28/22.45  Lemma 43: ifeq(product(X, Y, additive_identity), true, ifeq(product(Z, Y, W), true, ifeq(sum(Z, X, V), true, product(V, Y, W), true), true), true) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, ifeq(product(Z, Y, W), true, ifeq(sum(Z, X, V), true, product(V, Y, W), true), true), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, ifeq(product(Z, Y, W), true, ifeq(true, true, ifeq(sum(Z, X, V), true, product(V, Y, W), true), true), true), true)
% 173.28/22.45  = { by axiom 1 (additive_identity2) R->L }
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, ifeq(product(Z, Y, W), true, ifeq(sum(W, additive_identity, W), true, ifeq(sum(Z, X, V), true, product(V, Y, W), true), true), true), true)
% 173.28/22.45  = { by axiom 20 (distributivity4) }
% 173.28/22.45    true
% 173.28/22.45  
% 173.28/22.45  Lemma 44: ifeq(product(X, Y, additive_identity), true, product(multiplicative_identity, Y, multiply(Y, inverse(X))), true) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, product(multiplicative_identity, Y, multiply(Y, inverse(X))), true)
% 173.28/22.45  = { by lemma 26 R->L }
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, product(multiplicative_identity, Y, multiply(inverse(X), Y)), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, ifeq(true, true, product(multiplicative_identity, Y, multiply(inverse(X), Y)), true), true)
% 173.28/22.45  = { by axiom 13 (closure_of_multiplication) R->L }
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, ifeq(product(inverse(X), Y, multiply(inverse(X), Y)), true, product(multiplicative_identity, Y, multiply(inverse(X), Y)), true), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, ifeq(product(inverse(X), Y, multiply(inverse(X), Y)), true, ifeq(true, true, product(multiplicative_identity, Y, multiply(inverse(X), Y)), true), true), true)
% 173.28/22.45  = { by axiom 8 (additive_inverse1) R->L }
% 173.28/22.45    ifeq(product(X, Y, additive_identity), true, ifeq(product(inverse(X), Y, multiply(inverse(X), Y)), true, ifeq(sum(inverse(X), X, multiplicative_identity), true, product(multiplicative_identity, Y, multiply(inverse(X), Y)), true), true), true)
% 173.28/22.45  = { by lemma 43 }
% 173.28/22.45    true
% 173.28/22.45  
% 173.28/22.45  Lemma 45: ifeq(sum(inverse(X), Y, multiplicative_identity), true, sum(additive_identity, Y, add(X, Y)), true) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq(sum(inverse(X), Y, multiplicative_identity), true, sum(additive_identity, Y, add(X, Y)), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(sum(inverse(X), Y, multiplicative_identity), true, ifeq(true, true, sum(additive_identity, Y, add(X, Y)), true), true)
% 173.28/22.45  = { by axiom 12 (closure_of_addition) R->L }
% 173.28/22.45    ifeq(sum(inverse(X), Y, multiplicative_identity), true, ifeq(sum(X, Y, add(X, Y)), true, sum(additive_identity, Y, add(X, Y)), true), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(true, true, ifeq(sum(inverse(X), Y, multiplicative_identity), true, ifeq(sum(X, Y, add(X, Y)), true, sum(additive_identity, Y, add(X, Y)), true), true), true)
% 173.28/22.45  = { by axiom 9 (multiplicative_inverse2) R->L }
% 173.28/22.45    ifeq(product(X, inverse(X), additive_identity), true, ifeq(sum(inverse(X), Y, multiplicative_identity), true, ifeq(sum(X, Y, add(X, Y)), true, sum(additive_identity, Y, add(X, Y)), true), true), true)
% 173.28/22.45  = { by lemma 40 }
% 173.28/22.45    true
% 173.28/22.45  
% 173.28/22.45  Lemma 46: ifeq(sum(inverse(y), X, multiplicative_identity), true, ifeq(sum(inverse(x), X, Y), true, sum(x_inverse_times_y_inverse, X, Y), true), true) = true.
% 173.28/22.45  Proof:
% 173.28/22.45    ifeq(sum(inverse(y), X, multiplicative_identity), true, ifeq(sum(inverse(x), X, Y), true, sum(x_inverse_times_y_inverse, X, Y), true), true)
% 173.28/22.45  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.45    ifeq(true, true, ifeq(sum(inverse(y), X, multiplicative_identity), true, ifeq(sum(inverse(x), X, Y), true, sum(x_inverse_times_y_inverse, X, Y), true), true), true)
% 173.28/22.45  = { by axiom 14 (x_inverse_times_y_inverse) R->L }
% 173.28/22.45    ifeq(product(inverse(x), inverse(y), x_inverse_times_y_inverse), true, ifeq(sum(inverse(y), X, multiplicative_identity), true, ifeq(sum(inverse(x), X, Y), true, sum(x_inverse_times_y_inverse, X, Y), true), true), true)
% 173.28/22.45  = { by lemma 40 }
% 173.28/22.48    true
% 173.28/22.48  
% 173.28/22.48  Goal 1 (prove_equation): inverse(x_plus_y) = x_inverse_times_y_inverse.
% 173.28/22.48  Proof:
% 173.28/22.48    inverse(x_plus_y)
% 173.28/22.48  = { by lemma 27 R->L }
% 173.28/22.48    ifeq2(product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.48    ifeq2(ifeq(true, true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by lemma 25 R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(x, inverse(x_plus_y))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by lemma 36 R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), add(x_plus_y, x))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 17 (addition_is_well_defined) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(true, true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 8 (additive_inverse1) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(true, true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 13 (closure_of_multiplication) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), multiply(y, inverse(x))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by lemma 34 R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(product(inverse(x), x_plus_y, multiply(y, inverse(x))), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by lemma 26 R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(product(inverse(x), x_plus_y, multiply(inverse(x), y)), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(ifeq(true, true, product(inverse(x), x_plus_y, multiply(inverse(x), y)), true), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 13 (closure_of_multiplication) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(ifeq(product(inverse(x), y, multiply(inverse(x), y)), true, product(inverse(x), x_plus_y, multiply(inverse(x), y)), true), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(ifeq(true, true, ifeq(product(inverse(x), y, multiply(inverse(x), y)), true, product(inverse(x), x_plus_y, multiply(inverse(x), y)), true), true), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.48  = { by axiom 10 (multiplicative_inverse1) R->L }
% 173.28/22.48    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(ifeq(product(inverse(x), x, additive_identity), true, ifeq(product(inverse(x), y, multiply(inverse(x), y)), true, product(inverse(x), x_plus_y, multiply(inverse(x), y)), true), true), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(ifeq(product(inverse(x), x, additive_identity), true, ifeq(product(inverse(x), y, multiply(inverse(x), y)), true, ifeq(true, true, product(inverse(x), x_plus_y, multiply(inverse(x), y)), true), true), true), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 31 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(ifeq(product(inverse(x), x, additive_identity), true, ifeq(product(inverse(x), y, multiply(inverse(x), y)), true, ifeq(sum(y, x, x_plus_y), true, product(inverse(x), x_plus_y, multiply(inverse(x), y)), true), true), true), true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 28 }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), ifeq2(true, true, multiply(x_plus_y, inverse(x)), multiply(y, inverse(x)))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), multiply(x_plus_y, inverse(x))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), multiply(x_plus_y, inverse(x))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(true, true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 31 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(ifeq(product(y, inverse(x), multiply(x_plus_y, inverse(x))), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, ifeq(sum(y, x, x_plus_y), true, sum(multiply(x_plus_y, inverse(x)), x, x_plus_y), true), true), true), true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 40 }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, ifeq2(true, true, x_plus_y, add(x_plus_y, x)), add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(x)), x, add(x_plus_y, x)), true, x_plus_y, add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 41 }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), ifeq2(true, true, x_plus_y, add(x_plus_y, x)))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(inverse(x_plus_y), x_plus_y)), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 26 }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, multiply(x_plus_y, inverse(x_plus_y))), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 32 }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), x, additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 30 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 38 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(true, true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 13 (closure_of_multiplication) R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_plus_y, x_inverse_times_y_inverse)), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 26 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x_plus_y)), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(true, true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 43 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, additive_identity), true, ifeq(product(x, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true, ifeq(sum(x, y, x_plus_y), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true), true), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 2 (x_plus_y) }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, additive_identity), true, ifeq(product(x, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true, ifeq(true, true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true), true), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, additive_identity), true, ifeq(product(x, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 13 (closure_of_multiplication) }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, additive_identity), true, ifeq(true, true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, additive_identity), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 26 }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, additive_identity), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 32 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by lemma 37 R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.49  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.49    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(true, true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.50  = { by axiom 12 (closure_of_addition) R->L }
% 173.28/22.50    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.50  = { by lemma 39 R->L }
% 173.28/22.50    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.50  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.50    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(true, true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.50  = { by axiom 12 (closure_of_addition) R->L }
% 173.28/22.50    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.50  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.50    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(true, true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.50  = { by axiom 7 (additive_inverse2) R->L }
% 173.28/22.50    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(true, true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by lemma 25 R->L }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(y))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by lemma 36 R->L }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), add(y, x_inverse_times_y_inverse))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(true, true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by lemma 46 R->L }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(ifeq(sum(inverse(y), inverse(inverse(y)), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(inverse(y)), add(inverse(x), y)), true, sum(x_inverse_times_y_inverse, inverse(inverse(y)), add(inverse(x), y)), true), true), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by axiom 7 (additive_inverse2) }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(ifeq(true, true, ifeq(sum(inverse(x), inverse(inverse(y)), add(inverse(x), y)), true, sum(x_inverse_times_y_inverse, inverse(inverse(y)), add(inverse(x), y)), true), true), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(ifeq(sum(inverse(x), inverse(inverse(y)), add(inverse(x), y)), true, sum(x_inverse_times_y_inverse, inverse(inverse(y)), add(inverse(x), y)), true), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by lemma 30 }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(ifeq(sum(inverse(x), inverse(inverse(y)), add(inverse(x), y)), true, sum(x_inverse_times_y_inverse, y, add(inverse(x), y)), true), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.51  = { by lemma 30 }
% 173.28/22.51    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(ifeq(sum(inverse(x), y, add(inverse(x), y)), true, sum(x_inverse_times_y_inverse, y, add(inverse(x), y)), true), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 12 (closure_of_addition) }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(ifeq(true, true, sum(x_inverse_times_y_inverse, y, add(inverse(x), y)), true), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(sum(x_inverse_times_y_inverse, y, add(inverse(x), y)), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by lemma 23 }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), ifeq2(sum(x_inverse_times_y_inverse, y, add(y, inverse(x))), true, add(y, x_inverse_times_y_inverse), add(y, inverse(x))))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by lemma 42 }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(y), add(y, inverse(x)))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by lemma 36 }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, multiply(inverse(x), inverse(y))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 18 (multiplication_is_well_defined) R->L }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, ifeq2(product(inverse(x), inverse(y), multiply(inverse(x), inverse(y))), true, ifeq2(product(inverse(x), inverse(y), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(inverse(x), inverse(y))), multiply(inverse(x), inverse(y)))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 14 (x_inverse_times_y_inverse) }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, ifeq2(product(inverse(x), inverse(y), multiply(inverse(x), inverse(y))), true, ifeq2(true, true, x_inverse_times_y_inverse, multiply(inverse(x), inverse(y))), multiply(inverse(x), inverse(y)))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, ifeq2(product(inverse(x), inverse(y), multiply(inverse(x), inverse(y))), true, x_inverse_times_y_inverse, multiply(inverse(x), inverse(y)))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 13 (closure_of_multiplication) }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, ifeq2(true, true, x_inverse_times_y_inverse, multiply(inverse(x), inverse(y)))), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(y), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(y), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by lemma 40 }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), ifeq2(true, true, multiplicative_identity, add(inverse(y), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(y), inverse(x_inverse_times_y_inverse), multiplicative_identity), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(y, inverse(x_inverse_times_y_inverse))), true), true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by lemma 45 }
% 173.28/22.52    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(true, true, add(y, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.52  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, add(y, inverse(x_inverse_times_y_inverse)))), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 35 }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, y)), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 26 }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(product(y, x_inverse_times_y_inverse, multiply(y, x_inverse_times_y_inverse)), true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 13 (closure_of_multiplication) }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(ifeq(true, true, product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 26 }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, ifeq2(product(x_plus_y, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true, multiply(x_inverse_times_y_inverse, x_plus_y), multiply(x, x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 34 }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x, x_inverse_times_y_inverse)), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 26 R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, x)), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 35 R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, add(x, inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(true, true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 45 R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), multiplicative_identity), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(true, true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 40 R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(true, true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 13 (closure_of_multiplication) R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), multiply(x_inverse_times_y_inverse, inverse(x))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 36 R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), multiply(inverse(x), add(x, x_inverse_times_y_inverse))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 18 (multiplication_is_well_defined) R->L }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), add(x, x_inverse_times_y_inverse), multiply(inverse(x), add(x, x_inverse_times_y_inverse))), true, ifeq2(product(inverse(x), add(x, x_inverse_times_y_inverse), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(inverse(x), add(x, x_inverse_times_y_inverse))), multiply(inverse(x), add(x, x_inverse_times_y_inverse)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 13 (closure_of_multiplication) }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(true, true, ifeq2(product(inverse(x), add(x, x_inverse_times_y_inverse), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(inverse(x), add(x, x_inverse_times_y_inverse))), multiply(inverse(x), add(x, x_inverse_times_y_inverse)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by axiom 6 (ifeq_axiom) }
% 173.28/22.53    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), add(x, x_inverse_times_y_inverse), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(inverse(x), add(x, x_inverse_times_y_inverse)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.53  = { by lemma 26 }
% 173.28/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), add(x, x_inverse_times_y_inverse), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.54  = { by axiom 6 (ifeq_axiom) R->L }
% 173.28/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(true, true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.54  = { by lemma 40 R->L }
% 173.28/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(product(inverse(y), inverse(x), x_inverse_times_y_inverse), true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, inverse(inverse(x)), add(inverse(y), x)), true), true), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.54  = { by axiom 11 (ifeq_axiom_001) R->L }
% 173.28/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(ifeq(true, true, product(inverse(y), inverse(x), x_inverse_times_y_inverse), true), true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, inverse(inverse(x)), add(inverse(y), x)), true), true), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.54  = { by axiom 14 (x_inverse_times_y_inverse) R->L }
% 173.28/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(ifeq(product(inverse(x), inverse(y), x_inverse_times_y_inverse), true, product(inverse(y), inverse(x), x_inverse_times_y_inverse), true), true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, inverse(inverse(x)), add(inverse(y), x)), true), true), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.54  = { by axiom 16 (commutativity_of_multiplication) }
% 173.28/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(true, true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, inverse(inverse(x)), add(inverse(y), x)), true), true), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.54  = { by axiom 11 (ifeq_axiom_001) }
% 173.28/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, inverse(inverse(x)), add(inverse(y), x)), true), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 173.28/22.54  = { by axiom 7 (additive_inverse2) }
% 174.08/22.54    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(true, true, ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, inverse(inverse(x)), add(inverse(y), x)), true), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.54  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, inverse(inverse(x)), add(inverse(y), x)), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by lemma 30 }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(sum(inverse(y), inverse(inverse(x)), add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, x, add(inverse(y), x)), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by lemma 30 }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(sum(inverse(y), x, add(inverse(y), x)), true, sum(x_inverse_times_y_inverse, x, add(inverse(y), x)), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by axiom 12 (closure_of_addition) }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(ifeq(true, true, sum(x_inverse_times_y_inverse, x, add(inverse(y), x)), true), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(sum(x_inverse_times_y_inverse, x, add(inverse(y), x)), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by lemma 23 }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), ifeq2(sum(x_inverse_times_y_inverse, x, add(x, inverse(y))), true, add(x, x_inverse_times_y_inverse), add(x, inverse(y))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by lemma 42 }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), add(x, inverse(y)), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by lemma 23 R->L }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), add(inverse(y), x), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by lemma 30 R->L }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(product(inverse(x), add(inverse(y), inverse(inverse(x))), x_inverse_times_y_inverse), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by axiom 11 (ifeq_axiom_001) R->L }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(ifeq(true, true, product(inverse(x), add(inverse(y), inverse(inverse(x))), x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by axiom 14 (x_inverse_times_y_inverse) R->L }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(ifeq(product(inverse(x), inverse(y), x_inverse_times_y_inverse), true, product(inverse(x), add(inverse(y), inverse(inverse(x))), x_inverse_times_y_inverse), true), true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.55  = { by lemma 33 }
% 174.08/22.55    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), ifeq2(true, true, x_inverse_times_y_inverse, multiply(add(x, x_inverse_times_y_inverse), inverse(x)))), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 6 (ifeq_axiom) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(ifeq(product(x_inverse_times_y_inverse, inverse(x), x_inverse_times_y_inverse), true, product(inverse(x), x_inverse_times_y_inverse, x_inverse_times_y_inverse), true), true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 16 (commutativity_of_multiplication) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(true, true, ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), multiplicative_identity), true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 7 (additive_inverse2) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(true, true, ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 12 (closure_of_addition) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(ifeq(true, true, sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), ifeq2(sum(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, multiplicative_identity, add(inverse(x), inverse(x_inverse_times_y_inverse)))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 39 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(sum(inverse(x), inverse(x_inverse_times_y_inverse), add(inverse(x), inverse(x_inverse_times_y_inverse))), true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 12 (closure_of_addition) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(ifeq(true, true, sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, ifeq2(sum(additive_identity, inverse(x_inverse_times_y_inverse), add(x, inverse(x_inverse_times_y_inverse))), true, add(x, inverse(x_inverse_times_y_inverse)), inverse(x_inverse_times_y_inverse)))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 37 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_inverse_times_y_inverse))), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 32 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(ifeq(product(x_plus_y, x_inverse_times_y_inverse, additive_identity), true, product(multiplicative_identity, x_inverse_times_y_inverse, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 44 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, ifeq2(true, true, multiply(x_inverse_times_y_inverse, inverse(x_plus_y)), x_inverse_times_y_inverse)), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 6 (ifeq_axiom) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(x_inverse_times_y_inverse, inverse(x_plus_y))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 36 R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), add(x_plus_y, x_inverse_times_y_inverse))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 6 (ifeq_axiom) R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(true, true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 46 R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(sum(inverse(y), x_plus_y, multiplicative_identity), true, ifeq(sum(inverse(x), x_plus_y, add(inverse(x), x_plus_y)), true, sum(x_inverse_times_y_inverse, x_plus_y, add(inverse(x), x_plus_y)), true), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 12 (closure_of_addition) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(sum(inverse(y), x_plus_y, multiplicative_identity), true, ifeq(true, true, sum(x_inverse_times_y_inverse, x_plus_y, add(inverse(x), x_plus_y)), true), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(sum(inverse(y), x_plus_y, multiplicative_identity), true, sum(x_inverse_times_y_inverse, x_plus_y, add(inverse(x), x_plus_y)), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 23 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(sum(inverse(y), x_plus_y, multiplicative_identity), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 11 (ifeq_axiom_001) R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(true, true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 12 (closure_of_addition) R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(x_plus_y, inverse(y))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 23 R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(y), x_plus_y)), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 30 R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(y), inverse(inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 42 R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), ifeq2(sum(multiply(inverse(y), inverse(inverse(inverse(x_plus_y)))), inverse(inverse(x_plus_y)), add(inverse(y), inverse(inverse(x_plus_y)))), true, add(inverse(inverse(x_plus_y)), multiply(inverse(y), inverse(inverse(inverse(x_plus_y))))), add(inverse(y), inverse(inverse(x_plus_y))))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 41 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), ifeq2(true, true, add(inverse(inverse(x_plus_y)), multiply(inverse(y), inverse(inverse(inverse(x_plus_y))))), add(inverse(y), inverse(inverse(x_plus_y))))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 6 (ifeq_axiom) }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), multiply(inverse(y), inverse(inverse(inverse(x_plus_y)))))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 30 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), multiply(inverse(y), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by lemma 26 }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), multiply(inverse(x_plus_y), inverse(y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.56  = { by axiom 6 (ifeq_axiom) R->L }
% 174.08/22.56    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(true, true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by lemma 44 R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), additive_identity), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by lemma 32 R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(x_plus_y, inverse(x_plus_y))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by lemma 26 R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), x_plus_y)), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by axiom 6 (ifeq_axiom) R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(true, true, x_plus_y, add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by lemma 41 R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, x_plus_y, add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by axiom 6 (ifeq_axiom) R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(true, true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by lemma 40 R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), multiply(x_plus_y, inverse(y))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, ifeq(sum(x, y, x_plus_y), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by axiom 2 (x_plus_y) }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), multiply(x_plus_y, inverse(y))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, ifeq(true, true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), multiply(x_plus_y, inverse(y))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by axiom 6 (ifeq_axiom) R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(true, true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by lemma 28 R->L }
% 174.08/22.57    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(ifeq(product(inverse(y), y, additive_identity), true, ifeq(product(inverse(y), x, multiply(inverse(y), x)), true, ifeq(sum(x, y, x_plus_y), true, product(inverse(y), x_plus_y, multiply(inverse(y), x)), true), true), true), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.57  = { by axiom 2 (x_plus_y) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(ifeq(product(inverse(y), y, additive_identity), true, ifeq(product(inverse(y), x, multiply(inverse(y), x)), true, ifeq(true, true, product(inverse(y), x_plus_y, multiply(inverse(y), x)), true), true), true), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(ifeq(product(inverse(y), y, additive_identity), true, ifeq(product(inverse(y), x, multiply(inverse(y), x)), true, product(inverse(y), x_plus_y, multiply(inverse(y), x)), true), true), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 10 (multiplicative_inverse1) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(ifeq(true, true, ifeq(product(inverse(y), x, multiply(inverse(y), x)), true, product(inverse(y), x_plus_y, multiply(inverse(y), x)), true), true), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(ifeq(product(inverse(y), x, multiply(inverse(y), x)), true, product(inverse(y), x_plus_y, multiply(inverse(y), x)), true), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 13 (closure_of_multiplication) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(ifeq(true, true, product(inverse(y), x_plus_y, multiply(inverse(y), x)), true), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(product(inverse(y), x_plus_y, multiply(inverse(y), x)), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by lemma 26 }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), ifeq2(product(inverse(y), x_plus_y, multiply(x, inverse(y))), true, multiply(x_plus_y, inverse(y)), multiply(x, inverse(y)))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by lemma 34 }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(product(x, inverse(y), multiply(x, inverse(y))), true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 13 (closure_of_multiplication) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(true, true, ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(sum(inverse(y), y, multiplicative_identity), true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 8 (additive_inverse1) }
% 174.08/22.58    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(ifeq(true, true, sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.58  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), ifeq2(sum(multiply(x_plus_y, inverse(y)), y, add(x_plus_y, y)), true, ifeq2(sum(multiply(x_plus_y, inverse(y)), y, x_plus_y), true, x_plus_y, add(x_plus_y, y)), add(x_plus_y, y)))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 17 (addition_is_well_defined) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(inverse(x_plus_y), add(x_plus_y, y))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 36 }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(product(y, inverse(x_plus_y), multiply(y, inverse(x_plus_y))), true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 13 (closure_of_multiplication) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(ifeq(true, true, product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), ifeq2(product(multiplicative_identity, inverse(x_plus_y), multiply(inverse(x_plus_y), inverse(y))), true, multiply(inverse(x_plus_y), inverse(y)), inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 38 }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(inverse(inverse(x_plus_y)), inverse(x_plus_y))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 30 }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), add(x_plus_y, inverse(x_plus_y))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 39 R->L }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), ifeq2(sum(x_plus_y, inverse(x_plus_y), add(x_plus_y, inverse(x_plus_y))), true, multiplicative_identity, add(x_plus_y, inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 12 (closure_of_addition) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), ifeq2(true, true, multiplicative_identity, add(x_plus_y, inverse(x_plus_y)))), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 6 (ifeq_axiom) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(ifeq(sum(x_plus_y, inverse(y), multiplicative_identity), true, sum(inverse(y), x_plus_y, multiplicative_identity), true), true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 15 (commutativity_of_addition) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(ifeq(true, true, sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 11 (ifeq_axiom_001) }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), ifeq2(sum(x_inverse_times_y_inverse, x_plus_y, add(x_plus_y, inverse(x))), true, add(x_plus_y, x_inverse_times_y_inverse), add(x_plus_y, inverse(x))))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 42 }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), add(x_plus_y, inverse(x)))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 36 }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x), inverse(x_plus_y))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 26 }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), inverse(x))), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 11 (ifeq_axiom_001) R->L }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, ifeq(true, true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), inverse(x))), true), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 13 (closure_of_multiplication) R->L }
% 174.08/22.59    ifeq2(ifeq(product(inverse(x_plus_y), inverse(inverse(x)), additive_identity), true, ifeq(product(inverse(x_plus_y), inverse(x), multiply(inverse(x_plus_y), inverse(x))), true, product(inverse(x_plus_y), multiplicative_identity, multiply(inverse(x_plus_y), inverse(x))), true), true), true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by lemma 29 }
% 174.08/22.59    ifeq2(true, true, x_inverse_times_y_inverse, inverse(x_plus_y))
% 174.08/22.59  = { by axiom 6 (ifeq_axiom) }
% 174.08/22.59    x_inverse_times_y_inverse
% 174.08/22.59  % SZS output end Proof
% 174.08/22.59  
% 174.08/22.59  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------