%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:34:43 PM UTC 2026
% Result : Unsatisfiable 213.56s 27.31s
% Output : Proof 214.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 23:03:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 213.56/27.31 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 213.56/27.31
% 213.56/27.31 % SZS status Unsatisfiable
% 213.56/27.31
% 214.34/27.42 % SZS output start Proof
% 214.34/27.42 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 214.34/27.42 Axiom 2 (right_inverse): sum(X, additive_inverse(X), additive_identity) = true.
% 214.34/27.42 Axiom 3 (additive_identity1): sum(additive_identity, X, X) = true.
% 214.34/27.42 Axiom 4 (left_inverse): sum(additive_inverse(X), X, additive_identity) = true.
% 214.34/27.43 Axiom 5 (a_times_b): product(a, b, c) = true.
% 214.34/27.43 Axiom 6 (a_inverse_times_b_inverse): product(additive_inverse(a), additive_inverse(b), d) = true.
% 214.34/27.43 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 214.34/27.43 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 214.34/27.43 Axiom 9 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 214.34/27.43 Axiom 10 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 214.34/27.43 Axiom 11 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 214.34/27.43 Axiom 12 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 214.34/27.43 Axiom 13 (cancellation1): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, W, Z), true, W, Y), Y) = Y.
% 214.34/27.43 Axiom 14 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 214.34/27.43 Axiom 15 (associativity_of_addition2): ifeq(sum(X, Y, Z), true, ifeq(sum(W, Z, V), true, ifeq(sum(W, X, U), true, sum(U, Y, V), true), true), true) = true.
% 214.34/27.43 Axiom 16 (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.
% 214.34/27.43 Axiom 17 (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.
% 214.34/27.43
% 214.34/27.43 Lemma 18: add(X, Y) = add(Y, X).
% 214.34/27.43 Proof:
% 214.34/27.43 add(X, Y)
% 214.34/27.43 = { by axiom 12 (addition_is_well_defined) R->L }
% 214.34/27.43 ifeq2(sum(Y, X, add(X, Y)), true, ifeq2(sum(Y, X, add(Y, X)), true, add(Y, X), add(X, Y)), add(X, Y))
% 214.34/27.43 = { by axiom 9 (closure_of_addition) }
% 214.34/27.43 ifeq2(sum(Y, X, add(X, Y)), true, ifeq2(true, true, add(Y, X), add(X, Y)), add(X, Y))
% 214.34/27.43 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.43 ifeq2(sum(Y, X, add(X, Y)), true, add(Y, X), add(X, Y))
% 214.34/27.43 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.43 ifeq2(ifeq(true, true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 214.34/27.43 = { by axiom 9 (closure_of_addition) R->L }
% 214.34/27.43 ifeq2(ifeq(sum(X, Y, add(X, Y)), true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 214.34/27.43 = { by axiom 11 (commutativity_of_addition) }
% 214.34/27.43 ifeq2(true, true, add(Y, X), add(X, Y))
% 214.34/27.43 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.43 add(Y, X)
% 214.34/27.43
% 214.34/27.43 Lemma 19: ifeq2(sum(X, Y, X), true, additive_identity, Y) = Y.
% 214.34/27.43 Proof:
% 214.34/27.43 ifeq2(sum(X, Y, X), true, additive_identity, Y)
% 214.34/27.43 = { by axiom 8 (ifeq_axiom) R->L }
% 214.34/27.43 ifeq2(sum(X, Y, X), true, ifeq2(true, true, additive_identity, Y), Y)
% 214.34/27.43 = { by axiom 1 (additive_identity2) R->L }
% 214.34/27.43 ifeq2(sum(X, Y, X), true, ifeq2(sum(X, additive_identity, X), true, additive_identity, Y), Y)
% 214.34/27.43 = { by axiom 13 (cancellation1) }
% 214.34/27.43 Y
% 214.34/27.43
% 214.34/27.43 Lemma 20: ifeq2(sum(X, Y, additive_identity), true, additive_inverse(X), Y) = Y.
% 214.34/27.43 Proof:
% 214.34/27.43 ifeq2(sum(X, Y, additive_identity), true, additive_inverse(X), Y)
% 214.34/27.43 = { by axiom 8 (ifeq_axiom) R->L }
% 214.34/27.43 ifeq2(sum(X, Y, additive_identity), true, ifeq2(true, true, additive_inverse(X), Y), Y)
% 214.34/27.43 = { by axiom 2 (right_inverse) R->L }
% 214.34/27.43 ifeq2(sum(X, Y, additive_identity), true, ifeq2(sum(X, additive_inverse(X), additive_identity), true, additive_inverse(X), Y), Y)
% 214.34/27.43 = { by axiom 13 (cancellation1) }
% 214.34/27.43 Y
% 214.34/27.43
% 214.34/27.43 Lemma 21: ifeq2(product(X, Y, Z), true, multiply(X, Y), Z) = Z.
% 214.34/27.43 Proof:
% 214.34/27.43 ifeq2(product(X, Y, Z), true, multiply(X, Y), Z)
% 214.34/27.43 = { by axiom 8 (ifeq_axiom) R->L }
% 214.34/27.43 ifeq2(product(X, Y, Z), true, ifeq2(true, true, multiply(X, Y), Z), Z)
% 214.34/27.43 = { by axiom 10 (closure_of_multiplication) R->L }
% 214.34/27.43 ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, multiply(X, Y)), true, multiply(X, Y), Z), Z)
% 214.34/27.43 = { by axiom 14 (multiplication_is_well_defined) }
% 214.34/27.44 Z
% 214.34/27.44
% 214.34/27.44 Goal 1 (prove_c_equals_d): c = d.
% 214.34/27.44 Proof:
% 214.34/27.44 c
% 214.34/27.44 = { by axiom 12 (addition_is_well_defined) R->L }
% 214.34/27.44 ifeq2(sum(additive_identity, c, c), true, ifeq2(sum(additive_identity, c, d), true, d, c), c)
% 214.34/27.44 = { by axiom 3 (additive_identity1) }
% 214.34/27.44 ifeq2(true, true, ifeq2(sum(additive_identity, c, d), true, d, c), c)
% 214.34/27.44 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.44 ifeq2(sum(additive_identity, c, d), true, d, c)
% 214.34/27.44 = { by lemma 20 R->L }
% 214.34/27.44 ifeq2(sum(additive_identity, ifeq2(sum(additive_inverse(c), c, additive_identity), true, additive_inverse(additive_inverse(c)), c), d), true, d, c)
% 214.34/27.44 = { by axiom 4 (left_inverse) }
% 214.34/27.44 ifeq2(sum(additive_identity, ifeq2(true, true, additive_inverse(additive_inverse(c)), c), d), true, d, c)
% 214.34/27.44 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.44 ifeq2(sum(additive_identity, additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 8 (ifeq_axiom) R->L }
% 214.34/27.44 ifeq2(sum(ifeq2(true, true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 9 (closure_of_addition) R->L }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), add(d, multiply(additive_inverse(a), additive_identity))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by lemma 21 R->L }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), add(ifeq2(product(additive_inverse(a), additive_inverse(b), d), true, multiply(additive_inverse(a), additive_inverse(b)), d), multiply(additive_inverse(a), additive_identity))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 6 (a_inverse_times_b_inverse) }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), add(ifeq2(true, true, multiply(additive_inverse(a), additive_inverse(b)), d), multiply(additive_inverse(a), additive_identity))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 14 (multiplication_is_well_defined) R->L }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true, ifeq2(product(additive_inverse(a), additive_inverse(b), d), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 6 (a_inverse_times_b_inverse) }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true, ifeq2(true, true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.44 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.44 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(true, true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 10 (closure_of_multiplication) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by lemma 18 R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_identity), multiply(additive_inverse(a), additive_inverse(b)))), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(true, true, ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_identity), multiply(additive_inverse(a), additive_inverse(b)))), true), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 10 (closure_of_multiplication) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_identity), multiply(additive_inverse(a), additive_inverse(b)))), true), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by lemma 18 R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, ifeq(true, true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true), true), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 9 (closure_of_addition) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, ifeq(sum(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true), true), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, ifeq(sum(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true, ifeq(true, true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true), true), true), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 1 (additive_identity2) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), additive_inverse(b), multiply(additive_inverse(a), additive_inverse(b))), true, ifeq(sum(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true, ifeq(sum(additive_inverse(b), additive_identity, additive_inverse(b)), true, product(additive_inverse(a), additive_inverse(b), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity))), true), true), true), true), true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 16 (distributivity2) }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), ifeq2(true, true, d, add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), additive_identity)))), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.45 ifeq2(sum(ifeq2(sum(d, multiply(additive_inverse(a), additive_identity), d), true, additive_identity, multiply(additive_inverse(a), additive_identity)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by lemma 19 }
% 214.34/27.45 ifeq2(sum(multiply(additive_inverse(a), additive_identity), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 8 (ifeq_axiom) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(true, true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.45 = { by axiom 16 (distributivity2) R->L }
% 214.34/27.45 ifeq2(sum(ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), d), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, ifeq(sum(b, additive_inverse(b), additive_identity), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 2 (right_inverse) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), d), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, ifeq(true, true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), d), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 6 (a_inverse_times_b_inverse) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(true, true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 10 (closure_of_multiplication) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(true, true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by lemma 20 R->L }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), additive_identity), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 8 (ifeq_axiom) R->L }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(true, true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 9 (closure_of_addition) R->L }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), add(c, multiply(additive_identity, b))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 14 (multiplication_is_well_defined) R->L }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(product(a, b, add(c, multiply(additive_identity, b))), true, ifeq2(product(a, b, c), true, c, add(c, multiply(additive_identity, b))), add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 5 (a_times_b) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(product(a, b, add(c, multiply(additive_identity, b))), true, ifeq2(true, true, c, add(c, multiply(additive_identity, b))), add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.46 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.46 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(product(a, b, add(c, multiply(additive_identity, b))), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.47 = { by lemma 18 R->L }
% 214.34/27.47 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(product(a, b, add(multiply(additive_identity, b), c)), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.47 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.47 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(true, true, product(a, b, add(multiply(additive_identity, b), c)), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.47 = { by axiom 10 (closure_of_multiplication) R->L }
% 214.34/27.47 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, product(a, b, add(multiply(additive_identity, b), c)), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.47 = { by lemma 18 R->L }
% 214.34/27.47 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, product(a, b, add(c, multiply(additive_identity, b))), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.47 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.47 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(true, true, product(a, b, add(c, multiply(additive_identity, b))), true), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.47 = { by axiom 9 (closure_of_addition) R->L }
% 214.34/27.47 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(sum(c, multiply(additive_identity, b), add(c, multiply(additive_identity, b))), true, product(a, b, add(c, multiply(additive_identity, b))), true), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(true, true, ifeq(sum(c, multiply(additive_identity, b), add(c, multiply(additive_identity, b))), true, product(a, b, add(c, multiply(additive_identity, b))), true), true), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 5 (a_times_b) R->L }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(a, b, c), true, ifeq(sum(c, multiply(additive_identity, b), add(c, multiply(additive_identity, b))), true, product(a, b, add(c, multiply(additive_identity, b))), true), true), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(a, b, c), true, ifeq(sum(c, multiply(additive_identity, b), add(c, multiply(additive_identity, b))), true, ifeq(true, true, product(a, b, add(c, multiply(additive_identity, b))), true), true), true), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 1 (additive_identity2) R->L }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(a, b, c), true, ifeq(sum(c, multiply(additive_identity, b), add(c, multiply(additive_identity, b))), true, ifeq(sum(a, additive_identity, a), true, product(a, b, add(c, multiply(additive_identity, b))), true), true), true), true), true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 17 (distributivity4) }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), ifeq2(true, true, c, add(c, multiply(additive_identity, b)))), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(sum(c, multiply(additive_identity, b), c), true, additive_identity, multiply(additive_identity, b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by lemma 19 }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), multiply(additive_identity, b)), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 8 (ifeq_axiom) R->L }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(true, true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 17 (distributivity4) R->L }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(product(a, b, c), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(sum(additive_inverse(a), a, additive_identity), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 5 (a_times_b) }
% 214.34/27.48 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(true, true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(sum(additive_inverse(a), a, additive_identity), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.48 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(sum(additive_inverse(a), a, additive_identity), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 4 (left_inverse) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(true, true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 9 (closure_of_addition) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(true, true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 10 (closure_of_multiplication) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(ifeq(true, true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by lemma 18 }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), ifeq2(product(additive_identity, b, add(c, multiply(additive_inverse(a), b))), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b)))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by lemma 21 }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(sum(c, multiply(additive_inverse(a), b), add(c, multiply(additive_inverse(a), b))), true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 9 (closure_of_addition) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(ifeq2(true, true, additive_inverse(c), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(sum(additive_inverse(c), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 9 (closure_of_addition) }
% 214.34/27.49 ifeq2(sum(ifeq2(ifeq(true, true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 7 (ifeq_axiom) }
% 214.34/27.49 ifeq2(sum(ifeq2(product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by lemma 18 }
% 214.34/27.49 ifeq2(sum(ifeq2(product(additive_inverse(a), additive_identity, add(d, additive_inverse(c))), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by lemma 21 }
% 214.34/27.49 ifeq2(sum(add(d, additive_inverse(c)), additive_inverse(additive_inverse(c)), d), true, d, c)
% 214.34/27.49 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.49 ifeq2(ifeq(true, true, sum(add(d, additive_inverse(c)), additive_inverse(additive_inverse(c)), d), true), true, d, c)
% 214.34/27.49 = { by axiom 9 (closure_of_addition) R->L }
% 214.34/27.49 ifeq2(ifeq(sum(d, additive_inverse(c), add(d, additive_inverse(c))), true, sum(add(d, additive_inverse(c)), additive_inverse(additive_inverse(c)), d), true), true, d, c)
% 214.34/27.49 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.49 ifeq2(ifeq(true, true, ifeq(sum(d, additive_inverse(c), add(d, additive_inverse(c))), true, sum(add(d, additive_inverse(c)), additive_inverse(additive_inverse(c)), d), true), true), true, d, c)
% 214.34/27.49 = { by axiom 2 (right_inverse) R->L }
% 214.34/27.49 ifeq2(ifeq(sum(additive_inverse(c), additive_inverse(additive_inverse(c)), additive_identity), true, ifeq(sum(d, additive_inverse(c), add(d, additive_inverse(c))), true, sum(add(d, additive_inverse(c)), additive_inverse(additive_inverse(c)), d), true), true), true, d, c)
% 214.34/27.49 = { by axiom 7 (ifeq_axiom) R->L }
% 214.34/27.49 ifeq2(ifeq(sum(additive_inverse(c), additive_inverse(additive_inverse(c)), additive_identity), true, ifeq(true, true, ifeq(sum(d, additive_inverse(c), add(d, additive_inverse(c))), true, sum(add(d, additive_inverse(c)), additive_inverse(additive_inverse(c)), d), true), true), true), true, d, c)
% 214.34/27.49 = { by axiom 1 (additive_identity2) R->L }
% 214.34/27.49 ifeq2(ifeq(sum(additive_inverse(c), additive_inverse(additive_inverse(c)), additive_identity), true, ifeq(sum(d, additive_identity, d), true, ifeq(sum(d, additive_inverse(c), add(d, additive_inverse(c))), true, sum(add(d, additive_inverse(c)), additive_inverse(additive_inverse(c)), d), true), true), true), true, d, c)
% 214.34/27.49 = { by axiom 15 (associativity_of_addition2) }
% 214.34/27.49 ifeq2(true, true, d, c)
% 214.34/27.49 = { by axiom 8 (ifeq_axiom) }
% 214.34/27.49 d
% 214.34/27.49 % SZS output end Proof
% 214.34/27.49
% 214.34/27.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------