%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:34:42 PM UTC 2026
% Result : Unsatisfiable 118.59s 15.46s
% Output : Proof 119.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 22:57:31 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 118.59/15.46 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
% 118.59/15.46
% 118.59/15.46 % SZS status Unsatisfiable
% 118.59/15.46
% 119.38/15.51 % SZS output start Proof
% 119.38/15.51 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 119.38/15.51 Axiom 2 (additive_identity1): sum(additive_identity, X, X) = true.
% 119.38/15.51 Axiom 3 (left_inverse): sum(additive_inverse(X), X, additive_identity) = true.
% 119.38/15.51 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 119.38/15.51 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 119.38/15.51 Axiom 6 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 119.38/15.51 Axiom 7 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 119.38/15.51 Axiom 8 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 119.38/15.51 Axiom 9 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 119.38/15.51 Axiom 10 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 119.38/15.51 Axiom 11 (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.
% 119.38/15.51 Axiom 12 (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.
% 119.38/15.51
% 119.38/15.51 Lemma 13: ifeq2(sum(X, Y, Z), true, add(X, Y), Z) = Z.
% 119.38/15.51 Proof:
% 119.38/15.51 ifeq2(sum(X, Y, Z), true, add(X, Y), Z)
% 119.38/15.51 = { by axiom 5 (ifeq_axiom) R->L }
% 119.38/15.51 ifeq2(sum(X, Y, Z), true, ifeq2(true, true, add(X, Y), Z), Z)
% 119.38/15.51 = { by axiom 6 (closure_of_addition) R->L }
% 119.38/15.51 ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, add(X, Y)), true, add(X, Y), Z), Z)
% 119.38/15.51 = { by axiom 9 (addition_is_well_defined) }
% 119.38/15.51 Z
% 119.38/15.51
% 119.38/15.51 Lemma 14: add(X, Y) = add(Y, X).
% 119.38/15.51 Proof:
% 119.38/15.51 add(X, Y)
% 119.38/15.52 = { by lemma 13 R->L }
% 119.38/15.52 ifeq2(sum(Y, X, add(X, Y)), true, add(Y, X), add(X, Y))
% 119.38/15.52 = { by axiom 4 (ifeq_axiom) R->L }
% 119.38/15.52 ifeq2(ifeq(true, true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 119.38/15.52 = { by axiom 6 (closure_of_addition) R->L }
% 119.38/15.52 ifeq2(ifeq(sum(X, Y, add(X, Y)), true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 119.38/15.52 = { by axiom 8 (commutativity_of_addition) }
% 119.38/15.52 ifeq2(true, true, add(Y, X), add(X, Y))
% 119.38/15.52 = { by axiom 5 (ifeq_axiom) }
% 119.38/15.52 add(Y, X)
% 119.38/15.52
% 119.38/15.52 Goal 1 (prove_a_times_0_is_0): product(a, additive_identity, additive_identity) = true.
% 119.38/15.52 Proof:
% 119.38/15.52 product(a, additive_identity, additive_identity)
% 119.38/15.52 = { by axiom 5 (ifeq_axiom) R->L }
% 119.38/15.52 product(a, additive_identity, ifeq2(true, true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by axiom 11 (associativity_of_addition2) R->L }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X))), true, ifeq(sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true, sum(additive_identity, multiply(a, additive_identity), add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X))), true), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by axiom 6 (closure_of_addition) }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(true, true, ifeq(sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true, sum(additive_identity, multiply(a, additive_identity), add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X))), true), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true, sum(additive_identity, multiply(a, additive_identity), add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by lemma 14 }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by axiom 4 (ifeq_axiom) R->L }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(ifeq(true, true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by axiom 6 (closure_of_addition) R->L }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by axiom 4 (ifeq_axiom) R->L }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(ifeq(true, true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.52 = { by axiom 3 (left_inverse) R->L }
% 119.38/15.52 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(ifeq(sum(additive_inverse(multiply(a, X)), multiply(a, X), additive_identity), true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 4 (ifeq_axiom) R->L }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(ifeq(sum(additive_inverse(multiply(a, X)), multiply(a, X), additive_identity), true, ifeq(true, true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 1 (additive_identity2) R->L }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(ifeq(sum(additive_inverse(multiply(a, X)), multiply(a, X), additive_identity), true, ifeq(sum(additive_identity, additive_identity, additive_identity), true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 11 (associativity_of_addition2) }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq(true, true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 5 (ifeq_axiom) R->L }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(true, true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 12 (distributivity2) R->L }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, ifeq(sum(X, additive_identity, X), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 1 (additive_identity2) }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, ifeq(true, true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 6 (closure_of_addition) }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, ifeq(true, true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, X, multiply(a, X)), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 7 (closure_of_multiplication) }
% 119.38/15.53 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(true, true, ifeq(product(a, X, multiply(a, X)), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.53 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.54 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(product(a, X, multiply(a, X)), true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 7 (closure_of_multiplication) }
% 119.38/15.54 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(ifeq(true, true, product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.54 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 5 (ifeq_axiom) R->L }
% 119.38/15.54 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true, ifeq2(true, true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 7 (closure_of_multiplication) R->L }
% 119.38/15.54 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(product(a, X, add(multiply(a, X), multiply(a, additive_identity))), true, ifeq2(product(a, X, multiply(a, X)), true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity))), add(multiply(a, X), multiply(a, additive_identity)))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 10 (multiplication_is_well_defined) }
% 119.38/15.54 product(a, additive_identity, ifeq2(ifeq(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 6 (closure_of_addition) }
% 119.38/15.54 product(a, additive_identity, ifeq2(ifeq(true, true, sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), add(multiply(a, X), add(additive_identity, additive_inverse(multiply(a, X))))), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by lemma 14 R->L }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X))), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 5 (ifeq_axiom) R->L }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(true, true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 11 (associativity_of_addition2) R->L }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(ifeq(sum(additive_inverse(multiply(a, X)), multiply(a, X), additive_identity), true, ifeq(sum(additive_identity, additive_identity, additive_identity), true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true), true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 1 (additive_identity2) }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(ifeq(sum(additive_inverse(multiply(a, X)), multiply(a, X), additive_identity), true, ifeq(true, true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true), true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(ifeq(sum(additive_inverse(multiply(a, X)), multiply(a, X), additive_identity), true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 3 (left_inverse) }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(ifeq(true, true, ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true), true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(ifeq(sum(additive_identity, additive_inverse(multiply(a, X)), add(additive_identity, additive_inverse(multiply(a, X)))), true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 6 (closure_of_addition) }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(ifeq(true, true, sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true), true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 4 (ifeq_axiom) }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), ifeq2(sum(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X), additive_identity), true, add(add(additive_identity, additive_inverse(multiply(a, X))), multiply(a, X)), additive_identity)), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by lemma 13 }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, additive_identity, multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 5 (ifeq_axiom) R->L }
% 119.38/15.54 product(a, additive_identity, ifeq2(true, true, ifeq2(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, additive_identity, multiply(a, additive_identity)), multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 2 (additive_identity1) R->L }
% 119.38/15.54 product(a, additive_identity, ifeq2(sum(additive_identity, multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq2(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, additive_identity, multiply(a, additive_identity)), multiply(a, additive_identity)))
% 119.38/15.54 = { by axiom 9 (addition_is_well_defined) }
% 119.38/15.54 product(a, additive_identity, multiply(a, additive_identity))
% 119.38/15.54 = { by axiom 7 (closure_of_multiplication) }
% 119.38/15.54 true
% 119.38/15.54 % SZS output end Proof
% 119.38/15.54
% 119.38/15.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------