%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 11.79s 2.02s
% Output : Proof 11.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 22:59:26 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.79/2.02 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 11.79/2.02
% 11.79/2.02 % SZS status Unsatisfiable
% 11.79/2.02
% 11.79/2.03 % SZS output start Proof
% 11.79/2.03 Axiom 1 (additive_identity1): sum(additive_identity, X, X) = true.
% 11.79/2.03 Axiom 2 (additive_inverse1): sum(additive_inverse(X), X, additive_identity) = true.
% 11.79/2.03 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 11.79/2.03 Axiom 4 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 11.79/2.04 Axiom 5 (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.
% 11.79/2.04 Axiom 6 (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.
% 11.79/2.04 Axiom 7 (distributivity1): ifeq(product(X, Y, Z), true, ifeq(product(X, W, V), true, ifeq(product(X, U, T), true, ifeq(sum(U, W, Y), true, sum(T, V, Z), true), true), true), true) = true.
% 11.79/2.04
% 11.79/2.04 Goal 1 (prove_a_times_additive_id_is_additive_id): product(a, additive_identity, additive_identity) = true.
% 11.79/2.04 Proof:
% 11.79/2.04 product(a, additive_identity, additive_identity)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(true, true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 5 (associativity_of_addition2) R->L }
% 11.79/2.04 ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, ifeq(sum(additive_identity, multiply(a, additive_identity), multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 1 (additive_identity1) }
% 11.79/2.04 ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, ifeq(true, true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) }
% 11.79/2.04 ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(true, true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(true, true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(true, true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(true, true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 1 (additive_identity1) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(additive_identity, additive_identity, additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true), true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 7 (distributivity1) }
% 11.79/2.04 ifeq(ifeq(true, true, ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) }
% 11.79/2.04 ifeq(ifeq(sum(additive_identity, multiply(a, additive_identity), additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(true, true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 7 (distributivity1) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(additive_identity, additive_identity, additive_identity), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 1 (additive_identity1) }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(true, true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) }
% 11.79/2.04 ifeq(ifeq(ifeq(ifeq(true, true, sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) }
% 11.79/2.04 ifeq(ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq(true, true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 2 (additive_inverse1) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq(sum(additive_inverse(multiply(a, additive_identity)), multiply(a, additive_identity), additive_identity), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq(true, true, ifeq(sum(additive_inverse(multiply(a, additive_identity)), multiply(a, additive_identity), additive_identity), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 2 (additive_inverse1) R->L }
% 11.79/2.04 ifeq(ifeq(ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), multiply(a, additive_identity)), true, ifeq(sum(additive_inverse(multiply(a, additive_identity)), multiply(a, additive_identity), additive_identity), true, ifeq(sum(additive_inverse(multiply(a, additive_identity)), multiply(a, additive_identity), additive_identity), true, sum(additive_identity, multiply(a, additive_identity), additive_identity), true), true), true), true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 5 (associativity_of_addition2) }
% 11.79/2.04 ifeq(ifeq(true, true, sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) }
% 11.79/2.04 ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true, product(a, additive_identity, additive_identity), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(true, true, ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true, product(a, additive_identity, additive_identity), true), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) R->L }
% 11.79/2.04 ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true, product(a, additive_identity, additive_identity), true), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(true, true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true, product(a, additive_identity, additive_identity), true), true), true)
% 11.79/2.04 = { by axiom 4 (closure_of_multiplication) R->L }
% 11.79/2.04 ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true, product(a, additive_identity, additive_identity), true), true), true)
% 11.79/2.04 = { by axiom 3 (ifeq_axiom) R->L }
% 11.79/2.04 ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true, ifeq(true, true, product(a, additive_identity, additive_identity), true), true), true), true)
% 11.79/2.04 = { by axiom 1 (additive_identity1) R->L }
% 11.79/2.04 ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(multiply(a, additive_identity), multiply(a, additive_identity), additive_identity), true, ifeq(sum(additive_identity, additive_identity, additive_identity), true, product(a, additive_identity, additive_identity), true), true), true), true)
% 11.79/2.04 = { by axiom 6 (distributivity2) }
% 11.79/2.04 true
% 11.79/2.04 % SZS output end Proof
% 11.79/2.04
% 11.79/2.04 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------