%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:34:51 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.49s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 23:01:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.49 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
% 0.13/0.49
% 0.13/0.49 % SZS status Unsatisfiable
% 0.13/0.49
% 0.77/0.50 % SZS output start Proof
% 0.77/0.50 Axiom 1 (multiplicative_identity1): product(additive_identity, X, additive_identity) = true.
% 0.77/0.50 Axiom 2 (additive_identity2): sum(X, additive_identity, X) = true.
% 0.77/0.50 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.77/0.50 Axiom 4 (some_property): ifeq(equalish(X, additive_identity), true, product(X, h(X, Y), Y), true) = true.
% 0.77/0.50 Axiom 5 (multiplication_is_well_defined): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 0.77/0.50 Axiom 6 (addition_is_well_defined): ifeq(sum(X, Y, Z), true, ifeq(sum(X, Y, W), true, equalish(W, Z), true), true) = true.
% 0.77/0.50
% 0.77/0.50 Goal 1 (a_not_additive_identity): equalish(a, additive_identity) = true.
% 0.77/0.50 Proof:
% 0.77/0.50 equalish(a, additive_identity)
% 0.77/0.50 = { by axiom 3 (ifeq_axiom) R->L }
% 0.77/0.50 ifeq(true, true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 4 (some_property) R->L }
% 0.77/0.50 ifeq(ifeq(equalish(additive_identity, additive_identity), true, product(additive_identity, h(additive_identity, a), a), true), true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 3 (ifeq_axiom) R->L }
% 0.77/0.50 ifeq(ifeq(ifeq(true, true, equalish(additive_identity, additive_identity), true), true, product(additive_identity, h(additive_identity, a), a), true), true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 2 (additive_identity2) R->L }
% 0.77/0.50 ifeq(ifeq(ifeq(sum(additive_identity, additive_identity, additive_identity), true, equalish(additive_identity, additive_identity), true), true, product(additive_identity, h(additive_identity, a), a), true), true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 3 (ifeq_axiom) R->L }
% 0.77/0.50 ifeq(ifeq(ifeq(true, true, ifeq(sum(additive_identity, additive_identity, additive_identity), true, equalish(additive_identity, additive_identity), true), true), true, product(additive_identity, h(additive_identity, a), a), true), true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 2 (additive_identity2) R->L }
% 0.77/0.50 ifeq(ifeq(ifeq(sum(additive_identity, additive_identity, additive_identity), true, ifeq(sum(additive_identity, additive_identity, additive_identity), true, equalish(additive_identity, additive_identity), true), true), true, product(additive_identity, h(additive_identity, a), a), true), true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 6 (addition_is_well_defined) }
% 0.77/0.50 ifeq(ifeq(true, true, product(additive_identity, h(additive_identity, a), a), true), true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 3 (ifeq_axiom) }
% 0.77/0.50 ifeq(product(additive_identity, h(additive_identity, a), a), true, equalish(a, additive_identity), true)
% 0.77/0.50 = { by axiom 3 (ifeq_axiom) R->L }
% 0.77/0.50 ifeq(true, true, ifeq(product(additive_identity, h(additive_identity, a), a), true, equalish(a, additive_identity), true), true)
% 0.77/0.50 = { by axiom 1 (multiplicative_identity1) R->L }
% 0.77/0.50 ifeq(product(additive_identity, h(additive_identity, a), additive_identity), true, ifeq(product(additive_identity, h(additive_identity, a), a), true, equalish(a, additive_identity), true), true)
% 0.77/0.50 = { by axiom 5 (multiplication_is_well_defined) }
% 0.77/0.50 true
% 0.77/0.50 % SZS output end Proof
% 0.77/0.50
% 0.77/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------