%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 143.68s 18.56s
% Output : Proof 143.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG039-2 : 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 : n007.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 23:00:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 143.68/18.56 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
% 143.68/18.56
% 143.68/18.56 % SZS status Unsatisfiable
% 143.68/18.56
% 143.68/18.57 % SZS output start Proof
% 143.68/18.57 Axiom 1 (multiplicative_identity1): product(additive_identity, X, additive_identity) = true.
% 143.68/18.57 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 143.68/18.57 Axiom 3 (clause35): equalish(multiply(X, X), X) = true.
% 143.68/18.57 Axiom 4 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 143.68/18.57 Axiom 5 (clause46): product(a, multiply(b, c), c) = true.
% 143.68/18.57 Axiom 6 (clause44): product(a, multiply(b, X), multiply(Y, X)) = true.
% 143.68/18.57 Axiom 7 (transitivity): ifeq(equalish(X, Y), true, ifeq(equalish(Z, X), true, equalish(Z, Y), true), true) = true.
% 143.68/18.57 Axiom 8 (product_substitution3): ifeq(product(X, Y, Z), true, ifeq(equalish(Z, W), true, product(X, Y, W), true), true) = true.
% 143.68/18.57 Axiom 9 (multiplication_is_well_defined): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 143.68/18.57
% 143.68/18.57 Goal 1 (prove_c_equals_d): equalish(c, d) = true.
% 143.68/18.57 Proof:
% 143.68/18.57 equalish(c, d)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(true, true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 9 (multiplication_is_well_defined) R->L }
% 143.68/18.58 ifeq(ifeq(product(additive_identity, c, additive_identity), true, ifeq(product(additive_identity, c, c), true, equalish(c, additive_identity), true), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 1 (multiplicative_identity1) }
% 143.68/18.58 ifeq(ifeq(true, true, ifeq(product(additive_identity, c, c), true, equalish(c, additive_identity), true), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(ifeq(product(additive_identity, c, c), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(true, true, product(additive_identity, c, c), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 9 (multiplication_is_well_defined) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(product(a, multiply(b, c), c), true, ifeq(product(a, multiply(b, c), multiply(additive_identity, c)), true, equalish(multiply(additive_identity, c), c), true), true), true, product(additive_identity, c, c), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 5 (clause46) }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(a, multiply(b, c), multiply(additive_identity, c)), true, equalish(multiply(additive_identity, c), c), true), true), true, product(additive_identity, c, c), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(product(a, multiply(b, c), multiply(additive_identity, c)), true, equalish(multiply(additive_identity, c), c), true), true, product(additive_identity, c, c), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 6 (clause44) }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(true, true, equalish(multiply(additive_identity, c), c), true), true, product(additive_identity, c, c), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(ifeq(ifeq(equalish(multiply(additive_identity, c), c), true, product(additive_identity, c, c), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(true, true, ifeq(equalish(multiply(additive_identity, c), c), true, product(additive_identity, c, c), true), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 4 (closure_of_multiplication) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(product(additive_identity, c, multiply(additive_identity, c)), true, ifeq(equalish(multiply(additive_identity, c), c), true, product(additive_identity, c, c), true), true), true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 8 (product_substitution3) }
% 143.68/18.58 ifeq(ifeq(true, true, equalish(c, additive_identity), true), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(equalish(c, additive_identity), true, equalish(c, d), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(true, true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 9 (multiplication_is_well_defined) R->L }
% 143.68/18.58 ifeq(ifeq(product(additive_identity, d, d), true, ifeq(product(additive_identity, d, additive_identity), true, equalish(additive_identity, d), true), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 1 (multiplicative_identity1) }
% 143.68/18.58 ifeq(ifeq(product(additive_identity, d, d), true, ifeq(true, true, equalish(additive_identity, d), true), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(ifeq(product(additive_identity, d, d), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(true, true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 7 (transitivity) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(equalish(multiply(d, d), d), true, ifeq(equalish(multiply(additive_identity, d), multiply(d, d)), true, equalish(multiply(additive_identity, d), d), true), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 3 (clause35) }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(equalish(multiply(additive_identity, d), multiply(d, d)), true, equalish(multiply(additive_identity, d), d), true), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(equalish(multiply(additive_identity, d), multiply(d, d)), true, equalish(multiply(additive_identity, d), d), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, equalish(multiply(additive_identity, d), multiply(d, d)), true), true, equalish(multiply(additive_identity, d), d), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 6 (clause44) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(ifeq(product(a, multiply(b, d), multiply(additive_identity, d)), true, equalish(multiply(additive_identity, d), multiply(d, d)), true), true, equalish(multiply(additive_identity, d), d), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(a, multiply(b, d), multiply(additive_identity, d)), true, equalish(multiply(additive_identity, d), multiply(d, d)), true), true), true, equalish(multiply(additive_identity, d), d), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 6 (clause44) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(ifeq(product(a, multiply(b, d), multiply(d, d)), true, ifeq(product(a, multiply(b, d), multiply(additive_identity, d)), true, equalish(multiply(additive_identity, d), multiply(d, d)), true), true), true, equalish(multiply(additive_identity, d), d), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 9 (multiplication_is_well_defined) }
% 143.68/18.58 ifeq(ifeq(ifeq(ifeq(true, true, equalish(multiply(additive_identity, d), d), true), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(ifeq(ifeq(equalish(multiply(additive_identity, d), d), true, product(additive_identity, d, d), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(true, true, ifeq(equalish(multiply(additive_identity, d), d), true, product(additive_identity, d, d), true), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 4 (closure_of_multiplication) R->L }
% 143.68/18.58 ifeq(ifeq(ifeq(product(additive_identity, d, multiply(additive_identity, d)), true, ifeq(equalish(multiply(additive_identity, d), d), true, product(additive_identity, d, d), true), true), true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 8 (product_substitution3) }
% 143.68/18.58 ifeq(ifeq(true, true, equalish(additive_identity, d), true), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 2 (ifeq_axiom) }
% 143.68/18.58 ifeq(equalish(additive_identity, d), true, ifeq(equalish(c, additive_identity), true, equalish(c, d), true), true)
% 143.68/18.58 = { by axiom 7 (transitivity) }
% 143.68/18.58 true
% 143.68/18.58 % SZS output end Proof
% 143.68/18.58
% 143.68/18.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------