%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 55.52s 7.49s
% Output : Proof 56.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 23:01:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.52/7.49 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
% 55.52/7.49
% 55.52/7.49 % SZS status Unsatisfiable
% 55.52/7.49
% 55.52/7.50 % SZS output start Proof
% 55.52/7.50 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 55.52/7.50 Axiom 2 (additive_identity1): sum(additive_identity, X, X) = true.
% 55.52/7.50 Axiom 3 (a_times_b): product(a, b, additive_identity) = true.
% 55.52/7.50 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 55.52/7.50 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 55.52/7.50 Axiom 6 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 55.52/7.50 Axiom 7 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 55.52/7.50 Axiom 8 (some_property): ifeq3(X, additive_identity, product(X, h(X, Y), Y), true) = true.
% 55.52/7.50 Axiom 9 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 55.52/7.50 Axiom 10 (associativity_of_multiplication1): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(product(U, W, X), true, product(U, V, Z), true), true), true) = true.
% 55.52/7.50 Axiom 11 (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.
% 55.52/7.50
% 55.52/7.50 Lemma 12: ifeq2(product(a, b, X), true, additive_identity, X) = X.
% 55.52/7.50 Proof:
% 55.52/7.50 ifeq2(product(a, b, X), true, additive_identity, X)
% 55.52/7.50 = { by axiom 5 (ifeq_axiom) R->L }
% 55.52/7.50 ifeq2(product(a, b, X), true, ifeq2(true, true, additive_identity, X), X)
% 55.52/7.50 = { by axiom 3 (a_times_b) R->L }
% 55.52/7.50 ifeq2(product(a, b, X), true, ifeq2(product(a, b, additive_identity), true, additive_identity, X), X)
% 55.52/7.50 = { by axiom 9 (multiplication_is_well_defined) }
% 56.32/7.50 X
% 56.32/7.50
% 56.32/7.50 Goal 1 (prove_b_is_additive_identity): b = additive_identity.
% 56.32/7.50 Proof:
% 56.32/7.50 b
% 56.32/7.50 = { by lemma 12 R->L }
% 56.32/7.50 ifeq2(product(a, b, b), true, additive_identity, b)
% 56.32/7.50 = { by axiom 9 (multiplication_is_well_defined) R->L }
% 56.32/7.50 ifeq2(product(a, b, ifeq2(product(additive_identity, h(additive_identity, b), b), true, ifeq2(product(additive_identity, h(additive_identity, b), multiply(additive_identity, h(additive_identity, b))), true, multiply(additive_identity, h(additive_identity, b)), b), b)), true, additive_identity, b)
% 56.32/7.50 = { by axiom 7 (closure_of_multiplication) }
% 56.32/7.50 ifeq2(product(a, b, ifeq2(product(additive_identity, h(additive_identity, b), b), true, ifeq2(true, true, multiply(additive_identity, h(additive_identity, b)), b), b)), true, additive_identity, b)
% 56.32/7.50 = { by axiom 5 (ifeq_axiom) }
% 56.32/7.50 ifeq2(product(a, b, ifeq2(product(additive_identity, h(additive_identity, b), b), true, multiply(additive_identity, h(additive_identity, b)), b)), true, additive_identity, b)
% 56.32/7.50 = { by axiom 6 (ifeq_axiom) R->L }
% 56.32/7.50 ifeq2(product(a, b, ifeq2(ifeq3(additive_identity, additive_identity, product(additive_identity, h(additive_identity, b), b), true), true, multiply(additive_identity, h(additive_identity, b)), b)), true, additive_identity, b)
% 56.32/7.50 = { by axiom 8 (some_property) }
% 56.32/7.50 ifeq2(product(a, b, ifeq2(true, true, multiply(additive_identity, h(additive_identity, b)), b)), true, additive_identity, b)
% 56.32/7.50 = { by axiom 5 (ifeq_axiom) }
% 56.32/7.50 ifeq2(product(a, b, multiply(additive_identity, h(additive_identity, b))), true, additive_identity, b)
% 56.32/7.50 = { by axiom 4 (ifeq_axiom) R->L }
% 56.32/7.50 ifeq2(ifeq(true, true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.50 = { by axiom 7 (closure_of_multiplication) R->L }
% 56.32/7.50 ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.50 = { by lemma 12 R->L }
% 56.32/7.50 ifeq2(ifeq(product(a, additive_identity, ifeq2(product(a, b, multiply(a, additive_identity)), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.50 = { by axiom 4 (ifeq_axiom) R->L }
% 56.32/7.50 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(true, true, product(a, b, multiply(a, additive_identity)), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.50 = { by axiom 7 (closure_of_multiplication) R->L }
% 56.32/7.50 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, product(a, b, multiply(a, additive_identity)), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 4 (ifeq_axiom) R->L }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(true, true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, product(a, b, multiply(a, additive_identity)), true), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 3 (a_times_b) R->L }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(product(a, b, additive_identity), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, product(a, b, multiply(a, additive_identity)), true), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 4 (ifeq_axiom) R->L }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(product(a, b, additive_identity), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(true, true, product(a, b, multiply(a, additive_identity)), true), true), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 2 (additive_identity1) R->L }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(product(a, b, additive_identity), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(additive_identity, b, b), true, product(a, b, multiply(a, additive_identity)), true), true), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 4 (ifeq_axiom) R->L }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(product(a, b, additive_identity), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(true, true, ifeq(sum(additive_identity, b, b), true, product(a, b, multiply(a, additive_identity)), true), true), true), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 1 (additive_identity2) R->L }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, ifeq2(ifeq(product(a, b, additive_identity), true, ifeq(product(a, additive_identity, multiply(a, additive_identity)), true, ifeq(sum(multiply(a, additive_identity), additive_identity, multiply(a, additive_identity)), true, ifeq(sum(additive_identity, b, b), true, product(a, b, multiply(a, additive_identity)), true), true), true), true), true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 11 (distributivity2) }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, ifeq2(true, true, additive_identity, multiply(a, additive_identity))), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 5 (ifeq_axiom) }
% 56.32/7.51 ifeq2(ifeq(product(a, additive_identity, additive_identity), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 4 (ifeq_axiom) R->L }
% 56.32/7.51 ifeq2(ifeq(true, true, ifeq(product(a, additive_identity, additive_identity), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 8 (some_property) R->L }
% 56.32/7.51 ifeq2(ifeq(ifeq3(additive_identity, additive_identity, product(additive_identity, h(additive_identity, b), b), true), true, ifeq(product(a, additive_identity, additive_identity), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 6 (ifeq_axiom) }
% 56.32/7.51 ifeq2(ifeq(product(additive_identity, h(additive_identity, b), b), true, ifeq(product(a, additive_identity, additive_identity), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 4 (ifeq_axiom) R->L }
% 56.32/7.51 ifeq2(ifeq(true, true, ifeq(product(additive_identity, h(additive_identity, b), b), true, ifeq(product(a, additive_identity, additive_identity), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 7 (closure_of_multiplication) R->L }
% 56.32/7.51 ifeq2(ifeq(product(additive_identity, h(additive_identity, b), multiply(additive_identity, h(additive_identity, b))), true, ifeq(product(additive_identity, h(additive_identity, b), b), true, ifeq(product(a, additive_identity, additive_identity), true, product(a, b, multiply(additive_identity, h(additive_identity, b))), true), true), true), true, additive_identity, b)
% 56.32/7.51 = { by axiom 10 (associativity_of_multiplication1) }
% 56.32/7.51 ifeq2(true, true, additive_identity, b)
% 56.32/7.51 = { by axiom 5 (ifeq_axiom) }
% 56.32/7.51 additive_identity
% 56.32/7.51 % SZS output end Proof
% 56.32/7.51
% 56.32/7.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------