%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 135.86s 17.61s
% Output : Proof 135.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n017.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 22:53:05 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 135.86/17.61 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
% 135.86/17.61
% 135.86/17.61 % SZS status Unsatisfiable
% 135.86/17.61
% 135.86/17.64 % SZS output start Proof
% 135.86/17.64 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 135.86/17.64 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 135.86/17.64 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 135.86/17.64 Axiom 4 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 135.86/17.64 Axiom 5 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 135.86/17.64 Axiom 6 (cancellation1): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, W, Z), true, W, Y), Y) = Y.
% 135.86/17.64 Axiom 7 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 135.86/17.64 Axiom 8 (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.
% 135.86/17.64
% 135.86/17.64 Goal 1 (prove_a_times_additive_id_is_additive_id): product(a, additive_identity, additive_identity) = true.
% 135.86/17.64 Proof:
% 135.86/17.64 product(a, additive_identity, additive_identity)
% 135.86/17.64 = { by axiom 3 (ifeq_axiom) R->L }
% 135.86/17.64 product(a, additive_identity, ifeq2(true, true, additive_identity, multiply(a, additive_identity)))
% 135.86/17.64 = { by axiom 4 (closure_of_addition) R->L }
% 135.86/17.64 product(a, additive_identity, ifeq2(sum(multiply(a, X), multiply(a, additive_identity), add(multiply(a, X), multiply(a, additive_identity))), true, additive_identity, multiply(a, additive_identity)))
% 135.86/17.64 = { by axiom 7 (multiplication_is_well_defined) R->L }
% 135.86/17.64 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.64 = { by axiom 5 (closure_of_multiplication) }
% 135.86/17.64 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.64 = { by axiom 3 (ifeq_axiom) }
% 135.86/17.64 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.64 = { by axiom 2 (ifeq_axiom) R->L }
% 135.86/17.64 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 5 (closure_of_multiplication) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 2 (ifeq_axiom) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 5 (closure_of_multiplication) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 2 (ifeq_axiom) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 4 (closure_of_addition) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 2 (ifeq_axiom) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 1 (additive_identity2) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(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, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 8 (distributivity2) }
% 135.86/17.65 product(a, additive_identity, ifeq2(sum(multiply(a, X), multiply(a, additive_identity), ifeq2(true, true, multiply(a, X), add(multiply(a, X), multiply(a, additive_identity)))), true, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 3 (ifeq_axiom) }
% 135.86/17.65 product(a, additive_identity, ifeq2(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, additive_identity, multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 3 (ifeq_axiom) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq2(true, true, additive_identity, multiply(a, additive_identity)), multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 1 (additive_identity2) R->L }
% 135.86/17.65 product(a, additive_identity, ifeq2(sum(multiply(a, X), multiply(a, additive_identity), multiply(a, X)), true, ifeq2(sum(multiply(a, X), additive_identity, multiply(a, X)), true, additive_identity, multiply(a, additive_identity)), multiply(a, additive_identity)))
% 135.86/17.65 = { by axiom 6 (cancellation1) }
% 135.86/17.65 product(a, additive_identity, multiply(a, additive_identity))
% 135.86/17.65 = { by axiom 5 (closure_of_multiplication) }
% 135.86/17.65 true
% 135.86/17.65 % SZS output end Proof
% 135.86/17.65
% 135.86/17.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------