%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL007-1 : 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 11:48:49 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:14:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44 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
% 0.10/0.44
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44
% 0.10/0.44 % SZS output start Proof
% 0.10/0.44 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.44 Axiom 2 (ec_4): is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))) = true.
% 0.10/0.44 Axiom 3 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 0.10/0.44 Axiom 4 (ec_5): is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))) = true.
% 0.10/0.44
% 0.10/0.44 Goal 1 (prove_ec_2): is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))) = true.
% 0.10/0.44 Proof:
% 0.10/0.44 is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))
% 0.10/0.44 = { by axiom 1 (ifeq_axiom) R->L }
% 0.10/0.44 ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true)
% 0.10/0.44 = { by axiom 4 (ec_5) R->L }
% 0.10/0.44 ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true)
% 0.10/0.44 = { by axiom 1 (ifeq_axiom) R->L }
% 0.10/0.44 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 0.10/0.44 = { by axiom 2 (ec_4) R->L }
% 0.10/0.44 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c)))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 0.10/0.44 = { by axiom 3 (condensed_detachment) }
% 0.10/0.44 true
% 0.10/0.44 % SZS output end Proof
% 0.10/0.44
% 0.10/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------