%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 09:37:05 AM UTC 2026
% Result : Unsatisfiable 25.97s 3.57s
% Output : Proof 25.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n011.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:28:50 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.97/3.57 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
% 25.97/3.57
% 25.97/3.57 % SZS status Unsatisfiable
% 25.97/3.57
% 25.97/3.57 % SZS output start Proof
% 25.97/3.57 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 25.97/3.57 Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 25.97/3.57 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 25.97/3.57 Axiom 4 (c_definition): apply(apply(apply(c, X), Y), Z) = apply(apply(X, Z), Y).
% 25.97/3.57 Axiom 5 (weak_fixed_point): ifeq(X, apply(fixed_pt, X), fixed_point(X), true) = true.
% 25.97/3.57
% 25.97/3.57 Goal 1 (prove_weak_fixed_point): fixed_point(apply(apply(apply(s, apply(c, apply(b, X))), apply(s, apply(c, apply(b, X)))), apply(s, apply(c, apply(b, X))))) = true.
% 25.97/3.57 The goal is true when:
% 25.97/3.57 X = fixed_pt
% 25.97/3.57
% 25.97/3.57 Proof:
% 25.97/3.57 fixed_point(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt)))))
% 25.97/3.57 = { by axiom 1 (ifeq_axiom) R->L }
% 25.97/3.57 ifeq(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt)))), apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt)))), fixed_point(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt))))), true)
% 25.97/3.57 = { by axiom 2 (s_definition) }
% 25.97/3.57 ifeq(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt)))), apply(apply(apply(c, apply(b, fixed_pt)), apply(s, apply(c, apply(b, fixed_pt)))), apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt))))), fixed_point(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt))))), true)
% 25.97/3.57 = { by axiom 4 (c_definition) }
% 25.97/3.57 ifeq(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt)))), apply(apply(apply(b, fixed_pt), apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt))))), apply(s, apply(c, apply(b, fixed_pt)))), fixed_point(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt))))), true)
% 25.97/3.57 = { by axiom 3 (b_definition) }
% 25.97/3.57 ifeq(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt)))), apply(fixed_pt, apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt))))), fixed_point(apply(apply(apply(s, apply(c, apply(b, fixed_pt))), apply(s, apply(c, apply(b, fixed_pt)))), apply(s, apply(c, apply(b, fixed_pt))))), true)
% 25.97/3.57 = { by axiom 5 (weak_fixed_point) }
% 25.97/3.57 true
% 25.97/3.57 % SZS output end Proof
% 25.97/3.57
% 25.97/3.57 RESULT: Unsatisfiable (the axioms are contradictory).
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