%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL042-4 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 09:37:14 AM UTC 2026
% Result : Unsatisfiable 4.39s 0.88s
% Output : Proof 4.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-4 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:36:18 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.39/0.88 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 4.39/0.88
% 4.39/0.88 % SZS status Unsatisfiable
% 4.39/0.88
% 4.39/0.88 % SZS output start Proof
% 4.39/0.88 Axiom 1 (w1_definition): apply(apply(w1, X), Y) = apply(apply(Y, X), X).
% 4.39/0.88 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 4.39/0.88 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 4.39/0.88 Axiom 4 (strong_fixed_point): ifeq(apply(X, fixed_pt), apply(fixed_pt, apply(X, fixed_pt)), fixed_point(X), true) = true.
% 4.39/0.88
% 4.39/0.88 Lemma 5: apply(apply(w1, Z), apply(apply(b, X), Y)) = apply(apply(X, apply(Y, Z)), Z).
% 4.39/0.88 Proof:
% 4.39/0.88 apply(apply(w1, Z), apply(apply(b, X), Y))
% 4.39/0.88 = { by axiom 1 (w1_definition) }
% 4.39/0.88 apply(apply(apply(apply(b, X), Y), Z), Z)
% 4.39/0.88 = { by axiom 3 (b_definition) }
% 4.39/0.88 apply(apply(X, apply(Y, Z)), Z)
% 4.39/0.88
% 4.39/0.88 Goal 1 (prove_strong_fixed_point): fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)) = true.
% 4.39/0.88 Proof:
% 4.39/0.88 fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b))
% 4.39/0.88 = { by axiom 2 (ifeq_axiom) R->L }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b)), apply(b, fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(w1, w1), apply(apply(apply(b, apply(b, w1)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(w1, w1), apply(apply(b, w1), apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by lemma 5 }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), w1), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 1 (w1_definition) }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), apply(apply(b, apply(b, fixed_pt)), w1)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 1 (w1_definition) }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(apply(b, apply(b, fixed_pt)), w1), apply(apply(b, apply(b, fixed_pt)), w1)), apply(apply(b, apply(b, fixed_pt)), w1)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(b, fixed_pt), apply(w1, apply(apply(b, apply(b, fixed_pt)), w1))), apply(apply(b, apply(b, fixed_pt)), w1)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), apply(apply(b, apply(b, fixed_pt)), w1))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 1 (w1_definition) R->L }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), w1)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by lemma 5 R->L }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, w1), apply(apply(b, w1), apply(b, apply(b, fixed_pt))))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) R->L }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, w1), apply(apply(apply(b, apply(b, w1)), b), apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) R->L }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b)), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 3 (b_definition) R->L }
% 4.39/0.88 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 4.39/0.88 = { by axiom 4 (strong_fixed_point) }
% 4.39/0.88 true
% 4.39/0.88 % SZS output end Proof
% 4.39/0.88
% 4.39/0.88 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------