%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL044-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 09:37:15 AM UTC 2026
% Result : Unsatisfiable 16.25s 2.36s
% Output : Proof 16.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-3 : 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 : n008.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 21:31:24 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.25/2.36 Command-line arguments: --flatten-regeneralise
% 16.25/2.36
% 16.25/2.36 % SZS status Unsatisfiable
% 16.25/2.36
% 16.25/2.37 % SZS output start Proof
% 16.25/2.37 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 16.25/2.37 Axiom 2 (n_definition): apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z).
% 16.25/2.37 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 16.25/2.37 Axiom 4 (strong_fixed_point): ifeq(apply(X, fixed_pt), apply(fixed_pt, apply(X, fixed_pt)), fixed_point(X), true) = true.
% 16.25/2.37
% 16.25/2.37 Lemma 5: apply(apply(apply(n, apply(b, X)), Z), Y) = apply(apply(X, apply(Y, Z)), Y).
% 16.25/2.37 Proof:
% 16.25/2.37 apply(apply(apply(n, apply(b, X)), Z), Y)
% 16.25/2.37 = { by axiom 2 (n_definition) }
% 16.25/2.37 apply(apply(apply(apply(b, X), Y), Z), Y)
% 16.25/2.37 = { by axiom 3 (b_definition) }
% 16.25/2.37 apply(apply(X, apply(Y, Z)), Y)
% 16.25/2.37
% 16.25/2.37 Lemma 6: apply(apply(apply(n, apply(n, apply(b, b))), X), Y) = apply(apply(X, Y), apply(X, Y)).
% 16.25/2.37 Proof:
% 16.25/2.37 apply(apply(apply(n, apply(n, apply(b, b))), X), Y)
% 16.25/2.37 = { by axiom 2 (n_definition) }
% 16.25/2.37 apply(apply(apply(apply(n, apply(b, b)), Y), X), Y)
% 16.25/2.37 = { by lemma 5 }
% 16.25/2.37 apply(apply(apply(b, apply(X, Y)), X), Y)
% 16.25/2.37 = { by axiom 3 (b_definition) }
% 16.25/2.37 apply(apply(X, Y), apply(X, Y))
% 16.25/2.37
% 16.25/2.37 Lemma 7: apply(apply(apply(n, apply(apply(b, b), X)), Z), Y) = apply(apply(X, Y), apply(Z, Y)).
% 16.25/2.37 Proof:
% 16.25/2.37 apply(apply(apply(n, apply(apply(b, b), X)), Z), Y)
% 16.25/2.37 = { by axiom 2 (n_definition) }
% 16.25/2.37 apply(apply(apply(apply(apply(b, b), X), Y), Z), Y)
% 16.25/2.37 = { by axiom 3 (b_definition) }
% 16.25/2.37 apply(apply(apply(b, apply(X, Y)), Z), Y)
% 16.25/2.37 = { by axiom 3 (b_definition) }
% 16.25/2.37 apply(apply(X, Y), apply(Z, Y))
% 16.25/2.37
% 16.25/2.37 Goal 1 (prove_strong_fixed_point): fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)) = true.
% 16.25/2.37 Proof:
% 16.25/2.37 fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b))
% 16.25/2.37 = { by axiom 1 (ifeq_axiom) R->L }
% 16.25/2.37 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.38 = { by axiom 3 (b_definition) }
% 16.25/2.38 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b), apply(b, fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.38 = { by axiom 3 (b_definition) }
% 16.25/2.38 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n), apply(b, apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.38 = { by lemma 7 }
% 16.25/2.38 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(apply(n, apply(n, apply(b, b))), n), apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.38 = { by lemma 6 }
% 16.25/2.38 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(n, apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt)))), apply(n, apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.38 = { by lemma 5 }
% 16.25/2.38 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(b, fixed_pt), apply(apply(n, apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt))))), apply(n, apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.38 = { by lemma 6 R->L }
% 16.25/2.38 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(b, fixed_pt), apply(apply(apply(n, apply(n, apply(b, b))), n), apply(b, apply(b, fixed_pt)))), apply(n, apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.38 = { by axiom 3 (b_definition) }
% 16.25/2.38 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(apply(n, apply(n, apply(b, b))), n), apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt))))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.39 = { by lemma 7 R->L }
% 16.25/2.39 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n), apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.39 = { by axiom 3 (b_definition) R->L }
% 16.25/2.39 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.39 = { by axiom 3 (b_definition) R->L }
% 16.25/2.39 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 16.25/2.39 = { by axiom 4 (strong_fixed_point) }
% 16.25/2.39 true
% 16.25/2.39 % SZS output end Proof
% 16.25/2.39
% 16.25/2.39 RESULT: Unsatisfiable (the axioms are contradictory).
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