%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 09:37:07 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.28s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 21:24:36 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.28 Command-line arguments: --flatten --complete-subsets
% 0.23/0.28
% 0.23/0.28 % SZS status Unsatisfiable
% 0.23/0.28
% 0.23/0.28 % SZS output start Proof
% 0.23/0.28 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.23/0.28 Axiom 2 (w_definition): apply(apply(w, X), Y) = apply(apply(X, Y), Y).
% 0.23/0.28 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.23/0.28 Axiom 4 (strong_fixed_point): ifeq(apply(X, fixed_pt), apply(fixed_pt, apply(X, fixed_pt)), fixed_point(X), true) = true.
% 0.23/0.28
% 0.23/0.28 Lemma 5: apply(apply(w, w), X) = apply(apply(X, X), X).
% 0.23/0.28 Proof:
% 0.23/0.28 apply(apply(w, w), X)
% 0.23/0.28 = { by axiom 2 (w_definition) }
% 0.23/0.28 apply(apply(w, X), X)
% 0.23/0.28 = { by axiom 2 (w_definition) }
% 0.23/0.28 apply(apply(X, X), X)
% 0.23/0.28
% 0.23/0.28 Goal 1 (prove_strong_fixed_point): fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))) = true.
% 0.23/0.28 Proof:
% 0.23/0.28 fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))))
% 0.23/0.28 = { by axiom 1 (ifeq_axiom) R->L }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 3 (b_definition) }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(apply(w, w), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by lemma 5 }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(apply(apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 3 (b_definition) }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(apply(apply(w, apply(apply(apply(b, b), b), fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 3 (b_definition) }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(apply(apply(w, apply(b, apply(b, fixed_pt))), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 2 (w_definition) }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(apply(apply(apply(b, apply(b, fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 3 (b_definition) }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(apply(apply(b, fixed_pt), apply(apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt))), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 3 (b_definition) }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(fixed_pt, apply(apply(apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt)), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt))), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by lemma 5 R->L }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(fixed_pt, apply(apply(w, w), apply(apply(apply(b, w), apply(apply(b, b), b)), fixed_pt))), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 3 (b_definition) R->L }
% 0.23/0.28 ifeq(apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b))), fixed_pt)), fixed_point(apply(apply(b, apply(w, w)), apply(apply(b, w), apply(apply(b, b), b)))), true)
% 0.23/0.28 = { by axiom 4 (strong_fixed_point) }
% 0.23/0.28 true
% 0.23/0.28 % SZS output end Proof
% 0.23/0.28
% 0.23/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
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