%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL006-5 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 09:37:09 AM UTC 2026
% Result : Unsatisfiable 4.28s 0.82s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 6 RR)
% Number of literals : 63 ( 62 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 143 ( 36 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c2,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
apply(strong_fixed_point,X2) = apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(X2,apply(strong_fixed_point,X2)) = apply(X2,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
cnf(c6,plain,
apply(apply(apply(s,apply(k,X2)),X4),X3) = apply(apply(apply(k,X2),X3),apply(X4,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,axiom,
apply(apply(k,X2),Y2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(c8,plain,
apply(apply(k,X3),X2) = X3,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(apply(k,X4),X2),apply(X3,X2)) = apply(X4,apply(X3,X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(apply(apply(s,apply(k,X4)),X3),X2) = apply(X4,apply(X3,X2)),
inference(transitivity,[status(thm)],[c6,c9]) ).
cnf(c11,plain,
apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X4) = apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(X4,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X4)) = apply(X4,apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X2) = apply(apply(apply(s,s),apply(s,k)),apply(apply(apply(s,apply(k,s)),k),X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c14,plain,
apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X3),X2) = apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(apply(s,apply(k,s)),k),X3)),X2),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(apply(apply(s,s),X2),X3) = apply(apply(s,X3),apply(X2,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c16,plain,
apply(apply(apply(apply(s,s),X2),X4),X3) = apply(apply(apply(s,X4),apply(X2,X4)),X3),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(s,X4),apply(X2,X4)),X3) = apply(apply(X4,X3),apply(apply(X2,X4),X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c18,plain,
apply(apply(apply(apply(s,s),X2),X4),X3) = apply(apply(X4,X3),apply(apply(X2,X4),X3)),
inference(transitivity,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X3),X2) = apply(apply(X3,X2),apply(apply(apply(s,k),X3),X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(apply(s,k),X3),X2) = apply(apply(k,X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c21,plain,
apply(apply(k,X2),apply(X3,X2)) = X2,
inference(substitution,[status(thm)],[c7]) ).
cnf(c22,plain,
apply(apply(apply(s,k),X3),X2) = X2,
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
apply(apply(X3,X2),apply(apply(apply(s,k),X3),X2)) = apply(apply(X3,X2),X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(apply(apply(apply(s,s),apply(s,k)),X3),X2) = apply(apply(X3,X2),X2),
inference(transitivity,[status(thm)],[c19,c23]) ).
cnf(c25,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(apply(s,apply(k,s)),k),X3)),X2) = apply(apply(apply(apply(apply(s,apply(k,s)),k),X3),X2),X2),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
apply(apply(apply(s,apply(k,s)),k),X2) = apply(s,apply(k,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c27,plain,
apply(apply(apply(apply(s,apply(k,s)),k),X3),X2) = apply(apply(s,apply(k,X3)),X2),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(apply(apply(apply(apply(s,apply(k,s)),k),X4),X3),X2) = apply(apply(apply(s,apply(k,X4)),X3),X2),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(apply(apply(s,apply(k,X4)),X3),X2) = apply(apply(apply(k,X4),X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c30,plain,
apply(apply(k,X3),X2) = X3,
inference(substitution,[status(thm)],[c7]) ).
cnf(c31,plain,
apply(apply(apply(k,X4),X2),apply(X3,X2)) = apply(X4,apply(X3,X2)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
apply(apply(apply(s,apply(k,X4)),X3),X2) = apply(X4,apply(X3,X2)),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
apply(apply(apply(apply(apply(s,apply(k,s)),k),X4),X3),X2) = apply(X4,apply(X3,X2)),
inference(transitivity,[status(thm)],[c28,c32]) ).
cnf(c34,plain,
apply(apply(apply(apply(apply(s,apply(k,s)),k),X3),X2),X2) = apply(X3,apply(X2,X2)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(apply(s,apply(k,s)),k),X3)),X2) = apply(X3,apply(X2,X2)),
inference(transitivity,[status(thm)],[c25,c34]) ).
cnf(c36,plain,
apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X3),X2) = apply(X3,apply(X2,X2)),
inference(transitivity,[status(thm)],[c14,c35]) ).
cnf(c37,plain,
apply(apply(apply(s,apply(apply(s,k),X4)),X3),X2) = apply(apply(apply(apply(s,k),X4),X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c38,plain,
apply(apply(apply(apply(s,k),X4),X2),apply(X3,X2)) = apply(X2,apply(X3,X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c39,plain,
apply(apply(apply(s,apply(apply(s,k),X4)),X3),X2) = apply(X2,apply(X3,X2)),
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),X4) = apply(X4,apply(apply(apply(s,k),X2),X4)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
apply(apply(apply(s,k),X2),X3) = X3,
inference(substitution,[status(thm)],[c22]) ).
cnf(c42,plain,
apply(X3,apply(apply(apply(s,k),X2),X3)) = apply(X3,X3),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
apply(apply(apply(s,apply(apply(s,k),X2)),apply(apply(s,k),X4)),X3) = apply(X3,X3),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
apply(X4,X4) = apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),X4),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
apply(X5,apply(X4,X4)) = apply(X5,apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),X4)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X5),X4) = apply(X5,apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),X4)),
inference(transitivity,[status(thm)],[c36,c45]) ).
cnf(c47,plain,
apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)) = apply(X4,apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4))),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
apply(X4,apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4))) = apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
apply(apply(apply(s,apply(apply(s,k),X2)),apply(apply(s,k),X4)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X3)) = apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X3),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X3)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c50,plain,
apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)) = apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X4) = apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c52,plain,
apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)) = apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X4),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
apply(apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X4)) = apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X4),
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
apply(X6,apply(apply(apply(s,apply(apply(s,k),X5)),apply(apply(s,k),X4)),apply(apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)),X6))) = apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X6),
inference(transitivity,[status(thm)],[c48,c53]) ).
cnf(c55,plain,
apply(X6,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X5)),apply(apply(s,k),X4)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X6)) = apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),X3)),apply(apply(s,k),X2)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X6),
inference(transitivity,[status(thm)],[c12,c54]) ).
cnf(c56,plain,
apply(X2,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X2)) = apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X2),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))) = strong_fixed_point,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c58,plain,
apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X2) = apply(strong_fixed_point,X2),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
apply(X2,apply(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k))),X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c56,c58]) ).
cnf(c60,plain,
apply(X2,apply(strong_fixed_point,X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c4,c59]) ).
cnf(c61,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) = apply(strong_fixed_point,fixed_pt),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
$false,
inference(resolution,[status(thm)],[c1,c62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-5 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n006.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 21:29:09 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.28/0.82 Command-line arguments: --flatten --complete-subsets
% 4.28/0.82
% 4.28/0.82 % SZS status Unsatisfiable
% 4.28/0.82
% 4.28/0.82 % SZS output start CNFRefutation
% See solution above
% 4.28/0.87
% 4.28/0.87 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------