%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 09:37:10 AM UTC 2026
% Result : Unsatisfiable 21.04s 2.95s
% Output : CNFRefutation 21.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 18 RR)
% Number of literals : 41 ( 40 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
Y != apply(combinator,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c2,axiom,
apply(apply(apply(b,X),Y2),Z) = apply(X,apply(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(c3,plain,
apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)) = apply(X3,apply(X2,apply(apply(b,X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,plain,
apply(X3,apply(X2,apply(apply(b,X3),X2))) = apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)),
inference(symmetry,[status(thm)],[c4]) ).
cnf(c6,plain,
apply(X4,apply(X3,apply(X2,apply(apply(b,X3),X2)))) = apply(X4,apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
apply(apply(l2,X2),Y2) = apply(Y2,apply(X2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_definition) ).
cnf(c8,plain,
apply(apply(l2,apply(apply(b,X3),X2)),X4) = apply(X4,apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(X4,apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2))) = apply(apply(l2,apply(apply(b,X3),X2)),X4),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(X4,apply(X3,apply(X2,apply(apply(b,X3),X2)))) = apply(apply(l2,apply(apply(b,X3),X2)),X4),
inference(transitivity,[status(thm)],[c6,c9]) ).
cnf(c11,plain,
apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(l2,apply(apply(b,apply(b,combinator)),l2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))) = apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(l2,apply(apply(b,apply(b,combinator)),l2)))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(l2,apply(l2,apply(apply(b,apply(b,combinator)),l2))),combinator) = apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(l2,apply(apply(b,apply(b,combinator)),l2)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c14,plain,
apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(apply(l2,apply(l2,apply(apply(b,apply(b,combinator)),l2))),combinator),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(apply(l2,X2),l2) = apply(l2,apply(X2,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c16,plain,
apply(apply(apply(l2,X3),l2),X2) = apply(apply(l2,apply(X3,X3)),X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(l2,apply(l2,X3)),X2) = apply(X2,apply(apply(l2,X3),apply(l2,X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c18,plain,
apply(apply(l2,X2),apply(l2,X2)) = apply(apply(l2,X2),apply(X2,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c19,plain,
apply(X2,apply(apply(l2,X3),apply(l2,X3))) = apply(X2,apply(apply(l2,X3),apply(X3,X3))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(l2,X2),apply(X2,X2)) = apply(apply(X2,X2),apply(X2,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c21,plain,
apply(X3,apply(apply(l2,X2),apply(X2,X2))) = apply(X3,apply(apply(X2,X2),apply(X2,X2))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
apply(apply(l2,apply(X2,X2)),X3) = apply(X3,apply(apply(X2,X2),apply(X2,X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c23,plain,
apply(X3,apply(apply(X2,X2),apply(X2,X2))) = apply(apply(l2,apply(X2,X2)),X3),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(X3,apply(apply(l2,X2),apply(X2,X2))) = apply(apply(l2,apply(X2,X2)),X3),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
apply(X2,apply(apply(l2,X3),apply(X3,X3))) = apply(apply(l2,apply(X3,X3)),X2),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
apply(X2,apply(apply(l2,X3),apply(l2,X3))) = apply(apply(l2,apply(X3,X3)),X2),
inference(transitivity,[status(thm)],[c19,c25]) ).
cnf(c27,plain,
apply(apply(l2,apply(l2,X3)),X2) = apply(apply(l2,apply(X3,X3)),X2),
inference(transitivity,[status(thm)],[c17,c26]) ).
cnf(c28,plain,
apply(apply(l2,apply(X3,X3)),X2) = apply(apply(l2,apply(l2,X3)),X2),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(apply(apply(l2,X3),l2),X2) = apply(apply(l2,apply(l2,X3)),X2),
inference(transitivity,[status(thm)],[c16,c28]) ).
cnf(c30,plain,
apply(apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),l2),combinator) = apply(apply(l2,apply(l2,apply(apply(b,apply(b,combinator)),l2))),combinator),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
apply(apply(l2,apply(l2,apply(apply(b,apply(b,combinator)),l2))),combinator) = apply(apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),l2),combinator),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
apply(l2,apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),l2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c33,plain,
apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),l2) = apply(l2,apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
apply(apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),l2),combinator) = apply(apply(l2,apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))),combinator),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
apply(apply(l2,apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))),combinator) = apply(combinator,apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c36,plain,
apply(apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),l2),combinator) = apply(combinator,apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))),
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
apply(apply(l2,apply(l2,apply(apply(b,apply(b,combinator)),l2))),combinator) = apply(combinator,apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))),
inference(transitivity,[status(thm)],[c31,c36]) ).
cnf(c38,plain,
apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(combinator,apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))),
inference(transitivity,[status(thm)],[c14,c37]) ).
cnf(c39,plain,
apply(combinator,apply(apply(l2,apply(apply(b,apply(b,combinator)),l2)),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))) = apply(combinator,apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))),
inference(transitivity,[status(thm)],[c12,c38]) ).
cnf(c40,plain,
apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2)))) = apply(combinator,apply(apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))),apply(apply(b,combinator),apply(l2,apply(apply(b,apply(b,combinator)),l2))))),
inference(transitivity,[status(thm)],[c3,c39]) ).
cnf(c41,plain,
$false,
inference(resolution,[status(thm)],[c1,c40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:29:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.04/2.95 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
% 21.04/2.95
% 21.04/2.95 % SZS status Unsatisfiable
% 21.04/2.95
% 21.04/2.95 % SZS output start CNFRefutation
% See solution above
% 21.04/2.98
% 21.04/2.98 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------