%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL037-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 09:37:13 AM UTC 2026
% Result : Unsatisfiable 1.85s 0.51s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 3 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c2,axiom,
apply(apply(apply(c,X),Y2),Z) = apply(apply(X,Z),Y2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
cnf(c3,plain,
apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))) = apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
apply(apply(apply(s,X2),Y2),Z2) = apply(apply(X2,Z2),apply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
cnf(c5,plain,
apply(apply(apply(s,apply(c,X2)),X4),X3) = apply(apply(apply(c,X2),X3),apply(X4,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
apply(apply(apply(c,X4),X2),apply(X3,X2)) = apply(apply(X4,apply(X3,X2)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
apply(apply(apply(s,apply(c,X4)),X3),X2) = apply(apply(X4,apply(X3,X2)),X2),
inference(transitivity,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
apply(apply(apply(s,apply(c,apply(b,X4))),X3),X2) = apply(apply(apply(b,X4),apply(X3,X2)),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,axiom,
apply(apply(apply(b,X2),Y2),Z2) = apply(X2,apply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(c10,plain,
apply(apply(apply(b,X4),apply(X3,X2)),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(apply(apply(s,apply(c,apply(b,X4))),X3),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))) = apply(apply(s,b),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))) = apply(apply(apply(s,b),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2) = apply(apply(apply(apply(s,b),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(apply(apply(s,b),X2),X3) = apply(apply(b,X3),apply(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c16,plain,
apply(apply(apply(apply(s,b),X3),X4),X2) = apply(apply(apply(b,X4),apply(X3,X4)),X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(b,X4),apply(X3,X4)),X2) = apply(X4,apply(apply(X3,X4),X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c18,plain,
apply(apply(apply(apply(s,b),X3),X4),X2) = apply(X4,apply(apply(X3,X4),X2)),
inference(transitivity,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
apply(apply(apply(apply(s,b),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2) = apply(f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))) = apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2) = apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
apply(f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)),apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2)) = apply(f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)),apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(apply(apply(s,b),apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2) = apply(f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)),apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)))),
inference(transitivity,[status(thm)],[c19,c22]) ).
cnf(c24,plain,
apply(apply(apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b))))),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))),X2) = apply(f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)),apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)))),
inference(transitivity,[status(thm)],[c14,c23]) ).
cnf(c25,plain,
apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2))) = apply(f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)),apply(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2),f(apply(apply(c,apply(apply(apply(s,apply(c,apply(b,apply(s,b)))),apply(s,apply(c,apply(b,apply(s,b))))),apply(s,apply(c,apply(b,apply(s,b)))))),X2)))),
inference(transitivity,[status(thm)],[c3,c24]) ).
cnf(c26,plain,
$false,
inference(resolution,[status(thm)],[c1,c25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n002.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:32:52 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.85/0.51 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
% 1.85/0.51
% 1.85/0.51 % SZS status Unsatisfiable
% 1.85/0.51
% 1.85/0.51 % SZS output start CNFRefutation
% See solution above
% 1.85/0.53
% 1.85/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------