%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL034-1 : TPTP v9.3.1. Released v1.0.0.
% 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 09:37:13 AM UTC 2026
% Result : Unsatisfiable 16.14s 2.34s
% Output : CNFRefutation 16.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 26 RR)
% Number of literals : 34 ( 33 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 17 ( 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(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,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))) = apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))) = apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,plain,
apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))) = apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
apply(apply(t,X2),Y2) = apply(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
cnf(c7,plain,
apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))) = apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))))) = apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,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(c10,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)],[c9]) ).
cnf(c11,axiom,
apply(m,X2) = apply(X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
cnf(c12,plain,
apply(m,apply(apply(b,X3),X2)) = apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)) = apply(m,apply(apply(b,X3),X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(X3,apply(X2,apply(apply(b,X3),X2))) = apply(m,apply(apply(b,X3),X2)),
inference(transitivity,[status(thm)],[c10,c13]) ).
cnf(c15,plain,
apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m))) = apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m)) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))) = apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m),
inference(substitution,[status(thm)],[c6]) ).
cnf(c18,plain,
apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m) = apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m)) = apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))) = apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))) = apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))))) = apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))) = apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))) = apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(transitivity,[status(thm)],[c24,c27]) ).
cnf(c29,plain,
apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(transitivity,[status(thm)],[c20,c28]) ).
cnf(c30,plain,
apply(m,apply(apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))),m)) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(transitivity,[status(thm)],[c16,c29]) ).
cnf(c31,plain,
apply(m,apply(apply(t,m),apply(b,f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(transitivity,[status(thm)],[c8,c30]) ).
cnf(c32,plain,
apply(m,apply(apply(apply(b,apply(t,m)),b),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(transitivity,[status(thm)],[c5,c31]) ).
cnf(c33,plain,
apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b)))) = apply(f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))),apply(apply(apply(b,m),apply(apply(b,apply(t,m)),b)),f(apply(apply(b,m),apply(apply(b,apply(t,m)),b))))),
inference(transitivity,[status(thm)],[c3,c32]) ).
cnf(c34,plain,
$false,
inference(resolution,[status(thm)],[c1,c33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL034-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n006.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:29:54 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.14/2.34 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
% 16.14/2.34
% 16.14/2.34 % SZS status Unsatisfiable
% 16.14/2.34
% 16.14/2.34 % SZS output start CNFRefutation
% See solution above
% 16.14/2.37
% 16.14/2.37 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------