%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL049-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 09:37:17 AM UTC 2026
% Result : Unsatisfiable 7.32s 1.22s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 18 RR)
% Number of literals : 32 ( 31 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 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 : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c2,axiom,
apply(apply(apply(b,X),Y2),Z) = apply(X,apply(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(c3,plain,
apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b)))) = apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b)))) = apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,plain,
apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b))))) = apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b)))))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
apply(apply(w,X2),Y2) = apply(apply(X2,Y2),Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
cnf(c7,plain,
apply(apply(w,apply(b,X3)),X2) = apply(apply(apply(b,X3),X2),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(b,X3),X2),X2) = apply(X3,apply(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
apply(apply(w,apply(b,X3)),X2) = apply(X3,apply(X2,X2)),
inference(transitivity,[status(thm)],[c7,c8]) ).
cnf(c10,axiom,
apply(m,X2) = apply(X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c11,plain,
apply(X2,X2) = apply(m,X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(X3,apply(X2,X2)) = apply(X3,apply(m,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(w,apply(b,X3)),X2) = apply(X3,apply(m,X2)),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
apply(apply(w,apply(b,X2)),apply(w,apply(b,X2))) = apply(X2,apply(m,apply(w,apply(b,X2)))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(X2,apply(m,apply(w,apply(b,X2)))) = apply(apply(w,apply(b,X2)),apply(w,apply(b,X2))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(m,apply(w,apply(b,X2))) = apply(apply(w,apply(b,X2)),apply(w,apply(b,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c17,plain,
apply(apply(w,apply(b,X2)),apply(w,apply(b,X2))) = apply(m,apply(w,apply(b,X2))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(X2,apply(m,apply(w,apply(b,X2)))) = apply(m,apply(w,apply(b,X2))),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b))))))) = apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b)))))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b)))))) = apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b))))))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b)))) = apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b))))) = apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b)))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b)))))) = apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b))))))) = apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b)))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b)))) = apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b))))) = apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b)))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b)))))) = apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b))))))) = apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(transitivity,[status(thm)],[c24,c27]) ).
cnf(c29,plain,
apply(m,apply(w,apply(b,f(apply(apply(b,m),apply(apply(b,w),b)))))) = apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(transitivity,[status(thm)],[c20,c28]) ).
cnf(c30,plain,
apply(m,apply(apply(apply(b,w),b),f(apply(apply(b,m),apply(apply(b,w),b))))) = apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(transitivity,[status(thm)],[c5,c29]) ).
cnf(c31,plain,
apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b)))) = apply(f(apply(apply(b,m),apply(apply(b,w),b))),apply(apply(apply(b,m),apply(apply(b,w),b)),f(apply(apply(b,m),apply(apply(b,w),b))))),
inference(transitivity,[status(thm)],[c3,c30]) ).
cnf(c32,plain,
$false,
inference(resolution,[status(thm)],[c1,c31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL049-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:34:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.32/1.22 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
% 7.32/1.22
% 7.32/1.22 % SZS status Unsatisfiable
% 7.32/1.22
% 7.32/1.22 % SZS output start CNFRefutation
% See solution above
% 7.32/1.24
% 7.32/1.24 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------