%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL003-20 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 09:37:07 AM UTC 2026
% Result : Unsatisfiable 1.24s 0.41s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 9 RR)
% Number of literals : 62 ( 61 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 0 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(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
apply(strong_fixed_point,X2) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(X2,apply(strong_fixed_point,X2)) = apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(c6,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2) = apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2)) = apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
apply(apply(w,X2),Y2) = apply(apply(X2,Y2),Y2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
cnf(c9,plain,
apply(apply(w,w),X2) = apply(apply(w,X2),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(apply(w,X2),X2) = apply(apply(X2,X2),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c11,plain,
apply(apply(w,w),X2) = apply(apply(X2,X2),X2),
inference(transitivity,[status(thm)],[c9,c10]) ).
cnf(c12,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)) = apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2))) = apply(X2,apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(b,apply(b,X2)),X4),X3) = apply(apply(b,X2),apply(X4,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,plain,
apply(apply(apply(apply(b,apply(b,X4)),X3),X2),X5) = apply(apply(apply(b,X4),apply(X3,X2)),X5),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(apply(apply(b,X5),apply(X4,X3)),X2) = apply(X5,apply(apply(X4,X3),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c17,plain,
apply(apply(apply(apply(b,apply(b,X5)),X4),X3),X2) = apply(X5,apply(apply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X3),X2) = apply(w,apply(apply(apply(apply(b,b),b),X3),X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X4),X3),X2) = apply(apply(w,apply(apply(apply(apply(b,b),b),X4),X3)),X2),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(w,apply(apply(apply(apply(b,b),b),X4),X3)),X2) = apply(apply(apply(apply(apply(apply(b,b),b),X4),X3),X2),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c21,plain,
apply(apply(w,w),b) = apply(apply(b,b),b),
inference(substitution,[status(thm)],[c11]) ).
cnf(c22,plain,
apply(apply(b,b),b) = apply(apply(w,w),b),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(apply(b,b),b),X2) = apply(apply(apply(w,w),b),X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(apply(apply(apply(b,b),b),X3),X2) = apply(apply(apply(apply(w,w),b),X3),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
apply(apply(apply(apply(apply(b,b),b),X4),X3),X2) = apply(apply(apply(apply(apply(w,w),b),X4),X3),X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
apply(apply(w,w),b) = apply(apply(w,b),b),
inference(substitution,[status(thm)],[c8]) ).
cnf(c27,plain,
apply(apply(apply(w,w),b),X2) = apply(apply(apply(w,b),b),X2),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(apply(apply(apply(w,w),b),X3),X2) = apply(apply(apply(apply(w,b),b),X3),X2),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(apply(apply(apply(apply(w,w),b),X4),X3),X2) = apply(apply(apply(apply(apply(w,b),b),X4),X3),X2),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
apply(apply(w,b),X2) = apply(apply(b,X2),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c31,plain,
apply(apply(apply(w,b),X3),X2) = apply(apply(apply(b,X3),X3),X2),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
apply(apply(apply(b,X3),X3),X2) = apply(X3,apply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c33,plain,
apply(apply(apply(w,b),X3),X2) = apply(X3,apply(X3,X2)),
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
apply(apply(apply(w,b),b),X2) = apply(b,apply(b,X2)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
apply(apply(apply(apply(w,b),b),X3),X2) = apply(apply(b,apply(b,X3)),X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
apply(apply(apply(apply(apply(w,b),b),X4),X3),X2) = apply(apply(apply(b,apply(b,X4)),X3),X2),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
apply(apply(apply(b,apply(b,X4)),X3),X2) = apply(apply(b,X4),apply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c38,plain,
apply(apply(apply(apply(apply(w,b),b),X4),X3),X2) = apply(apply(b,X4),apply(X3,X2)),
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
apply(apply(apply(apply(apply(w,w),b),X4),X3),X2) = apply(apply(b,X4),apply(X3,X2)),
inference(transitivity,[status(thm)],[c29,c38]) ).
cnf(c40,plain,
apply(apply(apply(apply(apply(b,b),b),X4),X3),X2) = apply(apply(b,X4),apply(X3,X2)),
inference(transitivity,[status(thm)],[c25,c39]) ).
cnf(c41,plain,
apply(apply(apply(apply(apply(apply(b,b),b),X4),X3),X2),X2) = apply(apply(apply(b,X4),apply(X3,X2)),X2),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
apply(apply(apply(b,X4),apply(X3,X2)),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c43,plain,
apply(apply(apply(apply(apply(apply(b,b),b),X4),X3),X2),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
apply(apply(w,apply(apply(apply(apply(b,b),b),X4),X3)),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(transitivity,[status(thm)],[c20,c43]) ).
cnf(c45,plain,
apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X4),X3),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(transitivity,[status(thm)],[c19,c44]) ).
cnf(c46,plain,
apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)) = apply(X2,apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
apply(X2,apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2))) = apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)) = apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c49,plain,
apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)) = apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2) = apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c51,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
apply(X2,apply(apply(apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2)),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2))) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2),
inference(transitivity,[status(thm)],[c47,c52]) ).
cnf(c54,plain,
apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),apply(apply(b,b),b)),X2))) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2),
inference(transitivity,[status(thm)],[c13,c53]) ).
cnf(c55,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2)) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2),
inference(transitivity,[status(thm)],[c7,c54]) ).
cnf(c56,plain,
apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))) = strong_fixed_point,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c57,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2) = apply(strong_fixed_point,X2),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),apply(apply(b,b),b))),X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c55,c57]) ).
cnf(c59,plain,
apply(X2,apply(strong_fixed_point,X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c4,c58]) ).
cnf(c60,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) = apply(strong_fixed_point,fixed_pt),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
$false,
inference(resolution,[status(thm)],[c1,c61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-20 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n007.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 21:26:55 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.24/0.41 Command-line arguments: --flatten --complete-subsets
% 1.24/0.41
% 1.24/0.41 % SZS status Unsatisfiable
% 1.24/0.41
% 1.24/0.41 % SZS output start CNFRefutation
% See solution above
% 1.24/0.46
% 1.24/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------