%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL003-13 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 09:37:06 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.16s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 6 RR)
% Number of literals : 44 ( 43 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; 4 con; 0-2 aty)
% Number of variables : 58 ( 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(apply(b,w),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(apply(b,w),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(apply(b,w),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(apply(b,w),b)),b)),X2) = apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2)) = apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),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(apply(b,w),b)),b),X2)) = apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),X2))) = apply(X2,apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(b,apply(apply(b,w),b)),b),X2) = apply(apply(apply(b,w),b),apply(b,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,plain,
apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),X3) = apply(apply(apply(apply(b,w),b),apply(b,X2)),X3),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X3),X2),X4) = apply(apply(apply(apply(apply(b,w),b),apply(b,X3)),X2),X4),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(b,w),b),X2) = apply(w,apply(b,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c18,plain,
apply(apply(apply(apply(b,w),b),X3),X2) = apply(apply(w,apply(b,X3)),X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(apply(w,apply(b,X3)),X2) = apply(apply(apply(b,X3),X2),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c20,plain,
apply(apply(apply(b,X3),X2),X2) = apply(X3,apply(X2,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c21,plain,
apply(apply(w,apply(b,X3)),X2) = apply(X3,apply(X2,X2)),
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
apply(apply(apply(apply(b,w),b),X3),X2) = apply(X3,apply(X2,X2)),
inference(transitivity,[status(thm)],[c18,c21]) ).
cnf(c23,plain,
apply(apply(apply(apply(b,w),b),apply(b,X3)),X2) = apply(apply(b,X3),apply(X2,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(apply(apply(apply(apply(b,w),b),apply(b,X4)),X3),X2) = apply(apply(apply(b,X4),apply(X3,X3)),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
apply(apply(apply(b,X4),apply(X3,X3)),X2) = apply(X4,apply(apply(X3,X3),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c26,plain,
apply(apply(apply(apply(apply(b,w),b),apply(b,X4)),X3),X2) = apply(X4,apply(apply(X3,X3),X2)),
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X4),X3),X2) = apply(X4,apply(apply(X3,X3),X2)),
inference(transitivity,[status(thm)],[c16,c26]) ).
cnf(c28,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)) = apply(X2,apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2))),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(X2,apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2))) = apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)) = apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c31,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)) = apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2) = apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c33,plain,
apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2),
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
apply(X2,apply(apply(apply(apply(apply(b,apply(apply(b,w),b)),b),X2),apply(apply(apply(b,apply(apply(b,w),b)),b),X2)),apply(apply(apply(b,apply(apply(b,w),b)),b),X2))) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2),
inference(transitivity,[status(thm)],[c29,c34]) ).
cnf(c36,plain,
apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(apply(b,w),b)),b),X2))) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2),
inference(transitivity,[status(thm)],[c13,c35]) ).
cnf(c37,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2)) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2),
inference(transitivity,[status(thm)],[c7,c36]) ).
cnf(c38,plain,
apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)) = strong_fixed_point,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c39,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2) = apply(strong_fixed_point,X2),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
apply(X2,apply(strong_fixed_point,X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c4,c40]) ).
cnf(c42,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) = apply(strong_fixed_point,fixed_pt),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
$false,
inference(resolution,[status(thm)],[c1,c43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL003-13 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Mon Sep 28 21:28:18 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.16 Command-line arguments: --flatten --complete-subsets
% 0.07/0.16
% 0.07/0.16 % SZS status Unsatisfiable
% 0.07/0.16
% 0.07/0.16 % SZS output start CNFRefutation
% See solution above
% 0.07/0.18
% 0.07/0.18 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------