%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 09:37:15 AM UTC 2026
% Result : Unsatisfiable 18.74s 2.72s
% Output : CNFRefutation 18.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 15 RR)
% Number of literals : 60 ( 59 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 73 ( 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/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c2,axiom,
apply(apply(w1,X),Y) = apply(apply(Y,X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).
cnf(c3,plain,
apply(apply(w1,X4),apply(apply(b,X3),X2)) = apply(apply(apply(apply(b,X3),X2),X4),X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
apply(apply(apply(b,X2),Y2),Z) = apply(X2,apply(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(c5,plain,
apply(apply(apply(b,X3),X2),X4) = apply(X3,apply(X2,X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
apply(apply(apply(apply(b,X3),X2),X4),X4) = apply(apply(X3,apply(X2,X4)),X4),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(apply(w1,X4),apply(apply(b,X3),X2)) = apply(apply(X3,apply(X2,X4)),X4),
inference(transitivity,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X2)))) = apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X2)))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(apply(w1,b),w1) = apply(apply(w1,b),b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
apply(apply(apply(w1,b),w1),X2) = apply(apply(apply(w1,b),b),X2),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(apply(w1,X2),b) = apply(apply(b,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
apply(apply(apply(w1,X3),b),X2) = apply(apply(apply(b,X3),X3),X2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(b,X3),X3),X2) = apply(X3,apply(X3,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c15,plain,
apply(apply(apply(w1,X3),b),X2) = apply(X3,apply(X3,X2)),
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
apply(apply(apply(w1,b),b),X2) = apply(b,apply(b,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(w1,b),w1),X2) = apply(b,apply(b,X2)),
inference(transitivity,[status(thm)],[c11,c16]) ).
cnf(c18,plain,
apply(b,apply(b,X2)) = apply(apply(apply(w1,b),w1),X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(apply(b,w1),apply(b,apply(b,X2))) = apply(apply(b,w1),apply(apply(apply(w1,b),w1),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X2)))) = apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(w1,b),w1),X2))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)),X2) = apply(apply(b,w1),apply(apply(apply(w1,b),w1),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c22,plain,
apply(apply(b,w1),apply(apply(apply(w1,b),w1),X2)) = apply(apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)),X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(w1,b),w1),X2))) = apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)),X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1))),X2) = apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c25,plain,
apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)),X2)) = apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1))),X2),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
apply(apply(w1,b),w1) = apply(apply(w1,b),b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)) = apply(apply(b,apply(b,w1)),apply(apply(w1,b),b)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1))) = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),b))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(apply(w1,b),b) = apply(apply(b,b),b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
apply(apply(b,apply(b,w1)),apply(apply(w1,b),b)) = apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),b))) = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
strong_fixed_point = apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c33,plain,
apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b))) = strong_fixed_point,
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),b))) = strong_fixed_point,
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1))) = strong_fixed_point,
inference(transitivity,[status(thm)],[c28,c34]) ).
cnf(c36,plain,
apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1))),X2) = apply(strong_fixed_point,X2),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(w1,b),w1)),X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c25,c36]) ).
cnf(c38,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(w1,b),w1),X2))) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c23,c37]) ).
cnf(c39,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X2)))) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c20,c38]) ).
cnf(c40,plain,
apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c9,c39]) ).
cnf(c41,plain,
apply(strong_fixed_point,X2) = apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
apply(X2,apply(strong_fixed_point,X2)) = apply(X2,apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
apply(apply(w1,X2),apply(apply(b,apply(b,X4)),X3)) = apply(apply(apply(b,X4),apply(X3,X2)),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c44,plain,
apply(apply(apply(b,X4),apply(X3,X2)),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c45,plain,
apply(apply(w1,X2),apply(apply(b,apply(b,X4)),X3)) = apply(X4,apply(apply(X3,X2),X2)),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
apply(apply(w1,X4),apply(apply(b,apply(b,X3)),X2)) = apply(X3,apply(apply(X2,X4),X4)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
apply(apply(w1,X3),X2) = apply(apply(X2,X3),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c48,plain,
apply(apply(X2,X3),X3) = apply(apply(w1,X3),X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
apply(X3,apply(apply(X2,X4),X4)) = apply(X3,apply(apply(w1,X4),X2)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
apply(apply(w1,X4),apply(apply(b,apply(b,X3)),X2)) = apply(X3,apply(apply(w1,X4),X2)),
inference(transitivity,[status(thm)],[c46,c49]) ).
cnf(c51,plain,
apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),apply(apply(b,apply(b,X2)),w1)) = apply(X2,apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
apply(X2,apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1)) = apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),apply(apply(b,apply(b,X2)),w1)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1) = apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),apply(apply(b,apply(b,X2)),w1)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),apply(apply(b,apply(b,X2)),w1)) = apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),apply(apply(b,apply(b,X2)),w1)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c54,c40]) ).
cnf(c56,plain,
apply(X2,apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c52,c55]) ).
cnf(c57,plain,
apply(X2,apply(strong_fixed_point,X2)) = apply(strong_fixed_point,X2),
inference(transitivity,[status(thm)],[c42,c56]) ).
cnf(c58,plain,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) = apply(strong_fixed_point,fixed_pt),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
$false,
inference(resolution,[status(thm)],[c1,c59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.24 % Computer : n010.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 21:30:47 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.74/2.72 Command-line arguments: --no-flatten-goal
% 18.74/2.72
% 18.74/2.72 % SZS status Unsatisfiable
% 18.74/2.72
% 18.74/2.72 % SZS output start CNFRefutation
% See solution above
% 18.74/2.73
% 18.74/2.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------