%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 0.21s 0.35s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 10 RR)
% Number of literals : 53 ( 52 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 79 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),true) = fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) = ifeq(apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(c6,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(X2,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2)) = apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2)) = apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2))) = apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
apply(apply(w,X2),Y2) = apply(apply(X2,Y2),Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
cnf(c11,plain,
apply(apply(w,apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),X3) = apply(apply(apply(apply(apply(b,apply(b,w)),b),apply(b,X2)),X3),X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(apply(apply(b,apply(b,X3)),X2),X4) = apply(apply(b,X3),apply(X2,X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c13,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)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(b,X5),apply(X4,X3)),X2) = apply(X5,apply(apply(X4,X3),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,plain,
apply(apply(apply(apply(b,apply(b,X5)),X4),X3),X2) = apply(X5,apply(apply(X4,X3),X2)),
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
apply(apply(apply(apply(b,apply(b,w)),b),apply(b,X3)),X2) = apply(w,apply(apply(b,apply(b,X3)),X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(apply(apply(b,apply(b,w)),b),apply(b,X3)),X2),X2) = apply(apply(w,apply(apply(b,apply(b,X3)),X2)),X2),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(apply(w,apply(apply(b,apply(b,X4)),X3)),X2) = apply(apply(apply(apply(b,apply(b,X4)),X3),X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c19,plain,
apply(apply(apply(b,apply(b,X4)),X3),X2) = apply(apply(b,X4),apply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c20,plain,
apply(apply(apply(apply(b,apply(b,X4)),X3),X2),X2) = apply(apply(apply(b,X4),apply(X3,X2)),X2),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(b,X4),apply(X3,X2)),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c22,plain,
apply(apply(apply(apply(b,apply(b,X4)),X3),X2),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
apply(apply(w,apply(apply(b,apply(b,X4)),X3)),X2) = apply(X4,apply(apply(X3,X2),X2)),
inference(transitivity,[status(thm)],[c18,c22]) ).
cnf(c24,plain,
apply(apply(w,apply(apply(b,apply(b,X3)),X2)),X2) = apply(X3,apply(apply(X2,X2),X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
apply(apply(w,w),X2) = apply(apply(w,X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c26,plain,
apply(apply(w,X2),X2) = apply(apply(X2,X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c27,plain,
apply(apply(w,w),X2) = apply(apply(X2,X2),X2),
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
apply(apply(X2,X2),X2) = apply(apply(w,w),X2),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(X3,apply(apply(X2,X2),X2)) = apply(X3,apply(apply(w,w),X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
apply(apply(w,apply(apply(b,apply(b,X3)),X2)),X2) = apply(X3,apply(apply(w,w),X2)),
inference(transitivity,[status(thm)],[c24,c29]) ).
cnf(c31,plain,
apply(apply(apply(apply(apply(b,apply(b,w)),b),apply(b,X3)),X2),X2) = apply(X3,apply(apply(w,w),X2)),
inference(transitivity,[status(thm)],[c17,c30]) ).
cnf(c32,plain,
apply(apply(w,apply(apply(apply(b,apply(b,w)),b),apply(b,X3))),X2) = apply(X3,apply(apply(w,w),X2)),
inference(transitivity,[status(thm)],[c11,c31]) ).
cnf(c33,plain,
apply(apply(w,apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))) = apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2)))) = apply(apply(w,apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))) = apply(apply(w,apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c36,plain,
apply(apply(w,apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))) = apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2)) = apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c38,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2)),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2) = apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c40,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2)) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2),
inference(transitivity,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
apply(apply(w,apply(apply(apply(b,apply(b,w)),b),apply(b,X2))),apply(apply(apply(b,apply(b,w)),b),apply(b,X2))) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2),
inference(transitivity,[status(thm)],[c36,c41]) ).
cnf(c43,plain,
apply(X2,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X2)))) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2),
inference(transitivity,[status(thm)],[c34,c42]) ).
cnf(c44,plain,
apply(X2,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X2))) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2),
inference(transitivity,[status(thm)],[c9,c43]) ).
cnf(c45,plain,
apply(X2,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2)) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),X2),
inference(transitivity,[status(thm)],[c7,c44]) ).
cnf(c46,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt)) = apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt) = apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),true) = ifeq(apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt)),fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),true),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,axiom,
ifeq(apply(Strong_fixed_point,fixed_pt),apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)),fixed_point(Strong_fixed_point),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(c50,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt)),fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),true) = true,
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),true) = true,
inference(transitivity,[status(thm)],[c48,c50]) ).
cnf(c52,plain,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) = true,
inference(transitivity,[status(thm)],[c4,c51]) ).
cnf(c53,plain,
$false,
inference(resolution,[status(thm)],[c1,c52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n020.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 21:29:34 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.35 Command-line arguments: --flatten-regeneralise
% 0.21/0.35
% 0.21/0.35 % SZS status Unsatisfiable
% 0.21/0.35
% 0.21/0.35 % SZS output start CNFRefutation
% See solution above
% 0.21/0.39
% 0.21/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------