%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL042-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 09:37:14 AM UTC 2026
% Result : Unsatisfiable 5.26s 0.96s
% Output : CNFRefutation 5.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 10 RR)
% Number of literals : 60 ( 59 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 : 92 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),true) = fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)) = ifeq(apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),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/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(c6,plain,
apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2) = apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(X2,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2)) = apply(X2,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2)) = apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
apply(X2,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2))) = apply(X2,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(apply(apply(b,apply(b,w1)),b),apply(b,X2)) = apply(apply(b,w1),apply(b,apply(b,X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c11,plain,
apply(apply(w1,X3),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2))) = apply(apply(w1,X3),apply(apply(b,w1),apply(b,apply(b,X2)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(X3,apply(apply(w1,X2),apply(apply(apply(b,apply(b,w1)),b),apply(b,X3)))) = apply(X3,apply(apply(w1,X2),apply(apply(b,w1),apply(b,apply(b,X3))))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
apply(apply(w1,X2),Y2) = apply(apply(Y2,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w1_definition) ).
cnf(c14,plain,
apply(apply(w1,X4),apply(apply(b,X3),X2)) = apply(apply(apply(apply(b,X3),X2),X4),X4),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(apply(apply(b,X4),X3),X2) = apply(X4,apply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c16,plain,
apply(apply(apply(apply(b,X4),X3),X2),X2) = apply(apply(X4,apply(X3,X2)),X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(w1,X2),apply(apply(b,X4),X3)) = apply(apply(X4,apply(X3,X2)),X2),
inference(transitivity,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
apply(apply(w1,X2),apply(apply(b,w1),apply(b,apply(b,X3)))) = apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),X2),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(X3,apply(apply(w1,X2),apply(apply(b,w1),apply(b,apply(b,X3))))) = apply(X3,apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(w1,X4),apply(apply(b,apply(b,X3)),X2)) = apply(apply(apply(apply(b,apply(b,X3)),X2),X4),X4),
inference(substitution,[status(thm)],[c13]) ).
cnf(c21,plain,
apply(apply(apply(b,apply(b,X3)),X2),X4) = apply(apply(b,X3),apply(X2,X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c22,plain,
apply(apply(apply(apply(b,apply(b,X3)),X2),X4),X4) = apply(apply(apply(b,X3),apply(X2,X4)),X4),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(apply(b,X3),apply(X2,X4)),X4) = apply(X3,apply(apply(X2,X4),X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c24,plain,
apply(apply(apply(apply(b,apply(b,X3)),X2),X4),X4) = apply(X3,apply(apply(X2,X4),X4)),
inference(transitivity,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
apply(apply(w1,X4),apply(apply(b,apply(b,X3)),X2)) = apply(X3,apply(apply(X2,X4),X4)),
inference(transitivity,[status(thm)],[c20,c24]) ).
cnf(c26,plain,
apply(apply(w1,X3),X2) = apply(apply(X2,X3),X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c27,plain,
apply(apply(X2,X3),X3) = apply(apply(w1,X3),X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(X3,apply(apply(X2,X4),X4)) = apply(X3,apply(apply(w1,X4),X2)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(apply(w1,X4),apply(apply(b,apply(b,X3)),X2)) = apply(X3,apply(apply(w1,X4),X2)),
inference(transitivity,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),apply(apply(b,apply(b,X3)),X2)) = apply(X3,apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),X2)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
apply(X3,apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),X2)) = apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),apply(apply(b,apply(b,X3)),X2)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),w1) = apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),apply(apply(b,apply(b,X3)),X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c33,plain,
apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),apply(apply(b,apply(b,X3)),X2)) = apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),w1),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
apply(X3,apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),X2)) = apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),w1),
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
apply(X3,apply(apply(w1,X2),apply(apply(b,w1),apply(b,apply(b,X3))))) = apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),w1),
inference(transitivity,[status(thm)],[c19,c34]) ).
cnf(c36,plain,
apply(X3,apply(apply(w1,X2),apply(apply(apply(b,apply(b,w1)),b),apply(b,X3)))) = apply(apply(w1,apply(apply(b,apply(b,X3)),X2)),w1),
inference(transitivity,[status(thm)],[c12,c35]) ).
cnf(c37,plain,
apply(X2,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2)))) = apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,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)],[c17]) ).
cnf(c39,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)],[c38]) ).
cnf(c40,plain,
apply(apply(apply(b,apply(b,w1)),b),apply(b,X2)) = apply(apply(b,w1),apply(b,apply(b,X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c41,plain,
apply(apply(b,w1),apply(b,apply(b,X2))) = apply(apply(apply(b,apply(b,w1)),b),apply(b,X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X2)))) = apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2)) = apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c44,plain,
apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2))) = apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2) = apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c46,plain,
apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2)) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2))) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2),
inference(transitivity,[status(thm)],[c44,c46]) ).
cnf(c48,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X2)))) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2),
inference(transitivity,[status(thm)],[c42,c47]) ).
cnf(c49,plain,
apply(apply(w1,apply(apply(b,apply(b,X2)),w1)),w1) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2),
inference(transitivity,[status(thm)],[c39,c48]) ).
cnf(c50,plain,
apply(X2,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X2)))) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2),
inference(transitivity,[status(thm)],[c37,c49]) ).
cnf(c51,plain,
apply(X2,apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X2))) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2),
inference(transitivity,[status(thm)],[c9,c50]) ).
cnf(c52,plain,
apply(X2,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2)) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),X2),
inference(transitivity,[status(thm)],[c7,c51]) ).
cnf(c53,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)) = apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt) = apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),true) = ifeq(apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)),fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),true),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,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/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(c57,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt)),fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),true) = true,
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq(apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),fixed_pt),fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)),true) = true,
inference(transitivity,[status(thm)],[c55,c57]) ).
cnf(c59,plain,
fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b)) = true,
inference(transitivity,[status(thm)],[c4,c58]) ).
cnf(c60,plain,
$false,
inference(resolution,[status(thm)],[c1,c59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n020.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 21:31:19 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.26/0.96 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 5.26/0.96
% 5.26/0.96 % SZS status Unsatisfiable
% 5.26/0.96
% 5.26/0.97 % SZS output start CNFRefutation
% See solution above
% 5.26/0.99
% 5.26/0.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------