%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:37:05 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 4 RR)
% Number of literals : 22 ( 21 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
cnf(c2,axiom,
weak_fixed_point(X2) = apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
apply(X2,weak_fixed_point(X2)) = apply(X2,apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i))),
inference(congruence,[status(thm)],[c2]) ).
cnf(c4,axiom,
apply(i,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
cnf(c5,plain,
apply(i,apply(apply(s,apply(b,X2)),i)) = apply(apply(s,apply(b,X2)),i),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
apply(apply(s,apply(b,X2)),i) = apply(i,apply(apply(s,apply(b,X2)),i)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i)) = apply(apply(apply(s,apply(b,X2)),i),apply(i,apply(apply(s,apply(b,X2)),i))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(X2,apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i))) = apply(X2,apply(apply(apply(s,apply(b,X2)),i),apply(i,apply(apply(s,apply(b,X2)),i)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
apply(apply(apply(b,X2),Y),Z) = apply(X2,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(c10,plain,
apply(apply(apply(b,X2),apply(apply(s,apply(b,X2)),i)),apply(i,apply(apply(s,apply(b,X2)),i))) = apply(X2,apply(apply(apply(s,apply(b,X2)),i),apply(i,apply(apply(s,apply(b,X2)),i)))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(X2,apply(apply(apply(s,apply(b,X2)),i),apply(i,apply(apply(s,apply(b,X2)),i)))) = apply(apply(apply(b,X2),apply(apply(s,apply(b,X2)),i)),apply(i,apply(apply(s,apply(b,X2)),i))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
apply(apply(apply(s,X2),Y2),Z2) = apply(apply(X2,Z2),apply(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
cnf(c13,plain,
apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i)) = apply(apply(apply(b,X2),apply(apply(s,apply(b,X2)),i)),apply(i,apply(apply(s,apply(b,X2)),i))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(b,X2),apply(apply(s,apply(b,X2)),i)),apply(i,apply(apply(s,apply(b,X2)),i))) = apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i)) = weak_fixed_point(X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c16,plain,
apply(apply(apply(b,X2),apply(apply(s,apply(b,X2)),i)),apply(i,apply(apply(s,apply(b,X2)),i))) = weak_fixed_point(X2),
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
apply(X2,apply(apply(apply(s,apply(b,X2)),i),apply(i,apply(apply(s,apply(b,X2)),i)))) = weak_fixed_point(X2),
inference(transitivity,[status(thm)],[c11,c16]) ).
cnf(c18,plain,
apply(X2,apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i))) = weak_fixed_point(X2),
inference(transitivity,[status(thm)],[c8,c17]) ).
cnf(c19,plain,
apply(X2,weak_fixed_point(X2)) = weak_fixed_point(X2),
inference(transitivity,[status(thm)],[c3,c18]) ).
cnf(c20,plain,
apply(fixed_pt,weak_fixed_point(fixed_pt)) = weak_fixed_point(fixed_pt),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
weak_fixed_point(fixed_pt) = apply(fixed_pt,weak_fixed_point(fixed_pt)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
$false,
inference(resolution,[status(thm)],[c1,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:24:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25 Command-line arguments: --no-flatten-goal
% 0.09/0.25
% 0.09/0.25 % SZS status Unsatisfiable
% 0.09/0.25
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25
% 0.09/0.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------