%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 : Fri Sep 25 01:01:31 PM UTC 2026
% Result : Unsatisfiable 5.84s 1.53s
% Output : CNFRefutation 5.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 8 RR)
% Number of literals : 15 ( 14 equ; 7 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 : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t13,plain,
apply(apply(X1,X2),apply(X3,X2)) = apply(apply(apply(s,X1),X3),X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t2,axiom,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t12,plain,
apply(apply(apply(c,X1),X2),X3) = apply(apply(X1,X3),X2),
inference(orient,[status(thm)],[t2]) ).
cnf(t1,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t11,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t1]) ).
cnf(u0,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
weak_fixed_point(X) = apply(apply(apply(s,apply(c,apply(b,X))),apply(s,apply(c,apply(b,X)))),apply(s,apply(c,apply(b,X)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) != apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
apply(fixed_pt,apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))) != apply(fixed_pt,apply(apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(g0_1,plain,
apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))) != apply(fixed_pt,apply(apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(rw,[status(thm)],[g0_0,t13]) ).
cnf(g0_2,plain,
apply(apply(apply(c,apply(b,fixed_pt)),apply(s,apply(c,apply(b,fixed_pt)))),apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(rw,[status(thm)],[g0_1,t13]) ).
cnf(g0_3,plain,
apply(apply(apply(b,fixed_pt),apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(rw,[status(thm)],[g0_2,t12]) ).
cnf(g0_4,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))) != apply(fixed_pt,apply(apply(apply(apply(s,s),s),apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(rw,[status(thm)],[g0_3,t11]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL002-5 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.56 % Computer : n003.cluster.edu
% 0.17/0.56 % Model : x86_64 x86_64
% 0.17/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.56 % Memory : 8046.5625MB
% 0.17/0.56 % OS : Linux 6.8.0-71-generic
% 0.17/0.56 % CPULimit : 300
% 0.17/0.56 % WCLimit : 300
% 0.17/0.56 % DateTime : Fri Sep 25 07:09:22 UTC 2026
% 0.17/0.57 % CPUTime :
% 0.17/0.57 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.84/1.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.84/1.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------