%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:01:30 PM UTC 2026
% Result : Unsatisfiable 4.10s 1.02s
% Output : CNFRefutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 16 RR)
% Number of literals : 31 ( 30 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
inference(orient,[status(thm)],[t3]) ).
cnf(t5,axiom,
sF1 = apply(s,apply(b,fixed_pt)),
introduced(definition) ).
cnf(t4,axiom,
sF0 = apply(b,fixed_pt),
introduced(definition) ).
cnf(t10,plain,
apply(b,fixed_pt) = sF0,
inference(orient,[status(thm)],[t4]) ).
cnf(t47,plain,
sF1 = apply(s,sF0),
inference(step,[status(thm)],[t5,t10]) ).
cnf(t11,plain,
apply(s,sF0) = sF1,
inference(orient,[status(thm)],[t47]) ).
cnf(t18,plain,
apply(apply(sF0,X1),apply(X2,X1)) = apply(apply(sF1,X2),X1),
inference(cp,[status(thm)],[t17,t11]) ).
cnf(t1,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t1]) ).
cnf(t13,plain,
apply(fixed_pt,apply(X1,X2)) = apply(apply(sF0,X1),X2),
inference(cp,[status(thm)],[t12,t10]) ).
cnf(t14,plain,
apply(apply(sF0,X1),X2) = apply(fixed_pt,apply(X1,X2)),
inference(orient,[status(thm)],[t13]) ).
cnf(t50,plain,
apply(fixed_pt,apply(X1,apply(X2,X1))) = apply(apply(sF1,X2),X1),
inference(step,[status(thm)],[t18,t14]) ).
cnf(t19,plain,
apply(fixed_pt,apply(X1,apply(X2,X1))) = apply(apply(sF1,X2),X1),
inference(orient,[status(thm)],[t50]) ).
cnf(t0,axiom,
apply(i,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
apply(i,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t21,plain,
apply(apply(sF1,i),X1) = apply(fixed_pt,apply(X1,X1)),
inference(cp,[status(thm)],[t19,t9]) ).
cnf(t6,axiom,
sF2 = apply(apply(s,apply(b,fixed_pt)),i),
introduced(definition) ).
cnf(t48,plain,
sF2 = apply(apply(s,sF0),i),
inference(step,[status(thm)],[t6,t10]) ).
cnf(t49,plain,
sF2 = apply(sF1,i),
inference(step,[status(thm)],[t48,t11]) ).
cnf(t16,plain,
apply(sF1,i) = sF2,
inference(orient,[status(thm)],[t49]) ).
cnf(t58,plain,
apply(sF2,X1) = apply(fixed_pt,apply(X1,X1)),
inference(step,[status(thm)],[t21,t16]) ).
cnf(t39,plain,
apply(fixed_pt,apply(X1,X1)) = apply(sF2,X1),
inference(orient,[status(thm)],[t58]) ).
cnf(u0,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
weak_fixed_point(X) = apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
apply(sF2,apply(apply(s,apply(b,fixed_pt)),i)) != apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)),
inference(rw,[status(thm)],[goal_0,t39]) ).
cnf(g0_1,plain,
apply(sF2,apply(apply(s,apply(b,fixed_pt)),i)) != apply(apply(apply(s,sF0),i),apply(apply(s,apply(b,fixed_pt)),i)),
inference(rw,[status(thm)],[g0_0,t10]) ).
cnf(g0_2,plain,
apply(sF2,apply(apply(s,apply(b,fixed_pt)),i)) != apply(apply(sF1,i),apply(apply(s,apply(b,fixed_pt)),i)),
inference(rw,[status(thm)],[g0_1,t11]) ).
cnf(g0_3,plain,
apply(sF2,apply(apply(s,apply(b,fixed_pt)),i)) != apply(sF2,apply(apply(s,apply(b,fixed_pt)),i)),
inference(rw,[status(thm)],[g0_2,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n001.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 07:13:25 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.10/1.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/1.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------