%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL003-18 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:01:32 PM UTC 2026
% Result : Unsatisfiable 3.23s 0.80s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 26 RR)
% Number of literals : 30 ( 29 equ; 21 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)) = strong_fixed_point,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t0,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t6,plain,
apply(apply(X1,X2),X2) = apply(apply(w,X1),X2),
inference(orient,[status(thm)],[t0]) ).
cnf(t16,plain,
apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(w,b),b)) = strong_fixed_point,
inference(step,[status(thm)],[t2,t6]) ).
cnf(t17,plain,
apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(w,w),b)) = strong_fixed_point,
inference(step,[status(thm)],[t16,t6]) ).
cnf(t13,plain,
apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(w,w),b)) = strong_fixed_point,
inference(orient,[status(thm)],[t17]) ).
cnf(t1,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t1]) ).
cnf(goal_0,negated_conjecture,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(w,w),b)),fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(g0_1,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(w,b),b)),fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_0,t6]) ).
cnf(g0_2,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_1,t6]) ).
cnf(g0_3,plain,
apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_2,t5]) ).
cnf(g0_4,plain,
apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_3,t5]) ).
cnf(g0_5,plain,
apply(fixed_pt,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_4,t5]) ).
cnf(g0_6,plain,
apply(fixed_pt,apply(apply(w,apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_5,t6]) ).
cnf(g0_7,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_6,t6]) ).
cnf(g0_8,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(w,w),b)),fixed_pt),
inference(rw,[status(thm)],[g0_7,t13]) ).
cnf(g0_9,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(w,b),b)),fixed_pt),
inference(rw,[status(thm)],[g0_8,t6]) ).
cnf(g0_10,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(b,w))),apply(apply(b,b),b)),fixed_pt),
inference(rw,[status(thm)],[g0_9,t6]) ).
cnf(g0_11,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(apply(apply(b,b),b),fixed_pt)),
inference(rw,[status(thm)],[g0_10,t5]) ).
cnf(g0_12,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(w,w)),apply(b,w)),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_11,t5]) ).
cnf(g0_13,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_12,t5]) ).
cnf(g0_14,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(w,apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_13,t6]) ).
cnf(g0_15,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_14,t6]) ).
cnf(g0_16,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(w,apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(b,apply(b,fixed_pt))))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_15,t5]) ).
cnf(g0_17,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_16,t6]) ).
cnf(g0_18,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,fixed_pt),apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_17,t5]) ).
cnf(g0_19,plain,
apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(fixed_pt,apply(apply(apply(apply(b,w),apply(b,apply(b,fixed_pt))),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),apply(apply(b,w),apply(b,apply(b,fixed_pt))))),
inference(rw,[status(thm)],[g0_18,t5]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL003-18 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 07:08:05 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.23/0.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.23/0.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------