%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 01:01:51 PM UTC 2026
% Result : Unsatisfiable 5.05s 16.18s
% Output : CNFRefutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 25 RR)
% Number of literals : 29 ( 28 equ; 22 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 3 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 : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b) = strong_fixed_point,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t15,plain,
apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b) = strong_fixed_point,
inference(orient,[status(thm)],[t2]) ).
cnf(t0,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)],[t0]) ).
cnf(t1,axiom,
apply(apply(apply(n,X1),X2),X3) = apply(apply(apply(X1,X3),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t6,plain,
apply(apply(apply(X1,X2),X3),X2) = apply(apply(apply(n,X1),X3),X2),
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(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[goal_0,t15]) ).
cnf(g0_1,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,fixed_pt))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_0,t5]) ).
cnf(g0_2,plain,
apply(fixed_pt,apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_1,t5]) ).
cnf(g0_3,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n)),apply(b,apply(b,fixed_pt))),n),apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_2,t6]) ).
cnf(g0_4,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt)))),n),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(apply(b,apply(apply(apply(apply(apply(b,b),n),apply(b,apply(b,fixed_pt))),n),apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_4,t6]) ).
cnf(g0_6,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(apply(b,apply(n,apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_5,t5]) ).
cnf(g0_7,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))),n),apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_6,t5]) ).
cnf(g0_8,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_7,t5]) ).
cnf(g0_9,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt),
inference(rw,[status(thm)],[g0_8,t15]) ).
cnf(g0_10,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,fixed_pt)),
inference(rw,[status(thm)],[g0_9,t5]) ).
cnf(g0_11,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_10,t5]) ).
cnf(g0_12,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n)),apply(b,apply(b,fixed_pt))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_11,t6]) ).
cnf(g0_13,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_12,t5]) ).
cnf(g0_14,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(apply(apply(apply(b,b),n),apply(b,apply(b,fixed_pt))),n),apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_13,t6]) ).
cnf(g0_15,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(apply(b,apply(n,apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_14,t5]) ).
cnf(g0_16,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_15,t5]) ).
cnf(g0_17,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_16,t5]) ).
cnf(g0_18,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(b,apply(b,fixed_pt)),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_17,t6]) ).
cnf(g0_19,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,fixed_pt),apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(rw,[status(thm)],[g0_18,t5]) ).
cnf(g0_20,plain,
apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))),
inference(rw,[status(thm)],[g0_19,t5]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/15.39 % Computer : n006.cluster.edu
% 0.09/15.39 % Model : x86_64 x86_64
% 0.09/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.39 % Memory : 8046.5625MB
% 0.09/15.39 % OS : Linux 6.8.0-71-generic
% 0.09/15.39 % CPULimit : 300
% 0.09/15.39 % WCLimit : 300
% 0.09/15.39 % DateTime : Fri Sep 25 07:20:13 UTC 2026
% 0.09/15.39 % CPUTime :
% 0.09/15.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.05/16.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.05/16.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------