%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 01:01:52 PM UTC 2026
% Result : Unsatisfiable 4.12s 1.12s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 31 RR)
% Number of literals : 35 ( 34 equ; 28 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(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),b) = strong_fixed_point,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),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/sandbox/benchmark/theBenchmark.p') ).
cnf(t3,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/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,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/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),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(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b),apply(b,fixed_pt))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_0,t3]) ).
cnf(g0_2,plain,
apply(fixed_pt,apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n),apply(b,apply(b,fixed_pt)))) != apply(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_1,t3]) ).
cnf(g0_3,plain,
apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b))))),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,t4]) ).
cnf(g0_4,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))),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,t4]) ).
cnf(g0_5,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),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,t3]) ).
cnf(g0_6,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(apply(n,apply(n,apply(b,b))),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,t3]) ).
cnf(g0_7,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(apply(apply(n,apply(b,b)),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_6,t4]) ).
cnf(g0_8,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_7,t4]) ).
cnf(g0_9,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_8,t3]) ).
cnf(g0_10,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_9,t3]) ).
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(strong_fixed_point,fixed_pt),
inference(rw,[status(thm)],[g0_10,t3]) ).
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(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b)),b),fixed_pt),
inference(rw,[status(thm)],[g0_11,t13]) ).
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(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n)),b),apply(b,fixed_pt)),
inference(rw,[status(thm)],[g0_12,t3]) ).
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(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_13,t3]) ).
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(apply(n,apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b))))),apply(b,apply(b,fixed_pt))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_14,t4]) ).
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(apply(apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))),n),apply(b,apply(b,fixed_pt))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_15,t4]) ).
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(apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n)),apply(b,apply(b,fixed_pt))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_16,t3]) ).
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(b,apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt)))),n),apply(b,apply(b,fixed_pt))),
inference(rw,[status(thm)],[g0_17,t3]) ).
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,apply(apply(apply(apply(n,apply(b,b)),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_18,t4]) ).
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(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_19,t4]) ).
cnf(g0_21,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_20,t3]) ).
cnf(g0_22,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_21,t3]) ).
cnf(g0_23,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_22,t3]) ).
cnf(g0_24,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_23,t4]) ).
cnf(g0_25,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_24,t3]) ).
cnf(g0_26,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_25,t3]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 07:23:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.12/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.12/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------