%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 : Sun Sep 27 06:57:29 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 36 ( 36 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 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 : 18 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(b,VAR_0),VAR_1),VAR_2) = apply(VAR_0,apply(VAR_1,VAR_2)),
file('theBenchmark.p',b_definition) ).
cnf(c_1,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(h_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(h,VAR_0),VAR_1),VAR_2) = apply(apply(apply(VAR_0,VAR_1),VAR_2),VAR_1),
file('theBenchmark.p',h_definition) ).
cnf(c_2,plain,
apply(apply(apply(h,A),B),C) = apply(apply(apply(A,B),C),B),
inference(clausify,[status(thm)],[h_definition]) ).
fof(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
inference(clausify,[status(thm)],[strong_fixed_point]) ).
fof(prove_strong_fixed_point,axiom,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_4,plain,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_253,plain,
apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_254,plain,
apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt)) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_253]) ).
cnf(c_255,plain,
apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_254]) ).
cnf(c_256,plain,
apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_255]) ).
cnf(c_257,plain,
apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b),apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_256]) ).
cnf(c_258,plain,
apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_257]) ).
cnf(c_5,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_9,plain,
apply(apply(apply(h,apply(b,A)),B),C) = apply(apply(A,apply(B,C)),B),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_259,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b)))),h),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_260,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_259]) ).
cnf(c_15,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_260]) ).
cnf(c_261,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b)))),h),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_262,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(apply(apply(b,h),apply(b,b)),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_261]) ).
cnf(c_43,plain,
apply(fixed_pt,apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h)) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_262]) ).
cnf(c_263,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_2,c_43]) ).
cnf(c_264,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_263]) ).
cnf(c_265,plain,
apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h),
inference(paramod,[status(thm)],[c_1,c_264]) ).
cnf(c_44,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_265]) ).
cnf(c_266,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(apply(apply(b,h),apply(b,b)),h),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_44]) ).
cnf(c_47,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,fixed_pt))),h) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_266]) ).
cnf(c_267,plain,
apply(apply(apply(apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h)),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_47]) ).
cnf(c_268,plain,
apply(apply(apply(b,apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_267]) ).
cnf(c_48,plain,
apply(apply(apply(apply(h,apply(apply(b,h),apply(b,b))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_268]) ).
cnf(c_269,plain,
apply(apply(apply(apply(apply(apply(b,h),apply(b,b)),h),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_48]) ).
cnf(c_270,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_269]) ).
cnf(c_214,plain,
apply(fixed_pt,apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(apply(b,b),h),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_2,c_214]) ).
cnf(c_272,plain,
apply(fixed_pt,apply(apply(apply(apply(b,apply(h,apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_271]) ).
cnf(c_273,plain,
apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_272]) ).
cnf(c_216,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,fixed_pt))),h),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_273]) ).
cnf(c_274,plain,
apply(apply(apply(apply(apply(apply(b,b),h),apply(b,apply(b,fixed_pt))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_2,c_216]) ).
cnf(c_275,plain,
apply(apply(apply(apply(b,apply(h,apply(b,apply(b,fixed_pt)))),h),apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_274]) ).
cnf(c_276,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_275]) ).
cnf(c_219,plain,
apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_276]) ).
cnf(c_251,plain,
apply(apply(apply(h,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(B,C),B)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_277,plain,
apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(h,apply(b,apply(b,fixed_pt))),apply(h,apply(b,apply(b,fixed_pt)))),apply(h,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_219]) ).
cnf(c_252,plain,
$false,
inference(resolve,[status(thm)],[c_251,c_277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL043-3 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 23:06:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 722046 was started by sandbox on n007,
% 0.08/0.36 % Sat Sep 26 23:06:10 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 16.
% 0.13/0.42 % Level of proof is 10.
% 0.13/0.42 % Maximum clause weight is 61.000.
% 0.13/0.42 % Given clauses 20.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------