%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL044-5 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 06:57:30 AM UTC 2026
% Result : Unsatisfiable 27.32s 7.78s
% Output : CNFRefutation 27.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 36 unt; 0 def)
% Number of atoms : 42 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 23 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 7 !; 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(n_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(n,VAR_0),VAR_1),VAR_2) = apply(apply(apply(VAR_0,VAR_2),VAR_1),VAR_2),
file('theBenchmark.p',n_definition) ).
cnf(c_2,plain,
apply(apply(apply(n,A),B),C) = apply(apply(apply(A,C),B),C),
inference(clausify,[status(thm)],[n_definition]) ).
fof(strong_fixed_point,axiom,
! [VAR_0] :
( fixed_point(VAR_0)
| apply(VAR_0,fixed_pt) != apply(fixed_pt,apply(VAR_0,fixed_pt)) ),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
( fixed_point(A)
| apply(A,fixed_pt) != apply(fixed_pt,apply(A,fixed_pt)) ),
inference(clausify,[status(thm)],[strong_fixed_point]) ).
cnf(c_4,plain,
( fixed_point(A)
| apply(fixed_pt,apply(A,fixed_pt)) != apply(A,fixed_pt) ),
inference(copy,[status(thm)],[c_3]) ).
fof(prove_strong_fixed_point,axiom,
~ fixed_point(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)),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_5,plain,
~ fixed_point(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)),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_8,plain,
apply(apply(apply(n,apply(apply(b,A),B)),C),D) = apply(apply(apply(A,apply(B,D)),C),D),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
apply(apply(apply(n,apply(b,A)),B),C) = apply(apply(A,apply(C,B)),C),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_10090,plain,
apply(apply(apply(n,apply(n,A)),B),C) = apply(apply(apply(apply(A,B),C),B),C),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_11,plain,
apply(apply(apply(apply(A,B),C),B),C) = apply(apply(apply(n,apply(n,A)),B),C),
inference(copy,[status(thm)],[c_10090]) ).
cnf(c_10091,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(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(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_10092,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(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(paramod,[status(thm)],[c_1,c_10091]) ).
cnf(c_10093,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(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(paramod,[status(thm)],[c_1,c_10092]) ).
cnf(c_10094,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(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(paramod,[status(thm)],[c_1,c_10093]) ).
cnf(c_20,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(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(paramod,[status(thm)],[c_1,c_10094]) ).
cnf(c_49,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(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(paramod,[status(thm)],[c_2,c_20]) ).
cnf(c_10095,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(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(paramod,[status(thm)],[c_2,c_49]) ).
cnf(c_10096,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(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(paramod,[status(thm)],[c_1,c_10095]) ).
cnf(c_10097,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(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(paramod,[status(thm)],[c_1,c_10096]) ).
cnf(c_51,plain,
apply(fixed_pt,apply(apply(apply(apply(n,apply(n,apply(b,b))),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(paramod,[status(thm)],[c_1,c_10097]) ).
cnf(c_53,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(n,apply(b,b)),apply(b,apply(b,fixed_pt))),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(paramod,[status(thm)],[c_2,c_51]) ).
cnf(c_10098,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(apply(b,b),n),apply(b,apply(b,fixed_pt))),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(paramod,[status(thm)],[c_2,c_53]) ).
cnf(c_10099,plain,
apply(fixed_pt,apply(apply(apply(apply(b,apply(n,apply(b,apply(b,fixed_pt)))),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(paramod,[status(thm)],[c_1,c_10098]) ).
cnf(c_10100,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(paramod,[status(thm)],[c_1,c_10099]) ).
cnf(c_55,plain,
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(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(copy,[status(thm)],[c_10100]) ).
cnf(c_147,plain,
apply(apply(apply(n,apply(apply(b,b),A)),B),C) = apply(apply(A,C),apply(B,C)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_223,plain,
apply(apply(apply(apply(n,apply(b,b)),A),B),C) = apply(apply(B,A),apply(B,C)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_224,plain,
apply(apply(apply(n,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(C,B),C)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_10101,plain,
apply(apply(apply(n,apply(A,B)),B),C) = apply(apply(apply(n,apply(n,A)),B),C),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_621,plain,
apply(apply(apply(n,apply(n,A)),B),C) = apply(apply(apply(n,apply(A,B)),B),C),
inference(copy,[status(thm)],[c_10101]) ).
cnf(c_1537,plain,
apply(apply(apply(n,apply(n,apply(b,b))),A),B) = apply(apply(A,B),apply(A,B)),
inference(paramod,[status(thm)],[c_223,c_2]) ).
cnf(c_1806,plain,
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(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(paramod,[status(thm)],[c_224,c_55]) ).
cnf(c_5091,plain,
apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),A))),B),C) = apply(apply(apply(A,C),apply(A,C)),apply(B,C)),
inference(paramod,[status(thm)],[c_1537,c_147]) ).
cnf(c_10102,plain,
apply(apply(apply(n,apply(apply(apply(b,apply(b,b)),apply(n,apply(n,apply(b,b)))),n)),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(paramod,[status(thm)],[c_621,c_1806]) ).
cnf(c_10088,plain,
apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),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(paramod,[status(thm)],[c_1,c_10102]) ).
cnf(c_10089,plain,
$false,
inference(resolve,[status(thm)],[c_10088,c_5091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL044-5 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.40 % Computer : n002.cluster.edu
% 0.09/0.40 % Model : x86_64 x86_64
% 0.09/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.40 % Memory : 8046.5625MB
% 0.09/0.40 % OS : Linux 6.8.0-71-generic
% 0.09/0.40 % CPULimit : 300
% 0.09/0.40 % WCLimit : 300
% 0.09/0.40 % DateTime : Sat Sep 26 23:11:06 UTC 2026
% 0.09/0.40 % CPUTime :
% 0.09/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.40 % Process 2916337 was started by sandbox on n002,
% 0.09/0.40 % Sat Sep 26 23:11:06 2026
% 0.09/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 27.32/7.78
% 27.32/7.78 % SZS status Unsatisfiable for theBenchmark
% 27.32/7.78
% 27.32/7.78 % Proof 1 at 3.06 (+ 0.41) seconds.
% 27.32/7.78 % Length of proof is 22.
% 27.32/7.78 % Level of proof is 9.
% 27.32/7.78 % Maximum clause weight is 57.000.
% 27.32/7.78 % Given clauses 152.
% 27.32/7.78
% 27.32/7.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------