%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL044-4 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 06:57:30 AM UTC 2026
% Result : Unsatisfiable 210.65s 28.17s
% Output : CNFRefutation 210.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 33 unt; 0 def)
% Number of atoms : 39 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 19 ~; 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 : 54 ( 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(apply(b,b),n))))),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(apply(b,b),n))))),n)),b)),b)),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_9,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_10,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_6558,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_12,plain,
apply(apply(apply(apply(A,B),C),B),C) = apply(apply(apply(n,apply(n,A)),B),C),
inference(copy,[status(thm)],[c_6558]) ).
cnf(c_6559,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(apply(b,b),n))))),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(apply(b,b),n))))),n)),b)),b),fixed_pt),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_6560,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),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(apply(b,b),n))))),n)),b)),b),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_6559]) ).
cnf(c_6561,plain,
apply(fixed_pt,apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),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(apply(b,b),n))))),n)),b)),b),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_6560]) ).
cnf(c_6562,plain,
apply(fixed_pt,apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),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(apply(b,b),n))))),n)),b),apply(b,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_6561]) ).
cnf(c_16,plain,
apply(fixed_pt,apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_6562]) ).
cnf(c_115,plain,
apply(apply(apply(n,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(C,B),C)),
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_267,plain,
apply(apply(apply(n,apply(apply(b,b),A)),B),C) = apply(apply(A,C),apply(B,C)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_6563,plain,
apply(apply(apply(n,apply(A,B)),B),C) = apply(apply(apply(n,apply(n,A)),B),C),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_497,plain,
apply(apply(apply(n,apply(n,A)),B),C) = apply(apply(apply(n,apply(A,B)),B),C),
inference(copy,[status(thm)],[c_6563]) ).
cnf(c_6564,plain,
apply(fixed_pt,apply(apply(apply(apply(apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))),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(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_12,c_16]) ).
cnf(c_6565,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(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_6564]) ).
cnf(c_6566,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(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_6565]) ).
cnf(c_6567,plain,
apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,b),n)),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(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_6566]) ).
cnf(c_520,plain,
apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_6567]) ).
cnf(c_6568,plain,
apply(apply(apply(n,apply(b,apply(b,A))),apply(B,C)),apply(D,C)) = apply(A,apply(apply(apply(apply(n,apply(apply(b,b),D)),B),C),apply(D,C))),
inference(paramod,[status(thm)],[c_267,c_115]) ).
cnf(c_3668,plain,
apply(A,apply(apply(apply(apply(n,apply(apply(b,b),B)),C),D),apply(B,D))) = apply(apply(apply(n,apply(b,apply(b,A))),apply(C,D)),apply(B,D)),
inference(copy,[status(thm)],[c_6568]) ).
cnf(c_3714,plain,
apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),A)),B))),C),D) = apply(apply(apply(A,D),apply(B,D)),apply(C,D)),
inference(paramod,[status(thm)],[c_267,c_267]) ).
cnf(c_3724,plain,
apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(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_3668,c_520]) ).
cnf(c_4887,plain,
apply(apply(apply(apply(n,apply(b,n)),A),n),B) = apply(apply(apply(n,apply(A,n)),n),B),
inference(paramod,[status(thm)],[c_10,c_497]) ).
cnf(c_6569,plain,
apply(apply(apply(apply(n,apply(b,n)),apply(apply(b,apply(b,b)),apply(n,apply(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_10,c_3724]) ).
cnf(c_6570,plain,
apply(apply(apply(n,apply(apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))),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_4887,c_6569]) ).
cnf(c_6571,plain,
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(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_6570]) ).
cnf(c_6557,plain,
$false,
inference(resolve,[status(thm)],[c_3714,c_6571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-4 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 23:06:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 722842 was started by sandbox2 on n007,
% 0.10/0.37 % Sat Sep 26 23:06:24 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 210.65/28.17
% 210.65/28.17 % SZS status Unsatisfiable for theBenchmark
% 210.65/28.17
% 210.65/28.17 % Proof 1 at 2.98 (+ 0.64) seconds.
% 210.65/28.17 % Length of proof is 18.
% 210.65/28.17 % Level of proof is 5.
% 210.65/28.17 % Maximum clause weight is 53.000.
% 210.65/28.17 % Given clauses 89.
% 210.65/28.17
% 210.65/28.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------