%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL044-8 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 5.83s 1.12s
% Output : CNFRefutation 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 37 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 21 ( 21 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 41 ( 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(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,
strong_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',strong_fixed_point) ).
cnf(c_3,plain,
strong_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)],[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_4356,plain,
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(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_4357,plain,
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(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_4356]) ).
cnf(c_4358,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(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_4357]) ).
cnf(c_4359,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(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_3,c_4358]) ).
cnf(c_4360,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(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_4359]) ).
cnf(c_4361,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(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_4360]) ).
cnf(c_5,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(copy,[status(thm)],[c_4361]) ).
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_4362,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_4362]) ).
cnf(c_15,plain,
apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,apply(b,b)),apply(n,apply(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(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_4363,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_2,c_15]) ).
cnf(c_4364,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_4363]) ).
cnf(c_4365,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_4364]) ).
cnf(c_45,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_4365]) ).
cnf(c_4366,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(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_2,c_45]) ).
cnf(c_4367,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(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_4366]) ).
cnf(c_4368,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(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_4367]) ).
cnf(c_47,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(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_4368]) ).
cnf(c_137,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_198,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_4369,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_482,plain,
apply(apply(apply(n,apply(n,A)),B),C) = apply(apply(apply(n,apply(A,B)),B),C),
inference(copy,[status(thm)],[c_4369]) ).
cnf(c_1398,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_137,c_47]) ).
cnf(c_2770,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_198,c_198]) ).
cnf(c_4370,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_482,c_1398]) ).
cnf(c_4354,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_4370]) ).
cnf(c_4355,plain,
$false,
inference(resolve,[status(thm)],[c_4354,c_2770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-8 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 26 23:09:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2752784 was started by sandbox2 on n020,
% 0.11/0.36 % Sat Sep 26 23:09:35 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 5.83/1.12
% 5.83/1.12 % SZS status Unsatisfiable for theBenchmark
% 5.83/1.12
% 5.83/1.12 % Proof 1 at 0.63 (+ 0.11) seconds.
% 5.83/1.12 % Length of proof is 18.
% 5.83/1.12 % Level of proof is 7.
% 5.83/1.12 % Maximum clause weight is 57.000.
% 5.83/1.12 % Given clauses 73.
% 5.83/1.12
% 5.83/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------