%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 25 ( 25 ~; 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 : 21 ( 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(apply(b,b),apply(apply(n,apply(apply(b,b),n)),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(apply(b,b),apply(apply(n,apply(apply(b,b),n)),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_262,plain,
apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),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_263,plain,
apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,fixed_pt)) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_262]) ).
cnf(c_264,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(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_263]) ).
cnf(c_265,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(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b)),b),fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_264]) ).
cnf(c_266,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(fixed_pt,apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_265]) ).
cnf(c_267,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(fixed_pt,apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_266]) ).
cnf(c_5,plain,
apply(fixed_pt,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(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt))),
inference(copy,[status(thm)],[c_267]) ).
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_268,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(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_269,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(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_268]) ).
cnf(c_270,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(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_269]) ).
cnf(c_15,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(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_270]) ).
cnf(c_271,plain,
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(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(paramod,[status(thm)],[c_2,c_15]) ).
cnf(c_272,plain,
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(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(paramod,[status(thm)],[c_1,c_271]) ).
cnf(c_273,plain,
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(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(paramod,[status(thm)],[c_1,c_272]) ).
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(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_273]) ).
cnf(c_274,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(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_2,c_45]) ).
cnf(c_275,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(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_274]) ).
cnf(c_276,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,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_275]) ).
cnf(c_48,plain,
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(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_276]) ).
cnf(c_128,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_277,plain,
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(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_2,c_48]) ).
cnf(c_278,plain,
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(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_277]) ).
cnf(c_279,plain,
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(paramod,[status(thm)],[c_1,c_278]) ).
cnf(c_260,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(copy,[status(thm)],[c_279]) ).
cnf(c_280,plain,
apply(A,apply(apply(C,B),C)) = apply(apply(apply(n,apply(b,apply(b,A))),B),C),
inference(copy,[status(thm)],[c_128]) ).
cnf(c_261,plain,
$false,
inference(resolve,[status(thm)],[c_260,c_280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 23:08:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2855602 was started by sandbox on n004,
% 0.11/0.38 % Sat Sep 26 23:08:09 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.44
% 0.11/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.44
% 0.11/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.11/0.44 % Length of proof is 12.
% 0.11/0.44 % Level of proof is 6.
% 0.11/0.44 % Maximum clause weight is 49.000.
% 0.11/0.44 % Given clauses 16.
% 0.11/0.44
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------