%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL044-9 : 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 : n026.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 0.15s 5.96s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% 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 : 24 ( 24 ~; 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 : 59 ( 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(n,apply(b,b)))))),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(n,apply(b,b)))))),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_2710,plain,
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(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_2711,plain,
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(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_2710]) ).
cnf(c_2712,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(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_2711]) ).
cnf(c_2713,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(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_3,c_2712]) ).
cnf(c_2714,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(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_2713]) ).
cnf(c_2715,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(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_2714]) ).
cnf(c_5,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(copy,[status(thm)],[c_2715]) ).
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_2716,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_2716]) ).
cnf(c_15,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_5]) ).
cnf(c_2717,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_15]) ).
cnf(c_2718,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_2717]) ).
cnf(c_2719,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_2718]) ).
cnf(c_45,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_2719]) ).
cnf(c_47,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_45]) ).
cnf(c_2720,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_47]) ).
cnf(c_2721,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_2720]) ).
cnf(c_2722,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_2721]) ).
cnf(c_49,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_2722]) ).
cnf(c_127,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_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_190,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_2723,plain,
apply(apply(apply(n,apply(A,apply(B,C))),C),D) = apply(apply(apply(apply(n,apply(apply(b,A),B)),D),C),D),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_198,plain,
apply(apply(apply(apply(n,apply(apply(b,A),B)),C),D),C) = apply(apply(apply(n,apply(A,apply(B,D))),D),C),
inference(copy,[status(thm)],[c_2723]) ).
cnf(c_2724,plain,
apply(apply(apply(apply(A,B),C),B),C) = apply(apply(apply(apply(n,A),C),B),C),
inference(paramod,[status(thm)],[c_2,c_11]) ).
cnf(c_2725,plain,
apply(apply(apply(n,apply(n,A)),B),C) = apply(apply(apply(apply(n,A),C),B),C),
inference(paramod,[status(thm)],[c_11,c_2724]) ).
cnf(c_478,plain,
apply(apply(apply(apply(n,A),B),C),B) = apply(apply(apply(n,apply(n,A)),C),B),
inference(copy,[status(thm)],[c_2725]) ).
cnf(c_528,plain,
apply(apply(apply(n,apply(n,apply(apply(b,A),B))),C),D) = apply(apply(apply(n,apply(A,apply(B,C))),C),D),
inference(paramod,[status(thm)],[c_478,c_198]) ).
cnf(c_1386,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_128,c_49]) ).
cnf(c_2726,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(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)))),
inference(paramod,[status(thm)],[c_127,c_1386]) ).
cnf(c_2727,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(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_478,c_2726]) ).
cnf(c_1798,plain,
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(copy,[status(thm)],[c_2727]) ).
cnf(c_2708,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(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_190,c_1798]) ).
cnf(c_2728,plain,
apply(apply(apply(n,apply(A,apply(B,C))),C),D) = apply(apply(apply(n,apply(n,apply(apply(b,A),B))),C),D),
inference(copy,[status(thm)],[c_528]) ).
cnf(c_2709,plain,
$false,
inference(resolve,[status(thm)],[c_2708,c_2728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-9 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n026.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 23:11:33 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 2186975 was started by sandbox2 on n026,
% 0.09/5.38 % Sat Sep 26 23:11:33 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.15/5.96
% 0.15/5.96 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.96
% 0.15/5.96 % Proof 1 at 0.48 (+ 0.08) seconds.
% 0.15/5.96 % Length of proof is 22.
% 0.15/5.96 % Level of proof is 9.
% 0.15/5.96 % Maximum clause weight is 57.000.
% 0.15/5.96 % Given clauses 55.
% 0.15/5.96
% 0.15/5.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------