%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL003-19 : 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 : n009.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 06:57:20 AM UTC 2026
% Result : Unsatisfiable 66.79s 10.16s
% Output : CNFRefutation 66.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 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 : 27 ( 0 sgn 5 !; 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(w_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(w,VAR_0),VAR_1) = apply(apply(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',w_definition) ).
cnf(c_2,plain,
apply(apply(w,A),B) = apply(apply(A,B),B),
inference(clausify,[status(thm)],[w_definition]) ).
fof(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c_3,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),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_14876,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_14877,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,fixed_pt)) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_14876]) ).
cnf(c_14878,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_14877]) ).
cnf(c_14879,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_14878]) ).
cnf(c_14880,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),fixed_pt)),
inference(paramod,[status(thm)],[c_3,c_14879]) ).
cnf(c_14881,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_14880]) ).
cnf(c_14882,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_1,c_14881]) ).
cnf(c_14883,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_14882]) ).
cnf(c_5,plain,
apply(fixed_pt,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_14883]) ).
cnf(c_9,plain,
apply(apply(w,apply(apply(b,A),B)),C) = apply(apply(A,apply(B,C)),C),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_11,plain,
apply(apply(w,w),A) = apply(apply(A,A),A),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_14884,plain,
apply(apply(w,w),apply(apply(b,A),B)) = apply(apply(A,apply(B,apply(apply(b,A),B))),apply(apply(b,A),B)),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_34,plain,
apply(apply(A,apply(B,apply(apply(b,A),B))),apply(apply(b,A),B)) = apply(apply(w,w),apply(apply(b,A),B)),
inference(copy,[status(thm)],[c_14884]) ).
cnf(c_100,plain,
apply(apply(w,apply(apply(b,apply(b,A)),B)),C) = apply(A,apply(apply(B,C),C)),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_4250,plain,
apply(apply(w,apply(apply(b,apply(b,A)),B)),C) = apply(A,apply(apply(w,B),C)),
inference(paramod,[status(thm)],[c_2,c_100]) ).
cnf(c_14885,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A)))) = apply(A,apply(apply(w,apply(apply(b,w),apply(b,apply(b,A)))),apply(apply(b,w),apply(b,apply(b,A))))),
inference(paramod,[status(thm)],[c_34,c_4250]) ).
cnf(c_14886,plain,
apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A)))) = apply(A,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A))))),
inference(paramod,[status(thm)],[c_2,c_14885]) ).
cnf(c_14874,plain,
apply(A,apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A))))) = apply(apply(w,w),apply(apply(b,w),apply(b,apply(b,A)))),
inference(copy,[status(thm)],[c_14886]) ).
cnf(c_14875,plain,
$false,
inference(resolve,[status(thm)],[c_14874,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-19 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 23:03:29 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 1360908 was started by sandbox2 on n009,
% 0.10/0.37 % Sat Sep 26 23:03:29 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).
% 66.79/10.16
% 66.79/10.16 % SZS status Unsatisfiable for theBenchmark
% 66.79/10.16
% 66.79/10.16 % Proof 1 at 8.57 (+ 1.13) seconds.
% 66.79/10.16 % Length of proof is 12.
% 66.79/10.16 % Level of proof is 5.
% 66.79/10.16 % Maximum clause weight is 29.000.
% 66.79/10.16 % Given clauses 101.
% 66.79/10.16
% 66.79/10.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------