%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL003-3 : TPTP v9.3.1. Released v1.0.0.
% 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 06:57:21 AM UTC 2026
% Result : Unsatisfiable 4.08s 0.97s
% Output : CNFRefutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 23 unt; 0 def)
% Number of atoms : 29 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 16 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 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 : 24 ( 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(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,
! [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(w,w)),apply(apply(b,apply(apply(b,w),b)),b))),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_5,plain,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_6,plain,
apply(apply(apply(b,A),apply(apply(b,B),C)),D) = apply(A,apply(B,apply(C,D))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
apply(apply(w,apply(b,A)),B) = apply(A,apply(B,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_16,plain,
apply(apply(w,w),A) = apply(apply(A,A),A),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_24,plain,
apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),fixed_pt)) != apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),fixed_pt),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_2732,plain,
apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))) != apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),fixed_pt),
inference(paramod,[status(thm)],[c_6,c_24]) ).
cnf(c_70,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),fixed_pt) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_2732]) ).
cnf(c_2733,plain,
apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_6,c_70]) ).
cnf(c_75,plain,
apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))) != apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(copy,[status(thm)],[c_2733]) ).
cnf(c_2734,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_75]) ).
cnf(c_76,plain,
apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_2734]) ).
cnf(c_2735,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))),
inference(paramod,[status(thm)],[c_1,c_76]) ).
cnf(c_80,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt)))),
inference(copy,[status(thm)],[c_2735]) ).
cnf(c_87,plain,
apply(apply(apply(b,A),apply(B,B)),B) = apply(A,apply(apply(w,w),B)),
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_2736,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))),
inference(paramod,[status(thm)],[c_16,c_80]) ).
cnf(c_788,plain,
apply(apply(apply(w,apply(b,apply(b,fixed_pt))),apply(w,apply(b,apply(b,fixed_pt)))),apply(w,apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))),
inference(copy,[status(thm)],[c_2736]) ).
cnf(c_2730,plain,
apply(apply(apply(w,apply(b,apply(b,A))),B),B) = apply(A,apply(apply(w,w),B)),
inference(paramod,[status(thm)],[c_11,c_87]) ).
cnf(c_2731,plain,
$false,
inference(resolve,[status(thm)],[c_2730,c_788]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 23:06:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2169974 was started by sandbox2 on n026,
% 0.08/0.37 % Sat Sep 26 23:06:42 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 4.08/0.97
% 4.08/0.97 % SZS status Unsatisfiable for theBenchmark
% 4.08/0.97
% 4.08/0.97 % Proof 1 at 0.47 (+ 0.12) seconds.
% 4.08/0.97 % Length of proof is 17.
% 4.08/0.97 % Level of proof is 8.
% 4.08/0.97 % Maximum clause weight is 77.000.
% 4.08/0.97 % Given clauses 63.
% 4.08/0.97
% 4.08/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------