%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 1.70s 0.62s
% Output : CNFRefutation 1.70s
% 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(apply(b,apply(w,w)),apply(apply(b,w),b))),b)),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_5,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b)),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_7,plain,
apply(apply(apply(b,apply(apply(b,A),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_18,plain,
apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt)) != apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_3428,plain,
apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,fixed_pt)))) != apply(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),fixed_pt),
inference(paramod,[status(thm)],[c_7,c_18]) ).
cnf(c_111,plain,
apply(apply(apply(b,apply(apply(b,apply(w,w)),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_3428]) ).
cnf(c_3429,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_7,c_111]) ).
cnf(c_116,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_3429]) ).
cnf(c_3430,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_116]) ).
cnf(c_117,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_3430]) ).
cnf(c_3431,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_117]) ).
cnf(c_121,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_3431]) ).
cnf(c_127,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_3432,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_121]) ).
cnf(c_621,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_3432]) ).
cnf(c_3426,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_127]) ).
cnf(c_3427,plain,
$false,
inference(resolve,[status(thm)],[c_3426,c_621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 23:03:46 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3319090 was started by sandbox on n005,
% 0.07/0.35 % Sat Sep 26 23:03:46 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 1.70/0.62
% 1.70/0.62 % SZS status Unsatisfiable for theBenchmark
% 1.70/0.62
% 1.70/0.62 % Proof 1 at 0.21 (+ 0.05) seconds.
% 1.70/0.62 % Length of proof is 17.
% 1.70/0.62 % Level of proof is 8.
% 1.70/0.62 % Maximum clause weight is 77.000.
% 1.70/0.62 % Given clauses 54.
% 1.70/0.62
% 1.70/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------