%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL003-2 : 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 3.53s 0.87s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 20 unt; 0 def)
% Number of atoms : 26 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 12 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 22 ( 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,w),apply(apply(b,b),b)))),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_5,plain,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b)))),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_8,plain,
apply(apply(w,apply(b,A)),B) = apply(A,apply(B,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_11,plain,
apply(apply(w,w),A) = apply(apply(A,A),A),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_521,plain,
apply(fixed_pt,apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),fixed_pt)) != apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),fixed_pt),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_522,plain,
apply(fixed_pt,apply(apply(w,w),apply(apply(apply(b,w),apply(apply(b,b),b)),fixed_pt))) != apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_521]) ).
cnf(c_523,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),fixed_pt)))) != apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_522]) ).
cnf(c_524,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(b,apply(w,w)),apply(apply(b,w),apply(apply(b,b),b))),fixed_pt),
inference(paramod,[status(thm)],[c_1,c_523]) ).
cnf(c_525,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),apply(apply(b,b),b)),fixed_pt)),
inference(paramod,[status(thm)],[c_1,c_524]) ).
cnf(c_526,plain,
apply(fixed_pt,apply(apply(w,w),apply(w,apply(b,apply(b,fixed_pt))))) != apply(apply(w,w),apply(w,apply(apply(apply(b,b),b),fixed_pt))),
inference(paramod,[status(thm)],[c_1,c_525]) ).
cnf(c_17,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(paramod,[status(thm)],[c_1,c_526]) ).
cnf(c_39,plain,
apply(apply(apply(w,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(B,B),C)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_527,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,A)))) = apply(A,apply(apply(apply(w,apply(b,apply(b,A))),apply(w,apply(b,apply(b,A)))),apply(w,apply(b,apply(b,A))))),
inference(paramod,[status(thm)],[c_39,c_11]) ).
cnf(c_528,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,A)))) = apply(A,apply(apply(w,w),apply(w,apply(b,apply(b,A))))),
inference(paramod,[status(thm)],[c_11,c_527]) ).
cnf(c_519,plain,
apply(A,apply(apply(w,w),apply(w,apply(b,apply(b,A))))) = apply(apply(w,w),apply(w,apply(b,apply(b,A)))),
inference(copy,[status(thm)],[c_528]) ).
cnf(c_520,plain,
$false,
inference(resolve,[status(thm)],[c_519,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 23:04:01 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 3319464 was started by sandbox on n005,
% 0.08/0.34 % Sat Sep 26 23:04:01 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 3.53/0.87
% 3.53/0.87 % SZS status Unsatisfiable for theBenchmark
% 3.53/0.87
% 3.53/0.87 % Proof 1 at 0.40 (+ 0.11) seconds.
% 3.53/0.87 % Length of proof is 11.
% 3.53/0.87 % Level of proof is 4.
% 3.53/0.87 % Maximum clause weight is 100.000.
% 3.53/0.87 % Given clauses 71.
% 3.53/0.87
% 3.53/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------