%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 08:16:15 AM UTC 2026
% Result : Unsatisfiable 0.23s 10.57s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 49 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 18 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inductive1,axiom,
! [VAR_0] :
( member(null_class,VAR_0)
| ~ inductive(VAR_0) ),
file('theBenchmark.p',inductive1) ).
cnf(c_3,plain,
( member(null_class,A)
| ~ inductive(A) ),
inference(clausify,[status(thm)],[inductive1]) ).
fof(omega_is_inductive1,axiom,
inductive(omega),
file('theBenchmark.p',omega_is_inductive1) ).
cnf(c_4,plain,
inductive(omega),
inference(clausify,[status(thm)],[omega_is_inductive1]) ).
cnf(c_51,plain,
member(null_class,omega),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(prove_omega_is_not_null_1,axiom,
omega = null_class,
file('theBenchmark.p',prove_omega_is_not_null_1) ).
cnf(c_53,plain,
omega = null_class,
inference(clausify,[status(thm)],[prove_omega_is_not_null_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_129,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_130,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_129]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_179,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_182,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(equal_implies_subclass1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass1) ).
cnf(c_200,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass1]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_204,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_219,plain,
member(null_class,null_class),
inference(paramod,[status(thm)],[c_53,c_51]) ).
cnf(c_319,plain,
( member(B,A)
| ~ member(B,null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_130,c_182]) ).
cnf(c_631,plain,
( member(null_class,A)
| null_class = A ),
inference(resolve,[status(thm)],[c_319,c_219]) ).
cnf(c_649,plain,
( subclass(null_class,A)
| member(null_class,A) ),
inference(resolve,[status(thm)],[c_631,c_200]) ).
cnf(c_694,plain,
( member(B,A)
| ~ member(B,null_class)
| member(null_class,A) ),
inference(resolve,[status(thm)],[c_649,c_204]) ).
cnf(c_707,plain,
( ~ member(null_class,null_class)
| member(null_class,A) ),
inference(factor,[status(thm)],[c_694]) ).
cnf(c_695,plain,
member(null_class,A),
inference(resolve,[status(thm)],[c_219,c_707]) ).
cnf(c_708,plain,
~ member(null_class,A),
inference(resolve,[status(thm)],[c_695,c_179]) ).
cnf(c_706,plain,
$false,
inference(resolve,[status(thm)],[c_695,c_708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/10.47 % Computer : n017.cluster.edu
% 0.19/10.47 % Model : x86_64 x86_64
% 0.19/10.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.47 % Memory : 8046.5625MB
% 0.19/10.47 % OS : Linux 6.8.0-71-generic
% 0.19/10.47 % CPULimit : 300
% 0.19/10.47 % WCLimit : 300
% 0.19/10.47 % DateTime : Sat Sep 26 02:06:43 UTC 2026
% 0.19/10.48 % CPUTime :
% 0.19/10.48 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/10.48 % Process 3743346 was started by sandbox2 on n017,
% 0.19/10.48 % Sat Sep 26 02:06:43 2026
% 0.19/10.48 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/10.49
% 0.19/10.49 % From the command line: assign(max_seconds, 300).
% 0.23/10.57
% 0.23/10.57 % SZS status Unsatisfiable for theBenchmark
% 0.23/10.57
% 0.23/10.57 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.23/10.57 % Length of proof is 17.
% 0.23/10.57 % Level of proof is 7.
% 0.23/10.57 % Maximum clause weight is 24.000.
% 0.23/10.57 % Given clauses 159.
% 0.23/10.57
% 0.23/10.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------