%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET184-6 : 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 : n013.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 08:35:59 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.62s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 34 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subclass_property2_2,axiom,
~ subclass(x,y),
file('theBenchmark.p',prove_subclass_property2_2) ).
cnf(c_36,plain,
~ subclass(x,y),
inference(clausify,[status(thm)],[prove_subclass_property2_2]) ).
fof(prove_subclass_property2_1,axiom,
intersection(x,y) = x,
file('theBenchmark.p',prove_subclass_property2_1) ).
cnf(c_37,plain,
intersection(x,y) = x,
inference(clausify,[status(thm)],[prove_subclass_property2_1]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_122,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(equal_implies_subclass2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass2) ).
cnf(c_140,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_143,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_144,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
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_145,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_303,plain,
subclass(x,intersection(x,y)),
inference(resolve,[status(thm)],[c_140,c_37]) ).
cnf(c_354,plain,
member(not_subclass_element(x,y),x),
inference(resolve,[status(thm)],[c_144,c_36]) ).
cnf(c_548,plain,
( member(A,intersection(x,y))
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_303,c_145]) ).
cnf(c_1311,plain,
member(not_subclass_element(x,y),intersection(x,y)),
inference(resolve,[status(thm)],[c_548,c_354]) ).
cnf(c_1321,plain,
member(not_subclass_element(x,y),y),
inference(resolve,[status(thm)],[c_1311,c_122]) ).
cnf(c_1327,plain,
subclass(x,y),
inference(resolve,[status(thm)],[c_1321,c_143]) ).
cnf(c_1326,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_1327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET184-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.53 % Computer : n013.cluster.edu
% 0.08/0.53 % Model : x86_64 x86_64
% 0.08/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.53 % Memory : 8046.5625MB
% 0.08/0.53 % OS : Linux 6.8.0-71-generic
% 0.08/0.53 % CPULimit : 300
% 0.08/0.53 % WCLimit : 300
% 0.08/0.53 % DateTime : Sat Sep 26 07:17:36 UTC 2026
% 0.08/0.54 % CPUTime :
% 0.08/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.54 % Process 2195720 was started by sandbox2 on n013,
% 0.08/0.54 % Sat Sep 26 07:17:36 2026
% 0.08/0.54 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.54
% 0.08/0.54 % From the command line: assign(max_seconds, 300).
% 0.13/0.62
% 0.13/0.62 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.62
% 0.13/0.62 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.13/0.62 % Length of proof is 13.
% 0.13/0.62 % Level of proof is 5.
% 0.13/0.62 % Maximum clause weight is 18.000.
% 0.13/0.62 % Given clauses 233.
% 0.13/0.62
% 0.13/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------