%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET067-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:35:36 AM UTC 2026
% Result : Unsatisfiable 25.79s 3.76s
% Output : CNFRefutation 25.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 19 unt; 0 def)
% Number of atoms : 59 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 21 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 7 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_in_unordered_pair1_1,axiom,
~ subclass(singleton(x),unordered_pair(x,y)),
file('theBenchmark.p',prove_singleton_in_unordered_pair1_1) ).
cnf(c_33,plain,
~ subclass(singleton(x),unordered_pair(x,y)),
inference(clausify,[status(thm)],[prove_singleton_in_unordered_pair1_1]) ).
fof(null_class_is_subclass,axiom,
! [VAR_0] : subclass(null_class,VAR_0),
file('theBenchmark.p',null_class_is_subclass) ).
cnf(c_40,plain,
subclass(null_class,A),
inference(clausify,[status(thm)],[null_class_is_subclass]) ).
fof(transitivity_of_subclass,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subclass(VAR_0,VAR_2)
| ~ subclass(VAR_1,VAR_2)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_subclass) ).
cnf(c_47,plain,
( subclass(A,C)
| ~ subclass(B,C)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_subclass]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_126,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_127,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_126]) ).
fof(unordered_pair2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_0,VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair2) ).
cnf(c_130,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_131,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_135,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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_136,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_137,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_138,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_217,plain,
~ subclass(unordered_pair(x,x),unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_127,c_33]) ).
cnf(c_218,plain,
( A = B
| ~ member(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_131]) ).
cnf(c_220,plain,
( subclass(A,B)
| ~ subclass(A,null_class) ),
inference(resolve,[status(thm)],[c_47,c_40]) ).
cnf(c_300,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_138,c_135]) ).
cnf(c_461,plain,
member(not_subclass_element(unordered_pair(x,x),unordered_pair(x,y)),unordered_pair(x,x)),
inference(resolve,[status(thm)],[c_217,c_137]) ).
cnf(c_487,plain,
( member(not_subclass_element(A,null_class),A)
| subclass(A,B) ),
inference(resolve,[status(thm)],[c_220,c_137]) ).
cnf(c_1039,plain,
member(not_subclass_element(unordered_pair(x,x),null_class),unordered_pair(x,x)),
inference(resolve,[status(thm)],[c_487,c_217]) ).
cnf(c_3356,plain,
member(not_subclass_element(unordered_pair(x,x),null_class),universal_class),
inference(resolve,[status(thm)],[c_1039,c_300]) ).
cnf(c_3359,plain,
not_subclass_element(unordered_pair(x,x),null_class) = x,
inference(resolve,[status(thm)],[c_1039,c_218]) ).
cnf(c_3368,plain,
member(x,universal_class),
inference(paramod,[status(thm)],[c_3359,c_3356]) ).
cnf(c_3380,plain,
member(x,unordered_pair(x,A)),
inference(resolve,[status(thm)],[c_3368,c_130]) ).
cnf(c_11438,plain,
not_subclass_element(unordered_pair(x,x),unordered_pair(x,y)) = x,
inference(resolve,[status(thm)],[c_461,c_218]) ).
cnf(c_11813,plain,
( subclass(unordered_pair(x,x),unordered_pair(x,y))
| ~ member(x,unordered_pair(x,y)) ),
inference(paramod,[status(thm)],[c_11438,c_136]) ).
cnf(c_11814,plain,
subclass(unordered_pair(x,x),unordered_pair(x,y)),
inference(resolve,[status(thm)],[c_3380,c_11813]) ).
cnf(c_11812,plain,
$false,
inference(resolve,[status(thm)],[c_217,c_11814]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET067-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 07:05:28 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3390241 was started by sandbox on n015,
% 0.18/0.44 % Sat Sep 26 07:05:28 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 25.79/3.76
% 25.79/3.76 % given #500 (T,wt=9): 3907 subset_relation = null_class | member(regular(subset_relation),intersection(subset_relation,subset_relation)). [resolve(3903,b,249,a),flip(c),merge(c)].
% 25.79/3.76
% 25.79/3.76 % SZS status Unsatisfiable for theBenchmark
% 25.79/3.76
% 25.79/3.76 % Proof 1 at 2.61 (+ 0.64) seconds.
% 25.79/3.76 % Length of proof is 24.
% 25.79/3.76 % Level of proof is 7.
% 25.79/3.76 % Maximum clause weight is 11.000.
% 25.79/3.76 % Given clauses 789.
% 25.79/3.76
% 25.79/3.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------