%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET123-6 : 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 : n009.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 08:35:51 AM UTC 2026
% Result : Unsatisfiable 67.70s 9.07s
% Output : CNFRefutation 67.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 30 unt; 0 def)
% Number of atoms : 66 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 29 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_set_builder_alternate_defn1_3,axiom,
~ member(x,z),
file('theBenchmark.p',prove_set_builder_alternate_defn1_3) ).
cnf(c_34,plain,
~ member(x,z),
inference(clausify,[status(thm)],[prove_set_builder_alternate_defn1_3]) ).
fof(prove_set_builder_alternate_defn1_2,axiom,
x != y,
file('theBenchmark.p',prove_set_builder_alternate_defn1_2) ).
cnf(c_35,plain,
x != y,
inference(clausify,[status(thm)],[prove_set_builder_alternate_defn1_2]) ).
cnf(c_36,plain,
y != x,
inference(copy,[status(thm)],[c_35]) ).
fof(prove_set_builder_alternate_defn1_1,axiom,
member(x,set_builder(y,z)),
file('theBenchmark.p',prove_set_builder_alternate_defn1_1) ).
cnf(c_37,plain,
member(x,set_builder(y,z)),
inference(clausify,[status(thm)],[prove_set_builder_alternate_defn1_1]) ).
fof(definition_of_set_builder,axiom,
! [VAR_0,VAR_1] : union(singleton(VAR_0),VAR_1) = set_builder(VAR_0,VAR_1),
file('theBenchmark.p',definition_of_set_builder) ).
cnf(c_38,plain,
union(singleton(A),B) = set_builder(A,B),
inference(clausify,[status(thm)],[definition_of_set_builder]) ).
cnf(c_39,plain,
set_builder(A,B) = union(singleton(A),B),
inference(copy,[status(thm)],[c_38]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : complement(intersection(complement(VAR_0),complement(VAR_1))) = union(VAR_0,VAR_1),
file('theBenchmark.p',union) ).
cnf(c_97,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_98,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_97]) ).
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| member(VAR_0,complement(VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',complement2) ).
cnf(c_99,plain,
( member(A,B)
| member(A,complement(B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_100,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_101,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_113,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_114,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_113]) ).
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_118,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_122,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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_125,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_3058,plain,
member(x,union(singleton(y),z)),
inference(paramod,[status(thm)],[c_39,c_37]) ).
cnf(c_3059,plain,
member(x,union(unordered_pair(y,y),z)),
inference(paramod,[status(thm)],[c_114,c_3058]) ).
cnf(c_159,plain,
member(x,complement(intersection(complement(unordered_pair(y,y)),complement(z)))),
inference(paramod,[status(thm)],[c_98,c_3059]) ).
cnf(c_3060,plain,
x != y,
inference(copy,[status(thm)],[c_36]) ).
cnf(c_3061,plain,
( x = A
| ~ member(x,unordered_pair(y,A)) ),
inference(resolve,[status(thm)],[c_118,c_3060]) ).
cnf(c_3062,plain,
x != y,
inference(copy,[status(thm)],[c_36]) ).
cnf(c_232,plain,
~ member(x,unordered_pair(y,y)),
inference(resolve,[status(thm)],[c_3061,c_3062]) ).
cnf(c_268,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_125,c_122]) ).
cnf(c_295,plain,
~ member(x,intersection(complement(unordered_pair(y,y)),complement(z))),
inference(resolve,[status(thm)],[c_159,c_100]) ).
cnf(c_400,plain,
member(x,universal_class),
inference(resolve,[status(thm)],[c_268,c_159]) ).
cnf(c_418,plain,
( member(x,A)
| member(x,complement(A)) ),
inference(resolve,[status(thm)],[c_400,c_99]) ).
cnf(c_1247,plain,
member(x,complement(unordered_pair(y,y))),
inference(resolve,[status(thm)],[c_418,c_232]) ).
cnf(c_1263,plain,
member(x,complement(z)),
inference(resolve,[status(thm)],[c_418,c_34]) ).
cnf(c_3063,plain,
( member(x,intersection(A,complement(z)))
| ~ member(x,A) ),
inference(resolve,[status(thm)],[c_101,c_1263]) ).
cnf(c_3064,plain,
~ member(x,complement(unordered_pair(y,y))),
inference(resolve,[status(thm)],[c_3063,c_295]) ).
cnf(c_3057,plain,
$false,
inference(resolve,[status(thm)],[c_1247,c_3064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET123-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n009.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:11:00 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 3649270 was started by sandbox on n009,
% 0.19/0.46 % Sat Sep 26 07:11:00 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 67.70/9.07
% 67.70/9.07 % SZS status Unsatisfiable for theBenchmark
% 67.70/9.07
% 67.70/9.07 % Proof 1 at 0.41 (+ 0.13) seconds.
% 67.70/9.07 % Length of proof is 25.
% 67.70/9.07 % Level of proof is 6.
% 67.70/9.07 % Maximum clause weight is 35.000.
% 67.70/9.07 % Given clauses 375.
% 67.70/9.07
% 67.70/9.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------