%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET096-7 : 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 08:35:45 AM UTC 2026
% Result : Unsatisfiable 1.29s 0.71s
% Output : CNFRefutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 16 unt; 0 def)
% Number of atoms : 60 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 25 |; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_two_subsets_of_singleton_3,axiom,
singleton(y) != x,
file('theBenchmark.p',prove_two_subsets_of_singleton_3) ).
cnf(c_33,plain,
singleton(y) != x,
inference(clausify,[status(thm)],[prove_two_subsets_of_singleton_3]) ).
fof(prove_two_subsets_of_singleton_2,axiom,
x != null_class,
file('theBenchmark.p',prove_two_subsets_of_singleton_2) ).
cnf(c_34,plain,
x != null_class,
inference(clausify,[status(thm)],[prove_two_subsets_of_singleton_2]) ).
fof(prove_two_subsets_of_singleton_1,axiom,
subclass(x,singleton(y)),
file('theBenchmark.p',prove_two_subsets_of_singleton_1) ).
cnf(c_35,plain,
subclass(x,singleton(y)),
inference(clausify,[status(thm)],[prove_two_subsets_of_singleton_1]) ).
fof(only_member_in_singleton,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ member(VAR_0,singleton(VAR_1)) ),
file('theBenchmark.p',only_member_in_singleton) ).
cnf(c_51,plain,
( A = B
| ~ member(A,singleton(B)) ),
inference(clausify,[status(thm)],[only_member_in_singleton]) ).
fof(unordered_pair_is_subset,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subclass(unordered_pair(VAR_0,VAR_2),VAR_1)
| ~ member(VAR_2,VAR_1)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',unordered_pair_is_subset) ).
cnf(c_57,plain,
( subclass(unordered_pair(A,C),B)
| ~ member(C,B)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[unordered_pair_is_subset]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_103,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_104,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_103]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_160,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_161,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_160]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_166,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
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_172,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_193,plain,
( subclass(unordered_pair(A,A),B)
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_1687,plain,
( x = singleton(y)
| ~ subclass(singleton(y),x) ),
inference(resolve,[status(thm)],[c_166,c_35]) ).
cnf(c_1688,plain,
( singleton(y) = x
| ~ subclass(singleton(y),x) ),
inference(copy,[status(thm)],[c_1687]) ).
cnf(c_749,plain,
~ subclass(singleton(y),x),
inference(resolve,[status(thm)],[c_33,c_1688]) ).
cnf(c_810,plain,
( member(A,singleton(y))
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_172,c_35]) ).
cnf(c_954,plain,
~ subclass(unordered_pair(y,y),x),
inference(paramod,[status(thm)],[c_161,c_749]) ).
cnf(c_1689,plain,
( null_class = x
| member(regular(x),singleton(y)) ),
inference(resolve,[status(thm)],[c_810,c_104]) ).
cnf(c_1690,plain,
( x = null_class
| member(regular(x),singleton(y)) ),
inference(copy,[status(thm)],[c_1689]) ).
cnf(c_1567,plain,
member(regular(x),singleton(y)),
inference(resolve,[status(thm)],[c_34,c_1690]) ).
cnf(c_1580,plain,
regular(x) = y,
inference(resolve,[status(thm)],[c_1567,c_51]) ).
cnf(c_1691,plain,
( member(y,x)
| null_class = x ),
inference(paramod,[status(thm)],[c_1580,c_104]) ).
cnf(c_1692,plain,
( member(y,x)
| x = null_class ),
inference(copy,[status(thm)],[c_1691]) ).
cnf(c_1678,plain,
member(y,x),
inference(resolve,[status(thm)],[c_34,c_1692]) ).
cnf(c_1693,plain,
subclass(unordered_pair(y,y),x),
inference(resolve,[status(thm)],[c_1678,c_193]) ).
cnf(c_1686,plain,
$false,
inference(resolve,[status(thm)],[c_954,c_1693]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 07:06:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2177849 was started by sandbox2 on n013,
% 0.10/0.37 % Sat Sep 26 07:06:07 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 1.29/0.71
% 1.29/0.71 % SZS status Unsatisfiable for theBenchmark
% 1.29/0.71
% 1.29/0.71 % Proof 1 at 0.23 (+ 0.08) seconds.
% 1.29/0.71 % Length of proof is 19.
% 1.29/0.71 % Level of proof is 5.
% 1.29/0.71 % Maximum clause weight is 21.000.
% 1.29/0.71 % Given clauses 262.
% 1.29/0.71
% 1.29/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------