%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET096-6 : 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 : n007.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 11.55s 1.95s
% Output : CNFRefutation 11.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 66 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 23 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_two_subsets_of_singleton_3,axiom,
singleton(y) != x,
file('theBenchmark.p',prove_two_subsets_of_singleton_3) ).
cnf(c_34,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_35,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_36,plain,
subclass(x,singleton(y)),
inference(clausify,[status(thm)],[prove_two_subsets_of_singleton_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_53,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_54,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_53]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_110,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_111,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_110]) ).
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_115,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
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_116,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
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_120,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_121,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_122,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_197,plain,
subclass(x,unordered_pair(y,y)),
inference(paramod,[status(thm)],[c_111,c_36]) ).
cnf(c_198,plain,
unordered_pair(y,y) != x,
inference(paramod,[status(thm)],[c_111,c_34]) ).
cnf(c_199,plain,
( A = B
| ~ member(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_115]) ).
cnf(c_326,plain,
( member(A,unordered_pair(y,y))
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_197,c_122]) ).
cnf(c_6470,plain,
( unordered_pair(y,y) = x
| ~ subclass(unordered_pair(y,y),x) ),
inference(resolve,[status(thm)],[c_197,c_116]) ).
cnf(c_327,plain,
~ subclass(unordered_pair(y,y),x),
inference(resolve,[status(thm)],[c_198,c_6470]) ).
cnf(c_506,plain,
member(not_subclass_element(unordered_pair(y,y),x),unordered_pair(y,y)),
inference(resolve,[status(thm)],[c_327,c_121]) ).
cnf(c_507,plain,
~ member(not_subclass_element(unordered_pair(y,y),x),x),
inference(resolve,[status(thm)],[c_120,c_327]) ).
cnf(c_6471,plain,
( null_class = x
| member(regular(x),unordered_pair(y,y)) ),
inference(resolve,[status(thm)],[c_326,c_54]) ).
cnf(c_6472,plain,
( x = null_class
| member(regular(x),unordered_pair(y,y)) ),
inference(copy,[status(thm)],[c_6471]) ).
cnf(c_2287,plain,
member(regular(x),unordered_pair(y,y)),
inference(resolve,[status(thm)],[c_35,c_6472]) ).
cnf(c_2291,plain,
regular(x) = y,
inference(resolve,[status(thm)],[c_2287,c_199]) ).
cnf(c_6473,plain,
( member(y,x)
| null_class = x ),
inference(paramod,[status(thm)],[c_2291,c_54]) ).
cnf(c_6474,plain,
( member(y,x)
| x = null_class ),
inference(copy,[status(thm)],[c_6473]) ).
cnf(c_2381,plain,
member(y,x),
inference(resolve,[status(thm)],[c_35,c_6474]) ).
cnf(c_6468,plain,
not_subclass_element(unordered_pair(y,y),x) = y,
inference(resolve,[status(thm)],[c_506,c_199]) ).
cnf(c_6475,plain,
~ member(y,x),
inference(paramod,[status(thm)],[c_6468,c_507]) ).
cnf(c_6469,plain,
$false,
inference(resolve,[status(thm)],[c_2381,c_6475]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET096-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 07:04:39 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3079383 was started by sandbox2 on n007,
% 0.19/0.45 % Sat Sep 26 07:04:39 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 11.55/1.95
% 11.55/1.95 % given #500 (F,wt=6): 3287 -subclass(universal_class,intersection(complement(omega),A)). [ur(122,b,413,a,c,347,a)].
% 11.55/1.95
% 11.55/1.95 % SZS status Unsatisfiable for theBenchmark
% 11.55/1.95
% 11.55/1.95 % Proof 1 at 1.17 (+ 0.29) seconds.
% 11.55/1.95 % Length of proof is 24.
% 11.55/1.95 % Level of proof is 7.
% 11.55/1.95 % Maximum clause weight is 11.000.
% 11.55/1.95 % Given clauses 619.
% 11.55/1.95
% 11.55/1.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------