%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET079-6 : 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 : n020.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 08:35:40 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 17 unt; 0 def)
% Number of atoms : 63 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 23 ~; 24 |; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 9 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_set_in_its_singleton_2,axiom,
singleton(x) = null_class,
file('theBenchmark.p',prove_corollary_to_set_in_its_singleton_2) ).
cnf(c_34,plain,
singleton(x) = null_class,
inference(clausify,[status(thm)],[prove_corollary_to_set_in_its_singleton_2]) ).
cnf(c_35,plain,
null_class = singleton(x),
inference(copy,[status(thm)],[c_34]) ).
fof(prove_corollary_to_set_in_its_singleton_1,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_corollary_to_set_in_its_singleton_1) ).
cnf(c_36,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_to_set_in_its_singleton_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_51,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_588,plain,
( intersection(A,regular(A)) = null_class
| A = singleton(x) ),
inference(paramod,[status(thm)],[c_35,c_51]) ).
cnf(c_589,plain,
( intersection(A,regular(A)) = singleton(x)
| A = singleton(x) ),
inference(paramod,[status(thm)],[c_35,c_588]) ).
cnf(c_52,plain,
( intersection(A,regular(A)) = singleton(x)
| singleton(x) = A ),
inference(copy,[status(thm)],[c_589]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_99,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_102,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_112,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_113,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_112]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_115,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
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_116,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
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_119,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
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_124,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_590,plain,
( intersection(A,regular(A)) = singleton(x)
| unordered_pair(x,x) = A ),
inference(paramod,[status(thm)],[c_113,c_52]) ).
cnf(c_201,plain,
( intersection(A,regular(A)) = unordered_pair(x,x)
| unordered_pair(x,x) = A ),
inference(paramod,[status(thm)],[c_113,c_590]) ).
cnf(c_209,plain,
~ member(x,complement(universal_class)),
inference(resolve,[status(thm)],[c_99,c_36]) ).
cnf(c_220,plain,
member(x,unordered_pair(A,x)),
inference(resolve,[status(thm)],[c_115,c_36]) ).
cnf(c_223,plain,
member(x,unordered_pair(x,A)),
inference(resolve,[status(thm)],[c_116,c_36]) ).
cnf(c_237,plain,
subclass(A,A),
inference(xxres,[status(thm)],[c_119]) ).
cnf(c_363,plain,
~ member(x,intersection(complement(universal_class),A)),
inference(resolve,[status(thm)],[c_102,c_209]) ).
cnf(c_591,plain,
( member(x,B)
| ~ subclass(unordered_pair(x,A),B) ),
inference(resolve,[status(thm)],[c_124,c_223]) ).
cnf(c_435,plain,
~ subclass(unordered_pair(x,A),complement(universal_class)),
inference(resolve,[status(thm)],[c_591,c_209]) ).
cnf(c_592,plain,
( ~ member(x,unordered_pair(x,x))
| unordered_pair(x,x) = complement(universal_class) ),
inference(paramod,[status(thm)],[c_201,c_363]) ).
cnf(c_593,plain,
( ~ member(x,unordered_pair(x,x))
| complement(universal_class) = unordered_pair(x,x) ),
inference(copy,[status(thm)],[c_592]) ).
cnf(c_532,plain,
complement(universal_class) = unordered_pair(x,x),
inference(resolve,[status(thm)],[c_220,c_593]) ).
cnf(c_586,plain,
~ subclass(unordered_pair(x,A),unordered_pair(x,x)),
inference(paramod,[status(thm)],[c_532,c_435]) ).
cnf(c_587,plain,
$false,
inference(resolve,[status(thm)],[c_586,c_237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET079-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:04:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 932470 was started by sandbox on n020,
% 0.09/0.36 % Sat Sep 26 07:04:48 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.46
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46
% 0.13/0.46 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.13/0.46 % Length of proof is 23.
% 0.13/0.46 % Level of proof is 6.
% 0.13/0.46 % Maximum clause weight is 13.000.
% 0.13/0.46 % Given clauses 129.
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------