%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET080-6 : 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 : n011.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 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 30 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 4 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inductive1,axiom,
! [VAR_0] :
( member(null_class,VAR_0)
| ~ inductive(VAR_0) ),
file('theBenchmark.p',inductive1) ).
cnf(c_3,plain,
( member(null_class,A)
| ~ inductive(A) ),
inference(clausify,[status(thm)],[inductive1]) ).
fof(omega_is_inductive1,axiom,
inductive(omega),
file('theBenchmark.p',omega_is_inductive1) ).
cnf(c_4,plain,
inductive(omega),
inference(clausify,[status(thm)],[omega_is_inductive1]) ).
cnf(c_32,plain,
member(null_class,omega),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(prove_null_class_in_its_singleton_1,axiom,
~ member(null_class,singleton(null_class)),
file('theBenchmark.p',prove_null_class_in_its_singleton_1) ).
cnf(c_34,plain,
~ member(null_class,singleton(null_class)),
inference(clausify,[status(thm)],[prove_null_class_in_its_singleton_1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_108,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_109,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_108]) ).
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_112,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_117,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_120,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_203,plain,
~ member(null_class,unordered_pair(null_class,null_class)),
inference(paramod,[status(thm)],[c_109,c_34]) ).
cnf(c_303,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_120,c_117]) ).
cnf(c_376,plain,
member(null_class,universal_class),
inference(resolve,[status(thm)],[c_303,c_32]) ).
cnf(c_381,plain,
member(null_class,unordered_pair(null_class,A)),
inference(resolve,[status(thm)],[c_376,c_112]) ).
cnf(c_382,plain,
$false,
inference(resolve,[status(thm)],[c_381,c_203]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET080-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.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 07:03:58 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 4036762 was started by sandbox2 on n011,
% 0.18/0.45 % Sat Sep 26 07:03:58 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.53
% 0.18/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.53
% 0.18/0.53 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.18/0.53 % Length of proof is 14.
% 0.18/0.53 % Level of proof is 4.
% 0.18/0.53 % Maximum clause weight is 18.000.
% 0.18/0.53 % Given clauses 108.
% 0.18/0.53
% 0.18/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------