%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET093-6 : 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 : n010.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 08:35:44 AM UTC 2026
% Result : Unsatisfiable 0.37s 0.60s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 15 unt; 0 def)
% Number of atoms : 23 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 5 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2_to_singletons_are_sets_2,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_corollary_2_to_singletons_are_sets_2) ).
cnf(c_34,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_2_to_singletons_are_sets_2]) ).
fof(prove_corollary_2_to_singletons_are_sets_1,axiom,
singleton(member_of(x)) = x,
file('theBenchmark.p',prove_corollary_2_to_singletons_are_sets_1) ).
cnf(c_35,plain,
singleton(member_of(x)) = x,
inference(clausify,[status(thm)],[prove_corollary_2_to_singletons_are_sets_1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_109,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_110,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_109]) ).
fof(unordered_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_111,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_118,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_121,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_196,plain,
unordered_pair(member_of(x),member_of(x)) = x,
inference(paramod,[status(thm)],[c_110,c_35]) ).
cnf(c_326,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_257,plain,
~ member(x,A),
inference(resolve,[status(thm)],[c_326,c_34]) ).
cnf(c_327,plain,
member(x,universal_class),
inference(paramod,[status(thm)],[c_196,c_111]) ).
cnf(c_325,plain,
$false,
inference(resolve,[status(thm)],[c_257,c_327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET093-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42 % Computer : n010.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Sat Sep 26 07:06:20 UTC 2026
% 0.09/0.42 % CPUTime :
% 0.09/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.43 % Process 2751364 was started by sandbox on n010,
% 0.09/0.43 % Sat Sep 26 07:06:20 2026
% 0.09/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.43
% 0.09/0.43 % From the command line: assign(max_seconds, 300).
% 0.37/0.60
% 0.37/0.60 % SZS status Unsatisfiable for theBenchmark
% 0.37/0.60
% 0.37/0.60 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.37/0.60 % Length of proof is 10.
% 0.37/0.60 % Level of proof is 3.
% 0.37/0.60 % Maximum clause weight is 9.000.
% 0.37/0.60 % Given clauses 97.
% 0.37/0.60
% 0.37/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------