%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET411-6 : 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 : n015.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 08:36:18 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.65s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 30 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 3 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_compose_condition_for_singleton_membership1_2,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_compose_condition_for_singleton_membership1_2) ).
cnf(c_36,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_compose_condition_for_singleton_membership1_2]) ).
fof(prove_compose_condition_for_singleton_membership1_1,axiom,
member(ordered_pair(x,y),singleton_relation),
file('theBenchmark.p',prove_compose_condition_for_singleton_membership1_1) ).
cnf(c_37,plain,
member(ordered_pair(x,y),singleton_relation),
inference(clausify,[status(thm)],[prove_compose_condition_for_singleton_membership1_1]) ).
fof(compose_can_define_singleton,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('theBenchmark.p',compose_can_define_singleton) ).
cnf(c_44,plain,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(clausify,[status(thm)],[compose_can_define_singleton]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_122,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(element_relation2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| ~ member(ordered_pair(VAR_0,VAR_1),element_relation) ),
file('theBenchmark.p',element_relation2) ).
cnf(c_125,plain,
( member(A,B)
| ~ member(ordered_pair(A,B),element_relation) ),
inference(clausify,[status(thm)],[element_relation2]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_142,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_145,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_240,plain,
( member(A,element_relation)
| ~ member(A,singleton_relation) ),
inference(paramod,[status(thm)],[c_44,c_122]) ).
cnf(c_381,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_145,c_142]) ).
cnf(c_468,plain,
member(ordered_pair(x,y),element_relation),
inference(resolve,[status(thm)],[c_240,c_37]) ).
cnf(c_664,plain,
member(x,y),
inference(resolve,[status(thm)],[c_468,c_125]) ).
cnf(c_690,plain,
member(x,universal_class),
inference(resolve,[status(thm)],[c_664,c_381]) ).
cnf(c_689,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n015.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sat Sep 26 07:44:00 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.57 % Process 3479855 was started by sandbox on n015,
% 0.08/0.57 % Sat Sep 26 07:44:00 2026
% 0.08/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.57
% 0.08/0.57 % From the command line: assign(max_seconds, 300).
% 0.12/0.65
% 0.12/0.65 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.65
% 0.12/0.65 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.12/0.65 % Length of proof is 12.
% 0.12/0.65 % Level of proof is 4.
% 0.12/0.65 % Maximum clause weight is 34.000.
% 0.12/0.65 % Given clauses 158.
% 0.12/0.65
% 0.12/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------