%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET147-6 : 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 08:35:54 AM UTC 2026
% Result : Unsatisfiable 22.18s 3.62s
% Output : CNFRefutation 22.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 60 ( 7 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 30 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_identity_for_intersection_1,axiom,
intersection(universal_class,x) != x,
file('theBenchmark.p',prove_identity_for_intersection_1) ).
cnf(c_36,plain,
intersection(universal_class,x) != x,
inference(clausify,[status(thm)],[prove_identity_for_intersection_1]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_120,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
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_121,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
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_138,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_141,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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_142,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_143,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_144,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_336,plain,
( member(not_subclass_element(intersection(A,B),C),B)
| subclass(intersection(A,B),C) ),
inference(resolve,[status(thm)],[c_143,c_121]) ).
cnf(c_337,plain,
( member(not_subclass_element(A,B),intersection(C,A))
| ~ member(not_subclass_element(A,B),C)
| subclass(A,B) ),
inference(resolve,[status(thm)],[c_143,c_120]) ).
cnf(c_353,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_427,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),universal_class) ),
inference(resolve,[status(thm)],[c_353,c_143]) ).
cnf(c_20087,plain,
( subclass(intersection(A,B),B)
| subclass(intersection(A,B),B) ),
inference(resolve,[status(thm)],[c_336,c_142]) ).
cnf(c_7398,plain,
subclass(intersection(A,B),B),
inference(copy,[status(thm)],[c_20087]) ).
cnf(c_20088,plain,
( A = intersection(B,A)
| ~ subclass(A,intersection(B,A)) ),
inference(resolve,[status(thm)],[c_7398,c_138]) ).
cnf(c_7442,plain,
( intersection(B,A) = A
| ~ subclass(A,intersection(B,A)) ),
inference(copy,[status(thm)],[c_20088]) ).
cnf(c_20089,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),intersection(universal_class,A))
| subclass(A,B) ),
inference(resolve,[status(thm)],[c_337,c_427]) ).
cnf(c_7460,plain,
( member(not_subclass_element(A,B),intersection(universal_class,A))
| subclass(A,B) ),
inference(copy,[status(thm)],[c_20089]) ).
cnf(c_20090,plain,
( subclass(A,intersection(universal_class,A))
| subclass(A,intersection(universal_class,A)) ),
inference(resolve,[status(thm)],[c_7460,c_142]) ).
cnf(c_20058,plain,
subclass(A,intersection(universal_class,A)),
inference(copy,[status(thm)],[c_20090]) ).
cnf(c_20085,plain,
intersection(universal_class,A) = A,
inference(resolve,[status(thm)],[c_20058,c_7442]) ).
cnf(c_20086,plain,
$false,
inference(resolve,[status(thm)],[c_20085,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET147-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 07:14:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 947122 was started by sandbox on n020,
% 0.12/0.38 % Sat Sep 26 07:14:48 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 22.18/3.62
% 22.18/3.62 % given #500 (T,wt=19): 5445 member(regular(element_relation),element_relation) | member(ordered_pair(null_class,omega),A). [resolve(4900,b,3706,a)].
% 22.18/3.62
% 22.18/3.62 % given #1000 (F,wt=34): 17672 -member(domain_of(inverse(intersection(choice,cross_product(omega,universal_class)))),null_class). [para(113(a,1),17650(a,1,1,1))].
% 22.18/3.62
% 22.18/3.62 % SZS status Unsatisfiable for theBenchmark
% 22.18/3.62
% 22.18/3.62 % Proof 1 at 2.54 (+ 0.64) seconds.
% 22.18/3.62 % Length of proof is 18.
% 22.18/3.62 % Level of proof is 6.
% 22.18/3.62 % Maximum clause weight is 27.000.
% 22.18/3.62 % Given clauses 1204.
% 22.18/3.62
% 22.18/3.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------