%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET244-6 : 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 : n001.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 08:36:06 AM UTC 2026
% Result : Unsatisfiable 37.73s 5.26s
% Output : CNFRefutation 37.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 64 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 23 ~; 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 4 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_restriction_with_universal_class_1,axiom,
restrict(universal_class,x,y) != cross_product(x,y),
file('theBenchmark.p',prove_restriction_with_universal_class_1) ).
cnf(c_36,plain,
restrict(universal_class,x,y) != cross_product(x,y),
inference(clausify,[status(thm)],[prove_restriction_with_universal_class_1]) ).
fof(restriction1,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(VAR_0,cross_product(VAR_1,VAR_2)) = restrict(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',restriction1) ).
cnf(c_112,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_113,plain,
restrict(A,B,C) = intersection(A,cross_product(B,C)),
inference(copy,[status(thm)],[c_112]) ).
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_214,plain,
intersection(universal_class,cross_product(x,y)) != cross_product(x,y),
inference(paramod,[status(thm)],[c_113,c_36]) ).
cnf(c_338,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_339,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_355,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_429,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),universal_class) ),
inference(resolve,[status(thm)],[c_355,c_143]) ).
cnf(c_20089,plain,
( subclass(intersection(A,B),B)
| subclass(intersection(A,B),B) ),
inference(resolve,[status(thm)],[c_338,c_142]) ).
cnf(c_7400,plain,
subclass(intersection(A,B),B),
inference(copy,[status(thm)],[c_20089]) ).
cnf(c_20090,plain,
( A = intersection(B,A)
| ~ subclass(A,intersection(B,A)) ),
inference(resolve,[status(thm)],[c_7400,c_138]) ).
cnf(c_7444,plain,
( intersection(B,A) = A
| ~ subclass(A,intersection(B,A)) ),
inference(copy,[status(thm)],[c_20090]) ).
cnf(c_20091,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),intersection(universal_class,A))
| subclass(A,B) ),
inference(resolve,[status(thm)],[c_339,c_429]) ).
cnf(c_7462,plain,
( member(not_subclass_element(A,B),intersection(universal_class,A))
| subclass(A,B) ),
inference(copy,[status(thm)],[c_20091]) ).
cnf(c_20092,plain,
( subclass(A,intersection(universal_class,A))
| subclass(A,intersection(universal_class,A)) ),
inference(resolve,[status(thm)],[c_7462,c_142]) ).
cnf(c_20060,plain,
subclass(A,intersection(universal_class,A)),
inference(copy,[status(thm)],[c_20092]) ).
cnf(c_20087,plain,
intersection(universal_class,A) = A,
inference(resolve,[status(thm)],[c_20060,c_7444]) ).
cnf(c_20088,plain,
$false,
inference(resolve,[status(thm)],[c_20087,c_214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET244-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 07:28:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1253348 was started by sandbox on n001,
% 0.10/0.37 % Sat Sep 26 07:28:42 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 37.73/5.26
% 37.73/5.26 % given #500 (A,wt=24): 313 subclass(image(A,B),range_of(restrict(A,B,universal_class))). [resolve(139,a,93,a(flip))].
% 37.73/5.26
% 37.73/5.26 % given #1000 (A,wt=25): 563 null_class = universal_class | member(power_class(regular(universal_class)),intersection(universal_class,universal_class)). [resolve(185,a,176,a)].
% 37.73/5.26
% 37.73/5.26 % SZS status Unsatisfiable for theBenchmark
% 37.73/5.26
% 37.73/5.26 % Proof 1 at 3.92 (+ 0.90) seconds.
% 37.73/5.26 % Length of proof is 21.
% 37.73/5.26 % Level of proof is 6.
% 37.73/5.26 % Maximum clause weight is 27.000.
% 37.73/5.26 % Given clauses 1206.
% 37.73/5.26
% 37.73/5.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------