%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET505-6 : 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 : n016.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 08:36:24 AM UTC 2026
% Result : Unsatisfiable 164.55s 22.51s
% Output : CNFRefutation 164.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 94 ( 32 unt; 0 def)
% Number of atoms : 166 ( 81 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 123 ( 51 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 150 ( 20 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2_to_universal_class_not_set_1,axiom,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_corollary_2_to_universal_class_not_set_1) ).
cnf(c_36,plain,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_corollary_2_to_universal_class_not_set_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_73,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_74,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_73]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_75,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_76,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_75]) ).
fof(domain1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_1,domain_of(VAR_0))
| restrict(VAR_0,singleton(VAR_1),universal_class) != null_class ),
file('theBenchmark.p',domain1) ).
cnf(c_109,plain,
( ~ member(B,domain_of(A))
| restrict(A,singleton(B),universal_class) != null_class ),
inference(clausify,[status(thm)],[domain1]) ).
fof(restriction2,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(cross_product(VAR_0,VAR_1),VAR_2) = restrict(VAR_2,VAR_0,VAR_1),
file('theBenchmark.p',restriction2) ).
cnf(c_110,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_111,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_110]) ).
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_62898,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_111,c_112]) ).
cnf(c_113,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_62898]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_119,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
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(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_122,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(cartesian_product1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product1) ).
cnf(c_129,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product1]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_130,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_131,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_130]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_132,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_133,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_132]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_135,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
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_136,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_137,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
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(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_62899,plain,
( ~ member(B,domain_of(A))
| restrict(A,unordered_pair(B,B),universal_class) != null_class ),
inference(paramod,[status(thm)],[c_133,c_109]) ).
cnf(c_225,plain,
( ~ member(A,domain_of(B))
| intersection(cross_product(unordered_pair(A,A),universal_class),B) != null_class ),
inference(paramod,[status(thm)],[c_111,c_62899]) ).
cnf(c_231,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_120]) ).
cnf(c_62900,plain,
( member(A,C)
| ~ member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_131,c_129]) ).
cnf(c_62901,plain,
( member(A,C)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_133,c_62900]) ).
cnf(c_233,plain,
( member(A,C)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_133,c_62901]) ).
cnf(c_62902,plain,
member(unordered_pair(singleton(universal_class),unordered_pair(universal_class,singleton(y))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_131,c_36]) ).
cnf(c_62903,plain,
member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,singleton(y))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_133,c_62902]) ).
cnf(c_250,plain,
member(unordered_pair(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(paramod,[status(thm)],[c_133,c_62903]) ).
cnf(c_62904,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_119,c_76]) ).
cnf(c_259,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_62904]) ).
cnf(c_62905,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_121,c_76]) ).
cnf(c_266,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_62905]) ).
cnf(c_62906,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_269,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_62906]) ).
cnf(c_62907,plain,
( null_class = unordered_pair(A,B)
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(resolve,[status(thm)],[c_137,c_76]) ).
cnf(c_281,plain,
( unordered_pair(A,B) = null_class
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_62907]) ).
cnf(c_282,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_308,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_62908,plain,
( null_class = domain_of(A)
| intersection(cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class),A) != null_class ),
inference(resolve,[status(thm)],[c_225,c_76]) ).
cnf(c_62909,plain,
( null_class = domain_of(A)
| intersection(A,cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class)) != null_class ),
inference(paramod,[status(thm)],[c_113,c_62908]) ).
cnf(c_366,plain,
( domain_of(A) = null_class
| intersection(A,cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class)) != null_class ),
inference(copy,[status(thm)],[c_62909]) ).
cnf(c_403,plain,
member(universal_class,universal_class),
inference(resolve,[status(thm)],[c_250,c_233]) ).
cnf(c_448,plain,
member(universal_class,unordered_pair(universal_class,A)),
inference(resolve,[status(thm)],[c_403,c_136]) ).
cnf(c_449,plain,
member(universal_class,unordered_pair(A,universal_class)),
inference(resolve,[status(thm)],[c_403,c_135]) ).
cnf(c_450,plain,
( member(universal_class,intersection(A,universal_class))
| ~ member(universal_class,A) ),
inference(resolve,[status(thm)],[c_403,c_120]) ).
cnf(c_547,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_308,c_76]) ).
cnf(c_620,plain,
( member(regular(A),intersection(universal_class,universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_547,c_231]) ).
cnf(c_1056,plain,
member(universal_class,intersection(unordered_pair(A,universal_class),universal_class)),
inference(resolve,[status(thm)],[c_450,c_449]) ).
cnf(c_62910,plain,
( intersection(unordered_pair(A,A),A) = null_class
| null_class = unordered_pair(A,A)
| unordered_pair(A,A) = null_class ),
inference(paramod,[status(thm)],[c_282,c_74]) ).
cnf(c_62911,plain,
( intersection(unordered_pair(A,A),A) = null_class
| unordered_pair(A,A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_62910]) ).
cnf(c_1338,plain,
( intersection(unordered_pair(A,A),A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_62911]) ).
cnf(c_62912,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| null_class = complement(intersection(universal_class,universal_class)) ),
inference(resolve,[status(thm)],[c_620,c_259]) ).
cnf(c_62913,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| complement(intersection(universal_class,universal_class)) = null_class ),
inference(copy,[status(thm)],[c_62912]) ).
cnf(c_1522,plain,
complement(intersection(universal_class,universal_class)) = null_class,
inference(copy,[status(thm)],[c_62913]) ).
cnf(c_1531,plain,
( ~ member(A,intersection(universal_class,universal_class))
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_1522,c_119]) ).
cnf(c_1552,plain,
( null_class = A
| ~ member(regular(A),null_class) ),
inference(resolve,[status(thm)],[c_1531,c_620]) ).
cnf(c_62914,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_1552,c_269]) ).
cnf(c_62915,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_62914]) ).
cnf(c_1561,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_62915]) ).
cnf(c_62916,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_1552,c_266]) ).
cnf(c_62917,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_62916]) ).
cnf(c_1562,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_62917]) ).
cnf(c_4076,plain,
domain_of(null_class) = null_class,
inference(resolve,[status(thm)],[c_366,c_1561]) ).
cnf(c_62918,plain,
( ~ member(A,null_class)
| intersection(cross_product(unordered_pair(A,A),universal_class),null_class) != null_class ),
inference(paramod,[status(thm)],[c_4076,c_225]) ).
cnf(c_62919,plain,
( ~ member(A,null_class)
| null_class != null_class ),
inference(paramod,[status(thm)],[c_1562,c_62918]) ).
cnf(c_4094,plain,
~ member(A,null_class),
inference(copy,[status(thm)],[c_62919]) ).
cnf(c_62920,plain,
( member(universal_class,null_class)
| unordered_pair(universal_class,universal_class) = null_class ),
inference(paramod,[status(thm)],[c_1338,c_1056]) ).
cnf(c_62804,plain,
unordered_pair(universal_class,universal_class) = null_class,
inference(resolve,[status(thm)],[c_4094,c_62920]) ).
cnf(c_62921,plain,
member(universal_class,null_class),
inference(paramod,[status(thm)],[c_62804,c_448]) ).
cnf(c_62897,plain,
$false,
inference(resolve,[status(thm)],[c_4094,c_62921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET505-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:54:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 344562 was started by sandbox on n016,
% 0.11/0.37 % Sat Sep 26 07:54:44 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 164.55/22.51
% 164.55/22.51 % given #500 (T,wt=9): 1348 member(null_class,intersection(intersection(universal_class,intersection(omega,omega)),omega)). [resolve(1265,a,265,a)].
% 164.55/22.51
% 164.55/22.51 % given #1000 (A,wt=17): 506 member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(y,y))),cross_product(unordered_pair(A,y),unordered_pair(A,y))). [resolve(433,a,232,a)].
% 164.55/22.51
% 164.55/22.51 % given #1500 (T,wt=11): 3597 member(null_class,intersection(intersection(omega,intersection(universal_class,unordered_pair(null_class,A))),omega)). [resolve(1319,a,265,a)].
% 164.55/22.51
% 164.55/22.51 % given #2000 (T,wt=11): 10260 member(null_class,intersection(intersection(omega,universal_class),intersection(unordered_pair(null_class,A),universal_class))). [resolve(712,a,1168,a)].
% 164.55/22.51
% 164.55/22.51 % given #2500 (T,wt=9): 57067 null_class = universal_class | member(null_class,complement(domain_of(regular(universal_class)))). [para(52412(a,1),562(a,2)),unit_del(b,4094)].
% 164.55/22.51
% 164.55/22.51 % given #3000 (A,wt=16): 1177 -member(unordered_pair(A,B),C) | member(unordered_pair(A,B),intersection(C,unordered_pair(D,unordered_pair(A,B)))). [resolve(275,a,120,b)].
% 164.55/22.51
% 164.55/22.51 % SZS status Unsatisfiable for theBenchmark
% 164.55/22.51
% 164.55/22.51 % Proof 1 at 15.69 (+ 5.69) seconds.
% 164.55/22.51 % Length of proof is 52.
% 164.55/22.51 % Level of proof is 11.
% 164.55/22.51 % Maximum clause weight is 17.000.
% 164.55/22.51 % Given clauses 3199.
% 164.55/22.51
% 164.55/22.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------