%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET503-6 : 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 08:36:24 AM UTC 2026
% Result : Unsatisfiable 215.16s 29.11s
% Output : CNFRefutation 215.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 27 unt; 0 def)
% Number of atoms : 151 ( 78 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 113 ( 46 ~; 67 |; 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 : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 124 ( 13 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_universal_class_not_set_1,axiom,
member(universal_class,x),
file('theBenchmark.p',prove_universal_class_not_set_1) ).
cnf(c_36,plain,
member(universal_class,x),
inference(clausify,[status(thm)],[prove_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_45585,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_45585]) ).
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(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_45586,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_45586]) ).
cnf(c_231,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_120]) ).
cnf(c_45587,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_119,c_76]) ).
cnf(c_258,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_45587]) ).
cnf(c_45588,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_121,c_76]) ).
cnf(c_267,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_45588]) ).
cnf(c_45589,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_270,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_45589]) ).
cnf(c_45590,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_282,plain,
( unordered_pair(A,B) = null_class
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_45590]) ).
cnf(c_283,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_282]) ).
cnf(c_309,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_45591,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_45592,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_45591]) ).
cnf(c_367,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_45592]) ).
cnf(c_378,plain,
member(universal_class,intersection(x,x)),
inference(resolve,[status(thm)],[c_231,c_36]) ).
cnf(c_460,plain,
member(universal_class,universal_class),
inference(resolve,[status(thm)],[c_309,c_378]) ).
cnf(c_461,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_309,c_76]) ).
cnf(c_488,plain,
member(universal_class,unordered_pair(universal_class,A)),
inference(resolve,[status(thm)],[c_460,c_136]) ).
cnf(c_489,plain,
member(universal_class,unordered_pair(A,universal_class)),
inference(resolve,[status(thm)],[c_460,c_135]) ).
cnf(c_490,plain,
( member(universal_class,intersection(A,universal_class))
| ~ member(universal_class,A) ),
inference(resolve,[status(thm)],[c_460,c_120]) ).
cnf(c_571,plain,
( member(regular(A),intersection(universal_class,universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_461,c_231]) ).
cnf(c_1285,plain,
member(universal_class,intersection(unordered_pair(A,universal_class),universal_class)),
inference(resolve,[status(thm)],[c_490,c_489]) ).
cnf(c_45593,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_283,c_74]) ).
cnf(c_45594,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_45593]) ).
cnf(c_1408,plain,
( intersection(unordered_pair(A,A),A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_45594]) ).
cnf(c_45595,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| null_class = complement(intersection(universal_class,universal_class)) ),
inference(resolve,[status(thm)],[c_571,c_258]) ).
cnf(c_45596,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| complement(intersection(universal_class,universal_class)) = null_class ),
inference(copy,[status(thm)],[c_45595]) ).
cnf(c_1624,plain,
complement(intersection(universal_class,universal_class)) = null_class,
inference(copy,[status(thm)],[c_45596]) ).
cnf(c_1633,plain,
( ~ member(A,intersection(universal_class,universal_class))
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_1624,c_119]) ).
cnf(c_1638,plain,
( null_class = A
| ~ member(regular(A),null_class) ),
inference(resolve,[status(thm)],[c_1633,c_571]) ).
cnf(c_45597,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_1638,c_270]) ).
cnf(c_45598,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_45597]) ).
cnf(c_1646,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_45598]) ).
cnf(c_45599,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_1638,c_267]) ).
cnf(c_45600,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_45599]) ).
cnf(c_1647,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_45600]) ).
cnf(c_4324,plain,
domain_of(null_class) = null_class,
inference(resolve,[status(thm)],[c_367,c_1646]) ).
cnf(c_45601,plain,
( ~ member(A,null_class)
| intersection(cross_product(unordered_pair(A,A),universal_class),null_class) != null_class ),
inference(paramod,[status(thm)],[c_4324,c_225]) ).
cnf(c_45602,plain,
( ~ member(A,null_class)
| null_class != null_class ),
inference(paramod,[status(thm)],[c_1647,c_45601]) ).
cnf(c_4342,plain,
~ member(A,null_class),
inference(copy,[status(thm)],[c_45602]) ).
cnf(c_45603,plain,
( member(universal_class,null_class)
| unordered_pair(universal_class,universal_class) = null_class ),
inference(paramod,[status(thm)],[c_1408,c_1285]) ).
cnf(c_45358,plain,
unordered_pair(universal_class,universal_class) = null_class,
inference(resolve,[status(thm)],[c_4342,c_45603]) ).
cnf(c_45604,plain,
member(universal_class,null_class),
inference(paramod,[status(thm)],[c_45358,c_488]) ).
cnf(c_45584,plain,
$false,
inference(resolve,[status(thm)],[c_4342,c_45604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET503-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 07:51:03 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1012007 was started by sandbox on n020,
% 0.10/0.36 % Sat Sep 26 07:51:03 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 215.16/29.11
% 215.16/29.11 % given #500 (A,wt=19): 357 -operation(intersection(successor_relation,cross_product(omega,universal_class))) | maps(intersection(successor_relation,cross_product(omega,universal_class)),domain_of(intersection(successor_relation,cross_product(omega,universal_class))),omega). [resolve(212,a,160,b)].
% 215.16/29.11
% 215.16/29.11 % given #1000 (T,wt=11): 1595 member(universal_class,intersection(intersection(unordered_pair(universal_class,A),unordered_pair(universal_class,A)),x)). [resolve(536,a,265,a)].
% 215.16/29.11
% 215.16/29.11 % given #1500 (T,wt=11): 3171 member(null_class,intersection(universal_class,intersection(omega,intersection(unordered_pair(A,null_class),universal_class)))). [resolve(1118,a,475,a)].
% 215.16/29.11
% 215.16/29.11 % given #2000 (T,wt=11): 4932 member(universal_class,intersection(x,intersection(intersection(universal_class,unordered_pair(universal_class,A)),universal_class))). [resolve(1437,a,261,a)].
% 215.16/29.11
% 215.16/29.11 % given #2500 (T,wt=11): 14217 member(universal_class,intersection(intersection(universal_class,unordered_pair(A,universal_class)),unordered_pair(universal_class,B))). [resolve(537,a,1392,a)].
% 215.16/29.11
% 215.16/29.11 % given #3000 (T,wt=11): 20395 singleton_relation = null_class | member(regular(singleton_relation),intersection(intersection(singleton_relation,universal_class),element_relation)). [resolve(565,b,654,a),flip(c),merge(c)].
% 215.16/29.11
% 215.16/29.11 % given #3500 (T,wt=11): 45052 null_class = universal_class | subclass(intersection(A,complement(complement(regular(universal_class)))),null_class). [resolve(43637,b,140,a)].
% 215.16/29.11
% 215.16/29.11 % SZS status Unsatisfiable for theBenchmark
% 215.16/29.11
% 215.16/29.11 % Proof 1 at 19.50 (+ 8.71) seconds.
% 215.16/29.11 % Length of proof is 48.
% 215.16/29.11 % Level of proof is 11.
% 215.16/29.11 % Maximum clause weight is 17.000.
% 215.16/29.11 % Given clauses 3519.
% 215.16/29.11
% 215.16/29.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------