%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET515-6 : 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 : n012.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 08:36:25 AM UTC 2026
% Result : Unsatisfiable 48.70s 7.33s
% Output : CNFRefutation 48.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 27 unt; 0 def)
% Number of atoms : 127 ( 65 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 93 ( 38 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 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 : 106 ( 11 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_no_class_belongs_to_itself_1,axiom,
member(x,x),
file('theBenchmark.p',prove_no_class_belongs_to_itself_1) ).
cnf(c_36,plain,
member(x,x),
inference(clausify,[status(thm)],[prove_no_class_belongs_to_itself_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_27811,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_27811]) ).
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(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_27812,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_27812]) ).
cnf(c_27813,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_27813]) ).
cnf(c_269,plain,
( member(x,intersection(A,x))
| ~ member(x,A) ),
inference(resolve,[status(thm)],[c_120,c_36]) ).
cnf(c_27814,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_274,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_27814]) ).
cnf(c_27815,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_287,plain,
( unordered_pair(A,B) = null_class
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_27815]) ).
cnf(c_288,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_287]) ).
cnf(c_314,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_422,plain,
( ~ member(B,domain_of(A))
| intersection(A,cross_product(unordered_pair(B,B),universal_class)) != null_class ),
inference(paramod,[status(thm)],[c_113,c_225]) ).
cnf(c_488,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_314,c_76]) ).
cnf(c_489,plain,
member(x,universal_class),
inference(resolve,[status(thm)],[c_314,c_36]) ).
cnf(c_507,plain,
member(x,unordered_pair(x,A)),
inference(resolve,[status(thm)],[c_489,c_136]) ).
cnf(c_508,plain,
member(x,unordered_pair(A,x)),
inference(resolve,[status(thm)],[c_489,c_135]) ).
cnf(c_674,plain,
member(x,intersection(unordered_pair(A,x),x)),
inference(resolve,[status(thm)],[c_269,c_508]) ).
cnf(c_27816,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_488,c_258]) ).
cnf(c_27817,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_27816]) ).
cnf(c_803,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_27817]) ).
cnf(c_27818,plain,
( ~ member(regular(A),complement(universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_488,c_119]) ).
cnf(c_824,plain,
( ~ member(regular(A),null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_803,c_27818]) ).
cnf(c_27819,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_824,c_274]) ).
cnf(c_27820,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_27819]) ).
cnf(c_943,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_27820]) ).
cnf(c_968,plain,
~ member(A,domain_of(null_class)),
inference(resolve,[status(thm)],[c_943,c_422]) ).
cnf(c_27821,plain,
null_class = domain_of(null_class),
inference(resolve,[status(thm)],[c_968,c_76]) ).
cnf(c_974,plain,
domain_of(null_class) = null_class,
inference(copy,[status(thm)],[c_27821]) ).
cnf(c_975,plain,
~ member(A,null_class),
inference(paramod,[status(thm)],[c_974,c_968]) ).
cnf(c_27822,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_288,c_74]) ).
cnf(c_27823,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_27822]) ).
cnf(c_1010,plain,
( intersection(unordered_pair(A,A),A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_27823]) ).
cnf(c_27824,plain,
( member(x,null_class)
| unordered_pair(x,x) = null_class ),
inference(paramod,[status(thm)],[c_1010,c_674]) ).
cnf(c_27457,plain,
unordered_pair(x,x) = null_class,
inference(resolve,[status(thm)],[c_975,c_27824]) ).
cnf(c_27825,plain,
member(x,null_class),
inference(paramod,[status(thm)],[c_27457,c_507]) ).
cnf(c_27810,plain,
$false,
inference(resolve,[status(thm)],[c_975,c_27825]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET515-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 26 07:50:50 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 55128 was started by sandbox on n012,
% 0.02/0.30 % Sat Sep 26 07:50:50 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 48.70/7.33
% 48.70/7.33 % given #500 (A,wt=41): 409 -compatible(intersection(successor_relation,cross_product(omega,universal_class)),A,B) | maps(intersection(successor_relation,cross_product(omega,universal_class)),domain_of(intersection(successor_relation,cross_product(omega,universal_class))),omega). [resolve(212,a,152,b)].
% 48.70/7.33
% 48.70/7.33 % given #1000 (A,wt=53): 681 -member(A,B) | member(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(A,A))),cross_product(unordered_pair(C,null_class),B)). [resolve(530,a,235,a)].
% 48.70/7.33
% 48.70/7.33 % given #1500 (A,wt=27): 904 member(null_class,A) | -member(null_class,B) | member(null_class,intersection(complement(A),B)). [resolve(534,a,120,a)].
% 48.70/7.33
% 48.70/7.33 % SZS status Unsatisfiable for theBenchmark
% 48.70/7.33
% 48.70/7.33 % Proof 1 at 6.09 (+ 0.89) seconds.
% 48.70/7.33 % Length of proof is 42.
% 48.70/7.33 % Level of proof is 10.
% 48.70/7.33 % Maximum clause weight is 33.000.
% 48.70/7.33 % Given clauses 1754.
% 48.70/7.33
% 48.70/7.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------