%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET067-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:35:36 AM UTC 2026
% Result : Unsatisfiable 12.24s 2.08s
% Output : CNFRefutation 12.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 24 unt; 0 def)
% Number of atoms : 134 ( 61 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 104 ( 45 ~; 59 |; 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 : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 107 ( 11 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_in_unordered_pair1_1,axiom,
~ subclass(singleton(x),unordered_pair(x,y)),
file('theBenchmark.p',prove_singleton_in_unordered_pair1_1) ).
cnf(c_34,plain,
~ subclass(singleton(x),unordered_pair(x,y)),
inference(clausify,[status(thm)],[prove_singleton_in_unordered_pair1_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_51,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_52,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_51]) ).
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_85,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_86,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_87,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_86]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_95,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
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_97,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_98,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_108,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_109,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_108]) ).
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_112,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_113,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
fof(equal_implies_subclass1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass1) ).
cnf(c_116,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass1]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_117,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_118,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_119,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_120,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_5523,plain,
( ~ member(B,domain_of(A))
| restrict(A,unordered_pair(B,B),universal_class) != null_class ),
inference(paramod,[status(thm)],[c_109,c_85]) ).
cnf(c_176,plain,
( ~ member(A,domain_of(B))
| intersection(cross_product(unordered_pair(A,A),universal_class),B) != null_class ),
inference(paramod,[status(thm)],[c_87,c_5523]) ).
cnf(c_195,plain,
~ subclass(unordered_pair(x,x),unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_109,c_34]) ).
cnf(c_196,plain,
( A = B
| ~ member(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_113]) ).
cnf(c_5524,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_95,c_52]) ).
cnf(c_203,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_5524]) ).
cnf(c_5525,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_97,c_52]) ).
cnf(c_213,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_5525]) ).
cnf(c_5526,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_98,c_52]) ).
cnf(c_215,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_5526]) ).
cnf(c_5527,plain,
( null_class = unordered_pair(A,B)
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(resolve,[status(thm)],[c_113,c_52]) ).
cnf(c_227,plain,
( unordered_pair(A,B) = null_class
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_5527]) ).
cnf(c_228,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_227]) ).
cnf(c_249,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_120,c_117]) ).
cnf(c_347,plain,
member(not_subclass_element(unordered_pair(x,x),unordered_pair(x,y)),unordered_pair(x,x)),
inference(resolve,[status(thm)],[c_195,c_119]) ).
cnf(c_348,plain,
~ member(not_subclass_element(unordered_pair(x,x),unordered_pair(x,y)),unordered_pair(x,y)),
inference(resolve,[status(thm)],[c_118,c_195]) ).
cnf(c_389,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_249,c_52]) ).
cnf(c_5528,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_389,c_203]) ).
cnf(c_5529,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_5528]) ).
cnf(c_611,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_5529]) ).
cnf(c_5530,plain,
( ~ member(regular(A),complement(universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_389,c_95]) ).
cnf(c_630,plain,
( ~ member(regular(A),null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_611,c_5530]) ).
cnf(c_5531,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_630,c_215]) ).
cnf(c_5532,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_5531]) ).
cnf(c_902,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_5532]) ).
cnf(c_5533,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_630,c_213]) ).
cnf(c_5534,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_5533]) ).
cnf(c_903,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_5534]) ).
cnf(c_954,plain,
( member(A,B)
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_902,c_97]) ).
cnf(c_955,plain,
~ member(A,domain_of(null_class)),
inference(resolve,[status(thm)],[c_903,c_176]) ).
cnf(c_969,plain,
~ member(A,null_class),
inference(resolve,[status(thm)],[c_954,c_955]) ).
cnf(c_5535,plain,
( null_class = unordered_pair(A,A)
| member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(paramod,[status(thm)],[c_228,c_389]) ).
cnf(c_5536,plain,
( unordered_pair(A,A) = null_class
| member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_5535]) ).
cnf(c_1015,plain,
( member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_5536]) ).
cnf(c_1756,plain,
( member(A,unordered_pair(A,B))
| unordered_pair(A,A) = null_class ),
inference(resolve,[status(thm)],[c_1015,c_112]) ).
cnf(c_5497,plain,
not_subclass_element(unordered_pair(x,x),unordered_pair(x,y)) = x,
inference(resolve,[status(thm)],[c_347,c_196]) ).
cnf(c_5537,plain,
( member(not_subclass_element(unordered_pair(x,x),unordered_pair(x,y)),A)
| ~ subclass(unordered_pair(x,x),A) ),
inference(resolve,[status(thm)],[c_120,c_347]) ).
cnf(c_5506,plain,
~ subclass(unordered_pair(x,x),null_class),
inference(resolve,[status(thm)],[c_5537,c_969]) ).
cnf(c_5517,plain,
~ member(x,unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_5497,c_348]) ).
cnf(c_5521,plain,
unordered_pair(x,x) != null_class,
inference(resolve,[status(thm)],[c_116,c_5506]) ).
cnf(c_5538,plain,
unordered_pair(x,x) = null_class,
inference(resolve,[status(thm)],[c_5517,c_1756]) ).
cnf(c_5522,plain,
$false,
inference(resolve,[status(thm)],[c_5521,c_5538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET067-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 07:02:04 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 665344 was started by sandbox2 on n019,
% 0.18/0.45 % Sat Sep 26 07:02:04 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 12.24/2.08
% 12.24/2.08 % given #500 (W,wt=17): 1826 unordered_pair(omega,universal_class) != unordered_pair(null_class,A). [ur(116,b,1037,a),flip(a)].
% 12.24/2.08
% 12.24/2.08 % SZS status Unsatisfiable for theBenchmark
% 12.24/2.08
% 12.24/2.08 % Proof 1 at 1.28 (+ 0.31) seconds.
% 12.24/2.08 % Length of proof is 44.
% 12.24/2.08 % Level of proof is 10.
% 12.24/2.08 % Maximum clause weight is 33.000.
% 12.24/2.08 % Given clauses 583.
% 12.24/2.08
% 12.24/2.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------