%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET516-6 : 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 : n009.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 1.80s 0.68s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 102 ( 51 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 75 ( 28 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 6 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_no_class_belongs_to_itself_1,axiom,
singleton(x) = x,
file('theBenchmark.p',prove_corollary_to_no_class_belongs_to_itself_1) ).
cnf(c_36,plain,
singleton(x) = x,
inference(clausify,[status(thm)],[prove_corollary_to_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(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(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_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_134,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
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_176,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_120]) ).
cnf(c_2924,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_119,c_76]) ).
cnf(c_234,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_2924]) ).
cnf(c_292,plain,
unordered_pair(x,x) = x,
inference(paramod,[status(thm)],[c_133,c_36]) ).
cnf(c_385,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_472,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_385,c_76]) ).
cnf(c_608,plain,
member(x,universal_class),
inference(paramod,[status(thm)],[c_292,c_134]) ).
cnf(c_2925,plain,
( A = x
| A = x
| ~ member(A,x) ),
inference(paramod,[status(thm)],[c_292,c_137]) ).
cnf(c_2926,plain,
( A = x
| x = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_2925]) ).
cnf(c_2927,plain,
( x = A
| x = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_2926]) ).
cnf(c_609,plain,
( x = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_2927]) ).
cnf(c_614,plain,
member(x,unordered_pair(x,A)),
inference(resolve,[status(thm)],[c_608,c_136]) ).
cnf(c_2928,plain,
( null_class = x
| x = regular(x) ),
inference(resolve,[status(thm)],[c_609,c_76]) ).
cnf(c_2929,plain,
( null_class = x
| regular(x) = x ),
inference(copy,[status(thm)],[c_2928]) ).
cnf(c_626,plain,
( x = null_class
| regular(x) = x ),
inference(copy,[status(thm)],[c_2929]) ).
cnf(c_848,plain,
member(x,x),
inference(paramod,[status(thm)],[c_292,c_614]) ).
cnf(c_850,plain,
member(x,intersection(x,x)),
inference(resolve,[status(thm)],[c_848,c_176]) ).
cnf(c_2930,plain,
( intersection(x,x) = null_class
| null_class = x
| x = null_class ),
inference(paramod,[status(thm)],[c_626,c_74]) ).
cnf(c_2931,plain,
( intersection(x,x) = null_class
| x = null_class
| x = null_class ),
inference(copy,[status(thm)],[c_2930]) ).
cnf(c_1241,plain,
( intersection(x,x) = null_class
| x = null_class ),
inference(copy,[status(thm)],[c_2931]) ).
cnf(c_2932,plain,
( null_class = complement(universal_class)
| complement(universal_class) = null_class ),
inference(resolve,[status(thm)],[c_234,c_472]) ).
cnf(c_2933,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_2932]) ).
cnf(c_1537,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_2933]) ).
cnf(c_1545,plain,
( ~ member(A,universal_class)
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_1537,c_119]) ).
cnf(c_2804,plain,
( member(x,null_class)
| x = null_class ),
inference(paramod,[status(thm)],[c_1241,c_850]) ).
cnf(c_2934,plain,
( ~ member(x,universal_class)
| x = null_class ),
inference(resolve,[status(thm)],[c_2804,c_1545]) ).
cnf(c_2806,plain,
x = null_class,
inference(resolve,[status(thm)],[c_608,c_2934]) ).
cnf(c_2848,plain,
member(x,null_class),
inference(paramod,[status(thm)],[c_2806,c_848]) ).
cnf(c_2935,plain,
~ member(x,universal_class),
inference(resolve,[status(thm)],[c_2848,c_1545]) ).
cnf(c_2923,plain,
$false,
inference(resolve,[status(thm)],[c_608,c_2935]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET516-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:50:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3741994 was started by sandbox2 on n009,
% 0.08/0.36 % Sat Sep 26 07:50:59 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 1.80/0.68
% 1.80/0.68 % SZS status Unsatisfiable for theBenchmark
% 1.80/0.68
% 1.80/0.68 % Proof 1 at 0.22 (+ 0.07) seconds.
% 1.80/0.68 % Length of proof is 32.
% 1.80/0.68 % Level of proof is 10.
% 1.80/0.68 % Maximum clause weight is 24.000.
% 1.80/0.68 % Given clauses 359.
% 1.80/0.68
% 1.80/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------