%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM156-1 : 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 : n010.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 08:16:13 AM UTC 2026
% Result : Unsatisfiable 97.09s 13.82s
% Output : CNFRefutation 97.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 33 unt; 0 def)
% Number of atoms : 65 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 25 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 56 ( 5 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inductive1,axiom,
! [VAR_0] :
( member(null_class,VAR_0)
| ~ inductive(VAR_0) ),
file('theBenchmark.p',inductive1) ).
cnf(c_3,plain,
( member(null_class,A)
| ~ inductive(A) ),
inference(clausify,[status(thm)],[inductive1]) ).
fof(omega_is_inductive1,axiom,
inductive(omega),
file('theBenchmark.p',omega_is_inductive1) ).
cnf(c_4,plain,
inductive(omega),
inference(clausify,[status(thm)],[omega_is_inductive1]) ).
cnf(c_51,plain,
member(null_class,omega),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(prove_null_class_is_kind_1_1,axiom,
~ member(null_class,kind_1_ordinals),
file('theBenchmark.p',prove_null_class_is_kind_1_1) ).
cnf(c_53,plain,
~ member(null_class,kind_1_ordinals),
inference(clausify,[status(thm)],[prove_null_class_is_kind_1_1]) ).
fof(kind_1_ordinals,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('theBenchmark.p',kind_1_ordinals) ).
cnf(c_77,plain,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
inference(clausify,[status(thm)],[kind_1_ordinals]) ).
cnf(c_78,plain,
kind_1_ordinals = union(singleton(null_class),image(successor_relation,ordinal_numbers)),
inference(copy,[status(thm)],[c_77]) ).
fof(image,axiom,
! [VAR_0,VAR_1] : range_of(restrict(VAR_0,VAR_1,universal_class)) = image(VAR_0,VAR_1),
file('theBenchmark.p',image) ).
cnf(c_152,plain,
range_of(restrict(A,B,universal_class)) = image(A,B),
inference(clausify,[status(thm)],[image]) ).
cnf(c_153,plain,
image(A,B) = range_of(restrict(A,B,universal_class)),
inference(copy,[status(thm)],[c_152]) ).
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_172,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_173,plain,
restrict(A,B,C) = intersection(A,cross_product(B,C)),
inference(copy,[status(thm)],[c_172]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : complement(intersection(complement(VAR_0),complement(VAR_1))) = union(VAR_0,VAR_1),
file('theBenchmark.p',union) ).
cnf(c_176,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_177,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_176]) ).
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| member(VAR_0,complement(VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',complement2) ).
cnf(c_178,plain,
( member(A,B)
| member(A,complement(B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_179,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
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_182,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_192,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_193,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_192]) ).
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_195,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_201,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_204,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_219,plain,
~ member(null_class,union(singleton(null_class),image(successor_relation,ordinal_numbers))),
inference(paramod,[status(thm)],[c_78,c_53]) ).
cnf(c_410,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_204,c_201]) ).
cnf(c_444,plain,
~ member(null_class,union(unordered_pair(null_class,null_class),image(successor_relation,ordinal_numbers))),
inference(paramod,[status(thm)],[c_193,c_219]) ).
cnf(c_445,plain,
~ member(null_class,union(unordered_pair(null_class,null_class),range_of(restrict(successor_relation,ordinal_numbers,universal_class)))),
inference(paramod,[status(thm)],[c_153,c_444]) ).
cnf(c_453,plain,
~ member(null_class,union(unordered_pair(null_class,null_class),range_of(intersection(successor_relation,cross_product(ordinal_numbers,universal_class))))),
inference(paramod,[status(thm)],[c_173,c_445]) ).
cnf(c_492,plain,
member(null_class,universal_class),
inference(resolve,[status(thm)],[c_410,c_51]) ).
cnf(c_496,plain,
member(null_class,unordered_pair(A,null_class)),
inference(resolve,[status(thm)],[c_492,c_195]) ).
cnf(c_501,plain,
( member(null_class,A)
| member(null_class,complement(A)) ),
inference(resolve,[status(thm)],[c_492,c_178]) ).
cnf(c_579,plain,
~ member(null_class,complement(intersection(complement(unordered_pair(null_class,null_class)),complement(range_of(intersection(successor_relation,cross_product(ordinal_numbers,universal_class))))))),
inference(paramod,[status(thm)],[c_177,c_453]) ).
cnf(c_944,plain,
member(null_class,intersection(complement(unordered_pair(null_class,null_class)),complement(range_of(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)))))),
inference(resolve,[status(thm)],[c_501,c_579]) ).
cnf(c_20931,plain,
member(null_class,complement(unordered_pair(null_class,null_class))),
inference(resolve,[status(thm)],[c_944,c_182]) ).
cnf(c_20953,plain,
~ member(null_class,unordered_pair(null_class,null_class)),
inference(resolve,[status(thm)],[c_20931,c_179]) ).
cnf(c_20952,plain,
$false,
inference(resolve,[status(thm)],[c_496,c_20953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM156-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 02:08:14 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2233684 was started by sandbox on n010,
% 0.16/0.44 % Sat Sep 26 02:08:14 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 97.09/13.82
% 97.09/13.82 % given #500 (W,wt=13): 961 member(image(A,null_class),universal_class) | recursion_equation_functions(A) = null_class. [resolve(505,a,231,b)].
% 97.09/13.82
% 97.09/13.82 % given #1000 (T,wt=13): 10316 member(power_class(omega),A) | member(not_subclass_element(universal_class,A),universal_class). [resolve(409,a,243,a)].
% 97.09/13.82
% 97.09/13.82 % given #1500 (A,wt=28): 627 null_class = universal_class | regular(universal_class) = null_class | -member(apply(choice,regular(universal_class)),A) | member(apply(choice,regular(universal_class)),intersection(A,regular(universal_class))). [resolve(225,c,180,b)].
% 97.09/13.82
% 97.09/13.82 % given #2000 (T,wt=15): 4111 member(complement(intersection(universal_class,universal_class)),unordered_pair(A,complement(universal_class))). [para(2189(a,1),2254(a,1))].
% 97.09/13.82
% 97.09/13.82 % SZS status Unsatisfiable for theBenchmark
% 97.09/13.82
% 97.09/13.82 % Proof 1 at 3.39 (+ 1.77) seconds.
% 97.09/13.82 % Length of proof is 32.
% 97.09/13.82 % Level of proof is 9.
% 97.09/13.82 % Maximum clause weight is 29.000.
% 97.09/13.82 % Given clauses 2445.
% 97.09/13.82
% 97.09/13.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------