%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET163-6 : 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 : n016.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 08:35:57 AM UTC 2026
% Result : Unsatisfiable 158.17s 26.50s
% Output : CNFRefutation 158.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 19 unt; 0 def)
% Number of atoms : 107 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 79 ( 31 ~; 48 |; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 9 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_union_with_universal_class_1,axiom,
union(universal_class,x) != universal_class,
file('theBenchmark.p',prove_union_with_universal_class_1) ).
cnf(c_36,plain,
union(universal_class,x) != universal_class,
inference(clausify,[status(thm)],[prove_union_with_universal_class_1]) ).
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(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_116,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_117,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_116]) ).
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_118,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_119,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_122,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_138,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
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(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_142,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_143,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_144,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_231,plain,
complement(intersection(complement(universal_class),complement(x))) != universal_class,
inference(paramod,[status(thm)],[c_117,c_36]) ).
cnf(c_23610,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_23610]) ).
cnf(c_303,plain,
( universal_class = A
| ~ subclass(universal_class,A) ),
inference(resolve,[status(thm)],[c_141,c_138]) ).
cnf(c_307,plain,
( member(not_subclass_element(intersection(A,B),C),A)
| subclass(intersection(A,B),C) ),
inference(resolve,[status(thm)],[c_143,c_122]) ).
cnf(c_311,plain,
( ~ member(not_subclass_element(complement(A),B),A)
| subclass(complement(A),B) ),
inference(resolve,[status(thm)],[c_143,c_119]) ).
cnf(c_317,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_439,plain,
( member(not_subclass_element(universal_class,A),universal_class)
| universal_class = A ),
inference(resolve,[status(thm)],[c_303,c_143]) ).
cnf(c_440,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),universal_class) ),
inference(resolve,[status(thm)],[c_317,c_143]) ).
cnf(c_441,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_317,c_76]) ).
cnf(c_23611,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_441,c_258]) ).
cnf(c_23612,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_23611]) ).
cnf(c_609,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_23612]) ).
cnf(c_626,plain,
complement(intersection(null_class,complement(x))) != universal_class,
inference(paramod,[status(thm)],[c_609,c_231]) ).
cnf(c_808,plain,
( member(not_subclass_element(universal_class,A),B)
| member(not_subclass_element(universal_class,A),complement(B))
| universal_class = A ),
inference(resolve,[status(thm)],[c_439,c_118]) ).
cnf(c_23613,plain,
( subclass(intersection(A,B),A)
| subclass(intersection(A,B),A) ),
inference(resolve,[status(thm)],[c_307,c_142]) ).
cnf(c_1513,plain,
subclass(intersection(A,B),A),
inference(copy,[status(thm)],[c_23613]) ).
cnf(c_23614,plain,
( subclass(complement(universal_class),A)
| subclass(complement(universal_class),A) ),
inference(resolve,[status(thm)],[c_311,c_440]) ).
cnf(c_23615,plain,
( subclass(complement(universal_class),A)
| subclass(null_class,A) ),
inference(paramod,[status(thm)],[c_609,c_23614]) ).
cnf(c_23616,plain,
( subclass(null_class,A)
| subclass(null_class,A) ),
inference(paramod,[status(thm)],[c_609,c_23615]) ).
cnf(c_1575,plain,
subclass(null_class,A),
inference(copy,[status(thm)],[c_23616]) ).
cnf(c_1576,plain,
( member(A,B)
| ~ member(A,null_class) ),
inference(resolve,[status(thm)],[c_1575,c_144]) ).
cnf(c_23617,plain,
( A = null_class
| ~ subclass(A,null_class) ),
inference(resolve,[status(thm)],[c_1575,c_138]) ).
cnf(c_1577,plain,
( null_class = A
| ~ subclass(A,null_class) ),
inference(copy,[status(thm)],[c_23617]) ).
cnf(c_23618,plain,
null_class = intersection(null_class,A),
inference(resolve,[status(thm)],[c_1577,c_1513]) ).
cnf(c_1601,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_23618]) ).
cnf(c_1609,plain,
complement(null_class) != universal_class,
inference(paramod,[status(thm)],[c_1601,c_626]) ).
cnf(c_23567,plain,
( member(not_subclass_element(universal_class,A),B)
| member(not_subclass_element(universal_class,A),complement(null_class))
| universal_class = A ),
inference(resolve,[status(thm)],[c_808,c_1576]) ).
cnf(c_23596,plain,
( member(not_subclass_element(universal_class,A),complement(null_class))
| universal_class = A ),
inference(factor,[status(thm)],[c_23567]) ).
cnf(c_23619,plain,
( subclass(universal_class,complement(null_class))
| universal_class = complement(null_class) ),
inference(resolve,[status(thm)],[c_23596,c_142]) ).
cnf(c_23620,plain,
( subclass(universal_class,complement(null_class))
| complement(null_class) = universal_class ),
inference(copy,[status(thm)],[c_23619]) ).
cnf(c_23603,plain,
subclass(universal_class,complement(null_class)),
inference(resolve,[status(thm)],[c_1609,c_23620]) ).
cnf(c_23621,plain,
universal_class = complement(null_class),
inference(resolve,[status(thm)],[c_23603,c_303]) ).
cnf(c_23622,plain,
complement(null_class) = universal_class,
inference(copy,[status(thm)],[c_23621]) ).
cnf(c_23609,plain,
$false,
inference(resolve,[status(thm)],[c_1609,c_23622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET163-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n016.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sat Sep 26 07:20:22 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.41 % Process 274845 was started by sandbox2 on n016,
% 0.13/5.41 % Sat Sep 26 07:20:22 2026
% 0.13/5.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.42
% 0.13/5.42 % From the command line: assign(max_seconds, 300).
% 158.17/26.50
% 158.17/26.50 % given #500 (A,wt=68): 421 complement(intersection(complement(intersection(cross_product(A,B),C)),complement(intersection(complement(cross_product(A,B)),complement(C))))) = complement(intersection(complement(intersection(C,cross_product(A,B))),complement(intersection(complement(cross_product(A,B)),complement(C))))). [para(254(a,1),117(a,2,1)),rewrite([117(7)])].
% 158.17/26.50
% 158.17/26.50 % given #1000 (T,wt=21): 835 member(not_subclass_element(A,B),universal_class) | -member(C,A) | member(C,B). [resolve(440,b,144,a)].
% 158.17/26.50
% 158.17/26.50 % SZS status Unsatisfiable for theBenchmark
% 158.17/26.50
% 158.17/26.50 % Proof 1 at 3.89 (+ 0.91) seconds.
% 158.17/26.50 % Length of proof is 35.
% 158.17/26.50 % Level of proof is 9.
% 158.17/26.50 % Maximum clause weight is 30.000.
% 158.17/26.50 % Given clauses 1091.
% 158.17/26.50
% 158.17/26.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------