%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Thu Sep 24 02:19:22 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 29
% Syntax : Number of formulae : 132 ( 24 unt; 11 def)
% Number of atoms : 384 ( 75 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 411 ( 159 ~; 171 |; 53 &)
% ( 22 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 236 ( 224 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f36,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f74,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f75,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f78,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f80,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f100,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f101,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
( ! [A,B,C] :
( ( ( in(sK3_skl(C,B,A),B)
| in(sK3_skl(C,B,A),A)
| in(sK3_skl(C,B,A),C) )
& ( ( ~ in(sK3_skl(C,B,A),B)
& ~ in(sK3_skl(C,B,A),A) )
| ~ in(sK3_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f109,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f110,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f112,plain,
( ! [A,B] :
( ( ~ in(sK4_skl(B,A),B)
& in(sK4_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(C,sK4_skl(B,A))],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( in(sK4_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(sK4_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f125,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f126,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK6_skl(C,B,A),B)
& in(sK6_skl(C,B,A),A) )
| in(sK6_skl(C,B,A),C) )
& ( in(sK6_skl(C,B,A),B)
| ~ in(sK6_skl(C,B,A),A)
| ~ in(sK6_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(D,sK6_skl(C,B,A))],[f126]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f143,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f144,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f145,plain,
! [A] :
( ! [B] : ~ empty(set_union2(A,B))
| empty(A) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f148,plain,
! [A] :
( ! [B] : ~ empty(set_union2(B,A))
| empty(A) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f157,plain,
? [A,B] :
( subset(singleton(A),B)
<~> in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f158,plain,
? [A,B] :
( ( ~ in(A,B)
| ~ subset(singleton(A),B) )
& ( in(A,B)
| subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
( ( ~ in(sK7_skl,sK8_skl)
| ~ subset(singleton(sK7_skl),sK8_skl) )
& ( in(sK7_skl,sK8_skl)
| subset(singleton(sK7_skl),sK8_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f158]) ).
fof(f160,plain,
( in(sK7_skl,sK8_skl)
| subset(singleton(sK7_skl),sK8_skl) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
( ~ in(sK7_skl,sK8_skl)
| ~ subset(singleton(sK7_skl),sK8_skl) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f174,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f175,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f179,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f194,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f198,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f217,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f229,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f230,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f234,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f244,definition,
( sQ0_spl
<=> subset(singleton(sK7_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ0_spl
| subset(singleton(sK7_skl),sK8_skl) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( sQ0_spl
| ~ subset(singleton(sK7_skl),sK8_skl) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
( sQ1_spl
<=> in(sK7_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ1_spl
| in(sK7_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f160,f244,f247]) ).
fof(f251,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f161,f244,f247]) ).
fof(f254,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f82]) ).
fof(f255,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f83]) ).
fof(f260,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f103]) ).
fof(f262,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f105]) ).
fof(f267,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f129]) ).
fof(f278,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f194,f78]) ).
fof(f287,plain,
! [X0] : X0 = set_union2(empty_set,X0),
inference(paramodulation,[status(thm)],[f179,f72]) ).
fof(f336,plain,
! [X0] : set_intersection2(empty_set,X0) = empty_set,
inference(resolution,[status(thm)],[f176,f278]) ).
fof(f339,plain,
! [X0,X1] :
( ~ subset(X0,set_intersection2(X0,X1))
| X0 = set_intersection2(X0,X1) ),
inference(resolution,[status(thm)],[f176,f78]) ).
fof(f354,plain,
! [X0,X1] :
( ~ subset(X0,set_difference(X0,X1))
| X0 = set_difference(X0,X1) ),
inference(resolution,[status(thm)],[f198,f78]) ).
fof(f361,plain,
! [X0,X1,X2] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f234,f113]) ).
fof(f459,plain,
! [X0] :
( ~ sQ1_spl
| in(sK7_skl,set_union2(sK8_skl,X0)) ),
inference(resolution,[status(thm)],[f361,f248]) ).
fof(f462,plain,
! [X0,X1] : in(X0,set_union2(singleton(X0),X1)),
inference(resolution,[status(thm)],[f361,f255]) ).
fof(f463,plain,
! [X0,X1] :
( ~ sQ1_spl
| in(sK7_skl,set_union2(set_union2(sK8_skl,X0),X1)) ),
inference(resolution,[status(thm)],[f459,f361]) ).
fof(f466,plain,
! [X0] :
( ~ sQ1_spl
| in(sK7_skl,set_union2(X0,sK8_skl)) ),
inference(paramodulation,[status(thm)],[f72,f459]) ).
fof(f473,plain,
! [X0] :
( ~ subset(empty_set,empty_set)
| empty_set = set_intersection2(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f336,f339]) ).
fof(f478,definition,
! [X0] :
( sQ2_spl
<=> empty_set = set_intersection2(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f481,definition,
( sQ3_spl
<=> subset(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ3_spl
| ~ subset(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f473,f478,f481]) ).
fof(f561,definition,
! [X0] :
( sQ6_spl
<=> in(sK7_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f562,plain,
! [X0] :
( ~ sQ6_spl
| in(sK7_skl,X0) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f586,plain,
! [X0] :
( ~ subset(empty_set,empty_set)
| empty_set = set_difference(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f217,f354]) ).
fof(f588,definition,
! [X0] :
( sQ7_spl
<=> empty_set = set_difference(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f586,f588,f481]) ).
fof(f592,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f194]) ).
fof(f593,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f606,plain,
! [X0,X1] :
( X0 = empty_set
| ~ empty(set_union2(X0,X1)) ),
inference(resolution,[status(thm)],[f146,f230]) ).
fof(f619,plain,
! [X0] :
( ~ empty(X0)
| empty(empty_set) ),
inference(paramodulation,[status(thm)],[f179,f149]) ).
fof(f623,definition,
( sQ8_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f626,definition,
! [X0] :
( sQ9_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f627,plain,
! [X0] :
( ~ sQ9_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f629,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f619,f623,f626]) ).
fof(f630,plain,
( ~ sQ0_spl
| set_union2(singleton(sK7_skl),sK8_skl) = sK8_skl ),
inference(resolution,[status(thm)],[f175,f245]) ).
fof(f722,plain,
( ~ sQ0_spl
| in(sK7_skl,sK8_skl) ),
inference(paramodulation,[status(thm)],[f630,f462]) ).
fof(f731,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f722,f247,f244]) ).
fof(f775,plain,
! [X0,X1] :
( ~ sQ1_spl
| in(sK7_skl,set_union2(X0,set_union2(X1,sK8_skl))) ),
inference(resolution,[status(thm)],[f466,f262]) ).
fof(f899,plain,
! [X0,X1] :
( sK4_skl(X1,singleton(X0)) = X0
| subset(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f114,f254]) ).
fof(f1015,plain,
! [X0] :
( empty_set = empty_set
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f287,f606]) ).
fof(f1023,definition,
( sQ12_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( sQ12_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1015,f626,f1023]) ).
fof(f1027,plain,
( ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f143,f627]) ).
fof(f1028,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1027]) ).
fof(f1364,plain,
! [X0,X1] :
( ~ sQ1_spl
| in(sK7_skl,X1)
| in(sK7_skl,set_union2(sK8_skl,X0)) ),
inference(resolution,[status(thm)],[f463,f260]) ).
fof(f1383,definition,
! [X0] :
( sQ15_spl
<=> in(sK7_skl,set_union2(sK8_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1386,plain,
( ~ sQ1_spl
| sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f1364,f1383,f561,f247]) ).
fof(f1387,plain,
! [X0,X1] :
( ~ sQ1_spl
| in(sK7_skl,set_union2(X1,sK8_skl))
| in(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f775,f260]) ).
fof(f1406,definition,
! [X1] :
( sQ16_spl
<=> in(sK7_skl,set_union2(X1,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1407,plain,
! [X0] :
( ~ sQ16_spl
| in(sK7_skl,set_union2(X0,sK8_skl)) ),
inference(component_clause,[status(thm)],[f1406]) ).
fof(f1409,plain,
( ~ sQ1_spl
| sQ16_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1387,f561,f1406,f247]) ).
fof(f1421,plain,
! [X0] :
( ~ sQ6_spl
| ~ in(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f562,f267]) ).
fof(f1434,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1421,f562]) ).
fof(f1435,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f1434]) ).
fof(f1440,plain,
! [X0] :
( ~ sQ16_spl
| in(sK7_skl,sK8_skl)
| in(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f1407,f260]) ).
fof(f1452,plain,
( ~ sQ16_spl
| sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1440,f561,f247,f1406]) ).
fof(f1470,plain,
( sQ0_spl
| sK4_skl(sK8_skl,singleton(sK7_skl)) = sK7_skl ),
inference(resolution,[status(thm)],[f899,f246]) ).
fof(f1685,plain,
( sQ0_spl
| ~ in(sK7_skl,sK8_skl)
| subset(singleton(sK7_skl),sK8_skl) ),
inference(paramodulation,[status(thm)],[f1470,f115]) ).
fof(f1691,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1685,f244,f247]) ).
fof(f1696,plain,
$false,
inference(sat_refutation,[status(thm)],[f250,f251,f484,f591,f593,f629,f731,f1026,f1028,f1386,f1409,f1435,f1452,f1691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:54:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.112316 seconds
% 0.12/0.47 % CPU time: 0.555244 seconds
% 0.12/0.47 % Total memory used: 112.242 MB
% 0.12/0.47 % Net memory used: 110.988 MB
%------------------------------------------------------------------------------