%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU138+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:19:20 PM UTC 2026
% Result : Theorem 0.27s 1.20s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 128 ( 31 unt; 11 def)
% Number of atoms : 404 ( 65 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 457 ( 181 ~; 186 |; 67 &)
% ( 20 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 244 ( 229 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f53,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,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)],[f6]) ).
fof(f68,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)],[f67]) ).
fof(f69,plain,
( ! [A,B,C] :
( ( ( in(sK1_skl(C,B,A),B)
| in(sK1_skl(C,B,A),A)
| in(sK1_skl(C,B,A),C) )
& ( ( ~ in(sK1_skl(C,B,A),B)
& ~ in(sK1_skl(C,B,A),A) )
| ~ in(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f68]) ).
fof(f75,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X2)
| in(sK1_skl(X0,X2,X1),X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f77,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)],[f76]) ).
fof(f78,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)],[f77]) ).
fof(f79,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_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,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,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_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f84,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_intersection2(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_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,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_intersection2(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_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f84]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ in(sK3_skl(X0,X2,X1),X2)
| ~ in(sK3_skl(X0,X2,X1),X1)
| ~ in(sK3_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X2,X1),X1)
| in(sK3_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f91,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X2,X1),X2)
| in(sK3_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f92,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)],[f9]) ).
fof(f93,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)],[f92]) ).
fof(f94,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK4_skl(C,B,A),B)
& in(sK4_skl(C,B,A),A) )
| in(sK4_skl(C,B,A),C) )
& ( in(sK4_skl(C,B,A),B)
| ~ in(sK4_skl(C,B,A),A)
| ~ in(sK4_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,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f93]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f114,plain,
! [A] : set_intersection2(A,A) = A,
inference(miniscoping,[status(thm)],[f19]) ).
fof(f115,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f133,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f140,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f141,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f148,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f152,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f159,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f160,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f161,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ( in(sK8_skl(B,A),B)
& in(sK8_skl(B,A),A) )
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(C,sK8_skl(B,A))],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( in(sK8_skl(X1,X0),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( in(sK8_skl(X1,X0),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f170,plain,
? [A,B] : set_difference(A,set_difference(A,B)) != set_intersection2(A,B),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f171,plain,
set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)) != set_intersection2(sK9_skl,sK10_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(A,sK9_skl),skolemize(B,sK10_skl)],[f170]) ).
fof(f172,plain,
set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)) != set_intersection2(sK9_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f192,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f65]) ).
fof(f197,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f87]) ).
fof(f199,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f95]) ).
fof(f200,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f96]) ).
fof(f201,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f97]) ).
fof(f212,plain,
! [X0,X1] :
( set_intersection2(X1,X0) = X0
| ~ subset(X0,X1) ),
inference(paramodulation,[status(thm)],[f56,f141]) ).
fof(f218,plain,
! [X0,X1] : ~ in(X0,set_intersection2(X1,empty_set)),
inference(resolution,[status(thm)],[f192,f197]) ).
fof(f220,plain,
! [X0,X1] : ~ in(X0,set_intersection2(X1,X0)),
inference(resolution,[status(thm)],[f54,f197]) ).
fof(f251,plain,
! [X0] : disjoint(empty_set,X0),
inference(resolution,[status(thm)],[f162,f192]) ).
fof(f254,plain,
! [X0] : disjoint(X0,empty_set),
inference(resolution,[status(thm)],[f163,f192]) ).
fof(f299,plain,
! [X0,X1] :
( in(sK1_skl(empty_set,X1,X0),X1)
| in(sK1_skl(empty_set,X1,X0),X0)
| empty_set = set_union2(X0,X1) ),
inference(resolution,[status(thm)],[f75,f192]) ).
fof(f410,plain,
! [X0] :
( in(sK1_skl(empty_set,empty_set,X0),X0)
| empty_set = set_union2(X0,empty_set) ),
inference(resolution,[status(thm)],[f299,f192]) ).
fof(f553,plain,
! [X0] : ~ in(X0,X0),
inference(paramodulation,[status(thm)],[f115,f220]) ).
fof(f581,plain,
! [X0,X1] : ~ in(X0,set_difference(X0,X1)),
inference(resolution,[status(thm)],[f199,f553]) ).
fof(f610,plain,
! [X0,X1,X2,X3] :
( in(sK3_skl(set_difference(X0,X1),X2,X3),X2)
| set_difference(X0,X1) = set_intersection2(X3,X2)
| ~ in(sK3_skl(set_difference(X0,X1),X2,X3),X1) ),
inference(resolution,[status(thm)],[f200,f91]) ).
fof(f693,plain,
! [X0] :
( in(sK1_skl(empty_set,empty_set,X0),X0)
| empty_set = X0 ),
inference(backward_demodulation,[status(thm)],[f133,f410]) ).
fof(f1177,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(resolution,[status(thm)],[f218,f693]) ).
fof(f1525,plain,
! [X0] :
( empty_set = empty_set
| ~ subset(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f1177,f212]) ).
fof(f1560,definition,
! [X0] :
( sQ2_spl
<=> ~ subset(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1561,plain,
! [X0] :
( ~ sQ2_spl
| ~ subset(empty_set,X0) ),
inference(component_clause,[status(thm)],[f1560]) ).
fof(f1563,definition,
( sQ3_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1566,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1525,f1560,f1563]) ).
fof(f1567,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1561,f148]) ).
fof(f1568,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1567]) ).
fof(f1578,definition,
( sQ5_spl
<=> subset(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1580,plain,
( sQ5_spl
| ~ subset(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f1578]) ).
fof(f1583,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1580,f152]) ).
fof(f1584,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1583]) ).
fof(f2412,plain,
( ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK10_skl)
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK9_skl)
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl))) ),
inference(resolution,[status(thm)],[f89,f172]) ).
fof(f2418,definition,
( sQ10_spl
<=> in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f2420,plain,
( sQ10_spl
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl))) ),
inference(component_clause,[status(thm)],[f2418]) ).
fof(f2421,definition,
( sQ11_spl
<=> in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f2423,plain,
( sQ11_spl
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK9_skl) ),
inference(component_clause,[status(thm)],[f2421]) ).
fof(f2424,definition,
( sQ12_spl
<=> in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f2426,plain,
( sQ12_spl
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK10_skl) ),
inference(component_clause,[status(thm)],[f2424]) ).
fof(f2427,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2412,f2418,f2421,f2424]) ).
fof(f2434,definition,
! [X0] :
( sQ13_spl
<=> ~ disjoint(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f2435,plain,
! [X0] :
( ~ sQ13_spl
| ~ disjoint(empty_set,X0) ),
inference(component_clause,[status(thm)],[f2434]) ).
fof(f2438,definition,
! [X0] :
( sQ14_spl
<=> ~ disjoint(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f2439,plain,
! [X0] :
( ~ sQ14_spl
| ~ disjoint(X0,empty_set) ),
inference(component_clause,[status(thm)],[f2438]) ).
fof(f2442,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2439,f254]) ).
fof(f2443,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f2442]) ).
fof(f2444,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2435,f251]) ).
fof(f2445,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f2444]) ).
fof(f2456,plain,
( sQ12_spl
| set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)) = set_intersection2(sK9_skl,sK10_skl)
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f2426,f610]) ).
fof(f2459,plain,
( sQ12_spl
| in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)))
| set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)) = set_intersection2(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f2426,f91]) ).
fof(f2468,definition,
( sQ15_spl
<=> in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2469,plain,
( ~ sQ15_spl
| in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f2468]) ).
fof(f2470,plain,
( sQ15_spl
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f2468]) ).
fof(f2471,definition,
( sQ16_spl
<=> set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)) = set_intersection2(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f2472,plain,
( ~ sQ16_spl
| set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)) = set_intersection2(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f2471]) ).
fof(f2474,plain,
( sQ12_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2456,f2468,f2471,f2424]) ).
fof(f2483,plain,
( sQ12_spl
| sQ10_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f2459,f2471,f2418,f2424]) ).
fof(f2486,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2472,f172]) ).
fof(f2487,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f2486]) ).
fof(f2492,plain,
! [X0] :
( sQ11_spl
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),X0)
| ~ subset(X0,sK9_skl) ),
inference(resolution,[status(thm)],[f2423,f80]) ).
fof(f2532,definition,
! [X0] :
( sQ20_spl
<=> in(sK2_skl(sK10_skl,set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl))),X0) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f2533,plain,
! [X0] :
( ~ sQ20_spl
| in(sK2_skl(sK10_skl,set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl))),X0) ),
inference(component_clause,[status(thm)],[f2532]) ).
fof(f2538,plain,
( ~ sQ20_spl
| $false ),
inference(resolution,[status(thm)],[f2533,f581]) ).
fof(f2549,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f2538]) ).
fof(f2569,plain,
( sQ15_spl
| in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK10_skl)
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK9_skl) ),
inference(resolution,[status(thm)],[f2470,f201]) ).
fof(f2578,plain,
( sQ15_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2569,f2421,f2424,f2468]) ).
fof(f2596,plain,
( sQ11_spl
| in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK9_skl)
| set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)) = set_intersection2(sK9_skl,sK10_skl)
| ~ subset(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK9_skl) ),
inference(resolution,[status(thm)],[f2492,f90]) ).
fof(f2641,plain,
( sQ11_spl
| sQ16_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2596,f1578,f2471,f2421]) ).
fof(f2827,plain,
( sQ10_spl
| in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),set_difference(sK9_skl,sK10_skl))
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK9_skl) ),
inference(resolution,[status(thm)],[f2420,f201]) ).
fof(f2842,plain,
( sQ10_spl
| sQ15_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2827,f2421,f2468,f2418]) ).
fof(f3208,plain,
( ~ sQ15_spl
| ~ in(sK3_skl(set_difference(sK9_skl,set_difference(sK9_skl,sK10_skl)),sK10_skl,sK9_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f2469,f200]) ).
fof(f3212,plain,
( ~ sQ15_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f3208,f2424,f2468]) ).
fof(f3213,plain,
$false,
inference(sat_refutation,[status(thm)],[f1566,f1568,f1584,f2427,f2443,f2445,f2474,f2483,f2487,f2549,f2578,f2641,f2842,f3212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU138+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:50:20 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.27/1.20 % Refutation found
% 0.27/1.20 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.27/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.17/1.25 % Elapsed time: 0.789185 seconds
% 1.17/1.25 % CPU time: 5.783281 seconds
% 1.17/1.25 % Total memory used: 144.353 MB
% 1.17/1.25 % Net memory used: 138.267 MB
%------------------------------------------------------------------------------