%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU109+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 : Tue Sep 29 12:47:15 PM UTC 2026
% Result : Theorem 2.68s 1.27s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 151 ( 24 unt; 16 def)
% Number of atoms : 431 ( 12 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 468 ( 188 ~; 196 |; 57 &)
% ( 21 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 0 sgn 94 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f31,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f32,axiom,
! [X0] :
( ( ~ empty(X0)
& preboolean(X0) )
=> in(empty_set,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(f35,conjecture,
! [X0] :
( ( ~ empty(X0)
& preboolean(X0) )
=> ! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> ( ~ empty(set_intersection2(X0,X1))
& preboolean(set_intersection2(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_finsub_1) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& preboolean(X0) )
=> ! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> ( ~ empty(set_intersection2(X0,X1))
& preboolean(set_intersection2(X0,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f45,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f75,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f76,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0] :
( in(empty_set,X0)
| empty(X0)
| ~ preboolean(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f78,plain,
! [X0] :
( in(empty_set,X0)
| empty(X0)
| ~ preboolean(X0) ),
inference(flattening,[],[f77]) ).
fof(f80,plain,
? [X0] :
( ? [X1] :
( ( empty(set_intersection2(X0,X1))
| ~ preboolean(set_intersection2(X0,X1)) )
& ~ empty(X1)
& preboolean(X1) )
& ~ empty(X0)
& preboolean(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f81,plain,
? [X0] :
( ? [X1] :
( ( empty(set_intersection2(X0,X1))
| ~ preboolean(set_intersection2(X0,X1)) )
& ~ empty(X1)
& preboolean(X1) )
& ~ empty(X0)
& preboolean(X0) ),
inference(flattening,[],[f80]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X0)
& in(sK0(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f93]) ).
fof(f105,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) )
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f106,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X3,X4] :
( ( in(set_union2(X3,X4),X0)
& in(set_difference(X3,X4),X0) )
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ preboolean(X0) ) ),
inference(rectify,[],[f105]) ).
fof(f107,plain,
! [X0] :
( ( preboolean(X0)
| ( ( ~ in(set_union2(sK11(X0),sK12(X0)),X0)
| ~ in(set_difference(sK11(X0),sK12(X0)),X0) )
& in(sK11(X0),X0)
& in(sK12(X0),X0) ) )
& ( ! [X3,X4] :
( ( in(set_union2(X3,X4),X0)
& in(set_difference(X3,X4),X0) )
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ preboolean(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X1,sK11(X0)),skolemize(X2,sK12(X0))],[f106]) ).
fof(f108,plain,
( ( empty(set_intersection2(sK13,sK14))
| ~ preboolean(set_intersection2(sK13,sK14)) )
& ~ empty(sK14)
& preboolean(sK14)
& ~ empty(sK13)
& preboolean(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f81]) ).
fof(f117,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f118,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f119,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f160,plain,
! [X3,X0,X4] :
( ~ preboolean(X0)
| ~ in(X3,X0)
| ~ in(X4,X0)
| in(set_difference(X3,X4),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f161,plain,
! [X3,X0,X4] :
( ~ preboolean(X0)
| ~ in(X3,X0)
| ~ in(X4,X0)
| in(set_union2(X3,X4),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f162,plain,
! [X0] :
( preboolean(X0)
| in(sK12(X0),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f163,plain,
! [X0] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f164,plain,
! [X0] :
( preboolean(X0)
| ~ in(set_union2(sK11(X0),sK12(X0)),X0)
| ~ in(set_difference(sK11(X0),sK12(X0)),X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f165,plain,
! [X0] :
( ~ preboolean(X0)
| empty(X0)
| in(empty_set,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f168,plain,
preboolean(sK13),
inference(cnf_transformation,[],[f108]) ).
fof(f169,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
preboolean(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f171,plain,
~ empty(sK14),
inference(cnf_transformation,[],[f108]) ).
fof(f172,plain,
( empty(set_intersection2(sK13,sK14))
| ~ preboolean(set_intersection2(sK13,sK14)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f181,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f183,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f119]) ).
fof(f184,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f118]) ).
fof(f185,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f117]) ).
fof(f203,definition,
( spl16_1
<=> preboolean(set_intersection2(sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f204,plain,
( ~ preboolean(set_intersection2(sK13,sK14))
| spl16_1 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f206,definition,
( spl16_2
<=> empty(set_intersection2(sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f207,plain,
( empty(set_intersection2(sK13,sK14))
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f208,plain,
( ~ spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f172,f206,f203]) ).
fof(f217,plain,
( in(sK11(set_intersection2(sK13,sK14)),set_intersection2(sK13,sK14))
| spl16_1 ),
inference(resolution,[],[f163,f204]) ).
fof(f225,plain,
( empty(sK13)
| in(empty_set,sK13) ),
inference(resolution,[],[f165,f168]) ).
fof(f226,plain,
( empty(sK14)
| in(empty_set,sK14) ),
inference(resolution,[],[f165,f170]) ).
fof(f228,definition,
( spl16_3
<=> in(empty_set,sK14) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f229,plain,
( in(empty_set,sK14)
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,definition,
( spl16_4
<=> empty(sK14) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f232,plain,
( empty(sK14)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f233,plain,
( spl16_3
| spl16_4 ),
inference(avatar_split_clause,[],[f226,f231,f228]) ).
fof(f235,definition,
( spl16_5
<=> in(empty_set,sK13) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
fof(f236,plain,
( in(empty_set,sK13)
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,definition,
( spl16_6
<=> empty(sK13) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
fof(f239,plain,
( empty(sK13)
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( spl16_5
| spl16_6 ),
inference(avatar_split_clause,[],[f225,f238,f235]) ).
fof(f281,plain,
( in(sK11(set_intersection2(sK13,sK14)),sK14)
| spl16_1 ),
inference(resolution,[],[f185,f217]) ).
fof(f307,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ empty(set_intersection2(X1,X2)) ),
inference(resolution,[],[f183,f181]) ).
fof(f313,plain,
! [X0,X1] :
( in(set_difference(X0,X1),sK13)
| ~ in(X1,sK13)
| ~ in(X0,sK13) ),
inference(resolution,[],[f160,f168]) ).
fof(f314,plain,
! [X0,X1] :
( in(set_difference(X0,X1),sK14)
| ~ in(X1,sK14)
| ~ in(X0,sK14) ),
inference(resolution,[],[f160,f170]) ).
fof(f322,plain,
! [X0,X1] :
( in(set_union2(X0,X1),sK13)
| ~ in(X1,sK13)
| ~ in(X0,sK13) ),
inference(resolution,[],[f161,f168]) ).
fof(f323,plain,
! [X0,X1] :
( in(set_union2(X0,X1),sK14)
| ~ in(X1,sK14)
| ~ in(X0,sK14) ),
inference(resolution,[],[f161,f170]) ).
fof(f332,definition,
( spl16_9
<=> in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
fof(f333,plain,
( ~ in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14))
| spl16_9 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f335,definition,
( spl16_10
<=> in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
fof(f336,plain,
( ~ in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14))
| spl16_10 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f338,plain,
( ~ in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK13)
| ~ in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK14)
| spl16_9 ),
inference(resolution,[],[f333,f183]) ).
fof(f340,definition,
( spl16_11
<=> in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK14) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
fof(f341,plain,
( ~ in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK14)
| spl16_11 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f343,definition,
( spl16_12
<=> in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
fof(f344,plain,
( ~ in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK13)
| spl16_12 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f345,plain,
( ~ spl16_11
| ~ spl16_12
| spl16_9 ),
inference(avatar_split_clause,[],[f338,f332,f343,f340]) ).
fof(f346,plain,
( ~ in(sK12(set_intersection2(sK13,sK14)),sK14)
| ~ in(sK11(set_intersection2(sK13,sK14)),sK14)
| spl16_11 ),
inference(resolution,[],[f341,f314]) ).
fof(f348,definition,
( spl16_13
<=> in(sK11(set_intersection2(sK13,sK14)),sK14) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
fof(f349,plain,
( ~ in(sK11(set_intersection2(sK13,sK14)),sK14)
| spl16_13 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f351,definition,
( spl16_14
<=> in(sK12(set_intersection2(sK13,sK14)),sK14) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
fof(f352,plain,
( ~ in(sK12(set_intersection2(sK13,sK14)),sK14)
| spl16_14 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f353,plain,
( ~ spl16_13
| ~ spl16_14
| spl16_11 ),
inference(avatar_split_clause,[],[f346,f340,f351,f348]) ).
fof(f354,plain,
( $false
| spl16_1
| spl16_13 ),
inference(resolution,[],[f349,f281]) ).
fof(f355,plain,
( spl16_1
| spl16_13 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f457,plain,
( ! [X0] :
( ~ in(empty_set,X0)
| ~ empty(set_intersection2(sK13,X0)) )
| ~ spl16_5 ),
inference(resolution,[],[f307,f236]) ).
fof(f485,plain,
( ~ empty(set_intersection2(sK13,sK14))
| ~ spl16_3
| ~ spl16_5 ),
inference(resolution,[],[f457,f229]) ).
fof(f523,plain,
( $false
| ~ spl16_2
| ~ spl16_3
| ~ spl16_5 ),
inference(resolution,[],[f485,f207]) ).
fof(f524,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_5 ),
inference(avatar_contradiction_clause,[],[f523]) ).
fof(f525,plain,
( ~ in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14))
| ~ in(set_difference(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),set_intersection2(sK13,sK14))
| spl16_1 ),
inference(resolution,[],[f204,f164]) ).
fof(f526,plain,
( in(sK11(set_intersection2(sK13,sK14)),set_intersection2(sK13,sK14))
| spl16_1 ),
inference(resolution,[],[f204,f163]) ).
fof(f527,plain,
( in(sK12(set_intersection2(sK13,sK14)),set_intersection2(sK13,sK14))
| spl16_1 ),
inference(resolution,[],[f204,f162]) ).
fof(f534,plain,
( in(sK11(set_intersection2(sK13,sK14)),sK13)
| spl16_1 ),
inference(resolution,[],[f526,f184]) ).
fof(f541,plain,
( in(sK12(set_intersection2(sK13,sK14)),sK14)
| spl16_1 ),
inference(resolution,[],[f527,f185]) ).
fof(f542,plain,
( in(sK12(set_intersection2(sK13,sK14)),sK13)
| spl16_1 ),
inference(resolution,[],[f527,f184]) ).
fof(f596,plain,
( $false
| spl16_1
| spl16_14 ),
inference(resolution,[],[f352,f541]) ).
fof(f597,plain,
( spl16_1
| spl16_14 ),
inference(avatar_contradiction_clause,[],[f596]) ).
fof(f598,plain,
( ~ in(sK12(set_intersection2(sK13,sK14)),sK13)
| ~ in(sK11(set_intersection2(sK13,sK14)),sK13)
| spl16_12 ),
inference(resolution,[],[f344,f313]) ).
fof(f600,definition,
( spl16_26
<=> in(sK11(set_intersection2(sK13,sK14)),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_26])],[avatar_definition]) ).
fof(f601,plain,
( ~ in(sK11(set_intersection2(sK13,sK14)),sK13)
| spl16_26 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f603,definition,
( spl16_27
<=> in(sK12(set_intersection2(sK13,sK14)),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_27])],[avatar_definition]) ).
fof(f604,plain,
( ~ in(sK12(set_intersection2(sK13,sK14)),sK13)
| spl16_27 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f605,plain,
( ~ spl16_26
| ~ spl16_27
| spl16_12 ),
inference(avatar_split_clause,[],[f598,f343,f603,f600]) ).
fof(f670,plain,
( $false
| spl16_1
| spl16_26 ),
inference(resolution,[],[f601,f534]) ).
fof(f671,plain,
( spl16_1
| spl16_26 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f672,plain,
( $false
| spl16_1
| spl16_27 ),
inference(resolution,[],[f604,f542]) ).
fof(f673,plain,
( spl16_1
| spl16_27 ),
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f674,plain,
( ~ spl16_9
| ~ spl16_10
| spl16_1 ),
inference(avatar_split_clause,[],[f525,f203,f335,f332]) ).
fof(f675,plain,
( ~ in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK13)
| ~ in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK14)
| spl16_10 ),
inference(resolution,[],[f336,f183]) ).
fof(f677,definition,
( spl16_34
<=> in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK14) ),
introduced(definition,[new_symbols(definition,[spl16_34])],[avatar_definition]) ).
fof(f678,plain,
( ~ in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK14)
| spl16_34 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f680,definition,
( spl16_35
<=> in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_35])],[avatar_definition]) ).
fof(f681,plain,
( ~ in(set_union2(sK11(set_intersection2(sK13,sK14)),sK12(set_intersection2(sK13,sK14))),sK13)
| spl16_35 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f682,plain,
( ~ spl16_34
| ~ spl16_35
| spl16_10 ),
inference(avatar_split_clause,[],[f675,f335,f680,f677]) ).
fof(f683,plain,
( ~ in(sK12(set_intersection2(sK13,sK14)),sK14)
| ~ in(sK11(set_intersection2(sK13,sK14)),sK14)
| spl16_34 ),
inference(resolution,[],[f678,f323]) ).
fof(f684,plain,
( ~ spl16_13
| ~ spl16_14
| spl16_34 ),
inference(avatar_split_clause,[],[f683,f677,f351,f348]) ).
fof(f693,plain,
( $false
| ~ spl16_6 ),
inference(resolution,[],[f239,f169]) ).
fof(f694,plain,
~ spl16_6,
inference(avatar_contradiction_clause,[],[f693]) ).
fof(f695,plain,
( $false
| ~ spl16_4 ),
inference(resolution,[],[f232,f171]) ).
fof(f696,plain,
~ spl16_4,
inference(avatar_contradiction_clause,[],[f695]) ).
fof(f797,plain,
( ~ in(sK12(set_intersection2(sK13,sK14)),sK13)
| ~ in(sK11(set_intersection2(sK13,sK14)),sK13)
| spl16_35 ),
inference(resolution,[],[f681,f322]) ).
fof(f798,plain,
( ~ spl16_26
| ~ spl16_27
| spl16_35 ),
inference(avatar_split_clause,[],[f797,f680,f603,f600]) ).
cnf(s1,plain,
( ~ spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f208]) ).
cnf(s2,plain,
( spl16_3
| spl16_4 ),
inference(sat_conversion,[],[f233]) ).
cnf(s3,plain,
( spl16_5
| spl16_6 ),
inference(sat_conversion,[],[f240]) ).
cnf(s6,plain,
( spl16_9
| ~ spl16_11
| ~ spl16_12 ),
inference(sat_conversion,[],[f345]) ).
cnf(s7,plain,
( spl16_11
| ~ spl16_13
| ~ spl16_14 ),
inference(sat_conversion,[],[f353]) ).
cnf(s8,plain,
( spl16_1
| spl16_13 ),
inference(sat_conversion,[],[f355]) ).
cnf(s19,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_5 ),
inference(sat_conversion,[],[f524]) ).
cnf(s22,plain,
( spl16_1
| spl16_14 ),
inference(sat_conversion,[],[f597]) ).
cnf(s23,plain,
( spl16_12
| ~ spl16_26
| ~ spl16_27 ),
inference(sat_conversion,[],[f605]) ).
cnf(s35,plain,
( spl16_1
| spl16_26 ),
inference(sat_conversion,[],[f671]) ).
cnf(s36,plain,
( spl16_1
| spl16_27 ),
inference(sat_conversion,[],[f673]) ).
cnf(s37,plain,
( spl16_1
| ~ spl16_9
| ~ spl16_10 ),
inference(sat_conversion,[],[f674]) ).
cnf(s38,plain,
( spl16_10
| ~ spl16_34
| ~ spl16_35 ),
inference(sat_conversion,[],[f682]) ).
cnf(s39,plain,
( ~ spl16_13
| ~ spl16_14
| spl16_34 ),
inference(sat_conversion,[],[f684]) ).
cnf(s44,plain,
~ spl16_6,
inference(sat_conversion,[],[f694]) ).
cnf(s45,plain,
~ spl16_4,
inference(sat_conversion,[],[f696]) ).
cnf(s50,plain,
( ~ spl16_26
| ~ spl16_27
| spl16_35 ),
inference(sat_conversion,[],[f798]) ).
cnf(s52,plain,
spl16_5,
inference(rat,[],[s3,s44]) ).
cnf(s53,plain,
spl16_3,
inference(rat,[],[s2,s45]) ).
cnf(s55,plain,
~ spl16_2,
inference(rat,[],[s19,s52,s53]) ).
cnf(s56,plain,
~ spl16_1,
inference(rat,[],[s1,s55]) ).
cnf(s57,plain,
spl16_27,
inference(rat,[],[s36,s56]) ).
cnf(s58,plain,
spl16_26,
inference(rat,[],[s35,s56]) ).
cnf(s60,plain,
spl16_14,
inference(rat,[],[s22,s56]) ).
cnf(s61,plain,
spl16_13,
inference(rat,[],[s8,s56]) ).
cnf(s62,plain,
spl16_35,
inference(rat,[],[s50,s57,s58]) ).
cnf(s63,plain,
spl16_12,
inference(rat,[],[s23,s57,s58]) ).
cnf(s64,plain,
spl16_34,
inference(rat,[],[s39,s60,s61]) ).
cnf(s65,plain,
spl16_11,
inference(rat,[],[s7,s60,s61]) ).
cnf(s66,plain,
spl16_10,
inference(rat,[],[s38,s62,s64]) ).
cnf(s67,plain,
spl16_9,
inference(rat,[],[s6,s63,s65]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s37,s56,s66,s67]) ).
fof(f799,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU109+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:35:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.68/1.27 % (3552145)Detected formulas, will run a generic FOF schedule.
% 2.68/1.27 % (3552153)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2967006440:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.27 % (3552153)Refutation not found, incomplete strategy
% 2.68/1.27 % (3552153)------------------------------
% 2.68/1.27 % (3552153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (3552153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (3552153)CaDiCaL version: 2.1.3
% 2.68/1.27 % (3552153)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.27 % (3552153)Time elapsed: 0.001 s
% 2.68/1.27 % (3552153)Peak memory usage: 88 MB
% 2.68/1.27 % (3552153)Instructions burned: 1 (million)
% 2.68/1.27 % (3552155)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3473087917:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.27 % (3552154)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=396797606:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.27 % (3552152)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2064494354:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.27 % (3552151)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=862134495:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.27 % (3552156)dis-21_1_sil=8000:lcm=predicate:random_seed=1633150194:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.68/1.27 % (3552150)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=839420004:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.27 % (3552156)First to succeed.
% 2.68/1.27 % (3552156)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3552145"
% 2.68/1.27 % (3552155)Also succeeded, but the first one will report.
% 2.68/1.27 % (3552154)Instruction limit reached!
% 2.68/1.27 % (3552154)------------------------------
% 2.68/1.27 % (3552154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (3552154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (3552154)CaDiCaL version: 2.1.3
% 2.68/1.27 % (3552154)Termination reason: Instruction limit
% 2.68/1.27 % (3552154)Termination phase: Saturation
% 2.68/1.27 % (3552154)Time elapsed: 0.072 s
% 2.68/1.27 % (3552154)Peak memory usage: 88 MB
% 2.68/1.27 % (3552154)Instructions burned: 120 (million)
% 2.68/1.27 % (3552153)------------------------------
% 2.68/1.27 % (3552153)------------------------------
% 2.68/1.27 % (3552165)lrs+10_1_sil=32000:urr=on:br=off:random_seed=21496511:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.68/1.27 % (3552164)lrs+10_1_sil=8000:sp=occurrence:random_seed=2482572893:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.68/1.27 % (3552165)Instruction limit reached!
% 2.68/1.27 % (3552165)------------------------------
% 2.68/1.27 % (3552165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.27 % (3552165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.27 % (3552165)CaDiCaL version: 2.1.3
% 2.68/1.27 % (3552165)Termination reason: Instruction limit
% 2.68/1.27 % (3552165)Termination phase: Saturation
% 2.68/1.27 % (3552165)Time elapsed: 0.042 s
% 2.68/1.27 % (3552165)Peak memory usage: 91 MB
% 2.68/1.27 % (3552165)Instructions burned: 159 (million)
% 2.68/1.27 % (3552156)Refutation found. Thanks to Tanya!
% 2.68/1.27 % SZS status Theorem for theBenchmark
% 2.68/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.36 % (3552156)------------------------------
% 3.44/1.36 % (3552156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.36 % (3552156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.36 % (3552156)CaDiCaL version: 2.1.3
% 3.44/1.36 % (3552156)Termination reason: Refutation
% 3.44/1.36 % (3552156)Time elapsed: 0.013 s
% 3.44/1.36 % (3552156)Peak memory usage: 89 MB
% 3.44/1.36 % (3552156)Instructions burned: 18 (million)
% 3.44/1.36 % (3552156)------------------------------
% 3.44/1.36 % (3552156)------------------------------
% 3.44/1.36 % (3552145)Success in time 0.419 s
% 3.44/1.36 % Vampire exiting
%------------------------------------------------------------------------------