%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU745^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Wed Sep 30 08:31:05 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 88 ( 30 unt; 0 typ; 10 def)
% Number of atoms : 839 ( 200 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 974 ( 148 ~; 130 |; 42 &; 588 @)
% ( 18 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 25 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 100 !; 22 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
binunion: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_4,type,
setminusI: $o ).
thf(func_def_6,type,
inComplementUnionImpNotIn1: $o ).
thf(f1,axiom,
( setminusI
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
( inComplementUnionImpNotIn1
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(f3,conjecture,
( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( setminusI
=> ( inComplementUnionImpNotIn1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( setminusI = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( inComplementUnionImpNotIn1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
=> ~ ( in @ X3 @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ( inComplementUnionImpNotIn1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f8]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(flattening,[],[f10]) ).
thf(f13,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( setminusI = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( inComplementUnionImpNotIn1 = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f16,plain,
( ( inComplementUnionImpNotIn1 = $true )
& ( setminusI = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
<=> ( inComplementUnionImpNotIn1 = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( inComplementUnionImpNotIn1 != $true ) )
& ( ( inComplementUnionImpNotIn1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( inComplementUnionImpNotIn1 != $true ) )
& ( ( inComplementUnionImpNotIn1 = $true )
| ? [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
= $true )
& ? [X6: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ ( setminus @ X4 @ ( binunion @ X5 @ X6 ) ) )
= $true )
& ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ X7 @ X4 )
= $true ) )
& ( ( in @ X6 @ ( powerset @ X4 ) )
= $true ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) ) )
| ( inComplementUnionImpNotIn1 != $true ) )
& ( ( inComplementUnionImpNotIn1 = $true )
| ( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( ( in @ sK2 @ ( powerset @ sK0 ) )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f20]) ).
thf(f22,plain,
( ( inComplementUnionImpNotIn1 = $true )
& ( setminusI = $true )
& ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) )
& ( ( in @ sK7 @ ( setminus @ sK4 @ sK5 ) )
!= $true )
& ( ( in @ sK7 @ sK4 )
= $true )
& ( ( in @ sK7 @ ( setminus @ sK4 @ ( binunion @ sK5 @ sK6 ) ) )
= $true )
& ( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f16]) ).
thf(f23,plain,
( ( ( setminusI = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
& ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
| ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f24,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[],[f23]) ).
thf(f25,plain,
( ( ( setminusI = $true )
| ( ( ( in @ sK8 @ ( setminus @ sK9 @ sK10 ) )
!= $true )
& ( ( in @ sK8 @ sK10 )
!= $true )
& ( $true
= ( in @ sK8 @ sK9 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f24]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( inComplementUnionImpNotIn1 != $true )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f32,plain,
( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( ( in @ sK7 @ ( setminus @ sK4 @ ( binunion @ sK5 @ sK6 ) ) )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( ( in @ sK7 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
( ( in @ sK7 @ ( setminus @ sK4 @ sK5 ) )
!= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f36,plain,
( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
setminusI = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f38,plain,
inComplementUnionImpNotIn1 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f39,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setminusI != $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f49,definition,
( spl11_2
<=> ( inComplementUnionImpNotIn1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f59,definition,
( spl11_4
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f60,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f61,plain,
( spl11_4
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f31,f49,f59]) ).
thf(f63,definition,
( spl11_5
<=> ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f65,plain,
( ( $true
= ( in @ sK5 @ ( powerset @ sK4 ) ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f66,plain,
spl11_5,
inference(avatar_split_clause,[],[f36,f63]) ).
thf(f68,definition,
( spl11_6
<=> ( ( in @ sK7 @ ( setminus @ sK4 @ ( binunion @ sK5 @ sK6 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f70,plain,
( ( ( in @ sK7 @ ( setminus @ sK4 @ ( binunion @ sK5 @ sK6 ) ) )
= $true )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,plain,
spl11_6,
inference(avatar_split_clause,[],[f33,f68]) ).
thf(f78,definition,
( spl11_8
<=> ( setminusI = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f92,definition,
( spl11_11
<=> ( ( in @ sK7 @ ( setminus @ sK4 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f94,plain,
( ( ( in @ sK7 @ ( setminus @ sK4 @ sK5 ) )
!= $true )
| spl11_11 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f95,plain,
~ spl11_11,
inference(avatar_split_clause,[],[f35,f92]) ).
thf(f101,plain,
spl11_8,
inference(avatar_split_clause,[],[f37,f78]) ).
thf(f103,definition,
( spl11_13
<=> ( ( in @ sK7 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f105,plain,
( ( ( in @ sK7 @ sK4 )
= $true )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f106,plain,
spl11_13,
inference(avatar_split_clause,[],[f34,f103]) ).
thf(f108,definition,
( spl11_14
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f109,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f108]) ).
thf(f110,plain,
( spl11_14
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f39,f78,f108]) ).
thf(f116,plain,
spl11_2,
inference(avatar_split_clause,[],[f38,f49]) ).
thf(f123,definition,
( spl11_17
<=> ( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
thf(f125,plain,
( ( ( in @ sK6 @ ( powerset @ sK4 ) )
= $true )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f126,plain,
spl11_17,
inference(avatar_split_clause,[],[f32,f123]) ).
thf(f129,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ( ( in @ sK6 @ ( powerset @ sK4 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK4 ) ) )
| ( ( in @ sK7 @ sK4 )
!= $true )
| ~ spl11_4
| ~ spl11_6 ),
inference(superposition,[],[f60,f70]) ).
thf(f130,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ( ( in @ sK6 @ ( powerset @ sK4 ) )
!= $true )
| ( ( in @ sK7 @ sK4 )
!= $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK4 ) ) )
| ~ spl11_4
| ~ spl11_6 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f131,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ( ( in @ sK7 @ sK4 )
!= $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK4 ) ) )
| ~ spl11_4
| ~ spl11_6
| ~ spl11_17 ),
inference(forward_subsumption_resolution,[],[f130,f125]) ).
thf(f132,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK4 ) ) )
| ~ spl11_4
| ~ spl11_6
| ~ spl11_13
| ~ spl11_17 ),
inference(forward_subsumption_resolution,[],[f131,f105]) ).
thf(f133,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6
| ~ spl11_13
| ~ spl11_17 ),
inference(forward_subsumption_resolution,[],[f132,f65]) ).
thf(f135,definition,
( spl11_18
<=> ( ( in @ sK7 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition]) ).
thf(f137,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| spl11_18 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f138,plain,
( ~ spl11_18
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6
| ~ spl11_13
| ~ spl11_17 ),
inference(avatar_split_clause,[],[f133,f123,f103,f68,f63,f59,f135]) ).
thf(f140,plain,
( ( $true != $true )
| ( ( in @ sK7 @ sK5 )
= $true )
| ( ( in @ sK7 @ sK4 )
!= $true )
| spl11_11
| ~ spl11_14 ),
inference(superposition,[],[f94,f109]) ).
thf(f141,plain,
( ( ( in @ sK7 @ sK5 )
= $true )
| ( ( in @ sK7 @ sK4 )
!= $true )
| spl11_11
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f144,plain,
( ( ( in @ sK7 @ sK4 )
!= $true )
| spl11_11
| ~ spl11_14
| spl11_18 ),
inference(forward_subsumption_resolution,[],[f141,f137]) ).
thf(f145,plain,
( $false
| spl11_11
| ~ spl11_13
| ~ spl11_14
| spl11_18 ),
inference(forward_subsumption_resolution,[],[f144,f105]) ).
thf(f146,plain,
( spl11_11
| ~ spl11_13
| ~ spl11_14
| spl11_18 ),
inference(avatar_contradiction_clause,[],[f145]) ).
cnf(s3,plain,
( ~ spl11_2
| spl11_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
spl11_5,
inference(sat_conversion,[],[f66]) ).
cnf(s5,plain,
spl11_6,
inference(sat_conversion,[],[f71]) ).
cnf(s9,plain,
~ spl11_11,
inference(sat_conversion,[],[f95]) ).
cnf(s11,plain,
spl11_8,
inference(sat_conversion,[],[f101]) ).
cnf(s12,plain,
spl11_13,
inference(sat_conversion,[],[f106]) ).
cnf(s13,plain,
( ~ spl11_8
| spl11_14 ),
inference(sat_conversion,[],[f110]) ).
cnf(s15,plain,
spl11_2,
inference(sat_conversion,[],[f116]) ).
cnf(s17,plain,
spl11_17,
inference(sat_conversion,[],[f126]) ).
cnf(s18,plain,
( ~ spl11_4
| ~ spl11_5
| ~ spl11_6
| ~ spl11_13
| ~ spl11_17
| ~ spl11_18 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
( spl11_11
| ~ spl11_13
| ~ spl11_14
| spl11_18 ),
inference(sat_conversion,[],[f146]) ).
cnf(s20,plain,
spl11_14,
inference(rat,[],[s13,s11]) ).
cnf(s21,plain,
spl11_18,
inference(rat,[],[s19,s20,s12,s9]) ).
cnf(s22,plain,
~ spl11_4,
inference(rat,[],[s18,s21,s17,s12,s5,s4]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s3,s22,s15]) ).
thf(f147,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU745^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 % Computer : n010.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Tue Sep 29 14:20:33 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 Running higher-order theorem proving
% 0.24/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.35 % (2930055)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.35 % (2930068)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=417098530:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.24/0.35 % (2930068) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2930055-2930068"...
% 0.24/0.35 % (2930071)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.35 % (2930068)...printing done.
% 0.24/0.35 % (2930071)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.35 % (2930068)Refutation found. Thanks to Tanya!
% 0.24/0.35 % SZS status Theorem for theBenchmark
% 0.24/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.35 % (2930068)------------------------------
% 0.24/0.35 % (2930068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.35 % (2930068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.35 % (2930068)CaDiCaL version: 2.1.3
% 0.24/0.35 % (2930068)Termination reason: Refutation
% 0.24/0.35 % (2930068)Time elapsed: 0.004 s
% 0.24/0.35 % (2930068)Peak memory usage: 13 MB
% 0.24/0.35 % (2930068)Instructions burned: 10 (million)
% 0.24/0.35 % (2930055)Success in time 0.034 s
% 0.24/0.35 % Vampire exiting
%------------------------------------------------------------------------------