%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU613^2 : 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 : n013.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 08:30:20 AM UTC 2026
% Result : Theorem 0.24s 0.29s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 91 ( 30 unt; 0 typ; 9 def)
% Number of atoms : 641 ( 161 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 787 ( 145 ~; 116 |; 31 &; 452 @)
% ( 14 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 21 con; 0-4 aty)
% Number of variables : 159 ( 0 sgn 99 !; 21 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrI: $o ).
thf(func_def_4,type,
binunion: $i > $i > $i ).
thf(func_def_5,type,
binunionIR: $o ).
thf(func_def_6,type,
symdiff: $i > $i > $i ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vOR: $o > $o > $o ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK3: $i > $o ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f2,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
= binunionIR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X1 ) ) ) )
= symdiff ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiff) ).
thf(f4,conjecture,
( dsetconstrI
=> ( binunionIR
=> ! [X0: $i,X2: $i,X1: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(f5,negated_conjecture,
~ ( dsetconstrI
=> ( binunionIR
=> ! [X0: $i,X2: $i,X1: $i] :
( ~ ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( symdiff @ X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ( dsetconstrI
=> ( binunionIR
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ( ( dsetconstrI = $true )
=> ( ( binunionIR = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1 @ X0 )
=> ( ( X2 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X2: $i > $o,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( X2 @ X1 )
= $true )
=> ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X1 ) ) ) )
= symdiff ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
= binunionIR ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( ( binunionIR = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
~ ( ( dsetconstrI = $true )
=> ( ( binunionIR = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f15,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
<=> ( binunionIR = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f16,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( binunionIR = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f17,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
& ( binunionIR = $true )
& ( dsetconstrI = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X2: $i > $o,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f19,plain,
( ( dsetconstrI = $true )
<=> ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
& ( binunionIR = $true )
& ( dsetconstrI = $true ) ),
inference(rectify,[],[f17]) ).
thf(f21,plain,
( ( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( $true
= ( in @ sK0 @ sK2 ) )
& ( binunionIR = $true )
& ( dsetconstrI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f20]) ).
thf(f22,plain,
( ( ( dsetconstrI = $true )
| ? [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
= $true )
& ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f23,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
!= $true )
| ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ( dsetconstrI = $true )
| ( ( ( sK3 @ sK5 )
= $true )
& ( ( in @ sK5
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK3 @ Y0 ) ) )
!= $true )
& ( ( in @ sK5 @ sK4 )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( X3 @ X5 )
!= $true )
| ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f23]) ).
thf(f25,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) )
| ( binunionIR != $true ) )
& ( ( binunionIR = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true ) )
| ( binunionIR != $true ) )
& ( ( binunionIR = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X5 ) )
& ( ( in @ X3 @ ( binunion @ X4 @ X5 ) )
!= $true ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true ) )
| ( binunionIR != $true ) )
& ( ( binunionIR = $true )
| ( ( ( in @ sK6 @ sK8 )
= $true )
& ( $true
!= ( in @ sK6 @ ( binunion @ sK7 @ sK8 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8)],[f26]) ).
thf(f28,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f29,plain,
binunionIR = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f30,plain,
( $true
= ( in @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f31,plain,
( ( in @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f32,plain,
( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f33,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( dsetconstrI != $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
| ( ( X3 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( binunionIR != $true ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f40,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f42,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( dsetconstrI != $true )
| ( ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) )
= $true )
| ( ( X3 @ X5 )
!= $true ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f45,definition,
( spl9_1
<=> ( dsetconstrI = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f49,definition,
( spl9_2
<=> ! [X4: $i,X5: $i,X3: $i > $o] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( ( X3 @ X5 )
!= $true )
| ( ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f50,plain,
( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) )
= $true )
| ( ( X3 @ X5 )
!= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f51,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f42,f49,f45]) ).
thf(f58,definition,
( spl9_4
<=> ( binunionIR = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f61,plain,
spl9_4,
inference(avatar_split_clause,[],[f29,f58]) ).
thf(f63,definition,
( spl9_5
<=> ( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f65,plain,
( ( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f66,plain,
spl9_5,
inference(avatar_split_clause,[],[f40,f63]) ).
thf(f68,definition,
( spl9_6
<=> ( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f70,plain,
( ( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true )
| spl9_6 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,plain,
~ spl9_6,
inference(avatar_split_clause,[],[f32,f68]) ).
thf(f83,definition,
( spl9_9
<=> ( ( in @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
thf(f85,plain,
( ( ( in @ sK0 @ sK1 )
!= $true )
| spl9_9 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f86,plain,
~ spl9_9,
inference(avatar_split_clause,[],[f31,f83]) ).
thf(f98,definition,
( spl9_12
<=> ( $true
= ( in @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
thf(f100,plain,
( ( $true
= ( in @ sK0 @ sK2 ) )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f98]) ).
thf(f101,plain,
spl9_12,
inference(avatar_split_clause,[],[f30,f98]) ).
thf(f103,definition,
( spl9_13
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
thf(f104,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f105,plain,
( spl9_13
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f39,f58,f103]) ).
thf(f106,plain,
spl9_1,
inference(avatar_split_clause,[],[f28,f45]) ).
thf(f109,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) )
@ X1 )
= ( symdiff @ X1 ) )
| ~ spl9_5 ),
inference(argument_congruence,[],[f65]) ).
thf(f110,plain,
( ! [X1: $i] :
( ( symdiff @ X1 )
= ( ^ [Y0: $i] :
( dsetconstr @ ( binunion @ X1 @ Y0 )
@ ^ [Y1: $i] :
( ~ ( in @ Y1 @ Y0 )
| ~ ( in @ Y1 @ X1 ) ) ) ) )
| ~ spl9_5 ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
( ! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( dsetconstr @ ( binunion @ X1 @ Y0 )
@ ^ [Y1: $i] :
( ~ ( in @ Y1 @ Y0 )
| ~ ( in @ Y1 @ X1 ) ) )
@ X2 )
= ( symdiff @ X1 @ X2 ) )
| ~ spl9_5 ),
inference(argument_congruence,[],[f110]) ).
thf(f112,plain,
( ! [X2: $i,X1: $i] :
( ( symdiff @ X1 @ X2 )
= ( dsetconstr @ ( binunion @ X1 @ X2 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ X2 )
| ~ ( in @ Y0 @ X1 ) ) ) )
| ~ spl9_5 ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ X1 )
| ~ ( in @ Y0 @ X0 ) )
@ X2 )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true ) )
| ~ spl9_2
| ~ spl9_5 ),
inference(superposition,[],[f50,f112]) ).
thf(f114,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
| ( ( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) )
!= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true ) )
| ~ spl9_2
| ~ spl9_5 ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( ~ ( in @ X2 @ X0 ) )
= $false )
| ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true ) )
| ~ spl9_2
| ~ spl9_5 ),
inference(or_proxy_clausification,[],[f114]) ).
thf(f118,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( symdiff @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
!= $true ) )
| ~ spl9_2
| ~ spl9_5 ),
inference(not_proxy_clausification,[],[f115]) ).
thf(f121,plain,
( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
!= $true )
| ( ( in @ sK0 @ sK1 )
= $true )
| ( $true != $true )
| ~ spl9_2
| ~ spl9_5
| spl9_6 ),
inference(superposition,[],[f70,f118]) ).
thf(f122,plain,
( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
!= $true )
| ( ( in @ sK0 @ sK1 )
= $true )
| ~ spl9_2
| ~ spl9_5
| spl9_6 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f123,plain,
( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
!= $true )
| ~ spl9_2
| ~ spl9_5
| spl9_6
| spl9_9 ),
inference(forward_subsumption_resolution,[],[f122,f85]) ).
thf(f125,definition,
( spl9_14
<=> ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition]) ).
thf(f127,plain,
( ( ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) )
!= $true )
| spl9_14 ),
inference(avatar_component_clause,[],[f125]) ).
thf(f128,plain,
( ~ spl9_14
| ~ spl9_2
| ~ spl9_5
| spl9_6
| spl9_9 ),
inference(avatar_split_clause,[],[f123,f83,f68,f63,f49,f125]) ).
thf(f129,plain,
( ( $true
!= ( in @ sK0 @ sK2 ) )
| ( $true != $true )
| ~ spl9_13
| spl9_14 ),
inference(superposition,[],[f127,f104]) ).
thf(f130,plain,
( ( $true
!= ( in @ sK0 @ sK2 ) )
| ~ spl9_13
| spl9_14 ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f131,plain,
( $false
| ~ spl9_12
| ~ spl9_13
| spl9_14 ),
inference(forward_subsumption_resolution,[],[f130,f100]) ).
thf(f132,plain,
( ~ spl9_12
| ~ spl9_13
| spl9_14 ),
inference(avatar_contradiction_clause,[],[f131]) ).
cnf(s1,plain,
( ~ spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
spl9_4,
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
spl9_5,
inference(sat_conversion,[],[f66]) ).
cnf(s5,plain,
~ spl9_6,
inference(sat_conversion,[],[f71]) ).
cnf(s8,plain,
~ spl9_9,
inference(sat_conversion,[],[f86]) ).
cnf(s11,plain,
spl9_12,
inference(sat_conversion,[],[f101]) ).
cnf(s12,plain,
( ~ spl9_4
| spl9_13 ),
inference(sat_conversion,[],[f105]) ).
cnf(s13,plain,
spl9_1,
inference(sat_conversion,[],[f106]) ).
cnf(s14,plain,
( ~ spl9_2
| ~ spl9_5
| spl9_6
| spl9_9
| ~ spl9_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s15,plain,
( ~ spl9_12
| ~ spl9_13
| spl9_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s16,plain,
spl9_13,
inference(rat,[],[s12,s3]) ).
cnf(s17,plain,
spl9_14,
inference(rat,[],[s15,s11,s16]) ).
cnf(s18,plain,
~ spl9_2,
inference(rat,[],[s14,s4,s8,s5,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18,s13]) ).
thf(f133,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU613^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:57:30 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.24/0.29 % (2160826)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.29 % (2160834)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=1545144594: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)
% 0.24/0.29 % (2160834) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2160826-2160834"...
% 0.24/0.29 % (2160834)...printing done.
% 0.24/0.29 % (2160833)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3587362384:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.29 % (2160836)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=370750944:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.29 % (2160834)Refutation found. Thanks to Tanya!
% 0.24/0.29 % SZS status Theorem for theBenchmark
% 0.24/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.29 % (2160834)------------------------------
% 0.24/0.29 % (2160834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.29 % (2160834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.29 % (2160834)CaDiCaL version: 2.1.3
% 0.24/0.29 % (2160834)Termination reason: Refutation
% 0.24/0.29 % (2160834)Time elapsed: 0.005 s
% 0.24/0.29 % (2160834)Peak memory usage: 13 MB
% 0.24/0.29 % (2160834)Instructions burned: 10 (million)
% 0.24/0.29 % (2160826)Success in time 0.031 s
% 0.24/0.29 % Vampire exiting
%------------------------------------------------------------------------------