%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU751^2 : 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 : n014.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 08:31:08 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 31
% Syntax : Number of formulae : 203 ( 60 unt; 0 typ; 24 def)
% Number of atoms : 2026 ( 495 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 2293 ( 367 ~; 335 |; 103 &;1347 @)
% ( 44 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 62 ( 59 usr; 55 con; 0-2 aty)
% Number of variables : 290 ( 0 sgn 240 !; 50 ?; 290 :)
% 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,
binintersect: $i > $i > $i ).
thf(func_def_4,type,
binintersectI: $o ).
thf(func_def_6,type,
setminus: $i > $i > $i ).
thf(func_def_7,type,
setminusER: $o ).
thf(func_def_8,type,
complementT_lem: $o ).
thf(func_def_9,type,
complementTE1: $o ).
thf(func_def_10,type,
binunionTILcontra: $o ).
thf(func_def_11,type,
binunionTIRcontra: $o ).
thf(f1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(f2,axiom,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f3,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) )
= complementT_lem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).
thf(f4,axiom,
( complementTE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTE1) ).
thf(f5,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X1 ) ) ) ) )
= binunionTILcontra ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(f6,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) )
= binunionTIRcontra ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(f7,conjecture,
( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1a) ).
thf(f8,negated_conjecture,
~ ( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ) ) )
= binunionTIRcontra ),
inference(rectify,[],[f6]) ).
thf(f10,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) )
<=> ( binunionTIRcontra = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( binintersectI
=> ( setminusER
=> ( complementT_lem
=> ( complementTE1
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f12,plain,
~ ( ( binintersectI = $true )
=> ( ( setminusER = $true )
=> ( ( complementT_lem = $true )
=> ( ( complementTE1 = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
=> ( $true
= ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) )
= complementT_lem ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
( ( complementT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
inference(rectify,[],[f1]) ).
thf(f16,plain,
( ( binintersectI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( complementTE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f18,plain,
( ( complementTE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f20,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ~ ( in @ X3 @ X0 ) ) ) ) )
= binunionTILcontra ),
inference(rectify,[],[f5]) ).
thf(f22,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) )
<=> ( binunionTILcontra = $true ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) )
<=> ( binunionTIRcontra = $true ) ),
inference(flattening,[],[f10]) ).
thf(f24,plain,
( ( complementTE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ) ),
inference(flattening,[],[f18]) ).
thf(f25,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[],[f20]) ).
thf(f26,plain,
( ! [X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
=> ( ( in @ X3 @ X0 )
!= $true ) ) ) ) )
<=> ( binunionTILcontra = $true ) ),
inference(flattening,[],[f22]) ).
thf(f27,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTE1 = $true )
& ( complementT_lem = $true )
& ( setminusER = $true )
& ( binintersectI = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f28,plain,
( ( binintersectI = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( complementT_lem = $true )
& ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
& ( $true
!= ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
& ( binunionTIRcontra = $true )
& ( complementTE1 = $true ) ),
inference(flattening,[],[f27]) ).
thf(f29,plain,
( ( complementT_lem = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f30,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binunionTIRcontra = $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f31,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
( ( complementTE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f33,plain,
( ( complementTE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f32]) ).
thf(f34,plain,
( ( binintersectI = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f35,plain,
( ( binintersectI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ),
inference(flattening,[],[f34]) ).
thf(f36,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f37,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( binunionTILcontra = $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f38,plain,
( ( binunionTILcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(flattening,[],[f37]) ).
thf(f39,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[],[f36]) ).
thf(f40,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( setminusER != $true ) ) ),
inference(rectify,[],[f39]) ).
thf(f41,plain,
( ( ( setminusER = $true )
| ( ( $true
= ( in @ sK1 @ ( setminus @ sK0 @ sK2 ) ) )
& ( $true
= ( in @ sK1 @ sK2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ( setminusER != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
thf(f42,plain,
( ( binintersectI = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( complementT_lem = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( complementTE1 = $true ) ),
inference(rectify,[],[f28]) ).
thf(f43,plain,
( ( binintersectI = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( complementT_lem = $true )
& ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK6 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) ) )
& ( $true
!= ( in @ sK6 @ ( binunion @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) ) )
& ( $true
= ( in @ sK6 @ sK3 ) )
& ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) )
& ( binunionTIRcontra = $true )
& ( complementTE1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f42]) ).
thf(f44,plain,
( ( ( complementT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
| ( complementT_lem != $true ) ) ),
inference(nnf_transformation,[],[f29]) ).
thf(f45,plain,
( ( ( complementT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) )
| ( complementT_lem != $true ) ) ),
inference(rectify,[],[f44]) ).
thf(f46,plain,
( ( ( complementT_lem = $true )
| ( ( $true
= ( in @ sK8 @ ( powerset @ sK7 ) ) )
& ( $true
!= ( in @ ( setminus @ sK7 @ sK8 ) @ ( powerset @ sK7 ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) )
| ( complementT_lem != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f45]) ).
thf(f47,plain,
( ( ( binintersectI = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) )
| ( binintersectI != $true ) ) ),
inference(nnf_transformation,[],[f35]) ).
thf(f48,plain,
( ( ( binintersectI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) ) )
| ( binintersectI != $true ) ) ),
inference(rectify,[],[f47]) ).
thf(f49,plain,
( ( ( binintersectI = $true )
| ( ( $true
= ( in @ sK10 @ sK11 ) )
& ( $true
= ( in @ sK10 @ sK9 ) )
& ( $true
!= ( in @ sK10 @ ( binintersect @ sK9 @ sK11 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) ) )
| ( binintersectI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f48]) ).
thf(f50,plain,
( ( ( binunionTIRcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionTIRcontra != $true ) ) ),
inference(nnf_transformation,[],[f31]) ).
thf(f51,plain,
( ( ( binunionTIRcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X6 ) ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) )
| ( binunionTIRcontra != $true ) ) ),
inference(rectify,[],[f50]) ).
thf(f52,plain,
( ( ( binunionTIRcontra = $true )
| ( ( $true
= ( in @ sK14 @ ( powerset @ sK12 ) ) )
& ( $true
= ( in @ sK15 @ sK12 ) )
& ( $true
!= ( in @ sK15 @ ( binunion @ sK13 @ sK14 ) ) )
& ( $true
= ( in @ sK15 @ sK14 ) )
& ( $true
= ( in @ sK13 @ ( powerset @ sK12 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X6 ) ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) ) )
| ( binunionTIRcontra != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f51]) ).
thf(f53,plain,
( ( ( binunionTILcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ( binunionTILcontra != $true ) ) ),
inference(nnf_transformation,[],[f38]) ).
thf(f54,plain,
( ( ( binunionTILcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( binunionTILcontra != $true ) ) ),
inference(rectify,[],[f53]) ).
thf(f55,plain,
( ( ( binunionTILcontra = $true )
| ( ( $true
= ( in @ sK18 @ ( powerset @ sK17 ) ) )
& ( $true
= ( in @ sK19 @ sK16 ) )
& ( $true
!= ( in @ sK19 @ ( binunion @ sK16 @ sK18 ) ) )
& ( $true
= ( in @ sK19 @ sK17 ) )
& ( $true
= ( in @ sK16 @ ( powerset @ sK17 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ! [X7: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( binunionTILcontra != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18),skolemize(X3,sK19)],[f54]) ).
thf(f56,plain,
( ( ( complementTE1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( complementTE1 != $true ) ) ),
inference(nnf_transformation,[],[f33]) ).
thf(f57,plain,
( ( ( complementTE1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) ) )
| ( complementTE1 != $true ) ) ),
inference(rectify,[],[f56]) ).
thf(f58,plain,
( ( ( complementTE1 = $true )
| ( ( $true
= ( in @ sK22 @ sK20 ) )
& ( $true
!= ( in @ sK22 @ sK21 ) )
& ( $true
!= ( in @ sK22 @ ( setminus @ sK20 @ sK21 ) ) )
& ( $true
= ( in @ sK21 @ ( powerset @ sK20 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) ) )
| ( complementTE1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22)],[f57]) ).
thf(f59,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setminusER != $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
!= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f62,plain,
complementTE1 = $true,
inference(cnf_transformation,[],[f43]) ).
thf(f63,plain,
binunionTIRcontra = $true,
inference(cnf_transformation,[],[f43]) ).
thf(f64,plain,
( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f65,plain,
( $true
= ( in @ sK6 @ sK3 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f66,plain,
( $true
!= ( in @ sK6 @ ( binunion @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f67,plain,
( $true
= ( in @ sK6 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f68,plain,
( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f69,plain,
complementT_lem = $true,
inference(cnf_transformation,[],[f43]) ).
thf(f70,plain,
setminusER = $true,
inference(cnf_transformation,[],[f43]) ).
thf(f71,plain,
binunionTILcontra = $true,
inference(cnf_transformation,[],[f43]) ).
thf(f72,plain,
binintersectI = $true,
inference(cnf_transformation,[],[f43]) ).
thf(f73,plain,
! [X2: $i,X3: $i] :
( ( complementT_lem != $true )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f76,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binintersectI != $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
!= ( in @ X4 @ X3 ) )
| ( $true
= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f80,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( binunionTIRcontra != $true )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( $true
!= ( in @ X7 @ X4 ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f86,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( binunionTILcontra != $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f92,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( complementTE1 != $true )
| ( $true
= ( in @ X5 @ X4 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f99,definition,
( spl23_1
<=> ( binunionTIRcontra = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
thf(f108,definition,
( spl23_3
<=> ( binunionTILcontra = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
thf(f117,definition,
( spl23_5
<=> ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
thf(f119,plain,
( ( $true
= ( in @ sK4 @ ( powerset @ sK3 ) ) )
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,plain,
spl23_5,
inference(avatar_split_clause,[],[f64,f117]) ).
thf(f127,definition,
( spl23_7
<=> ( $true
= ( in @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_7])],[avatar_definition]) ).
thf(f129,plain,
( ( $true
= ( in @ sK6 @ sK3 ) )
| ~ spl23_7 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f130,plain,
spl23_7,
inference(avatar_split_clause,[],[f65,f127]) ).
thf(f132,definition,
( spl23_8
<=> ( $true
= ( in @ sK6 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition]) ).
thf(f134,plain,
( ( $true
= ( in @ sK6 @ ( setminus @ sK3 @ ( binintersect @ sK4 @ sK5 ) ) ) )
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f135,plain,
spl23_8,
inference(avatar_split_clause,[],[f67,f132]) ).
thf(f137,definition,
( spl23_9
<=> ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_9])],[avatar_definition]) ).
thf(f138,plain,
( ! [X2: $i,X3: $i] :
( ( $true
= ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) )
| ~ spl23_9 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,definition,
( spl23_10
<=> ( complementT_lem = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_10])],[avatar_definition]) ).
thf(f143,plain,
( spl23_9
| ~ spl23_10 ),
inference(avatar_split_clause,[],[f73,f140,f137]) ).
thf(f149,definition,
( spl23_12
<=> ( complementTE1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_12])],[avatar_definition]) ).
thf(f163,definition,
( spl23_15
<=> ( setminusER = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_15])],[avatar_definition]) ).
thf(f167,plain,
spl23_3,
inference(avatar_split_clause,[],[f71,f108]) ).
thf(f173,plain,
spl23_15,
inference(avatar_split_clause,[],[f70,f163]) ).
thf(f175,definition,
( spl23_17
<=> ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_17])],[avatar_definition]) ).
thf(f177,plain,
( ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ~ spl23_17 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f178,plain,
spl23_17,
inference(avatar_split_clause,[],[f68,f175]) ).
thf(f180,definition,
( spl23_18
<=> ( binintersectI = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_18])],[avatar_definition]) ).
thf(f194,definition,
( spl23_21
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) )
| ( $true
= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_21])],[avatar_definition]) ).
thf(f195,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( setminus @ X3 @ X4 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X3 ) ) )
| ( $true
= ( in @ X5 @ X4 ) )
| ( $true
!= ( in @ X5 @ X3 ) ) )
| ~ spl23_21 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f196,plain,
( ~ spl23_12
| spl23_21 ),
inference(avatar_split_clause,[],[f92,f194,f149]) ).
thf(f218,definition,
( spl23_26
<=> ( $true
= ( in @ sK6 @ ( binunion @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_26])],[avatar_definition]) ).
thf(f220,plain,
( ( $true
!= ( in @ sK6 @ ( binunion @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) ) )
| spl23_26 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,plain,
~ spl23_26,
inference(avatar_split_clause,[],[f66,f218]) ).
thf(f222,plain,
spl23_12,
inference(avatar_split_clause,[],[f62,f149]) ).
thf(f229,definition,
( spl23_28
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
!= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_28])],[avatar_definition]) ).
thf(f230,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( setminus @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) ) )
| ~ spl23_28 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f231,plain,
( ~ spl23_15
| spl23_28 ),
inference(avatar_split_clause,[],[f59,f229,f163]) ).
thf(f233,definition,
( spl23_29
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X7 @ X6 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_29])],[avatar_definition]) ).
thf(f234,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X5 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X4 ) ) )
| ( $true
!= ( in @ X7 @ X6 ) ) )
| ~ spl23_29 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f235,plain,
( ~ spl23_1
| spl23_29 ),
inference(avatar_split_clause,[],[f80,f233,f99]) ).
thf(f241,plain,
spl23_18,
inference(avatar_split_clause,[],[f72,f180]) ).
thf(f243,definition,
( spl23_31
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_31])],[avatar_definition]) ).
thf(f244,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( binintersect @ X3 @ X5 ) ) )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true
!= ( in @ X4 @ X3 ) ) )
| ~ spl23_31 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f245,plain,
( spl23_31
| ~ spl23_18 ),
inference(avatar_split_clause,[],[f76,f180,f243]) ).
thf(f256,plain,
spl23_1,
inference(avatar_split_clause,[],[f63,f99]) ).
thf(f257,plain,
spl23_10,
inference(avatar_split_clause,[],[f69,f140]) ).
thf(f269,definition,
( spl23_36
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_36])],[avatar_definition]) ).
thf(f270,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X7 @ ( binunion @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ~ spl23_36 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f271,plain,
( spl23_36
| ~ spl23_3 ),
inference(avatar_split_clause,[],[f86,f108,f269]) ).
thf(f288,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK6 @ ( binintersect @ sK4 @ sK5 ) ) )
| ~ spl23_8
| ~ spl23_28 ),
inference(superposition,[],[f230,f134]) ).
thf(f289,plain,
( ( $true
!= ( in @ sK6 @ ( binintersect @ sK4 @ sK5 ) ) )
| ~ spl23_8
| ~ spl23_28 ),
inference(trivial_inequality_removal,[],[f288]) ).
thf(f291,definition,
( spl23_39
<=> ( $true
= ( in @ sK6 @ ( binintersect @ sK4 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_39])],[avatar_definition]) ).
thf(f293,plain,
( ( $true
!= ( in @ sK6 @ ( binintersect @ sK4 @ sK5 ) ) )
| spl23_39 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f294,plain,
( ~ spl23_39
| ~ spl23_8
| ~ spl23_28 ),
inference(avatar_split_clause,[],[f289,f229,f132,f291]) ).
thf(f296,plain,
( ( $true
!= ( in @ sK6 @ sK5 ) )
| ( $true
!= ( in @ sK6 @ sK4 ) )
| ( $true != $true )
| ~ spl23_31
| spl23_39 ),
inference(superposition,[],[f293,f244]) ).
thf(f297,plain,
( ( $true
!= ( in @ sK6 @ sK5 ) )
| ( $true
!= ( in @ sK6 @ sK4 ) )
| ~ spl23_31
| spl23_39 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f299,definition,
( spl23_40
<=> ( $true
= ( in @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_40])],[avatar_definition]) ).
thf(f303,definition,
( spl23_41
<=> ( $true
= ( in @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_41])],[avatar_definition]) ).
thf(f306,plain,
( ~ spl23_40
| ~ spl23_41
| ~ spl23_31
| spl23_39 ),
inference(avatar_split_clause,[],[f297,f291,f243,f303,f299]) ).
thf(f307,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ sK6 @ X0 ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK5 ) @ ( powerset @ X0 ) ) ) )
| spl23_26
| ~ spl23_29 ),
inference(superposition,[],[f220,f234]) ).
thf(f308,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK5 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) ) )
| ( $true
!= ( in @ sK6 @ X0 ) ) )
| spl23_26
| ~ spl23_29 ),
inference(trivial_inequality_removal,[],[f307]) ).
thf(f310,definition,
( spl23_42
<=> ( $true
= ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_42])],[avatar_definition]) ).
thf(f312,plain,
( ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) ) )
| spl23_42 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f314,definition,
( spl23_43
<=> ! [X0: $i] :
( ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK6 @ X0 ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK5 ) @ ( powerset @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_43])],[avatar_definition]) ).
thf(f315,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( setminus @ sK3 @ sK5 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK6 @ X0 ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ X0 ) ) ) )
| ~ spl23_43 ),
inference(avatar_component_clause,[],[f314]) ).
thf(f316,plain,
( ~ spl23_42
| spl23_43
| spl23_26
| ~ spl23_29 ),
inference(avatar_split_clause,[],[f308,f233,f218,f314,f310]) ).
thf(f317,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) ) )
| ( $true
!= ( in @ sK6 @ X0 ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK5 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ X0 ) ) ) )
| spl23_26
| ~ spl23_36 ),
inference(superposition,[],[f220,f270]) ).
thf(f318,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK6 @ X0 ) )
| ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK5 ) @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ X0 ) ) ) )
| spl23_26
| ~ spl23_36 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f320,definition,
( spl23_44
<=> ( $true
= ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_44])],[avatar_definition]) ).
thf(f322,plain,
( ( $true
!= ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) ) )
| spl23_44 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f323,plain,
( spl23_43
| ~ spl23_44
| spl23_26
| ~ spl23_36 ),
inference(avatar_split_clause,[],[f318,f269,f218,f320,f314]) ).
thf(f324,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ( $true
= ( in @ sK6 @ sK5 ) )
| ~ spl23_21
| spl23_42 ),
inference(superposition,[],[f312,f195]) ).
thf(f325,plain,
( ( $true
= ( in @ sK6 @ sK5 ) )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl23_21
| spl23_42 ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f326,plain,
( ( $true
= ( in @ sK6 @ sK5 ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl23_17
| ~ spl23_21
| spl23_42 ),
inference(forward_subsumption_resolution,[],[f325,f177]) ).
thf(f327,plain,
( ( $true
= ( in @ sK6 @ sK5 ) )
| ~ spl23_7
| ~ spl23_17
| ~ spl23_21
| spl23_42 ),
inference(forward_subsumption_resolution,[],[f326,f129]) ).
thf(f328,plain,
( spl23_41
| ~ spl23_7
| ~ spl23_17
| ~ spl23_21
| spl23_42 ),
inference(avatar_split_clause,[],[f327,f310,f194,f175,f127,f303]) ).
thf(f329,plain,
( ( $true
!= ( in @ sK6 @ sK3 ) )
| ( $true
= ( in @ sK6 @ sK4 ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) )
| ( $true != $true )
| ~ spl23_21
| spl23_44 ),
inference(superposition,[],[f322,f195]) ).
thf(f330,plain,
( ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ( $true
= ( in @ sK6 @ sK4 ) )
| ~ spl23_21
| spl23_44 ),
inference(trivial_inequality_removal,[],[f329]) ).
thf(f331,plain,
( ( $true
!= ( in @ sK6 @ sK3 ) )
| ( $true
= ( in @ sK6 @ sK4 ) )
| ~ spl23_5
| ~ spl23_21
| spl23_44 ),
inference(forward_subsumption_resolution,[],[f330,f119]) ).
thf(f332,plain,
( ( $true
= ( in @ sK6 @ sK4 ) )
| ~ spl23_5
| ~ spl23_7
| ~ spl23_21
| spl23_44 ),
inference(forward_subsumption_resolution,[],[f331,f129]) ).
thf(f333,plain,
( spl23_40
| ~ spl23_5
| ~ spl23_7
| ~ spl23_21
| spl23_44 ),
inference(avatar_split_clause,[],[f332,f320,f194,f127,f117,f299]) ).
thf(f334,plain,
( ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ sK3 ) ) )
| ( $true != $true )
| ~ spl23_9
| ~ spl23_43 ),
inference(superposition,[],[f315,f138]) ).
thf(f335,plain,
( ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl23_9
| ~ spl23_43 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f336,plain,
( ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl23_9
| ~ spl23_17
| ~ spl23_43 ),
inference(forward_subsumption_resolution,[],[f335,f177]) ).
thf(f337,plain,
( ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ sK3 ) ) )
| ~ spl23_7
| ~ spl23_9
| ~ spl23_17
| ~ spl23_43 ),
inference(forward_subsumption_resolution,[],[f336,f129]) ).
thf(f339,definition,
( spl23_45
<=> ( $true
= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_45])],[avatar_definition]) ).
thf(f341,plain,
( ( $true
!= ( in @ ( setminus @ sK3 @ sK4 ) @ ( powerset @ sK3 ) ) )
| spl23_45 ),
inference(avatar_component_clause,[],[f339]) ).
thf(f342,plain,
( ~ spl23_45
| ~ spl23_7
| ~ spl23_9
| ~ spl23_17
| ~ spl23_43 ),
inference(avatar_split_clause,[],[f337,f314,f175,f137,f127,f339]) ).
thf(f346,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) )
| ~ spl23_9
| spl23_45 ),
inference(superposition,[],[f341,f138]) ).
thf(f347,plain,
( ( $true
!= ( in @ sK4 @ ( powerset @ sK3 ) ) )
| ~ spl23_9
| spl23_45 ),
inference(trivial_inequality_removal,[],[f346]) ).
thf(f348,plain,
( $false
| ~ spl23_5
| ~ spl23_9
| spl23_45 ),
inference(forward_subsumption_resolution,[],[f347,f119]) ).
thf(f349,plain,
( ~ spl23_5
| ~ spl23_9
| spl23_45 ),
inference(avatar_contradiction_clause,[],[f348]) ).
cnf(s3,plain,
spl23_5,
inference(sat_conversion,[],[f120]) ).
cnf(s5,plain,
spl23_7,
inference(sat_conversion,[],[f130]) ).
cnf(s6,plain,
spl23_8,
inference(sat_conversion,[],[f135]) ).
cnf(s7,plain,
( spl23_9
| ~ spl23_10 ),
inference(sat_conversion,[],[f143]) ).
cnf(s11,plain,
spl23_3,
inference(sat_conversion,[],[f167]) ).
cnf(s13,plain,
spl23_15,
inference(sat_conversion,[],[f173]) ).
cnf(s14,plain,
spl23_17,
inference(sat_conversion,[],[f178]) ).
cnf(s17,plain,
( ~ spl23_12
| spl23_21 ),
inference(sat_conversion,[],[f196]) ).
cnf(s22,plain,
~ spl23_26,
inference(sat_conversion,[],[f221]) ).
cnf(s23,plain,
spl23_12,
inference(sat_conversion,[],[f222]) ).
cnf(s25,plain,
( ~ spl23_15
| spl23_28 ),
inference(sat_conversion,[],[f231]) ).
cnf(s26,plain,
( ~ spl23_1
| spl23_29 ),
inference(sat_conversion,[],[f235]) ).
cnf(s28,plain,
spl23_18,
inference(sat_conversion,[],[f241]) ).
cnf(s29,plain,
( ~ spl23_18
| spl23_31 ),
inference(sat_conversion,[],[f245]) ).
cnf(s32,plain,
spl23_1,
inference(sat_conversion,[],[f256]) ).
cnf(s33,plain,
spl23_10,
inference(sat_conversion,[],[f257]) ).
cnf(s36,plain,
( ~ spl23_3
| spl23_36 ),
inference(sat_conversion,[],[f271]) ).
cnf(s39,plain,
( ~ spl23_8
| ~ spl23_28
| ~ spl23_39 ),
inference(sat_conversion,[],[f294]) ).
cnf(s40,plain,
( ~ spl23_31
| spl23_39
| ~ spl23_40
| ~ spl23_41 ),
inference(sat_conversion,[],[f306]) ).
cnf(s41,plain,
( spl23_26
| ~ spl23_29
| ~ spl23_42
| spl23_43 ),
inference(sat_conversion,[],[f316]) ).
cnf(s42,plain,
( spl23_26
| ~ spl23_36
| spl23_43
| ~ spl23_44 ),
inference(sat_conversion,[],[f323]) ).
cnf(s43,plain,
( ~ spl23_7
| ~ spl23_17
| ~ spl23_21
| spl23_41
| spl23_42 ),
inference(sat_conversion,[],[f328]) ).
cnf(s44,plain,
( ~ spl23_5
| ~ spl23_7
| ~ spl23_21
| spl23_40
| spl23_44 ),
inference(sat_conversion,[],[f333]) ).
cnf(s45,plain,
( ~ spl23_7
| ~ spl23_9
| ~ spl23_17
| ~ spl23_43
| ~ spl23_45 ),
inference(sat_conversion,[],[f342]) ).
cnf(s47,plain,
( ~ spl23_5
| ~ spl23_9
| spl23_45 ),
inference(sat_conversion,[],[f349]) ).
cnf(s48,plain,
spl23_31,
inference(rat,[],[s29,s28]) ).
cnf(s49,plain,
spl23_29,
inference(rat,[],[s26,s32]) ).
cnf(s50,plain,
spl23_21,
inference(rat,[],[s17,s23]) ).
cnf(s51,plain,
spl23_28,
inference(rat,[],[s25,s13]) ).
cnf(s52,plain,
spl23_36,
inference(rat,[],[s36,s11]) ).
cnf(s53,plain,
spl23_9,
inference(rat,[],[s7,s33]) ).
cnf(s54,plain,
~ spl23_39,
inference(rat,[],[s39,s51,s6]) ).
cnf(s55,plain,
spl23_45,
inference(rat,[],[s47,s53,s3]) ).
cnf(s56,plain,
~ spl23_43,
inference(rat,[],[s45,s5,s53,s14,s55]) ).
cnf(s57,plain,
~ spl23_44,
inference(rat,[],[s42,s52,s22,s56]) ).
cnf(s58,plain,
~ spl23_42,
inference(rat,[],[s41,s22,s49,s56]) ).
cnf(s59,plain,
spl23_40,
inference(rat,[],[s44,s3,s5,s50,s57]) ).
cnf(s60,plain,
spl23_41,
inference(rat,[],[s43,s5,s14,s50,s58]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s40,s54,s48,s60,s59]) ).
thf(f350,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU751^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n014.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 14:21:00 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 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
% 0.19/0.29 % (2735713)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.29 % (2735734)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1075452608:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.29 % (2735735)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.29 % (2735735)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
% 0.19/0.29 % (2735730)lrs+10_16_si=on:nwc=1.5:random_seed=3640085735:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.29 % (2735731)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2120160829:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.29 % (2735729)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1442302229:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.29 % (2735732)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=2001627728: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)
% 0.19/0.29 % (2735733)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1494649519:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.29 % (2735735)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2821958161:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.29 % (2735731)Instruction limit reached!
% 0.19/0.29 % (2735731)------------------------------
% 0.19/0.29 % (2735731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2735731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2735731)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2735731)Termination reason: Instruction limit
% 0.19/0.29 % (2735731)Termination phase: Property scanning
% 0.19/0.29 % (2735731)Time elapsed: 0.002 s
% 0.19/0.29 % (2735731)Peak memory usage: 10 MB
% 0.19/0.29 % (2735731)Instructions burned: 4 (million)
% 0.19/0.29 % (2735732) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2735713-2735732"...
% 0.19/0.29 % (2735730)Instruction limit reached!
% 0.19/0.29 % (2735730)------------------------------
% 0.19/0.29 % (2735730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2735730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2735730)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2735730)Termination reason: Instruction limit
% 0.19/0.29 % (2735730)Termination phase: Saturation
% 0.19/0.29 % (2735730)Time elapsed: 0.009 s
% 0.19/0.29 % (2735730)Peak memory usage: 12 MB
% 0.19/0.29 % (2735730)Instructions burned: 18 (million)
% 0.19/0.29 % (2735733) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2735713-2735733"...
% 0.19/0.29 % (2735732)...printing done.
% 0.19/0.29 % (2735732)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (2735732)------------------------------
% 0.19/0.29 % (2735732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2735732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2735732)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2735732)Termination reason: Refutation
% 0.19/0.29 % (2735732)Time elapsed: 0.013 s
% 0.19/0.29 % (2735732)Peak memory usage: 13 MB
% 0.19/0.29 % (2735732)Instructions burned: 23 (million)
% 0.19/0.29 % (2735713)Success in time 0.051 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------