%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU754^2 : 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 : n009.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 08:31:09 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 27
% Syntax : Number of formulae : 182 ( 53 unt; 0 typ; 21 def)
% Number of atoms : 1785 ( 435 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 2002 ( 341 ~; 306 |; 90 &;1140 @)
% ( 39 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 56 ( 53 usr; 49 con; 0-2 aty)
% Number of variables : 267 ( 0 sgn 221 !; 46 ?; 267 :)
% 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,
setminusI: $o ).
thf(func_def_8,type,
setminusER: $o ).
thf(func_def_9,type,
binunionTILcontra: $o ).
thf(func_def_10,type,
binunionTIRcontra: $o ).
thf(f1,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(f2,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f3,axiom,
( setminusER
= ( ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f4,axiom,
( binunionTILcontra
= ( ! [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 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(f5,axiom,
( binunionTIRcontra
= ( ! [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 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(f6,conjecture,
( binintersectI
=> ( setminusI
=> ( setminusER
=> ( 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 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a) ).
thf(f7,negated_conjecture,
~ ( binintersectI
=> ( setminusI
=> ( setminusER
=> ( 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 @ ( binunion @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
= binintersectI ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true ) ) )
<=> ( binintersectI = $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( binintersectI
=> ( setminusI
=> ( setminusER
=> ( 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 @ ( binunion @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f11,plain,
~ ( ( binintersectI = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ! [X1: $i,X0: $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 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( binunionTILcontra
= ( ! [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 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f13,plain,
( ( binunionTILcontra = $true )
<=> ! [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 @ X1 )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( binunionTIRcontra
= ( ! [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 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f15,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ~ ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f17,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> ( in @ X1 @ ( setminus @ X2 @ X0 ) ) ) )
= setminusI ),
inference(rectify,[],[f2]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( binunionTILcontra = $true )
<=> ! [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 @ X1 )
!= $true ) ) ) ) ) ),
inference(flattening,[],[f13]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
=> ( ( in @ X3 @ X2 )
!= $true ) ) ) ) )
<=> ( binunionTIRcontra = $true ) ),
inference(flattening,[],[f15]) ).
thf(f22,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f17]) ).
thf(f23,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f24,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binintersectI = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f25,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binintersectI = $true )
& ( setminusER = $true )
& ( binunionTILcontra = $true )
& ( setminusI = $true )
& ( binunionTIRcontra = $true ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f27,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( binintersectI = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f29,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true ) )
<=> ( binintersectI = $true ) ),
inference(flattening,[],[f28]) ).
thf(f30,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
<=> ( binunionTIRcontra = $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f31,plain,
( ( binunionTIRcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f33,plain,
( ( binunionTILcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f34,plain,
( ( binunionTILcontra = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) ) ),
inference(flattening,[],[f33]) ).
thf(f35,plain,
( ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f29]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
& ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ ( binintersect @ X4 @ X3 ) )
!= $true ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true ) )
| ( binintersectI != $true ) )
& ( ( binintersectI = $true )
| ( ( $true
= ( in @ sK2 @ sK0 ) )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f36]) ).
thf(f38,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binintersect @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectI = $true )
& ( setminusER = $true )
& ( binunionTILcontra = $true )
& ( setminusI = $true )
& ( binunionTIRcontra = $true ) ),
inference(rectify,[],[f25]) ).
thf(f39,plain,
( ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
& ( $true
= ( in @ sK6 @ sK3 ) )
& ( ( in @ sK6 @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) )
!= $true )
& ( ( in @ sK6 @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) )
= $true )
& ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
& ( binintersectI = $true )
& ( setminusER = $true )
& ( binunionTILcontra = $true )
& ( setminusI = $true )
& ( binunionTIRcontra = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f38]) ).
thf(f40,plain,
( ( ( binunionTIRcontra = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ! [X2: $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
!= $true ) ) )
| ( binunionTIRcontra != $true ) ) ),
inference(nnf_transformation,[],[f31]) ).
thf(f41,plain,
( ( ( binunionTIRcontra = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X0 @ X2 ) ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) ) )
| ( binunionTIRcontra != $true ) ) ),
inference(rectify,[],[f40]) ).
thf(f42,plain,
( ( ( binunionTIRcontra = $true )
| ( ( ( in @ sK7 @ ( powerset @ sK8 ) )
= $true )
& ( ( in @ sK10 @ ( binunion @ sK7 @ sK9 ) )
!= $true )
& ( ( in @ sK10 @ sK8 )
= $true )
& ( $true
= ( in @ sK10 @ sK9 ) )
& ( $true
= ( in @ sK9 @ ( powerset @ sK8 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) ) )
| ( binunionTIRcontra != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f41]) ).
thf(f43,plain,
( ( ( binunionTILcontra = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
= $true ) ) ) )
| ( binunionTILcontra != $true ) ) ),
inference(nnf_transformation,[],[f34]) ).
thf(f44,plain,
( ( ( binunionTILcontra = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
!= $true ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) ) ) ) )
| ( binunionTILcontra != $true ) ) ),
inference(rectify,[],[f43]) ).
thf(f45,plain,
( ( ( binunionTILcontra = $true )
| ( ( ( in @ sK12 @ ( powerset @ sK11 ) )
= $true )
& ( $true
= ( in @ sK13 @ ( powerset @ sK11 ) ) )
& ( ( in @ sK14 @ sK12 )
= $true )
& ( ( in @ sK14 @ sK11 )
= $true )
& ( ( in @ sK14 @ ( binunion @ sK12 @ sK13 ) )
!= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) ) ) ) )
| ( binunionTILcontra != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f44]) ).
thf(f46,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
& ( ( in @ X1 @ X2 )
= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X2 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[],[f27]) ).
thf(f47,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[],[f46]) ).
thf(f48,plain,
( ( ( setminusI = $true )
| ( ( $true
!= ( in @ sK17 @ sK15 ) )
& ( ( in @ sK17 @ ( setminus @ sK16 @ sK15 ) )
!= $true )
& ( ( in @ sK17 @ sK16 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X0,sK15),skolemize(X1,sK16),skolemize(X2,sK17)],[f47]) ).
thf(f49,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f32]) ).
thf(f50,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
= $true )
& ( ( in @ X5 @ X4 )
= $true ) ) ) ),
inference(rectify,[],[f49]) ).
thf(f51,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( ( in @ sK20 @ ( setminus @ sK18 @ sK19 ) )
= $true )
& ( ( in @ sK20 @ sK19 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X3,sK18),skolemize(X4,sK19),skolemize(X5,sK20)],[f50]) ).
thf(f55,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( binintersectI != $true ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f56,plain,
binunionTIRcontra = $true,
inference(cnf_transformation,[],[f39]) ).
thf(f57,plain,
setminusI = $true,
inference(cnf_transformation,[],[f39]) ).
thf(f58,plain,
binunionTILcontra = $true,
inference(cnf_transformation,[],[f39]) ).
thf(f59,plain,
setminusER = $true,
inference(cnf_transformation,[],[f39]) ).
thf(f60,plain,
binintersectI = $true,
inference(cnf_transformation,[],[f39]) ).
thf(f61,plain,
( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ),
inference(cnf_transformation,[],[f39]) ).
thf(f62,plain,
( ( in @ sK6 @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) )
= $true ),
inference(cnf_transformation,[],[f39]) ).
thf(f63,plain,
( ( in @ sK6 @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) )
!= $true ),
inference(cnf_transformation,[],[f39]) ).
thf(f64,plain,
( $true
= ( in @ sK6 @ sK3 ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f65,plain,
( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f66,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
= $true )
| ( binunionTIRcontra != $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f72,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( binunionTILcontra != $true )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
| ( ( in @ X7 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f78,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setminusI != $true )
| ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f84,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( setminusER != $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f91,definition,
( spl21_2
<=> ( setminusI = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
thf(f101,definition,
( spl21_4
<=> ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
thf(f103,plain,
( ( ( in @ sK4 @ ( powerset @ sK3 ) )
= $true )
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f104,plain,
spl21_4,
inference(avatar_split_clause,[],[f61,f101]) ).
thf(f106,definition,
( spl21_5
<=> ( binunionTIRcontra = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
thf(f109,plain,
spl21_5,
inference(avatar_split_clause,[],[f56,f106]) ).
thf(f111,definition,
( spl21_6
<=> ( setminusER = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
thf(f115,definition,
( spl21_7
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_7])],[avatar_definition]) ).
thf(f116,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true )
| ( ( in @ X2 @ X1 )
!= $true ) )
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f115]) ).
thf(f117,plain,
( ~ spl21_6
| spl21_7 ),
inference(avatar_split_clause,[],[f84,f115,f111]) ).
thf(f119,definition,
( spl21_8
<=> ( binunionTILcontra = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
thf(f138,definition,
( spl21_12
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
= $true )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
thf(f139,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setminus @ X4 @ X3 ) )
= $true )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) )
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f140,plain,
( ~ spl21_2
| spl21_12 ),
inference(avatar_split_clause,[],[f78,f138,f91]) ).
thf(f146,plain,
spl21_2,
inference(avatar_split_clause,[],[f57,f91]) ).
thf(f163,definition,
( spl21_17
<=> ( $true
= ( in @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_17])],[avatar_definition]) ).
thf(f165,plain,
( ( $true
= ( in @ sK6 @ sK3 ) )
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f163]) ).
thf(f166,plain,
spl21_17,
inference(avatar_split_clause,[],[f64,f163]) ).
thf(f177,definition,
( spl21_20
<=> ( binintersectI = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_20])],[avatar_definition]) ).
thf(f181,plain,
spl21_20,
inference(avatar_split_clause,[],[f60,f177]) ).
thf(f183,definition,
( spl21_21
<=> ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_21])],[avatar_definition]) ).
thf(f185,plain,
( ( $true
= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ~ spl21_21 ),
inference(avatar_component_clause,[],[f183]) ).
thf(f186,plain,
spl21_21,
inference(avatar_split_clause,[],[f65,f183]) ).
thf(f193,definition,
( spl21_23
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_23])],[avatar_definition]) ).
thf(f194,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binunion @ X4 @ X6 ) )
= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) )
| ~ spl21_23 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f195,plain,
( ~ spl21_5
| spl21_23 ),
inference(avatar_split_clause,[],[f66,f193,f106]) ).
thf(f202,definition,
( spl21_25
<=> ( ( in @ sK6 @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_25])],[avatar_definition]) ).
thf(f204,plain,
( ( ( in @ sK6 @ ( setminus @ sK3 @ ( binunion @ sK4 @ sK5 ) ) )
= $true )
| ~ spl21_25 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f205,plain,
spl21_25,
inference(avatar_split_clause,[],[f62,f202]) ).
thf(f207,definition,
( spl21_26
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_26])],[avatar_definition]) ).
thf(f208,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f209,plain,
( spl21_26
| ~ spl21_20 ),
inference(avatar_split_clause,[],[f55,f177,f207]) ).
thf(f221,definition,
( spl21_29
<=> ( ( in @ sK6 @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_29])],[avatar_definition]) ).
thf(f223,plain,
( ( ( in @ sK6 @ ( binintersect @ ( setminus @ sK3 @ sK4 ) @ ( setminus @ sK3 @ sK5 ) ) )
!= $true )
| spl21_29 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f224,plain,
~ spl21_29,
inference(avatar_split_clause,[],[f63,f221]) ).
thf(f235,plain,
spl21_6,
inference(avatar_split_clause,[],[f59,f111]) ).
thf(f237,definition,
( spl21_32
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_32])],[avatar_definition]) ).
thf(f238,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X7 @ ( binunion @ X5 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ( in @ X6 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f239,plain,
( spl21_32
| ~ spl21_8 ),
inference(avatar_split_clause,[],[f72,f119,f237]) ).
thf(f245,plain,
spl21_8,
inference(avatar_split_clause,[],[f58,f119]) ).
thf(f251,plain,
( ( $true != $true )
| ( ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) )
!= $true )
| ( ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) )
!= $true )
| ~ spl21_26
| spl21_29 ),
inference(superposition,[],[f223,f208]) ).
thf(f252,plain,
( ( ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) )
!= $true )
| ( ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) )
!= $true )
| ~ spl21_26
| spl21_29 ),
inference(trivial_inequality_removal,[],[f251]) ).
thf(f254,definition,
( spl21_34
<=> ( ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_34])],[avatar_definition]) ).
thf(f256,plain,
( ( ( in @ sK6 @ ( setminus @ sK3 @ sK4 ) )
!= $true )
| spl21_34 ),
inference(avatar_component_clause,[],[f254]) ).
thf(f258,definition,
( spl21_35
<=> ( ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_35])],[avatar_definition]) ).
thf(f260,plain,
( ( ( in @ sK6 @ ( setminus @ sK3 @ sK5 ) )
!= $true )
| spl21_35 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f261,plain,
( ~ spl21_34
| ~ spl21_35
| ~ spl21_26
| spl21_29 ),
inference(avatar_split_clause,[],[f252,f221,f207,f258,f254]) ).
thf(f262,plain,
( ( $true != $true )
| ( $true
= ( in @ sK6 @ sK4 ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl21_12
| spl21_34 ),
inference(superposition,[],[f256,f139]) ).
thf(f263,plain,
( ( $true
= ( in @ sK6 @ sK4 ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl21_12
| spl21_34 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f264,plain,
( ( $true
= ( in @ sK6 @ sK4 ) )
| ~ spl21_12
| ~ spl21_17
| spl21_34 ),
inference(forward_subsumption_resolution,[],[f263,f165]) ).
thf(f266,definition,
( spl21_36
<=> ( $true
= ( in @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_36])],[avatar_definition]) ).
thf(f268,plain,
( ( $true
= ( in @ sK6 @ sK4 ) )
| ~ spl21_36 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f269,plain,
( spl21_36
| ~ spl21_12
| ~ spl21_17
| spl21_34 ),
inference(avatar_split_clause,[],[f264,f254,f163,f138,f266]) ).
thf(f271,plain,
( ( $true != $true )
| ( ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) )
!= $true )
| ~ spl21_7
| ~ spl21_25 ),
inference(superposition,[],[f116,f204]) ).
thf(f273,plain,
( ( ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) )
!= $true )
| ~ spl21_7
| ~ spl21_25 ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f276,definition,
( spl21_37
<=> ( ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_37])],[avatar_definition]) ).
thf(f278,plain,
( ( ( in @ sK6 @ ( binunion @ sK4 @ sK5 ) )
!= $true )
| spl21_37 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f279,plain,
( ~ spl21_37
| ~ spl21_7
| ~ spl21_25 ),
inference(avatar_split_clause,[],[f273,f202,f115,f276]) ).
thf(f281,plain,
( ( $true
!= ( in @ sK6 @ sK3 ) )
| ( ( in @ sK6 @ sK5 )
= $true )
| ( $true != $true )
| ~ spl21_12
| spl21_35 ),
inference(superposition,[],[f260,f139]) ).
thf(f282,plain,
( ( $true
!= ( in @ sK6 @ sK3 ) )
| ( ( in @ sK6 @ sK5 )
= $true )
| ~ spl21_12
| spl21_35 ),
inference(trivial_inequality_removal,[],[f281]) ).
thf(f283,plain,
( ( ( in @ sK6 @ sK5 )
= $true )
| ~ spl21_12
| ~ spl21_17
| spl21_35 ),
inference(forward_subsumption_resolution,[],[f282,f165]) ).
thf(f285,definition,
( spl21_38
<=> ( ( in @ sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_38])],[avatar_definition]) ).
thf(f288,plain,
( spl21_38
| ~ spl21_12
| ~ spl21_17
| spl21_35 ),
inference(avatar_split_clause,[],[f283,f258,f163,f138,f285]) ).
thf(f294,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK6 @ sK4 ) )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK6 @ X0 )
!= $true )
| ( ( in @ sK5 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true ) )
| ~ spl21_32
| spl21_37 ),
inference(superposition,[],[f278,f238]) ).
thf(f295,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK6 @ X0 )
!= $true )
| ( ( in @ sK6 @ sK5 )
!= $true )
| ( ( in @ sK5 @ ( powerset @ X0 ) )
!= $true )
| ( $true != $true ) )
| ~ spl21_23
| spl21_37 ),
inference(superposition,[],[f278,f194]) ).
thf(f296,plain,
( ! [X0: $i] :
( ( ( in @ sK5 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ sK5 )
!= $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK6 @ X0 )
!= $true ) )
| ~ spl21_23
| spl21_37 ),
inference(trivial_inequality_removal,[],[f295]) ).
thf(f297,plain,
( ! [X0: $i] :
( ( ( in @ sK5 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( $true
!= ( in @ sK6 @ sK4 ) )
| ( ( in @ sK6 @ X0 )
!= $true ) )
| ~ spl21_32
| spl21_37 ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f298,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK5 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ X0 )
!= $true ) )
| ~ spl21_32
| ~ spl21_36
| spl21_37 ),
inference(forward_subsumption_resolution,[],[f297,f268]) ).
thf(f299,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl21_4
| ~ spl21_32
| ~ spl21_36
| spl21_37 ),
inference(superposition,[],[f298,f103]) ).
thf(f300,plain,
( ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl21_4
| ~ spl21_32
| ~ spl21_36
| spl21_37 ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f301,plain,
( ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl21_4
| ~ spl21_21
| ~ spl21_32
| ~ spl21_36
| spl21_37 ),
inference(forward_subsumption_resolution,[],[f300,f185]) ).
thf(f302,plain,
( $false
| ~ spl21_4
| ~ spl21_17
| ~ spl21_21
| ~ spl21_32
| ~ spl21_36
| spl21_37 ),
inference(forward_subsumption_resolution,[],[f301,f165]) ).
thf(f303,plain,
( ~ spl21_4
| ~ spl21_17
| ~ spl21_21
| ~ spl21_32
| ~ spl21_36
| spl21_37 ),
inference(avatar_contradiction_clause,[],[f302]) ).
thf(f305,definition,
( spl21_39
<=> ! [X0: $i] :
( ( ( in @ sK5 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ X0 )
!= $true )
| ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_39])],[avatar_definition]) ).
thf(f306,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK4 @ ( powerset @ X0 ) ) )
| ( ( in @ sK5 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ X0 )
!= $true ) )
| ~ spl21_39 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f308,plain,
( spl21_39
| ~ spl21_38
| ~ spl21_23
| spl21_37 ),
inference(avatar_split_clause,[],[f296,f276,f193,f285,f305]) ).
thf(f313,plain,
( ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ( $true != $true )
| ~ spl21_4
| ~ spl21_39 ),
inference(superposition,[],[f306,f103]) ).
thf(f314,plain,
( ( $true
!= ( in @ sK5 @ ( powerset @ sK3 ) ) )
| ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl21_4
| ~ spl21_39 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f315,plain,
( ( $true
!= ( in @ sK6 @ sK3 ) )
| ~ spl21_4
| ~ spl21_21
| ~ spl21_39 ),
inference(forward_subsumption_resolution,[],[f314,f185]) ).
thf(f316,plain,
( $false
| ~ spl21_4
| ~ spl21_17
| ~ spl21_21
| ~ spl21_39 ),
inference(forward_subsumption_resolution,[],[f315,f165]) ).
thf(f317,plain,
( ~ spl21_4
| ~ spl21_17
| ~ spl21_21
| ~ spl21_39 ),
inference(avatar_contradiction_clause,[],[f316]) ).
cnf(s3,plain,
spl21_4,
inference(sat_conversion,[],[f104]) ).
cnf(s4,plain,
spl21_5,
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( ~ spl21_6
| spl21_7 ),
inference(sat_conversion,[],[f117]) ).
cnf(s9,plain,
( ~ spl21_2
| spl21_12 ),
inference(sat_conversion,[],[f140]) ).
cnf(s11,plain,
spl21_2,
inference(sat_conversion,[],[f146]) ).
cnf(s15,plain,
spl21_17,
inference(sat_conversion,[],[f166]) ).
cnf(s18,plain,
spl21_20,
inference(sat_conversion,[],[f181]) ).
cnf(s19,plain,
spl21_21,
inference(sat_conversion,[],[f186]) ).
cnf(s21,plain,
( ~ spl21_5
| spl21_23 ),
inference(sat_conversion,[],[f195]) ).
cnf(s23,plain,
spl21_25,
inference(sat_conversion,[],[f205]) ).
cnf(s24,plain,
( ~ spl21_20
| spl21_26 ),
inference(sat_conversion,[],[f209]) ).
cnf(s27,plain,
~ spl21_29,
inference(sat_conversion,[],[f224]) ).
cnf(s30,plain,
spl21_6,
inference(sat_conversion,[],[f235]) ).
cnf(s31,plain,
( ~ spl21_8
| spl21_32 ),
inference(sat_conversion,[],[f239]) ).
cnf(s33,plain,
spl21_8,
inference(sat_conversion,[],[f245]) ).
cnf(s34,plain,
( ~ spl21_26
| spl21_29
| ~ spl21_34
| ~ spl21_35 ),
inference(sat_conversion,[],[f261]) ).
cnf(s35,plain,
( ~ spl21_12
| ~ spl21_17
| spl21_34
| spl21_36 ),
inference(sat_conversion,[],[f269]) ).
cnf(s36,plain,
( ~ spl21_7
| ~ spl21_25
| ~ spl21_37 ),
inference(sat_conversion,[],[f279]) ).
cnf(s38,plain,
( ~ spl21_12
| ~ spl21_17
| spl21_35
| spl21_38 ),
inference(sat_conversion,[],[f288]) ).
cnf(s40,plain,
( ~ spl21_4
| ~ spl21_17
| ~ spl21_21
| ~ spl21_32
| ~ spl21_36
| spl21_37 ),
inference(sat_conversion,[],[f303]) ).
cnf(s42,plain,
( ~ spl21_23
| spl21_37
| ~ spl21_38
| spl21_39 ),
inference(sat_conversion,[],[f308]) ).
cnf(s44,plain,
( ~ spl21_4
| ~ spl21_17
| ~ spl21_21
| ~ spl21_39 ),
inference(sat_conversion,[],[f317]) ).
cnf(s45,plain,
spl21_32,
inference(rat,[],[s31,s33]) ).
cnf(s46,plain,
spl21_26,
inference(rat,[],[s24,s18]) ).
cnf(s47,plain,
spl21_12,
inference(rat,[],[s9,s11]) ).
cnf(s48,plain,
spl21_7,
inference(rat,[],[s5,s30]) ).
cnf(s49,plain,
~ spl21_37,
inference(rat,[],[s36,s23,s48]) ).
cnf(s50,plain,
spl21_23,
inference(rat,[],[s21,s4]) ).
cnf(s51,plain,
~ spl21_39,
inference(rat,[],[s44,s15,s19,s3]) ).
cnf(s52,plain,
~ spl21_36,
inference(rat,[],[s40,s49,s15,s45,s19,s3]) ).
cnf(s53,plain,
~ spl21_38,
inference(rat,[],[s42,s50,s49,s51]) ).
cnf(s54,plain,
spl21_34,
inference(rat,[],[s35,s47,s15,s52]) ).
cnf(s55,plain,
spl21_35,
inference(rat,[],[s38,s47,s15,s53]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s34,s46,s27,s55,s54]) ).
thf(f318,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU754^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:22:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.27 % (4071494)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (4071502)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=894995327: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)
% 0.21/0.27 % (4071505)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (4071505)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
% 0.21/0.27 % (4071502) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4071494-4071502"...
% 0.21/0.27 % (4071499)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3855892977:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (4071500)lrs+10_16_si=on:nwc=1.5:random_seed=22260644:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (4071503)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2431616604:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (4071501)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3027444128:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (4071504)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4027480687:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (4071502)...printing done.
% 0.21/0.27 % (4071505)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=3191949413:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (4071502)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (4071502)------------------------------
% 0.21/0.28 % (4071502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (4071502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (4071502)CaDiCaL version: 2.1.3
% 0.21/0.28 % (4071502)Termination reason: Refutation
% 0.21/0.28 % (4071502)Time elapsed: 0.007 s
% 0.21/0.28 % (4071502)Peak memory usage: 13 MB
% 0.21/0.28 % (4071502)Instructions burned: 22 (million)
% 0.21/0.28 % (4071494)Success in time 0.038 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------