%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU752^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 27
% Syntax : Number of formulae : 175 ( 54 unt; 0 typ; 21 def)
% Number of atoms : 1664 ( 412 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 1866 ( 300 ~; 270 |; 81 &;1093 @)
% ( 39 <=>; 83 =>; 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 : 262 ( 0 sgn 220 !; 42 ?; 262 :)
% 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,
binunionE: $o ).
thf(func_def_5,type,
binintersect: $i > $i > $i ).
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,
binintersectTELcontra: $o ).
thf(func_def_10,type,
binintersectTERcontra: $o ).
thf(f1,axiom,
( binunionE
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(f3,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(f4,axiom,
( binintersectTELcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(f5,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) )
= binintersectTERcontra ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(f6,conjecture,
( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b) ).
thf(f7,negated_conjecture,
~ ( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( binintersectTELcontra
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X1 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
( ( binintersectTELcontra = $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 @ X1 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) )
= setminusI ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X0 @ X2 ) )
= setminusER ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
=> ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ~ ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) )
= binintersectTERcontra ),
inference(rectify,[],[f5]) ).
thf(f15,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 @ X2 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
<=> ( binintersectTERcontra = $true ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f17,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( binunionE
=> ( setminusI
=> ( setminusER
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( binunionE = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,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 @ X1 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
<=> ( binintersectTELcontra = $true ) ),
inference(flattening,[],[f9]) ).
thf(f21,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
!= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f22,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
=> ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(flattening,[],[f13]) ).
thf(f23,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X2 )
!= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) )
<=> ( binintersectTERcontra = $true ) ),
inference(flattening,[],[f15]) ).
thf(f24,plain,
( ( binunionE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f25,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true ) )
<=> ( binunionE = $true ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binintersectTERcontra = $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f27,plain,
( ( binintersectTERcontra = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f29,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( binunionE = $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f30,plain,
( ( binunionE = $true )
& ( binintersectTELcontra = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binunion @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X1 @ ( binintersect @ X0 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( setminusER = $true )
& ( binintersectTERcontra = $true )
& ( setminusI = $true ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
( ( setminusI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f32,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
<=> ( setminusI = $true ) ),
inference(flattening,[],[f31]) ).
thf(f33,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binintersectTELcontra = $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f34,plain,
( ( binintersectTELcontra = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f33]) ).
thf(f35,plain,
( ( ( binintersectTELcontra = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binintersectTELcontra != $true ) ) ),
inference(nnf_transformation,[],[f34]) ).
thf(f36,plain,
( ( ( binintersectTELcontra = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
& ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true ) )
| ( binintersectTELcontra != $true ) ) ),
inference(rectify,[],[f35]) ).
thf(f37,plain,
( ( ( binintersectTELcontra = $true )
| ( ( ( in @ sK3 @ sK0 )
!= $true )
& ( ( in @ sK3 @ ( binintersect @ sK0 @ sK2 ) )
= $true )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true ) )
| ( binintersectTELcontra != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f36]) ).
thf(f38,plain,
( ( binunionE = $true )
& ( binintersectTELcontra = $true )
& ( $true
= ( in @ sK7 @ ( binunion @ ( setminus @ sK5 @ sK4 ) @ ( setminus @ sK5 @ sK6 ) ) ) )
& ( ( in @ sK7 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) )
!= $true )
& ( ( in @ sK7 @ sK5 )
= $true )
& ( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true )
& ( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true )
& ( setminusER = $true )
& ( binintersectTERcontra = $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f30]) ).
thf(f39,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
!= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[],[f25]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
& ( $true
!= ( in @ X4 @ X3 ) )
& ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ( ( ( in @ sK9 @ sK10 )
!= $true )
& ( ( in @ sK9 @ sK8 )
!= $true )
& ( ( in @ sK9 @ ( binunion @ sK10 @ sK8 ) )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X3,sK8),skolemize(X4,sK9),skolemize(X5,sK10)],[f40]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f32]) ).
thf(f43,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true )
& ( ( in @ X5 @ ( setminus @ X3 @ X4 ) )
!= $true ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f44,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) )
| ( setminusI != $true ) )
& ( ( setminusI = $true )
| ( ( ( in @ sK13 @ sK12 )
!= $true )
& ( $true
= ( in @ sK13 @ sK11 ) )
& ( ( in @ sK13 @ ( setminus @ sK11 @ sK12 ) )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X3,sK11),skolemize(X4,sK12),skolemize(X5,sK13)],[f43]) ).
thf(f45,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f28]) ).
thf(f46,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
& ( ( in @ X3 @ X5 )
= $true ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f47,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( ( in @ sK14 @ ( setminus @ sK15 @ sK16 ) )
= $true )
& ( ( in @ sK14 @ sK16 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X3,sK14),skolemize(X4,sK15),skolemize(X5,sK16)],[f46]) ).
thf(f48,plain,
( ( ( binintersectTERcontra = $true )
| ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true ) ) ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) )
| ( binintersectTERcontra != $true ) ) ),
inference(nnf_transformation,[],[f27]) ).
thf(f49,plain,
( ( ( binintersectTERcontra = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ ( binintersect @ X0 @ X2 ) )
= $true ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true ) ) ) )
| ( binintersectTERcontra != $true ) ) ),
inference(rectify,[],[f48]) ).
thf(f50,plain,
( ( ( binintersectTERcontra = $true )
| ( ( $true
= ( in @ sK17 @ ( powerset @ sK18 ) ) )
& ( ( in @ sK19 @ ( powerset @ sK18 ) )
= $true )
& ( ( in @ sK20 @ sK19 )
!= $true )
& ( ( in @ sK20 @ sK18 )
= $true )
& ( ( in @ sK20 @ ( binintersect @ sK17 @ sK19 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true ) ) ) )
| ( binintersectTERcontra != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19,sK20]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19),skolemize(X3,sK20)],[f49]) ).
thf(f51,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( binintersectTELcontra != $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f57,plain,
setminusI = $true,
inference(cnf_transformation,[],[f38]) ).
thf(f58,plain,
binintersectTERcontra = $true,
inference(cnf_transformation,[],[f38]) ).
thf(f59,plain,
setminusER = $true,
inference(cnf_transformation,[],[f38]) ).
thf(f60,plain,
( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f61,plain,
( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f62,plain,
( ( in @ sK7 @ sK5 )
= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f63,plain,
( ( in @ sK7 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) )
!= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f64,plain,
( $true
= ( in @ sK7 @ ( binunion @ ( setminus @ sK5 @ sK4 ) @ ( setminus @ sK5 @ sK6 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f65,plain,
binintersectTELcontra = $true,
inference(cnf_transformation,[],[f38]) ).
thf(f66,plain,
binunionE = $true,
inference(cnf_transformation,[],[f38]) ).
thf(f70,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( binunionE != $true ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f74,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( setminusI != $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f77,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( setminusER != $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f78,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( binintersectTERcontra != $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ X6 )
= $true ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f90,definition,
( spl21_2
<=> ( setminusER = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
thf(f100,definition,
( spl21_4
<=> ( binunionE = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
thf(f109,definition,
( spl21_6
<=> ( binintersectTELcontra = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
thf(f123,definition,
( spl21_9
<=> ( setminusI = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
thf(f132,definition,
( spl21_11
<=> ( $true
= ( in @ sK7 @ ( binunion @ ( setminus @ sK5 @ sK4 ) @ ( setminus @ sK5 @ sK6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_11])],[avatar_definition]) ).
thf(f134,plain,
( ( $true
= ( in @ sK7 @ ( binunion @ ( setminus @ sK5 @ sK4 ) @ ( setminus @ sK5 @ sK6 ) ) ) )
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f135,plain,
spl21_11,
inference(avatar_split_clause,[],[f64,f132]) ).
thf(f137,definition,
( spl21_12
<=> ( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
thf(f139,plain,
( ( ( in @ sK6 @ ( powerset @ sK5 ) )
= $true )
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,plain,
spl21_12,
inference(avatar_split_clause,[],[f61,f137]) ).
thf(f147,definition,
( spl21_14
<=> ( binintersectTERcontra = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_14])],[avatar_definition]) ).
thf(f150,plain,
spl21_14,
inference(avatar_split_clause,[],[f58,f147]) ).
thf(f161,plain,
spl21_4,
inference(avatar_split_clause,[],[f66,f100]) ).
thf(f168,definition,
( spl21_18
<=> ( ( in @ sK7 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_18])],[avatar_definition]) ).
thf(f170,plain,
( ( ( in @ sK7 @ sK5 )
= $true )
| ~ spl21_18 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f171,plain,
spl21_18,
inference(avatar_split_clause,[],[f62,f168]) ).
thf(f188,definition,
( spl21_22
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_22])],[avatar_definition]) ).
thf(f189,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f190,plain,
( ~ spl21_9
| spl21_22 ),
inference(avatar_split_clause,[],[f74,f188,f123]) ).
thf(f196,plain,
spl21_9,
inference(avatar_split_clause,[],[f57,f123]) ).
thf(f203,definition,
( spl21_25
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X6 )
= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_25])],[avatar_definition]) ).
thf(f204,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X6 )
= $true ) )
| ~ spl21_25 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f205,plain,
( spl21_25
| ~ spl21_14 ),
inference(avatar_split_clause,[],[f78,f147,f203]) ).
thf(f212,definition,
( spl21_27
<=> ( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_27])],[avatar_definition]) ).
thf(f214,plain,
( ( ( in @ sK4 @ ( powerset @ sK5 ) )
= $true )
| ~ spl21_27 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f215,plain,
spl21_27,
inference(avatar_split_clause,[],[f60,f212]) ).
thf(f216,plain,
spl21_2,
inference(avatar_split_clause,[],[f59,f90]) ).
thf(f217,plain,
spl21_6,
inference(avatar_split_clause,[],[f65,f109]) ).
thf(f224,definition,
( spl21_29
<=> ( ( in @ sK7 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_29])],[avatar_definition]) ).
thf(f226,plain,
( ( ( in @ sK7 @ ( setminus @ sK5 @ ( binintersect @ sK4 @ sK6 ) ) )
!= $true )
| spl21_29 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f227,plain,
~ spl21_29,
inference(avatar_split_clause,[],[f63,f224]) ).
thf(f229,definition,
( spl21_30
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_30])],[avatar_definition]) ).
thf(f230,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ~ spl21_30 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f231,plain,
( spl21_30
| ~ spl21_2 ),
inference(avatar_split_clause,[],[f77,f90,f229]) ).
thf(f233,definition,
( spl21_31
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_31])],[avatar_definition]) ).
thf(f234,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( in @ X7 @ ( binintersect @ X4 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X4 )
= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) )
| ~ spl21_31 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f235,plain,
( spl21_31
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f51,f109,f233]) ).
thf(f237,definition,
( spl21_32
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X2 )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_32])],[avatar_definition]) ).
thf(f238,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( ( in @ X1 @ X2 )
= $true ) )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f239,plain,
( spl21_32
| ~ spl21_4 ),
inference(avatar_split_clause,[],[f70,f100,f237]) ).
thf(f250,plain,
( ( $true != $true )
| ( ( in @ sK7 @ sK5 )
!= $true )
| ( ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) )
= $true )
| ~ spl21_22
| spl21_29 ),
inference(superposition,[],[f226,f189]) ).
thf(f252,plain,
( ( ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) )
= $true )
| ( ( in @ sK7 @ sK5 )
!= $true )
| ~ spl21_22
| spl21_29 ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f253,plain,
( ( ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) )
= $true )
| ~ spl21_18
| ~ spl21_22
| spl21_29 ),
inference(forward_subsumption_resolution,[],[f252,f170]) ).
thf(f255,definition,
( spl21_34
<=> ( ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_34])],[avatar_definition]) ).
thf(f257,plain,
( ( ( in @ sK7 @ ( binintersect @ sK4 @ sK6 ) )
= $true )
| ~ spl21_34 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f258,plain,
( spl21_34
| ~ spl21_18
| ~ spl21_22
| spl21_29 ),
inference(avatar_split_clause,[],[f253,f224,f188,f168,f255]) ).
thf(f259,plain,
( ( ( in @ sK7 @ ( setminus @ sK5 @ sK6 ) )
= $true )
| ( ( in @ sK7 @ ( setminus @ sK5 @ sK4 ) )
= $true )
| ( $true != $true )
| ~ spl21_11
| ~ spl21_32 ),
inference(superposition,[],[f238,f134]) ).
thf(f260,plain,
( ( ( in @ sK7 @ ( setminus @ sK5 @ sK4 ) )
= $true )
| ( ( in @ sK7 @ ( setminus @ sK5 @ sK6 ) )
= $true )
| ~ spl21_11
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f262,definition,
( spl21_35
<=> ( ( in @ sK7 @ ( setminus @ sK5 @ sK6 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_35])],[avatar_definition]) ).
thf(f264,plain,
( ( ( in @ sK7 @ ( setminus @ sK5 @ sK6 ) )
= $true )
| ~ spl21_35 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f266,definition,
( spl21_36
<=> ( ( in @ sK7 @ ( setminus @ sK5 @ sK4 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_36])],[avatar_definition]) ).
thf(f268,plain,
( ( ( in @ sK7 @ ( setminus @ sK5 @ sK4 ) )
= $true )
| ~ spl21_36 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f269,plain,
( spl21_35
| spl21_36
| ~ spl21_11
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f260,f237,f132,f266,f262]) ).
thf(f270,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK7 @ sK6 )
= $true )
| ( ( in @ sK4 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ X0 )
!= $true ) )
| ~ spl21_25
| ~ spl21_34 ),
inference(superposition,[],[f204,f257]) ).
thf(f271,plain,
( ! [X0: $i] :
( ( ( in @ sK4 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ X0 )
!= $true )
| ( ( in @ sK7 @ sK6 )
= $true ) )
| ~ spl21_25
| ~ spl21_34 ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f273,definition,
( spl21_37
<=> ! [X0: $i] :
( ( ( in @ sK4 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ X0 )
!= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl21_37])],[avatar_definition]) ).
thf(f274,plain,
( ! [X0: $i] :
( ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK4 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ X0 )
!= $true ) )
| ~ spl21_37 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f276,definition,
( spl21_38
<=> ( ( in @ sK7 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_38])],[avatar_definition]) ).
thf(f279,plain,
( spl21_37
| spl21_38
| ~ spl21_25
| ~ spl21_34 ),
inference(avatar_split_clause,[],[f271,f255,f203,f276,f273]) ).
thf(f280,plain,
( ! [X0: $i] :
( ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ sK4 )
= $true )
| ( ( in @ sK4 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl21_31
| ~ spl21_34 ),
inference(superposition,[],[f234,f257]) ).
thf(f281,plain,
( ! [X0: $i] :
( ( ( in @ sK4 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ sK4 )
= $true )
| ( ( in @ sK6 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ sK7 @ X0 )
!= $true ) )
| ~ spl21_31
| ~ spl21_34 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f283,definition,
( spl21_39
<=> ( ( in @ sK7 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_39])],[avatar_definition]) ).
thf(f286,plain,
( spl21_37
| spl21_39
| ~ spl21_31
| ~ spl21_34 ),
inference(avatar_split_clause,[],[f281,f255,f233,f283,f273]) ).
thf(f287,plain,
( ( ( in @ sK7 @ sK6 )
!= $true )
| ( $true != $true )
| ~ spl21_30
| ~ spl21_35 ),
inference(superposition,[],[f230,f264]) ).
thf(f288,plain,
( ( ( in @ sK7 @ sK6 )
!= $true )
| ~ spl21_30
| ~ spl21_35 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f289,plain,
( ~ spl21_38
| ~ spl21_30
| ~ spl21_35 ),
inference(avatar_split_clause,[],[f288,f262,f229,f276]) ).
thf(f290,plain,
( ( $true != $true )
| ( ( in @ sK7 @ sK5 )
!= $true )
| ( ( in @ sK4 @ ( powerset @ sK5 ) )
!= $true )
| ~ spl21_12
| ~ spl21_37 ),
inference(superposition,[],[f274,f139]) ).
thf(f291,plain,
( ( ( in @ sK7 @ sK5 )
!= $true )
| ( ( in @ sK4 @ ( powerset @ sK5 ) )
!= $true )
| ~ spl21_12
| ~ spl21_37 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f292,plain,
( ( ( in @ sK4 @ ( powerset @ sK5 ) )
!= $true )
| ~ spl21_12
| ~ spl21_18
| ~ spl21_37 ),
inference(forward_subsumption_resolution,[],[f291,f170]) ).
thf(f293,plain,
( $false
| ~ spl21_12
| ~ spl21_18
| ~ spl21_27
| ~ spl21_37 ),
inference(forward_subsumption_resolution,[],[f292,f214]) ).
thf(f294,plain,
( ~ spl21_12
| ~ spl21_18
| ~ spl21_27
| ~ spl21_37 ),
inference(avatar_contradiction_clause,[],[f293]) ).
thf(f299,plain,
( ( $true != $true )
| ( ( in @ sK7 @ sK4 )
!= $true )
| ~ spl21_30
| ~ spl21_36 ),
inference(superposition,[],[f230,f268]) ).
thf(f300,plain,
( ( ( in @ sK7 @ sK4 )
!= $true )
| ~ spl21_30
| ~ spl21_36 ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f301,plain,
( ~ spl21_39
| ~ spl21_30
| ~ spl21_36 ),
inference(avatar_split_clause,[],[f300,f266,f229,f283]) ).
cnf(s7,plain,
spl21_11,
inference(sat_conversion,[],[f135]) ).
cnf(s8,plain,
spl21_12,
inference(sat_conversion,[],[f140]) ).
cnf(s10,plain,
spl21_14,
inference(sat_conversion,[],[f150]) ).
cnf(s13,plain,
spl21_4,
inference(sat_conversion,[],[f161]) ).
cnf(s15,plain,
spl21_18,
inference(sat_conversion,[],[f171]) ).
cnf(s19,plain,
( ~ spl21_9
| spl21_22 ),
inference(sat_conversion,[],[f190]) ).
cnf(s21,plain,
spl21_9,
inference(sat_conversion,[],[f196]) ).
cnf(s23,plain,
( ~ spl21_14
| spl21_25 ),
inference(sat_conversion,[],[f205]) ).
cnf(s25,plain,
spl21_27,
inference(sat_conversion,[],[f215]) ).
cnf(s26,plain,
spl21_2,
inference(sat_conversion,[],[f216]) ).
cnf(s27,plain,
spl21_6,
inference(sat_conversion,[],[f217]) ).
cnf(s29,plain,
~ spl21_29,
inference(sat_conversion,[],[f227]) ).
cnf(s30,plain,
( ~ spl21_2
| spl21_30 ),
inference(sat_conversion,[],[f231]) ).
cnf(s31,plain,
( ~ spl21_6
| spl21_31 ),
inference(sat_conversion,[],[f235]) ).
cnf(s32,plain,
( ~ spl21_4
| spl21_32 ),
inference(sat_conversion,[],[f239]) ).
cnf(s34,plain,
( ~ spl21_18
| ~ spl21_22
| spl21_29
| spl21_34 ),
inference(sat_conversion,[],[f258]) ).
cnf(s35,plain,
( ~ spl21_11
| ~ spl21_32
| spl21_35
| spl21_36 ),
inference(sat_conversion,[],[f269]) ).
cnf(s36,plain,
( ~ spl21_25
| ~ spl21_34
| spl21_37
| spl21_38 ),
inference(sat_conversion,[],[f279]) ).
cnf(s37,plain,
( ~ spl21_31
| ~ spl21_34
| spl21_37
| spl21_39 ),
inference(sat_conversion,[],[f286]) ).
cnf(s38,plain,
( ~ spl21_30
| ~ spl21_35
| ~ spl21_38 ),
inference(sat_conversion,[],[f289]) ).
cnf(s39,plain,
( ~ spl21_12
| ~ spl21_18
| ~ spl21_27
| ~ spl21_37 ),
inference(sat_conversion,[],[f294]) ).
cnf(s41,plain,
( ~ spl21_30
| ~ spl21_36
| ~ spl21_39 ),
inference(sat_conversion,[],[f301]) ).
cnf(s42,plain,
spl21_31,
inference(rat,[],[s31,s27]) ).
cnf(s43,plain,
spl21_30,
inference(rat,[],[s30,s26]) ).
cnf(s44,plain,
spl21_22,
inference(rat,[],[s19,s21]) ).
cnf(s45,plain,
spl21_34,
inference(rat,[],[s34,s44,s29,s15]) ).
cnf(s46,plain,
spl21_32,
inference(rat,[],[s32,s13]) ).
cnf(s47,plain,
spl21_25,
inference(rat,[],[s23,s10]) ).
cnf(s48,plain,
~ spl21_37,
inference(rat,[],[s39,s15,s25,s8]) ).
cnf(s49,plain,
spl21_39,
inference(rat,[],[s37,s45,s42,s48]) ).
cnf(s50,plain,
spl21_38,
inference(rat,[],[s36,s47,s45,s48]) ).
cnf(s51,plain,
~ spl21_36,
inference(rat,[],[s41,s43,s49]) ).
cnf(s52,plain,
~ spl21_35,
inference(rat,[],[s38,s43,s50]) ).
cnf(s53,plain,
~ spl21_11,
inference(rat,[],[s35,s51,s46,s52]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s7,s53]) ).
thf(f302,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU752^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:23:29 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (2577897)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2577905)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=3606536696: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)
% 0.21/0.29 % (2577908)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (2577908)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
% 0.21/0.29 % (2577905) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2577897-2577905"...
% 0.21/0.29 % (2577904)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2925417161:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (2577902)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1514881331:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2577903)lrs+10_16_si=on:nwc=1.5:random_seed=2076221751:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (2577907)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=828262690:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (2577906)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2645272150:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2577908)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=1334466339:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (2577905)...printing done.
% 0.21/0.29 % (2577904)Instruction limit reached!
% 0.21/0.29 % (2577904)------------------------------
% 0.21/0.29 % (2577904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2577904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2577904)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2577904)Termination reason: Instruction limit
% 0.21/0.29 % (2577904)Termination phase: Saturation
% 0.21/0.29 % (2577904)Time elapsed: 0.002 s
% 0.21/0.29 % (2577904)Peak memory usage: 11 MB
% 0.21/0.29 % (2577904)Instructions burned: 4 (million)
% 0.21/0.29 % (2577905)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (2577905)------------------------------
% 0.21/0.30 % (2577905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2577905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2577905)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2577905)Termination reason: Refutation
% 0.21/0.30 % (2577905)Time elapsed: 0.007 s
% 0.21/0.30 % (2577905)Peak memory usage: 13 MB
% 0.21/0.30 % (2577905)Instructions burned: 20 (million)
% 0.21/0.30 % (2577897)Success in time 0.044 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------