%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU732^2 : 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 : n006.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 08:31:01 AM UTC 2026
% Result : Theorem 0.33s 0.39s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 35
% Syntax : Number of formulae : 214 ( 70 unt; 0 typ; 32 def)
% Number of atoms : 1283 ( 256 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 1492 ( 211 ~; 231 |; 18 &; 839 @)
% ( 22 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 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 : 55 ( 51 usr; 41 con; 0-4 aty)
% ( 63 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 192 ( 0 sgn 114 !; 8 ?; 192 :)
% 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,
binintersect: $i > $i > $i ).
thf(func_def_3,type,
setminus: $i > $i > $i ).
thf(func_def_4,type,
setminusER: $o ).
thf(func_def_6,type,
binintersectTELcontra: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sF4: $o ).
thf(func_def_23,type,
sF6: $o ).
thf(func_def_24,type,
sF7: $o ).
thf(func_def_25,type,
sF8: $o ).
thf(func_def_27,type,
sF10: $o ).
thf(func_def_29,type,
sF12: $o ).
thf(func_def_30,type,
sF13: $o ).
thf(f1,axiom,
( setminusER
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f2,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/sandbox2/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(f3,conjecture,
( setminusER
=> ( binintersectTELcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(f4,negated_conjecture,
~ ( setminusER
=> ( binintersectTELcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,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,[],[f2]) ).
thf(f8,plain,
( binintersectTELcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( setminusER
=> ( binintersectTELcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( setminusER = $true )
=> ( ( 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 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( ( setminusER = $true )
=> ( ( 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 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
!= $true ) ) ) ) ) ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectTELcontra = $true )
& ( setminusER = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f13,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 @ ( binintersect @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) )
& ( setminusER = $true )
& ( binintersectTELcontra = $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) )
= $true )
& ( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true )
& ( setminusER = $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)],[f13]) ).
thf(f15,plain,
( binintersectTELcontra
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
binintersectTELcontra = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f17,plain,
setminusER = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
( ( in @ sK3 @ ( setminus @ sK0 @ sK1 ) )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( ( in @ sK3 @ ( binintersect @ sK1 @ sK2 ) )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( $true
= ( in @ sK2 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f26,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f16]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f17]) ).
thf(f28,definition,
( sF4
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= sF4 ),
inference(reorient_equations,[],[f28]) ).
thf(f30,plain,
$true = sF4,
inference(definition_folding,[],[f26,f29]) ).
thf(f31,definition,
( sF5
= ( powerset @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f32,plain,
( ( powerset @ sK0 )
= sF5 ),
inference(reorient_equations,[],[f31]) ).
thf(f33,definition,
( sF6
= ( in @ sK1 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f34,plain,
( ( in @ sK1 @ sF5 )
= sF6 ),
inference(reorient_equations,[],[f33]) ).
thf(f35,plain,
sF6 = $true,
inference(definition_folding,[],[f22,f34,f32]) ).
thf(f36,definition,
( sF7
= ( in @ sK2 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f37,plain,
sF7 = $true,
inference(definition_folding,[],[f21,f36,f32]) ).
thf(f38,definition,
( sF8
= ( in @ sK3 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f39,plain,
sF8 = $true,
inference(definition_folding,[],[f20,f38]) ).
thf(f40,definition,
( sF9
= ( binintersect @ sK1 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f41,plain,
( ( binintersect @ sK1 @ sK2 )
= sF9 ),
inference(reorient_equations,[],[f40]) ).
thf(f42,definition,
( sF10
= ( in @ sK3 @ sF9 ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f43,plain,
sF10 = $true,
inference(definition_folding,[],[f19,f42,f41]) ).
thf(f44,definition,
( sF11
= ( setminus @ sK0 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
thf(f45,definition,
( sF12
= ( in @ sK3 @ sF11 ) ),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
thf(f46,plain,
sF12 = $true,
inference(definition_folding,[],[f18,f45,f44]) ).
thf(f47,definition,
( sF13
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
thf(f48,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) )
= sF13 ),
inference(reorient_equations,[],[f47]) ).
thf(f49,plain,
$true = sF13,
inference(definition_folding,[],[f27,f48]) ).
thf(f51,plain,
( ( ( in @ sK2 @ sF5 )
= $true )
| ( sF7 = $false ) ),
inference(iff_proxy_clausification,[],[f36]) ).
thf(f53,plain,
( ( sF10 = $false )
| ( ( in @ sK3 @ sF9 )
= $true ) ),
inference(iff_proxy_clausification,[],[f42]) ).
thf(f54,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) ) )
= $true )
| ( $false = sF13 ) ),
inference(iff_proxy_clausification,[],[f48]) ).
thf(f65,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setminus @ Y2 @ Y0 ) )
=> ~ ( in @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true )
| ( $false = sF13 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f66,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setminus @ Y1 @ X1 ) )
=> ~ ( in @ Y0 @ X1 ) ) ) )
= $true )
| ( $false = sF13 ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( $false = sF13 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setminus @ Y1 @ X1 ) )
=> ~ ( in @ Y0 @ X1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setminus @ Y0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) )
= $true )
| ( $false = sF13 ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ X2 @ ( setminus @ Y0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
@ X3 )
= $true )
| ( $false = sF13 ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ ( setminus @ X3 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) )
| ( $false = sF13 ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( in @ X2 @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( setminus @ X3 @ X1 ) ) )
| ( $false = sF13 ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false = sF13 )
| ( $false
= ( in @ X2 @ ( setminus @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
= $true )
| ( $false = sF4 ) ),
inference(iff_proxy_clausification,[],[f29]) ).
thf(f93,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ~ ( in @ Y3 @ Y0 )
=> ~ ( in @ Y3 @ ( binintersect @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f94,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ X1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) ) )
= $true )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ~ ( in @ Y2 @ X1 )
=> ~ ( in @ Y2 @ ( binintersect @ X1 @ Y1 ) ) ) ) ) ) ) )
@ X2 )
= $true )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( $false = sF4 )
| ( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) ) ) )
| ( $false = sF4 )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ~ ( in @ Y1 @ X1 )
=> ~ ( in @ Y1 @ ( binintersect @ X1 @ Y0 ) ) ) ) ) )
@ X3 )
= $true )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ~ ( in @ Y0 @ X1 )
=> ~ ( in @ Y0 @ ( binintersect @ X1 @ X3 ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( in @ X4 @ X2 )
=> ( ~ ( in @ X4 @ X1 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( in @ X4 @ X1 )
=> ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false = sF4 )
| ( ( ~ ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( ~ ( in @ X4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
| ( $false = sF4 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( ~ ( in @ X4 @ X1 ) ) )
| ( $false
= ( in @ X4 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $true
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X4 @ X2 ) )
| ( $false
= ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f105]) ).
thf(f108,plain,
( ( sF12 = $false )
| ( ( in @ sK3 @ sF11 )
= $true ) ),
inference(iff_proxy_clausification,[],[f45]) ).
thf(f109,plain,
( ( ( in @ sK1 @ sF5 )
= $true )
| ( sF6 = $false ) ),
inference(iff_proxy_clausification,[],[f34]) ).
thf(f112,plain,
( ( $true
= ( in @ sK3 @ sK0 ) )
| ( sF8 = $false ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f114,definition,
( spl21_1
<=> ( ( in @ sK2 @ sF5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
thf(f116,plain,
( ( ( in @ sK2 @ sF5 )
= $true )
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f118,definition,
( spl21_2
<=> ( sF7 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
thf(f120,plain,
( ( sF7 = $false )
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f121,plain,
( spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f51,f118,f114]) ).
thf(f127,definition,
( spl21_4
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
thf(f129,plain,
( ( sF7 = $true )
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f131,plain,
spl21_4,
inference(avatar_split_clause,[],[f37,f127]) ).
thf(f133,definition,
( spl21_5
<=> ( sF10 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
thf(f135,plain,
( ( sF10 = $false )
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f137,definition,
( spl21_6
<=> ( ( in @ sK3 @ sF9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
thf(f139,plain,
( ( ( in @ sK3 @ sF9 )
= $true )
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f140,plain,
( spl21_5
| spl21_6 ),
inference(avatar_split_clause,[],[f53,f137,f133]) ).
thf(f142,definition,
( spl21_7
<=> ( sF10 = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_7])],[avatar_definition]) ).
thf(f144,plain,
( ( sF10 = $true )
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f142]) ).
thf(f155,definition,
( spl21_10
<=> ( $true = sF13 ) ),
introduced(definition,[new_symbols(definition,[spl21_10])],[avatar_definition]) ).
thf(f157,plain,
( ( $true = sF13 )
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f155]) ).
thf(f165,definition,
( spl21_12
<=> ( $false = sF13 ) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
thf(f167,plain,
( ( $false = sF13 )
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f169,definition,
( spl21_13
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X2 @ X1 )
= $false )
| ( $false
= ( in @ X2 @ ( setminus @ X3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_13])],[avatar_definition]) ).
thf(f170,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setminus @ X3 @ X1 ) ) )
| ( ( in @ X2 @ X1 )
= $false ) )
| ~ spl21_13 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f171,plain,
( spl21_12
| spl21_13 ),
inference(avatar_split_clause,[],[f72,f169,f165]) ).
thf(f173,definition,
( spl21_14
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl21_14])],[avatar_definition]) ).
thf(f175,plain,
( ( $true = sF4 )
| ~ spl21_14 ),
inference(avatar_component_clause,[],[f173]) ).
thf(f202,definition,
( spl21_20
<=> ! [X4: $i,X3: $i,X2: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
| ( $true
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl21_20])],[avatar_definition]) ).
thf(f203,plain,
( ! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X4 @ ( binintersect @ X1 @ X3 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ X4 @ X1 ) )
| ( $false
= ( in @ X4 @ X2 ) ) )
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f205,definition,
( spl21_21
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl21_21])],[avatar_definition]) ).
thf(f207,plain,
( ( $false = sF4 )
| ~ spl21_21 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f208,plain,
( spl21_20
| spl21_21 ),
inference(avatar_split_clause,[],[f106,f205,f202]) ).
thf(f209,plain,
spl21_10,
inference(avatar_split_clause,[],[f49,f155]) ).
thf(f211,definition,
( spl21_22
<=> ( ( in @ sK3 @ sF11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_22])],[avatar_definition]) ).
thf(f213,plain,
( ( ( in @ sK3 @ sF11 )
= $true )
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f211]) ).
thf(f215,definition,
( spl21_23
<=> ( sF12 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_23])],[avatar_definition]) ).
thf(f217,plain,
( ( sF12 = $false )
| ~ spl21_23 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f218,plain,
( spl21_22
| spl21_23 ),
inference(avatar_split_clause,[],[f108,f215,f211]) ).
thf(f220,definition,
( spl21_24
<=> ( sF12 = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_24])],[avatar_definition]) ).
thf(f222,plain,
( ( sF12 = $true )
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f229,definition,
( spl21_26
<=> ( ( in @ sK1 @ sF5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl21_26])],[avatar_definition]) ).
thf(f230,plain,
( ( ( in @ sK1 @ sF5 )
!= $false )
| spl21_26 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f231,plain,
( ( ( in @ sK1 @ sF5 )
= $false )
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f233,definition,
( spl21_27
<=> ( sF6 = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_27])],[avatar_definition]) ).
thf(f235,plain,
( ( sF6 = $true )
| ~ spl21_27 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f238,definition,
( spl21_28
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_28])],[avatar_definition]) ).
thf(f240,plain,
( ( sF6 = $false )
| ~ spl21_28 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f242,definition,
( spl21_29
<=> ( ( in @ sK1 @ sF5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl21_29])],[avatar_definition]) ).
thf(f244,plain,
( ( ( in @ sK1 @ sF5 )
= $true )
| ~ spl21_29 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f245,plain,
( spl21_28
| spl21_29 ),
inference(avatar_split_clause,[],[f109,f242,f238]) ).
thf(f247,definition,
( spl21_30
<=> ( sF8 = $false ) ),
introduced(definition,[new_symbols(definition,[spl21_30])],[avatar_definition]) ).
thf(f249,plain,
( ( sF8 = $false )
| ~ spl21_30 ),
inference(avatar_component_clause,[],[f247]) ).
thf(f251,definition,
( spl21_31
<=> ( $true
= ( in @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl21_31])],[avatar_definition]) ).
thf(f253,plain,
( ( $true
= ( in @ sK3 @ sK0 ) )
| ~ spl21_31 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f254,plain,
( spl21_30
| spl21_31 ),
inference(avatar_split_clause,[],[f112,f251,f247]) ).
thf(f256,definition,
( spl21_32
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(definition,[spl21_32])],[avatar_definition]) ).
thf(f258,plain,
( ( sF8 = $true )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f264,plain,
spl21_24,
inference(avatar_split_clause,[],[f46,f220]) ).
thf(f265,plain,
spl21_14,
inference(avatar_split_clause,[],[f30,f173]) ).
thf(f266,plain,
spl21_27,
inference(avatar_split_clause,[],[f35,f233]) ).
thf(f267,plain,
spl21_32,
inference(avatar_split_clause,[],[f39,f256]) ).
thf(f268,plain,
spl21_7,
inference(avatar_split_clause,[],[f43,f142]) ).
thf(f269,plain,
( ( $false = $true )
| ~ spl21_2
| ~ spl21_4 ),
inference(forward_demodulation,[],[f129,f120]) ).
thf(f270,plain,
( $false
| ~ spl21_2
| ~ spl21_4 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f271,plain,
( ~ spl21_2
| ~ spl21_4 ),
inference(avatar_contradiction_clause,[],[f270]) ).
thf(f283,plain,
( ( $false = $true )
| ~ spl21_5
| ~ spl21_7 ),
inference(forward_demodulation,[],[f144,f135]) ).
thf(f284,plain,
( $false
| ~ spl21_5
| ~ spl21_7 ),
inference(trivial_inequality_removal,[],[f283]) ).
thf(f285,plain,
( ~ spl21_5
| ~ spl21_7 ),
inference(avatar_contradiction_clause,[],[f284]) ).
thf(f290,plain,
( ( $false = $true )
| ~ spl21_27
| ~ spl21_28 ),
inference(forward_demodulation,[],[f240,f235]) ).
thf(f291,plain,
( $false
| ~ spl21_27
| ~ spl21_28 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f292,plain,
( ~ spl21_27
| ~ spl21_28 ),
inference(avatar_contradiction_clause,[],[f291]) ).
thf(f296,plain,
( ( $false = $true )
| ~ spl21_30
| ~ spl21_32 ),
inference(forward_demodulation,[],[f258,f249]) ).
thf(f297,plain,
( $false
| ~ spl21_30
| ~ spl21_32 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f298,plain,
( ~ spl21_30
| ~ spl21_32 ),
inference(avatar_contradiction_clause,[],[f297]) ).
thf(f301,plain,
( ( $false = $true )
| ~ spl21_10
| ~ spl21_12 ),
inference(forward_demodulation,[],[f157,f167]) ).
thf(f302,plain,
( $false
| ~ spl21_10
| ~ spl21_12 ),
inference(trivial_inequality_removal,[],[f301]) ).
thf(f303,plain,
( ~ spl21_10
| ~ spl21_12 ),
inference(avatar_contradiction_clause,[],[f302]) ).
thf(f308,plain,
( ( $false = $true )
| ~ spl21_26
| ~ spl21_29 ),
inference(forward_demodulation,[],[f244,f231]) ).
thf(f309,plain,
( $false
| ~ spl21_26
| ~ spl21_29 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f310,plain,
( ~ spl21_26
| ~ spl21_29 ),
inference(avatar_contradiction_clause,[],[f309]) ).
thf(f313,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF11 )
= $false )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl21_13 ),
inference(constrained_superposition,[],[f170,f44]) ).
thf(f318,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false = $true )
| ~ spl21_13
| ~ spl21_22 ),
inference(constrained_superposition,[],[f213,f313]) ).
thf(f319,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ~ spl21_13
| ~ spl21_22 ),
inference(trivial_inequality_removal,[],[f318]) ).
thf(f324,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ sK1 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ X1 ) )
| ( ( in @ sK2 @ ( powerset @ X1 ) )
= $false )
| ( $false
= ( in @ X0 @ sF9 ) )
| ( ( in @ X0 @ sK1 )
= $true ) )
| ~ spl21_20 ),
inference(constrained_superposition,[],[f203,f41]) ).
thf(f329,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $true )
| ( $false
= ( in @ X0 @ sF9 ) )
| ( ( in @ sK1 @ sF5 )
= $false )
| ( $false
= ( in @ sK2 @ sF5 ) ) )
| ~ spl21_20 ),
inference(constrained_superposition,[],[f324,f32]) ).
thf(f332,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $true )
| ( $false
= ( in @ X0 @ sF9 ) )
| ( $false
= ( in @ sK2 @ sF5 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl21_20
| spl21_26 ),
inference(forward_subsumption_resolution,[],[f329,f230]) ).
thf(f333,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sF9 ) )
| ( $false = $true )
| ( ( in @ X0 @ sK1 )
= $true ) )
| ~ spl21_1
| ~ spl21_20
| spl21_26 ),
inference(forward_demodulation,[],[f332,f116]) ).
thf(f334,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sF9 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( in @ X0 @ sK1 )
= $true ) )
| ~ spl21_1
| ~ spl21_20
| spl21_26 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f337,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( in @ sK3 @ sK1 )
= $true )
| ~ spl21_1
| ~ spl21_6
| ~ spl21_20
| spl21_26 ),
inference(constrained_superposition,[],[f139,f334]) ).
thf(f340,plain,
( ( $false
= ( in @ sK3 @ sK0 ) )
| ( ( in @ sK3 @ sK1 )
= $true )
| ~ spl21_1
| ~ spl21_6
| ~ spl21_20
| spl21_26 ),
inference(trivial_inequality_removal,[],[f337]) ).
thf(f343,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ( $false = $true )
| ~ spl21_1
| ~ spl21_6
| ~ spl21_20
| spl21_26
| ~ spl21_31 ),
inference(forward_demodulation,[],[f340,f253]) ).
thf(f344,plain,
( ( ( in @ sK3 @ sK1 )
= $true )
| ~ spl21_1
| ~ spl21_6
| ~ spl21_20
| spl21_26
| ~ spl21_31 ),
inference(trivial_inequality_removal,[],[f343]) ).
thf(f348,plain,
( ( $false = $true )
| ~ spl21_1
| ~ spl21_6
| ~ spl21_13
| ~ spl21_20
| ~ spl21_22
| spl21_26
| ~ spl21_31 ),
inference(forward_demodulation,[],[f344,f319]) ).
thf(f349,plain,
( $false
| ~ spl21_1
| ~ spl21_6
| ~ spl21_13
| ~ spl21_20
| ~ spl21_22
| spl21_26
| ~ spl21_31 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f350,plain,
( ~ spl21_1
| ~ spl21_6
| ~ spl21_13
| ~ spl21_20
| ~ spl21_22
| spl21_26
| ~ spl21_31 ),
inference(avatar_contradiction_clause,[],[f349]) ).
thf(f351,plain,
( ( $false = $true )
| ~ spl21_14
| ~ spl21_21 ),
inference(forward_demodulation,[],[f207,f175]) ).
thf(f352,plain,
( $false
| ~ spl21_14
| ~ spl21_21 ),
inference(trivial_inequality_removal,[],[f351]) ).
thf(f353,plain,
( ~ spl21_14
| ~ spl21_21 ),
inference(avatar_contradiction_clause,[],[f352]) ).
thf(f355,plain,
( ( $false = $true )
| ~ spl21_23
| ~ spl21_24 ),
inference(forward_demodulation,[],[f217,f222]) ).
thf(f356,plain,
( $false
| ~ spl21_23
| ~ spl21_24 ),
inference(trivial_inequality_removal,[],[f355]) ).
thf(f357,plain,
( ~ spl21_23
| ~ spl21_24 ),
inference(avatar_contradiction_clause,[],[f356]) ).
cnf(s1,plain,
( spl21_1
| spl21_2 ),
inference(sat_conversion,[],[f121]) ).
cnf(s3,plain,
spl21_4,
inference(sat_conversion,[],[f131]) ).
cnf(s4,plain,
( spl21_5
| spl21_6 ),
inference(sat_conversion,[],[f140]) ).
cnf(s8,plain,
( spl21_12
| spl21_13 ),
inference(sat_conversion,[],[f171]) ).
cnf(s14,plain,
( spl21_20
| spl21_21 ),
inference(sat_conversion,[],[f208]) ).
cnf(s15,plain,
spl21_10,
inference(sat_conversion,[],[f209]) ).
cnf(s16,plain,
( spl21_22
| spl21_23 ),
inference(sat_conversion,[],[f218]) ).
cnf(s19,plain,
( spl21_28
| spl21_29 ),
inference(sat_conversion,[],[f245]) ).
cnf(s20,plain,
( spl21_30
| spl21_31 ),
inference(sat_conversion,[],[f254]) ).
cnf(s22,plain,
spl21_24,
inference(sat_conversion,[],[f264]) ).
cnf(s23,plain,
spl21_14,
inference(sat_conversion,[],[f265]) ).
cnf(s24,plain,
spl21_27,
inference(sat_conversion,[],[f266]) ).
cnf(s25,plain,
spl21_32,
inference(sat_conversion,[],[f267]) ).
cnf(s26,plain,
spl21_7,
inference(sat_conversion,[],[f268]) ).
cnf(s27,plain,
( ~ spl21_2
| ~ spl21_4 ),
inference(sat_conversion,[],[f271]) ).
cnf(s28,plain,
( ~ spl21_5
| ~ spl21_7 ),
inference(sat_conversion,[],[f285]) ).
cnf(s29,plain,
( ~ spl21_27
| ~ spl21_28 ),
inference(sat_conversion,[],[f292]) ).
cnf(s30,plain,
( ~ spl21_30
| ~ spl21_32 ),
inference(sat_conversion,[],[f298]) ).
cnf(s31,plain,
( ~ spl21_10
| ~ spl21_12 ),
inference(sat_conversion,[],[f303]) ).
cnf(s32,plain,
( ~ spl21_26
| ~ spl21_29 ),
inference(sat_conversion,[],[f310]) ).
cnf(s34,plain,
( ~ spl21_1
| ~ spl21_6
| ~ spl21_13
| ~ spl21_20
| ~ spl21_22
| spl21_26
| ~ spl21_31 ),
inference(sat_conversion,[],[f350]) ).
cnf(s35,plain,
( ~ spl21_14
| ~ spl21_21 ),
inference(sat_conversion,[],[f353]) ).
cnf(s36,plain,
( ~ spl21_23
| ~ spl21_24 ),
inference(sat_conversion,[],[f357]) ).
cnf(s37,plain,
~ spl21_5,
inference(rat,[],[s28,s26]) ).
cnf(s38,plain,
~ spl21_30,
inference(rat,[],[s30,s25]) ).
cnf(s39,plain,
~ spl21_28,
inference(rat,[],[s29,s24]) ).
cnf(s40,plain,
~ spl21_21,
inference(rat,[],[s35,s23]) ).
cnf(s41,plain,
~ spl21_23,
inference(rat,[],[s36,s22]) ).
cnf(s42,plain,
spl21_31,
inference(rat,[],[s20,s38]) ).
cnf(s43,plain,
spl21_29,
inference(rat,[],[s19,s39]) ).
cnf(s44,plain,
~ spl21_26,
inference(rat,[],[s32,s43]) ).
cnf(s45,plain,
spl21_22,
inference(rat,[],[s16,s41]) ).
cnf(s46,plain,
~ spl21_12,
inference(rat,[],[s31,s15]) ).
cnf(s47,plain,
spl21_20,
inference(rat,[],[s14,s40]) ).
cnf(s48,plain,
spl21_13,
inference(rat,[],[s8,s46]) ).
cnf(s49,plain,
spl21_6,
inference(rat,[],[s4,s37]) ).
cnf(s50,plain,
~ spl21_1,
inference(rat,[],[s34,s42,s44,s45,s47,s48,s49]) ).
cnf(s51,plain,
~ spl21_2,
inference(rat,[],[s27,s3]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s1,s51,s50]) ).
thf(f358,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU732^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n006.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 14:17:40 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.33 Running higher-order theorem proving
% 0.27/0.34 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
% 0.33/0.39 % (788920)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.39 % (788931)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.39 % (788931)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
% 0.33/0.39 % (788931)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=3781160665:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.39 % (788931) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-788920-788931"...
% 0.33/0.39 % (788926)lrs+10_16_si=on:nwc=1.5:random_seed=2980328023:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.39 % (788931)...printing done.
% 0.33/0.39 % (788925)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3425957687:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.39 % (788931)Refutation found. Thanks to Tanya!
% 0.33/0.39 % SZS status Theorem for theBenchmark
% 0.33/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.40 % (788931)------------------------------
% 0.33/0.40 % (788931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.40 % (788931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.40 % (788931)CaDiCaL version: 2.1.3
% 0.33/0.40 % (788931)Termination reason: Refutation
% 0.33/0.40 % (788931)Time elapsed: 0.011 s
% 0.33/0.40 % (788931)Peak memory usage: 13 MB
% 0.33/0.40 % (788931)Instructions burned: 19 (million)
% 0.33/0.40 % (788920)Success in time 0.036 s
% 0.33/0.40 % Vampire exiting
%------------------------------------------------------------------------------