%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU649^2 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:31 AM UTC 2026
% Result : Theorem 0.33s 0.30s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 213 ( 64 unt; 0 typ; 23 def)
% Number of atoms : 1407 ( 368 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 1581 ( 170 ~; 304 |; 18 &; 874 @)
% ( 17 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 49 ( 45 usr; 35 con; 0-4 aty)
% ( 86 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 243 ( 0 sgn 139 !; 4 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setext: $o ).
thf(func_def_5,type,
setadjoinIL: $o ).
thf(func_def_6,type,
uniqinunit: $o ).
thf(func_def_7,type,
eqinunit: $o ).
thf(func_def_8,type,
upairset2E: $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
sF2: $o ).
thf(func_def_22,type,
sF3: $o ).
thf(func_def_25,type,
sF6: $o ).
thf(func_def_26,type,
sF7: $o ).
thf(func_def_27,type,
sF8: $o ).
thf(func_def_36,type,
sK17: $i > $i > $i ).
thf(func_def_37,type,
sK18: $i > $i > $i ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( X0 = X1 ) ) )
= setext ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(f2,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f3,axiom,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f5,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X2 = X0 ) ) )
= upairset2E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(f6,conjecture,
( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(f7,negated_conjecture,
~ ( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
~ ( setext
=> ( setadjoinIL
=> ( uniqinunit
=> ( eqinunit
=> ( upairset2E
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
~ ( ( setext = $true )
=> ( ( setadjoinIL = $true )
=> ( ( uniqinunit = $true )
=> ( ( eqinunit = $true )
=> ( ( upairset2E = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) )
= setext ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f16,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( ( X0 = X1 )
| ( X1 = X2 ) ) )
= upairset2E ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f19,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 = X1 ) )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( uniqinunit = $true )
& ( setadjoinIL = $true )
& ( setext = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f21,plain,
( ( setext = $true )
& ? [X0: $i,X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
!= ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 = X1 ) )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( setadjoinIL = $true )
& ( uniqinunit = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( setext = $true )
& ( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK0 = sK1 )
& ( upairset2E = $true )
& ( eqinunit = $true )
& ( setadjoinIL = $true )
& ( uniqinunit = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
thf(f23,plain,
( setext
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f24,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f25,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f26,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f28,plain,
upairset2E = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f29,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f31,plain,
setext = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
( upairset2E
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f33,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f37,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f23,f31]) ).
thf(f38,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f24,f26]) ).
thf(f39,plain,
( ( setadjoin @ sK1 @ ( setadjoin @ sK1 @ emptyset ) )
!= ( setadjoin @ sK1 @ emptyset ) ),
inference(definition_unfolding,[],[f30,f29]) ).
thf(f40,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f32,f28]) ).
thf(f41,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f33,f25]) ).
thf(f43,definition,
( sF2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) )
= sF2 ),
inference(reorient_equations,[],[f43]) ).
thf(f45,plain,
$true = sF2,
inference(definition_folding,[],[f37,f44]) ).
thf(f46,definition,
( sF3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f47,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) )
= sF3 ),
inference(reorient_equations,[],[f46]) ).
thf(f48,plain,
$true = sF3,
inference(definition_folding,[],[f38,f47]) ).
thf(f49,definition,
( sF4
= ( setadjoin @ sK1 @ emptyset ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f50,definition,
( sF5
= ( setadjoin @ sK1 @ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f51,plain,
( ( setadjoin @ sK1 @ sF4 )
= sF5 ),
inference(reorient_equations,[],[f50]) ).
thf(f52,plain,
sF4 != sF5,
inference(definition_folding,[],[f39,f49,f51,f49]) ).
thf(f53,definition,
( sF6
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f54,plain,
sF6 = $true,
inference(definition_folding,[],[f40,f53]) ).
thf(f55,definition,
( sF7
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f56,plain,
$true = sF7,
inference(definition_folding,[],[f41,f55]) ).
thf(f60,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) )
| ( $false = sF3 ) ),
inference(iff_proxy_clausification,[],[f47]) ).
thf(f66,plain,
! [X1: $i] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f67,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f71,plain,
( ( $false = sF7 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f55]) ).
thf(f72,plain,
! [X1: $i] :
( ( $false = sF7 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X1: $i] :
( ( $false = sF7 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) )
| ( $false = sF7 ) ),
inference(pi_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) )
| ( $false = sF7 ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( $false = sF7 )
| ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 )
| ( $false = sF7 ) ),
inference(equality_proxy_clausification,[],[f76]) ).
thf(f100,plain,
( ( $false = sF2 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f44]) ).
thf(f117,plain,
! [X1: $i] :
( ( $false = sF2 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f118,plain,
! [X1: $i] :
( ( $false = sF2 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( Y0 = X1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) ) )
| ( $false = sF2 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK17 @ X1 @ X2 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( X2 = X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK17 @ X1 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $false = sF2 ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( X1 = X2 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK17 @ X1 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK17 @ X1 @ X2 ) ) )
| ( $false = sF2 )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK18 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) ) )
| ( $false
= ( ( in @ ( sK17 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) ) )
| ( $false = sF2 )
| ( X1 = X2 ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( ( in @ ( sK17 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) ) )
| ( $false
= ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) )
| ( $false = sF2 ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( X1 = X2 )
| ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false
= ( ( in @ ( sK17 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f129,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false = sF2 )
| ( X1 = X2 )
| ( $false
= ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
= $true )
| ( X1 = X2 )
| ( $true
= ( in @ ( sK17 @ X1 @ X2 ) @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f128]) ).
thf(f131,plain,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) )
| ( $false = sF2 )
| ( $false
= ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f132,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 )
| ( $true
= ( in @ ( sK17 @ X1 @ X2 ) @ X1 ) )
| ( $false = sF2 ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f134,plain,
( ( sF6 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y1 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f53]) ).
thf(f135,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y1 ) ) ) ) )
@ X1 ) )
| ( sF6 = $false ) ),
inference(pi_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y0 = X1 )
| ( Y1 = Y0 ) ) ) ) )
= $true )
| ( sF6 = $false ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y0 = X1 )
| ( Y1 = Y0 ) ) ) )
@ X2 ) )
| ( sF6 = $false ) ),
inference(pi_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( Y0 = X2 ) ) ) ) )
| ( sF6 = $false ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( Y0 = X2 ) ) )
@ X3 ) )
| ( sF6 = $false ) ),
inference(pi_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF6 = $false )
| ( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X3 = X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( X2 = X1 )
| ( X3 = X2 ) ) )
| ( sF6 = $false )
| ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( $true
= ( X2 = X1 ) )
| ( sF6 = $false )
| ( $true
= ( X3 = X2 ) ) ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( X1 = X2 )
| ( sF6 = $false )
| ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( $true
= ( X3 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( X1 = X2 )
| ( sF6 = $false )
| ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( X2 = X3 ) ),
inference(equality_proxy_clausification,[],[f143]) ).
thf(f158,definition,
( spl22_1
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
thf(f160,plain,
( ( $true = sF3 )
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f167,definition,
( spl22_3
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
thf(f169,plain,
( ( $false = sF3 )
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f171,definition,
( spl22_4
<=> ! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
thf(f172,plain,
( ! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) )
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f171]) ).
thf(f173,plain,
( spl22_3
| spl22_4 ),
inference(avatar_split_clause,[],[f69,f171,f167]) ).
thf(f175,definition,
( spl22_5
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl22_5])],[avatar_definition]) ).
thf(f177,plain,
( ( $false = sF7 )
| ~ spl22_5 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f179,definition,
( spl22_6
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
thf(f180,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
| ( X1 = X2 ) )
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f179]) ).
thf(f181,plain,
( spl22_5
| spl22_6 ),
inference(avatar_split_clause,[],[f77,f179,f175]) ).
thf(f187,definition,
( spl22_8
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
thf(f189,plain,
( ( $true = sF7 )
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f196,plain,
spl22_1,
inference(avatar_split_clause,[],[f48,f158]) ).
thf(f219,plain,
spl22_8,
inference(avatar_split_clause,[],[f56,f187]) ).
thf(f222,definition,
( spl22_15
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl22_15])],[avatar_definition]) ).
thf(f224,plain,
( ( $true = sF2 )
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f239,definition,
( spl22_19
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl22_19])],[avatar_definition]) ).
thf(f241,plain,
( ( $false = sF2 )
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f243,definition,
( spl22_20
<=> ! [X2: $i,X1: $i] :
( ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( in @ ( sK17 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_20])],[avatar_definition]) ).
thf(f244,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK17 @ X1 @ X2 ) @ X1 ) )
| ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
= $true )
| ( X1 = X2 ) )
| ~ spl22_20 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f245,plain,
( spl22_19
| spl22_20 ),
inference(avatar_split_clause,[],[f130,f243,f239]) ).
thf(f247,definition,
( spl22_21
<=> ! [X2: $i,X1: $i] :
( ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false
= ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_21])],[avatar_definition]) ).
thf(f248,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 )
| ( ( in @ ( sK18 @ X1 @ X2 ) @ X2 )
= $true ) )
| ~ spl22_21 ),
inference(avatar_component_clause,[],[f247]) ).
thf(f249,plain,
( spl22_21
| spl22_19 ),
inference(avatar_split_clause,[],[f129,f239,f247]) ).
thf(f251,definition,
( spl22_22
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ ( sK17 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_22])],[avatar_definition]) ).
thf(f252,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK17 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X2 ) )
| ~ spl22_22 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f253,plain,
( spl22_19
| spl22_22 ),
inference(avatar_split_clause,[],[f132,f251,f239]) ).
thf(f255,definition,
( spl22_23
<=> ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( $false
= ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl22_23])],[avatar_definition]) ).
thf(f256,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( in @ ( sK18 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK17 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X2 ) )
| ~ spl22_23 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f257,plain,
( spl22_23
| spl22_19 ),
inference(avatar_split_clause,[],[f131,f239,f255]) ).
thf(f259,definition,
( spl22_24
<=> ( sF6 = $false ) ),
introduced(definition,[new_symbols(definition,[spl22_24])],[avatar_definition]) ).
thf(f261,plain,
( ( sF6 = $false )
| ~ spl22_24 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f263,definition,
( spl22_25
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( X1 = X2 )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl22_25])],[avatar_definition]) ).
thf(f264,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X2 = X3 ) )
| ~ spl22_25 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f265,plain,
( spl22_24
| spl22_25 ),
inference(avatar_split_clause,[],[f144,f263,f259]) ).
thf(f271,definition,
( spl22_27
<=> ( sF6 = $true ) ),
introduced(definition,[new_symbols(definition,[spl22_27])],[avatar_definition]) ).
thf(f273,plain,
( ( sF6 = $true )
| ~ spl22_27 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f285,plain,
spl22_15,
inference(avatar_split_clause,[],[f45,f222]) ).
thf(f286,plain,
spl22_27,
inference(avatar_split_clause,[],[f54,f271]) ).
thf(f287,plain,
( ( $false = $true )
| ~ spl22_1
| ~ spl22_3 ),
inference(forward_demodulation,[],[f169,f160]) ).
thf(f288,plain,
( $false
| ~ spl22_1
| ~ spl22_3 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f289,plain,
( ~ spl22_1
| ~ spl22_3 ),
inference(avatar_contradiction_clause,[],[f288]) ).
thf(f291,plain,
( ( $false = $true )
| ~ spl22_5
| ~ spl22_8 ),
inference(forward_demodulation,[],[f189,f177]) ).
thf(f292,plain,
( $false
| ~ spl22_5
| ~ spl22_8 ),
inference(trivial_inequality_removal,[],[f291]) ).
thf(f293,plain,
( ~ spl22_5
| ~ spl22_8 ),
inference(avatar_contradiction_clause,[],[f292]) ).
thf(f312,plain,
( ( $false = $true )
| ~ spl22_24
| ~ spl22_27 ),
inference(forward_demodulation,[],[f273,f261]) ).
thf(f313,plain,
( $false
| ~ spl22_24
| ~ spl22_27 ),
inference(trivial_inequality_removal,[],[f312]) ).
thf(f314,plain,
( ~ spl22_24
| ~ spl22_27 ),
inference(avatar_contradiction_clause,[],[f313]) ).
thf(f317,plain,
( ( $false = $true )
| ~ spl22_15
| ~ spl22_19 ),
inference(forward_demodulation,[],[f241,f224]) ).
thf(f318,plain,
( $false
| ~ spl22_15
| ~ spl22_19 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f319,plain,
( ~ spl22_15
| ~ spl22_19 ),
inference(avatar_contradiction_clause,[],[f318]) ).
thf(f321,plain,
( ( $true
= ( in @ sK1 @ sF4 ) )
| ~ spl22_4 ),
inference(constrained_superposition,[],[f172,f49]) ).
thf(f322,plain,
( ( $true
= ( in @ sK1 @ sF5 ) )
| ~ spl22_4 ),
inference(constrained_superposition,[],[f172,f51]) ).
thf(f323,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF4 )
= $false )
| ( sK1 = X0 ) )
| ~ spl22_6 ),
inference(constrained_superposition,[],[f180,f49]) ).
thf(f333,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ ( setadjoin @ X1 @ sF4 ) ) )
| ( X0 = X1 )
| ( sK1 = X0 ) )
| ~ spl22_25 ),
inference(constrained_superposition,[],[f264,f49]) ).
thf(f346,plain,
( ! [X0: $i] :
( ( sK1 = X0 )
| ( $false
= ( in @ X0 @ sF5 ) )
| ( sK1 = X0 ) )
| ~ spl22_25 ),
inference(constrained_superposition,[],[f333,f51]) ).
thf(f348,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sF5 ) )
| ( sK1 = X0 ) )
| ~ spl22_25 ),
inference(duplicate_literal_removal,[],[f346]) ).
thf(f367,plain,
( ! [X0: $i] :
( ( sF5 = X0 )
| ( $false = $true )
| ( $true
= ( in @ ( sK18 @ sF5 @ X0 ) @ X0 ) )
| ( ( sK17 @ sF5 @ X0 )
= sK1 ) )
| ~ spl22_20
| ~ spl22_25 ),
inference(constrained_superposition,[],[f348,f244]) ).
thf(f368,plain,
( ! [X0: $i] :
( ( $true
= ( in @ ( sK18 @ sF5 @ X0 ) @ X0 ) )
| ( ( sK17 @ sF5 @ X0 )
= sK1 )
| ( sF5 = X0 ) )
| ~ spl22_20
| ~ spl22_25 ),
inference(trivial_inequality_removal,[],[f367]) ).
thf(f385,plain,
( ( ( sK18 @ sF5 @ sF4 )
= sK1 )
| ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ( sF4 = sF5 )
| ( $false = $true )
| ~ spl22_6
| ~ spl22_20
| ~ spl22_25 ),
inference(constrained_superposition,[],[f323,f368]) ).
thf(f389,plain,
( ( ( sK18 @ sF5 @ sF4 )
= sK1 )
| ( sF4 = sF5 )
| ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_6
| ~ spl22_20
| ~ spl22_25 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f395,plain,
( ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ( ( sK18 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_6
| ~ spl22_20
| ~ spl22_25 ),
inference(forward_subsumption_resolution,[],[f389,f52]) ).
thf(f397,definition,
( spl22_30
<=> ( ( sK17 @ sF5 @ sF4 )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl22_30])],[avatar_definition]) ).
thf(f399,plain,
( ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_30 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f401,definition,
( spl22_31
<=> ( ( sK18 @ sF5 @ sF4 )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl22_31])],[avatar_definition]) ).
thf(f403,plain,
( ( ( sK18 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_31 ),
inference(avatar_component_clause,[],[f401]) ).
thf(f405,plain,
( spl22_30
| spl22_31
| ~ spl22_6
| ~ spl22_20
| ~ spl22_25 ),
inference(avatar_split_clause,[],[f395,f263,f243,f179,f401,f397]) ).
thf(f436,plain,
( ( $false
= ( in @ sK1 @ sF4 ) )
| ( ( in @ ( sK18 @ sF5 @ sF4 ) @ sF4 )
= $true )
| ( sF4 = sF5 )
| ~ spl22_21
| ~ spl22_30 ),
inference(constrained_superposition,[],[f248,f399]) ).
thf(f447,plain,
( ( ( in @ ( sK18 @ sF5 @ sF4 ) @ sF4 )
= $true )
| ( $false
= ( in @ sK1 @ sF4 ) )
| ~ spl22_21
| ~ spl22_30 ),
inference(forward_subsumption_resolution,[],[f436,f52]) ).
thf(f448,plain,
( ( $false = $true )
| ( ( in @ ( sK18 @ sF5 @ sF4 ) @ sF4 )
= $true )
| ~ spl22_4
| ~ spl22_21
| ~ spl22_30 ),
inference(forward_demodulation,[],[f447,f321]) ).
thf(f449,plain,
( ( ( in @ ( sK18 @ sF5 @ sF4 ) @ sF4 )
= $true )
| ~ spl22_4
| ~ spl22_21
| ~ spl22_30 ),
inference(trivial_inequality_removal,[],[f448]) ).
thf(f460,plain,
( ! [X0: $i] :
( ( ( in @ ( sK18 @ sF5 @ X0 ) @ sF5 )
= $false )
| ( ( sK17 @ sF5 @ X0 )
= sK1 )
| ( sF5 = X0 )
| ( $false = $true ) )
| ~ spl22_22
| ~ spl22_25 ),
inference(constrained_superposition,[],[f348,f252]) ).
thf(f461,plain,
( ! [X0: $i] :
( ( ( in @ ( sK18 @ sF5 @ X0 ) @ sF5 )
= $false )
| ( ( sK17 @ sF5 @ X0 )
= sK1 )
| ( sF5 = X0 ) )
| ~ spl22_22
| ~ spl22_25 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f472,plain,
( ( ( sK18 @ sF5 @ sF4 )
= sK1 )
| ( $false = $true )
| ~ spl22_4
| ~ spl22_6
| ~ spl22_21
| ~ spl22_30 ),
inference(constrained_superposition,[],[f323,f449]) ).
thf(f473,plain,
( ( ( sK18 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_4
| ~ spl22_6
| ~ spl22_21
| ~ spl22_30 ),
inference(trivial_inequality_removal,[],[f472]) ).
thf(f475,plain,
( spl22_31
| ~ spl22_4
| ~ spl22_6
| ~ spl22_21
| ~ spl22_30 ),
inference(avatar_split_clause,[],[f473,f397,f247,f179,f171,f401]) ).
thf(f488,plain,
( ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ( sF4 = sF5 )
| ( $false
= ( in @ sK1 @ sF5 ) )
| ~ spl22_22
| ~ spl22_25
| ~ spl22_31 ),
inference(constrained_superposition,[],[f461,f403]) ).
thf(f505,plain,
( ( sF4 = sF5 )
| ( $false
= ( in @ sK1 @ sF5 ) )
| ( $false
= ( in @ ( sK17 @ sF5 @ sF4 ) @ sF4 ) )
| ~ spl22_23
| ~ spl22_31 ),
inference(constrained_superposition,[],[f256,f403]) ).
thf(f518,plain,
( ( $false
= ( in @ sK1 @ sF5 ) )
| ( $false
= ( in @ ( sK17 @ sF5 @ sF4 ) @ sF4 ) )
| ~ spl22_23
| ~ spl22_31 ),
inference(forward_subsumption_resolution,[],[f505,f52]) ).
thf(f521,plain,
( ( $false = $true )
| ( $false
= ( in @ ( sK17 @ sF5 @ sF4 ) @ sF4 ) )
| ~ spl22_4
| ~ spl22_23
| ~ spl22_31 ),
inference(forward_demodulation,[],[f518,f322]) ).
thf(f522,plain,
( ( $false
= ( in @ ( sK17 @ sF5 @ sF4 ) @ sF4 ) )
| ~ spl22_4
| ~ spl22_23
| ~ spl22_31 ),
inference(trivial_inequality_removal,[],[f521]) ).
thf(f525,plain,
( ( $false
= ( in @ sK1 @ sF4 ) )
| ~ spl22_4
| ~ spl22_23
| ~ spl22_30
| ~ spl22_31 ),
inference(forward_demodulation,[],[f522,f399]) ).
thf(f526,plain,
( ( $false = $true )
| ~ spl22_4
| ~ spl22_23
| ~ spl22_30
| ~ spl22_31 ),
inference(forward_demodulation,[],[f525,f321]) ).
thf(f527,plain,
( $false
| ~ spl22_4
| ~ spl22_23
| ~ spl22_30
| ~ spl22_31 ),
inference(trivial_inequality_removal,[],[f526]) ).
thf(f528,plain,
( ~ spl22_4
| ~ spl22_23
| ~ spl22_30
| ~ spl22_31 ),
inference(avatar_contradiction_clause,[],[f527]) ).
thf(f529,plain,
( ( $false
= ( in @ sK1 @ sF5 ) )
| ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_22
| ~ spl22_25
| ~ spl22_31 ),
inference(forward_subsumption_resolution,[],[f488,f52]) ).
thf(f530,plain,
( ( $false = $true )
| ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_4
| ~ spl22_22
| ~ spl22_25
| ~ spl22_31 ),
inference(forward_demodulation,[],[f529,f322]) ).
thf(f531,plain,
( ( ( sK17 @ sF5 @ sF4 )
= sK1 )
| ~ spl22_4
| ~ spl22_22
| ~ spl22_25
| ~ spl22_31 ),
inference(trivial_inequality_removal,[],[f530]) ).
thf(f532,plain,
( spl22_30
| ~ spl22_4
| ~ spl22_22
| ~ spl22_25
| ~ spl22_31 ),
inference(avatar_split_clause,[],[f531,f401,f263,f251,f171,f397]) ).
cnf(s2,plain,
( spl22_3
| spl22_4 ),
inference(sat_conversion,[],[f173]) ).
cnf(s3,plain,
( spl22_5
| spl22_6 ),
inference(sat_conversion,[],[f181]) ).
cnf(s6,plain,
spl22_1,
inference(sat_conversion,[],[f196]) ).
cnf(s10,plain,
spl22_8,
inference(sat_conversion,[],[f219]) ).
cnf(s15,plain,
( spl22_19
| spl22_20 ),
inference(sat_conversion,[],[f245]) ).
cnf(s16,plain,
( spl22_19
| spl22_21 ),
inference(sat_conversion,[],[f249]) ).
cnf(s17,plain,
( spl22_19
| spl22_22 ),
inference(sat_conversion,[],[f253]) ).
cnf(s18,plain,
( spl22_19
| spl22_23 ),
inference(sat_conversion,[],[f257]) ).
cnf(s19,plain,
( spl22_24
| spl22_25 ),
inference(sat_conversion,[],[f265]) ).
cnf(s23,plain,
spl22_15,
inference(sat_conversion,[],[f285]) ).
cnf(s24,plain,
spl22_27,
inference(sat_conversion,[],[f286]) ).
cnf(s25,plain,
( ~ spl22_1
| ~ spl22_3 ),
inference(sat_conversion,[],[f289]) ).
cnf(s26,plain,
( ~ spl22_5
| ~ spl22_8 ),
inference(sat_conversion,[],[f293]) ).
cnf(s28,plain,
( ~ spl22_24
| ~ spl22_27 ),
inference(sat_conversion,[],[f314]) ).
cnf(s29,plain,
( ~ spl22_15
| ~ spl22_19 ),
inference(sat_conversion,[],[f319]) ).
cnf(s33,plain,
( ~ spl22_6
| ~ spl22_20
| ~ spl22_25
| spl22_30
| spl22_31 ),
inference(sat_conversion,[],[f405]) ).
cnf(s36,plain,
( ~ spl22_4
| ~ spl22_6
| ~ spl22_21
| ~ spl22_30
| spl22_31 ),
inference(sat_conversion,[],[f475]) ).
cnf(s39,plain,
( ~ spl22_4
| ~ spl22_23
| ~ spl22_30
| ~ spl22_31 ),
inference(sat_conversion,[],[f528]) ).
cnf(s40,plain,
( ~ spl22_4
| ~ spl22_22
| ~ spl22_25
| spl22_30
| ~ spl22_31 ),
inference(sat_conversion,[],[f532]) ).
cnf(s41,plain,
~ spl22_24,
inference(rat,[],[s28,s24]) ).
cnf(s42,plain,
~ spl22_19,
inference(rat,[],[s29,s23]) ).
cnf(s43,plain,
spl22_25,
inference(rat,[],[s19,s41]) ).
cnf(s44,plain,
spl22_23,
inference(rat,[],[s18,s42]) ).
cnf(s45,plain,
spl22_22,
inference(rat,[],[s17,s42]) ).
cnf(s46,plain,
spl22_21,
inference(rat,[],[s16,s42]) ).
cnf(s47,plain,
spl22_20,
inference(rat,[],[s15,s42]) ).
cnf(s49,plain,
~ spl22_5,
inference(rat,[],[s26,s10]) ).
cnf(s51,plain,
~ spl22_3,
inference(rat,[],[s25,s6]) ).
cnf(s52,plain,
spl22_6,
inference(rat,[],[s3,s49]) ).
cnf(s53,plain,
spl22_4,
inference(rat,[],[s2,s51]) ).
cnf(s54,plain,
spl22_30,
inference(rat,[],[s33,s40,s43,s47,s52,s45,s53]) ).
cnf(s55,plain,
~ spl22_31,
inference(rat,[],[s39,s53,s44,s54]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s36,s53,s52,s46,s55,s54]) ).
thf(f533,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU649^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n015.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 14:05:48 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.22 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
% 0.33/0.30 % (3576026)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.30 % (3576034)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=1874643746: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)
% 0.33/0.30 % (3576037)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.30 % (3576037)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
% 0.33/0.30 % (3576033)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1673190296:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.30 % (3576035)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=573177986:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.30 % (3576036)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1790039624:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.30 % (3576032)lrs+10_16_si=on:nwc=1.5:random_seed=3346346416:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.30 % (3576037)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=1860482342:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.30 % (3576033)Instruction limit reached!
% 0.33/0.30 % (3576033)------------------------------
% 0.33/0.30 % (3576033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.30 % (3576033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.30 % (3576033)CaDiCaL version: 2.1.3
% 0.33/0.30 % (3576033)Termination reason: Instruction limit
% 0.33/0.30 % (3576033)Termination phase: Saturation
% 0.33/0.30 % (3576033)Time elapsed: 0.002 s
% 0.33/0.30 % (3576033)Peak memory usage: 12 MB
% 0.33/0.30 % (3576033)Instructions burned: 3 (million)
% 0.33/0.30 % (3576032)Instruction limit reached!
% 0.33/0.30 % (3576032)------------------------------
% 0.33/0.30 % (3576032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.30 % (3576032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.30 % (3576032)CaDiCaL version: 2.1.3
% 0.33/0.30 % (3576032)Termination reason: Instruction limit
% 0.33/0.30 % (3576032)Termination phase: Saturation
% 0.33/0.30 % (3576032)Time elapsed: 0.011 s
% 0.33/0.30 % (3576032)Peak memory usage: 12 MB
% 0.33/0.30 % (3576032)Instructions burned: 19 (million)
% 0.33/0.30 % (3576031)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2920248745:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.30 % (3576035)Instruction limit reached!
% 0.33/0.30 % (3576035)------------------------------
% 0.33/0.30 % (3576035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.30 % (3576035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.30 % (3576035)CaDiCaL version: 2.1.3
% 0.33/0.30 % (3576035)Termination reason: Instruction limit
% 0.33/0.30 % (3576035)Termination phase: Saturation
% 0.33/0.30 % (3576035)Time elapsed: 0.014 s
% 0.33/0.30 % (3576035)Peak memory usage: 12 MB
% 0.33/0.30 % (3576035)Instructions burned: 26 (million)
% 0.33/0.30 % (3576037) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3576026-3576037"...
% 0.33/0.30 % (3576037)...printing done.
% 0.33/0.30 % (3576037)Refutation found. Thanks to Tanya!
% 0.33/0.30 % SZS status Theorem for theBenchmark
% 0.33/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.30 % (3576037)------------------------------
% 0.33/0.30 % (3576037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.30 % (3576037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.30 % (3576037)CaDiCaL version: 2.1.3
% 0.33/0.30 % (3576037)Termination reason: Refutation
% 0.33/0.30 % (3576037)Time elapsed: 0.023 s
% 0.33/0.30 % (3576037)Peak memory usage: 13 MB
% 0.33/0.30 % (3576037)Instructions burned: 34 (million)
% 0.33/0.30 % (3576026)Success in time 0.071 s
% 0.33/0.30 % Vampire exiting
%------------------------------------------------------------------------------