%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU731^2 : 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 : n019.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 08:31:00 AM UTC 2026
% Result : Theorem 0.74s 0.38s
% Output : Refutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 42
% Syntax : Number of formulae : 352 ( 79 unt; 0 typ; 37 def)
% Number of atoms : 3792 ( 770 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 4777 ( 528 ~; 995 |; 20 &;2826 @)
% ( 29 <=>; 265 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 61 ( 57 usr; 46 con; 0-4 aty)
% ( 114 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 399 ( 0 sgn 265 !; 6 ?; 399 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_3,type,
complementT_lem: $o ).
thf(func_def_5,type,
setextT: $o ).
thf(func_def_6,type,
doubleComplementI1: $o ).
thf(func_def_7,type,
doubleComplementE1: $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
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_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_20,type,
sF2: $o ).
thf(func_def_22,type,
sF4: $o ).
thf(func_def_25,type,
sF7: $o ).
thf(func_def_26,type,
sF8: $o ).
thf(func_def_27,type,
sF9: $o ).
thf(func_def_36,type,
sK18: $i > $i > $i > $i ).
thf(func_def_37,type,
sK19: $i > $i > $i > $i ).
thf(f1,axiom,
( complementT_lem
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).
thf(f2,axiom,
( setextT
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT) ).
thf(f3,axiom,
( doubleComplementI1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(f4,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) )
= doubleComplementE1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(f5,conjecture,
( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(f6,negated_conjecture,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( doubleComplementI1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
( doubleComplementI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( setextT
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X0 ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
= X0 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
~ ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
= X0 ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f14,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) )
=> ( in @ X2 @ X0 ) ) ) )
= doubleComplementE1 ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
!= X0 ) )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( setextT = $true )
& ( complementT_lem = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f18,plain,
( ( complementT_lem = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
!= X0 ) )
& ( doubleComplementI1 = $true )
& ( doubleComplementE1 = $true )
& ( setextT = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( complementT_lem = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 ) )
& ( doubleComplementI1 = $true )
& ( doubleComplementE1 = $true )
& ( setextT = $true ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( complementT_lem = $true )
& ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true )
& ( ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) )
!= sK1 )
& ( doubleComplementI1 = $true )
& ( doubleComplementE1 = $true )
& ( setextT = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f19]) ).
thf(f21,plain,
( doubleComplementI1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f22,plain,
setextT = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f23,plain,
doubleComplementE1 = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f24,plain,
doubleComplementI1 = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f25,plain,
( ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) )
!= sK1 ),
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
( ( in @ sK1 @ ( powerset @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
complementT_lem = $true,
inference(cnf_transformation,[],[f20]) ).
thf(f28,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f30,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f21,f24]) ).
thf(f34,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f27]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f29,f23]) ).
thf(f36,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f30,f22]) ).
thf(f37,definition,
( sF2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= sF2 ),
inference(reorient_equations,[],[f37]) ).
thf(f39,plain,
$true = sF2,
inference(definition_folding,[],[f33,f38]) ).
thf(f40,definition,
( sF3
= ( powerset @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f41,plain,
( ( powerset @ sK0 )
= sF3 ),
inference(reorient_equations,[],[f40]) ).
thf(f42,definition,
( sF4
= ( in @ sK1 @ sF3 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f43,plain,
( ( in @ sK1 @ sF3 )
= sF4 ),
inference(reorient_equations,[],[f42]) ).
thf(f44,plain,
sF4 = $true,
inference(definition_folding,[],[f26,f43,f41]) ).
thf(f45,definition,
( sF5
= ( setminus @ sK0 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f46,definition,
( sF6
= ( setminus @ sK0 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f47,plain,
sF6 != sK1,
inference(definition_folding,[],[f25,f46,f45]) ).
thf(f48,definition,
( sF7
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f49,plain,
sF7 = $true,
inference(definition_folding,[],[f34,f48]) ).
thf(f50,definition,
( sF8
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f51,plain,
sF8 = $true,
inference(definition_folding,[],[f35,f50]) ).
thf(f52,definition,
( sF9
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f53,plain,
sF9 = $true,
inference(definition_folding,[],[f36,f52]) ).
thf(f55,plain,
( ( sF8 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f50]) ).
thf(f56,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ ( setminus @ Y0 @ ( setminus @ Y0 @ Y1 ) ) )
=> ( in @ Y2 @ Y1 ) ) ) ) ) )
@ X1 )
= $true )
| ( sF8 = $false ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ ( setminus @ X1 @ ( setminus @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
| ( sF8 = $false ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( sF8 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ ( setminus @ X1 @ ( setminus @ X1 @ Y0 ) ) )
=> ( in @ Y1 @ Y0 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ Y0 @ X2 ) ) ) ) ) )
| ( sF8 = $false ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ Y0 @ X2 ) ) ) )
= $true )
| ( sF8 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ Y0 @ X2 ) ) )
@ X3 )
= $true )
| ( sF8 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF8 = $false )
| ( $true
= ( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X3 @ X2 ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
=> ( in @ X3 @ X2 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X1 )
= $false )
| ( sF8 = $false ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
= $false )
| ( ( in @ X3 @ X1 )
= $false )
| ( sF8 = $false ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f77,plain,
( ( ( in @ sK1 @ sF3 )
= $true )
| ( sF4 = $false ) ),
inference(iff_proxy_clausification,[],[f43]) ).
thf(f79,plain,
( ( $false = sF2 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f93,plain,
! [X1: $i] :
( ( $false = sF2 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f94,plain,
! [X1: $i] :
( ( $false = sF2 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ) ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( $false = sF2 ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF2 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) )
@ X3 ) )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF2 )
| ( ( ( in @ X3 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( ( in @ X3 @ X1 )
=> ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) )
= $true )
| ( $false = sF2 ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF2 )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
= $true )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f103,plain,
( ( sF7 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f48]) ).
thf(f104,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true )
| ( sF7 = $false ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ Y0 ) @ ( powerset @ X1 ) ) ) )
= $true )
| ( sF7 = $false ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ Y0 ) @ ( powerset @ X1 ) ) )
@ X2 )
= $true )
| ( sF7 = $false ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X1: $i] :
( ( sF7 = $false )
| ( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) )
| ( sF7 = $false ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f116,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
= $true )
| ( sF9 = $false ) ),
inference(iff_proxy_clausification,[],[f52]) ).
thf(f117,plain,
! [X1: $i] :
( ( sF9 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( ( sF9 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( sF9 = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) )
=> ( Y0 = Y1 ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) ) )
=> ( X2 = Y0 ) ) ) ) ) ) )
| ( sF9 = $false ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( ( sF9 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) ) )
=> ( X2 = Y0 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ X2 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X2 ) ) ) )
=> ( X2 = Y0 ) ) ) )
@ X3 )
= $true )
| ( sF9 = $false ) ),
inference(pi_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) )
= $true )
| ( sF9 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X2 ) ) ) )
=> ( X2 = X3 ) )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) ) )
| ( sF9 = $false ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF9 = $false )
| ( ( X2 = X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) ) ) )
| ( sF9 = $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK18 @ X3 @ X1 @ X2 ) )
= $false )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false ) ),
inference(sigma_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( X2 = X3 )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X2 ) ) )
@ ( sK19 @ X3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK18 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 ) ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( sF9 = $false )
| ( $false
= ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) ) ) )
| ( X2 = X3 )
| ( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 ) )
= $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( sF9 = $false ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF9 = $false )
| ( X2 = X3 )
| ( ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
= $false )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X2 = X3 )
| ( sF9 = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF9 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF9 = $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
= $false )
| ( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF9 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 ) )
= $false )
| ( X2 = X3 )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( sF9 = $false )
| ( X2 = X3 )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( X2 = X3 )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( sF9 = $false ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 ) )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false )
| ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X2 = X3 ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 ) )
= $false )
| ( sF9 = $false )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF9 = $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( X2 = X3 )
| ( sF9 = $false )
| ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( sF9 = $false )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f171,definition,
( spl23_1
<=> ( sF8 = $false ) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
thf(f173,plain,
( ( sF8 = $false )
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f171]) ).
thf(f175,definition,
( spl23_2
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
= $false )
| ( ( in @ X3 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
thf(f176,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
= $false )
| ( ( in @ X3 @ X2 )
= $true )
| ( ( in @ X3 @ X1 )
= $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f177,plain,
( spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f64,f175,f171]) ).
thf(f179,definition,
( spl23_3
<=> ( sF8 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
thf(f181,plain,
( ( sF8 = $true )
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f179]) ).
thf(f203,definition,
( spl23_8
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition]) ).
thf(f205,plain,
( ( sF4 = $true )
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f212,definition,
( spl23_10
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl23_10])],[avatar_definition]) ).
thf(f214,plain,
( ( sF4 = $false )
| ~ spl23_10 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f216,definition,
( spl23_11
<=> ( ( in @ sK1 @ sF3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl23_11])],[avatar_definition]) ).
thf(f218,plain,
( ( ( in @ sK1 @ sF3 )
= $true )
| ~ spl23_11 ),
inference(avatar_component_clause,[],[f216]) ).
thf(f219,plain,
( spl23_10
| spl23_11 ),
inference(avatar_split_clause,[],[f77,f216,f212]) ).
thf(f225,definition,
( spl23_13
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl23_13])],[avatar_definition]) ).
thf(f227,plain,
( ( $true = sF2 )
| ~ spl23_13 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f245,definition,
( spl23_17
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl23_17])],[avatar_definition]) ).
thf(f247,plain,
( ( $false = sF2 )
| ~ spl23_17 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f249,definition,
( spl23_18
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
= $true )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl23_18])],[avatar_definition]) ).
thf(f250,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X1 @ ( powerset @ X2 ) )
= $false )
| ( ( in @ X3 @ X2 )
= $false ) )
| ~ spl23_18 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f251,plain,
( spl23_17
| spl23_18 ),
inference(avatar_split_clause,[],[f101,f249,f245]) ).
thf(f252,plain,
spl23_3,
inference(avatar_split_clause,[],[f51,f179]) ).
thf(f254,definition,
( spl23_19
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_19])],[avatar_definition]) ).
thf(f255,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl23_19 ),
inference(avatar_component_clause,[],[f254]) ).
thf(f257,definition,
( spl23_20
<=> ( sF7 = $false ) ),
introduced(definition,[new_symbols(definition,[spl23_20])],[avatar_definition]) ).
thf(f259,plain,
( ( sF7 = $false )
| ~ spl23_20 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f260,plain,
( spl23_19
| spl23_20 ),
inference(avatar_split_clause,[],[f108,f257,f254]) ).
thf(f266,definition,
( spl23_22
<=> ( sF7 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_22])],[avatar_definition]) ).
thf(f268,plain,
( ( sF7 = $true )
| ~ spl23_22 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f276,definition,
( spl23_24
<=> ( sF9 = $false ) ),
introduced(definition,[new_symbols(definition,[spl23_24])],[avatar_definition]) ).
thf(f278,plain,
( ( sF9 = $false )
| ~ spl23_24 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f280,definition,
( spl23_25
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_25])],[avatar_definition]) ).
thf(f281,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl23_25 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f282,plain,
( spl23_24
| spl23_25 ),
inference(avatar_split_clause,[],[f134,f280,f276]) ).
thf(f284,definition,
( spl23_26
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_26])],[avatar_definition]) ).
thf(f285,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true )
| ( X2 = X3 )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl23_26 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f286,plain,
( spl23_26
| spl23_24 ),
inference(avatar_split_clause,[],[f136,f276,f284]) ).
thf(f288,definition,
( spl23_27
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_27])],[avatar_definition]) ).
thf(f289,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
| ~ spl23_27 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f290,plain,
( spl23_24
| spl23_27 ),
inference(avatar_split_clause,[],[f135,f288,f276]) ).
thf(f292,definition,
( spl23_28
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_28])],[avatar_definition]) ).
thf(f293,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 ) )
| ~ spl23_28 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f294,plain,
( spl23_24
| spl23_28 ),
inference(avatar_split_clause,[],[f140,f292,f276]) ).
thf(f296,definition,
( spl23_29
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_29])],[avatar_definition]) ).
thf(f297,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false ) )
| ~ spl23_29 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f298,plain,
( spl23_29
| spl23_24 ),
inference(avatar_split_clause,[],[f139,f276,f296]) ).
thf(f300,definition,
( spl23_30
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_30])],[avatar_definition]) ).
thf(f301,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 ) )
| ~ spl23_30 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f302,plain,
( spl23_24
| spl23_30 ),
inference(avatar_split_clause,[],[f144,f300,f276]) ).
thf(f304,definition,
( spl23_31
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_31])],[avatar_definition]) ).
thf(f305,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X3 )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false ) )
| ~ spl23_31 ),
inference(avatar_component_clause,[],[f304]) ).
thf(f306,plain,
( spl23_24
| spl23_31 ),
inference(avatar_split_clause,[],[f143,f304,f276]) ).
thf(f308,definition,
( spl23_32
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( X2 = X3 )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl23_32])],[avatar_definition]) ).
thf(f309,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X2 )
= $true )
| ( X2 = X3 )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl23_32 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f310,plain,
( spl23_32
| spl23_24 ),
inference(avatar_split_clause,[],[f146,f276,f308]) ).
thf(f312,definition,
( spl23_33
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X2 = X3 )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl23_33])],[avatar_definition]) ).
thf(f313,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK18 @ X3 @ X1 @ X2 ) @ X3 )
= $false )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( X2 = X3 ) )
| ~ spl23_33 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f314,plain,
( spl23_33
| spl23_24 ),
inference(avatar_split_clause,[],[f145,f276,f312]) ).
thf(f316,definition,
( spl23_34
<=> ( sF9 = $true ) ),
introduced(definition,[new_symbols(definition,[spl23_34])],[avatar_definition]) ).
thf(f318,plain,
( ( sF9 = $true )
| ~ spl23_34 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f342,plain,
spl23_13,
inference(avatar_split_clause,[],[f39,f225]) ).
thf(f343,plain,
spl23_8,
inference(avatar_split_clause,[],[f44,f203]) ).
thf(f344,plain,
spl23_22,
inference(avatar_split_clause,[],[f49,f266]) ).
thf(f345,plain,
spl23_34,
inference(avatar_split_clause,[],[f53,f316]) ).
thf(f346,plain,
( ( $true = $false )
| ~ spl23_8
| ~ spl23_10 ),
inference(forward_demodulation,[],[f214,f205]) ).
thf(f347,plain,
( $false
| ~ spl23_8
| ~ spl23_10 ),
inference(trivial_inequality_removal,[],[f346]) ).
thf(f348,plain,
( ~ spl23_8
| ~ spl23_10 ),
inference(avatar_contradiction_clause,[],[f347]) ).
thf(f359,plain,
( ( $true = $false )
| ~ spl23_13
| ~ spl23_17 ),
inference(forward_demodulation,[],[f227,f247]) ).
thf(f360,plain,
( $false
| ~ spl23_13
| ~ spl23_17 ),
inference(trivial_inequality_removal,[],[f359]) ).
thf(f361,plain,
( ~ spl23_13
| ~ spl23_17 ),
inference(avatar_contradiction_clause,[],[f360]) ).
thf(f364,plain,
( ( $true = $false )
| ~ spl23_24
| ~ spl23_34 ),
inference(forward_demodulation,[],[f278,f318]) ).
thf(f365,plain,
( $false
| ~ spl23_24
| ~ spl23_34 ),
inference(trivial_inequality_removal,[],[f364]) ).
thf(f366,plain,
( ~ spl23_24
| ~ spl23_34 ),
inference(avatar_contradiction_clause,[],[f365]) ).
thf(f378,definition,
( spl23_40
<=> ( ( in @ sF5 @ sF3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl23_40])],[avatar_definition]) ).
thf(f380,plain,
( ( ( in @ sF5 @ sF3 )
= $false )
| ~ spl23_40 ),
inference(avatar_component_clause,[],[f378]) ).
thf(f382,definition,
( spl23_41
<=> ( $true
= ( in @ sF6 @ sF3 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_41])],[avatar_definition]) ).
thf(f384,plain,
( ( $true
= ( in @ sF6 @ sF3 ) )
| ~ spl23_41 ),
inference(avatar_component_clause,[],[f382]) ).
thf(f386,plain,
( ( $true = $false )
| ~ spl23_20
| ~ spl23_22 ),
inference(forward_demodulation,[],[f259,f268]) ).
thf(f387,plain,
( $false
| ~ spl23_20
| ~ spl23_22 ),
inference(trivial_inequality_removal,[],[f386]) ).
thf(f388,plain,
( ~ spl23_20
| ~ spl23_22 ),
inference(avatar_contradiction_clause,[],[f387]) ).
thf(f393,plain,
( ( $true
= ( in @ sF5 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl23_19 ),
inference(constrained_superposition,[],[f255,f45]) ).
thf(f394,plain,
( ( $true
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ sF5 @ ( powerset @ sK0 ) )
= $false )
| ~ spl23_19 ),
inference(constrained_superposition,[],[f255,f46]) ).
thf(f395,plain,
( ( ( in @ sF5 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ sF6 @ sF3 ) )
| ~ spl23_19 ),
inference(forward_demodulation,[],[f394,f41]) ).
thf(f396,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ sF5 @ sF3 ) )
| ~ spl23_19 ),
inference(forward_demodulation,[],[f393,f41]) ).
thf(f397,plain,
( ( $true
= ( in @ sF6 @ sF3 ) )
| ( ( in @ sF5 @ sF3 )
= $false )
| ~ spl23_19 ),
inference(forward_demodulation,[],[f395,f41]) ).
thf(f398,plain,
( ( $true
= ( in @ sF5 @ sF3 ) )
| ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_19 ),
inference(forward_demodulation,[],[f396,f41]) ).
thf(f399,plain,
( ( $true = $false )
| ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_19
| ~ spl23_40 ),
inference(forward_demodulation,[],[f398,f380]) ).
thf(f400,plain,
( ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_19
| ~ spl23_40 ),
inference(trivial_inequality_removal,[],[f399]) ).
thf(f401,plain,
( ( $true = $false )
| ~ spl23_11
| ~ spl23_19
| ~ spl23_40 ),
inference(forward_demodulation,[],[f400,f218]) ).
thf(f402,plain,
( $false
| ~ spl23_11
| ~ spl23_19
| ~ spl23_40 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f403,plain,
( ~ spl23_11
| ~ spl23_19
| ~ spl23_40 ),
inference(avatar_contradiction_clause,[],[f402]) ).
thf(f406,plain,
( spl23_40
| spl23_41
| ~ spl23_19 ),
inference(avatar_split_clause,[],[f397,f254,f382,f378]) ).
thf(f423,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ sK0 @ sF5 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ X0 @ sK1 )
= $false ) )
| ~ spl23_18 ),
inference(constrained_superposition,[],[f250,f45]) ).
thf(f432,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( in @ X0 @ sF6 )
= $true )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) )
| ~ spl23_18 ),
inference(forward_demodulation,[],[f423,f46]) ).
thf(f434,plain,
( ! [X0: $i] :
( ( ( in @ sK1 @ sF3 )
= $false )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ X0 @ sF6 )
= $true ) )
| ~ spl23_18 ),
inference(forward_demodulation,[],[f432,f41]) ).
thf(f435,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ X0 @ sF6 )
= $true )
| ( $true = $false ) )
| ~ spl23_11
| ~ spl23_18 ),
inference(forward_demodulation,[],[f434,f218]) ).
thf(f436,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF6 )
= $true )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( in @ X0 @ sK0 )
= $false ) )
| ~ spl23_11
| ~ spl23_18 ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f514,plain,
( ( $true = $false )
| ~ spl23_1
| ~ spl23_3 ),
inference(forward_demodulation,[],[f173,f181]) ).
thf(f515,plain,
( $false
| ~ spl23_1
| ~ spl23_3 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f516,plain,
( ~ spl23_1
| ~ spl23_3 ),
inference(avatar_contradiction_clause,[],[f515]) ).
thf(f518,plain,
( ! [X0: $i] :
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ ( setminus @ sK0 @ sF5 ) ) )
| ( ( in @ X0 @ sK0 )
= $false ) )
| ~ spl23_2 ),
inference(constrained_superposition,[],[f176,f45]) ).
thf(f545,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK0 )
= $false )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( $false
= ( in @ X0 @ ( setminus @ sK0 @ sF5 ) ) )
| ( ( in @ sK1 @ sF3 )
= $false ) )
| ~ spl23_2 ),
inference(forward_demodulation,[],[f518,f41]) ).
thf(f547,plain,
( ! [X0: $i] :
( ( ( in @ sK1 @ sF3 )
= $false )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( ( in @ X0 @ sF6 )
= $false )
| ( ( in @ X0 @ sK0 )
= $false ) )
| ~ spl23_2 ),
inference(forward_demodulation,[],[f545,f46]) ).
thf(f548,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF6 )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( $true
= ( in @ X0 @ sK1 ) )
| ( $true = $false ) )
| ~ spl23_2
| ~ spl23_11 ),
inference(forward_demodulation,[],[f547,f218]) ).
thf(f549,plain,
( ! [X0: $i] :
( ( $true
= ( in @ X0 @ sK1 ) )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ X0 @ sF6 )
= $false ) )
| ~ spl23_2
| ~ spl23_11 ),
inference(trivial_inequality_removal,[],[f548]) ).
thf(f550,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK18 @ X0 @ X1 @ sK1 ) @ X1 ) )
| ( ( in @ sK1 @ ( powerset @ X1 ) )
= $false )
| ( $true = $false )
| ( $false
= ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sF6 ) )
| ( ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false )
| ( sK1 = X0 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_27 ),
inference(constrained_superposition,[],[f549,f289]) ).
thf(f552,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK18 @ X0 @ X1 @ sK1 ) @ X1 ) )
| ( ( in @ sK1 @ ( powerset @ X1 ) )
= $false )
| ( $false
= ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sF6 ) )
| ( ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sK0 )
= $false )
| ( sK1 = X0 )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_27 ),
inference(trivial_inequality_removal,[],[f550]) ).
thf(f627,plain,
( ! [X0: $i,X1: $i] :
( ( sK1 = X0 )
| ( ( in @ sK1 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false )
| ( $true = $false )
| ( ( in @ ( sK18 @ X0 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( $false
= ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sF6 ) )
| ( ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sK0 )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_32 ),
inference(constrained_superposition,[],[f549,f309]) ).
thf(f640,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sF6 ) )
| ( ( in @ ( sK18 @ X0 @ X1 @ sK1 ) @ sK1 )
= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false )
| ( sK1 = X0 )
| ( ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ X1 ) )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_32 ),
inference(trivial_inequality_removal,[],[f627]) ).
thf(f663,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sF6 ) )
| ( ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sK0 )
= $false )
| ( sK1 = X0 )
| ( ( in @ sK1 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ ( sK18 @ X0 @ X1 @ sK1 ) @ X0 )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_33 ),
inference(constrained_superposition,[],[f549,f313]) ).
thf(f667,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sF6 ) )
| ( ( in @ ( sK19 @ X0 @ X1 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ X1 ) )
= $false )
| ( ( in @ ( sK18 @ X0 @ X1 @ sK1 ) @ X0 )
= $false )
| ( sK1 = X0 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_33 ),
inference(trivial_inequality_removal,[],[f663]) ).
thf(f979,plain,
( ! [X0: $i] :
( ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( sF6 = sK1 )
| ( sF6 = sK1 )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( $true = $false )
| ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sK1 )
= $true )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sK1 )
= $true ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_30
| ~ spl23_32 ),
inference(constrained_superposition,[],[f640,f301]) ).
thf(f994,plain,
( ! [X0: $i] :
( ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sK1 )
= $true )
| ( $true = $false )
| ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( sF6 = sK1 )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_30
| ~ spl23_32 ),
inference(duplicate_literal_removal,[],[f979]) ).
thf(f995,plain,
( ! [X0: $i] :
( ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sK1 )
= $true )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( sF6 = sK1 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_30
| ~ spl23_32 ),
inference(trivial_inequality_removal,[],[f994]) ).
thf(f1021,plain,
( ! [X0: $i] :
( ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sK1 )
= $true ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_30
| ~ spl23_32 ),
inference(forward_subsumption_resolution,[],[f995,f47]) ).
thf(f1045,plain,
( ( $true = $false )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ( sF6 = sK1 )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(constrained_superposition,[],[f1021,f293]) ).
thf(f1055,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( $true = $false )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ( sF6 = sK1 )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(duplicate_literal_removal,[],[f1045]) ).
thf(f1056,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ( sF6 = sK1 )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(trivial_inequality_removal,[],[f1055]) ).
thf(f1066,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(forward_subsumption_resolution,[],[f1056,f47]) ).
thf(f1072,plain,
( ( ( in @ sK1 @ sF3 )
= $false )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(forward_demodulation,[],[f1066,f41]) ).
thf(f1080,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(forward_demodulation,[],[f1072,f218]) ).
thf(f1081,plain,
( ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(trivial_inequality_removal,[],[f1080]) ).
thf(f1090,plain,
( ( ( in @ sF6 @ sF3 )
= $false )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32 ),
inference(forward_demodulation,[],[f1081,f41]) ).
thf(f1098,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32
| ~ spl23_41 ),
inference(forward_demodulation,[],[f1090,f384]) ).
thf(f1099,plain,
( ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32
| ~ spl23_41 ),
inference(trivial_inequality_removal,[],[f1098]) ).
thf(f1107,definition,
( spl23_62
<=> ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_62])],[avatar_definition]) ).
thf(f1109,plain,
( ( $true
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 ) )
| ~ spl23_62 ),
inference(avatar_component_clause,[],[f1107]) ).
thf(f1111,definition,
( spl23_63
<=> ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) ) ),
introduced(definition,[new_symbols(definition,[spl23_63])],[avatar_definition]) ).
thf(f1113,plain,
( ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ~ spl23_63 ),
inference(avatar_component_clause,[],[f1111]) ).
thf(f1120,plain,
( spl23_62
| ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32
| ~ spl23_41 ),
inference(avatar_split_clause,[],[f1099,f382,f308,f300,f292,f216,f175,f1107]) ).
thf(f1234,plain,
( ! [X0: $i] :
( ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( sF6 = sK1 )
| ( sF6 = sK1 )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( $true = $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_31
| ~ spl23_33 ),
inference(constrained_superposition,[],[f305,f667]) ).
thf(f1246,plain,
( ! [X0: $i] :
( ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( $true = $false )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( sF6 = sK1 )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_31
| ~ spl23_33 ),
inference(duplicate_literal_removal,[],[f1234]) ).
thf(f1247,plain,
( ! [X0: $i] :
( ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sF6 )
= $false )
| ( sF6 = sK1 )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_31
| ~ spl23_33 ),
inference(trivial_inequality_removal,[],[f1246]) ).
thf(f1270,plain,
( ! [X0: $i] :
( ( ( in @ ( sK19 @ sF6 @ X0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ ( sK18 @ sF6 @ X0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ sF6 @ ( powerset @ X0 ) )
= $false ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_31
| ~ spl23_33 ),
inference(forward_subsumption_resolution,[],[f1247,f47]) ).
thf(f1273,plain,
( ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true = $false )
| ( sF6 = sK1 )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33 ),
inference(constrained_superposition,[],[f1270,f297]) ).
thf(f1287,plain,
( ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( sF6 = sK1 )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33 ),
inference(duplicate_literal_removal,[],[f1273]) ).
thf(f1288,plain,
( ( sF6 = sK1 )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33 ),
inference(trivial_inequality_removal,[],[f1287]) ).
thf(f1294,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33 ),
inference(forward_subsumption_resolution,[],[f1288,f47]) ).
thf(f1298,plain,
( ( ( in @ sF6 @ sF3 )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33 ),
inference(forward_demodulation,[],[f1294,f41]) ).
thf(f1302,plain,
( ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true = $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33
| ~ spl23_41 ),
inference(forward_demodulation,[],[f1298,f384]) ).
thf(f1303,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33
| ~ spl23_41 ),
inference(trivial_inequality_removal,[],[f1302]) ).
thf(f1309,plain,
( ( ( in @ sK1 @ sF3 )
= $false )
| ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33
| ~ spl23_41 ),
inference(forward_demodulation,[],[f1303,f41]) ).
thf(f1315,plain,
( ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ( $true = $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33
| ~ spl23_41 ),
inference(forward_demodulation,[],[f1309,f218]) ).
thf(f1316,plain,
( ( $false
= ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sF6 ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33
| ~ spl23_41 ),
inference(trivial_inequality_removal,[],[f1315]) ).
thf(f1322,plain,
( spl23_63
| ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33
| ~ spl23_41 ),
inference(avatar_split_clause,[],[f1316,f382,f312,f304,f296,f216,f175,f1111]) ).
thf(f1324,plain,
( ( $true = $false )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_63 ),
inference(constrained_superposition,[],[f1113,f436]) ).
thf(f1327,plain,
( ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK1 )
= $false )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_63 ),
inference(trivial_inequality_removal,[],[f1324]) ).
thf(f1330,plain,
( ( $true = $false )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_62
| ~ spl23_63 ),
inference(forward_demodulation,[],[f1327,f1109]) ).
thf(f1331,plain,
( ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_62
| ~ spl23_63 ),
inference(trivial_inequality_removal,[],[f1330]) ).
thf(f1336,plain,
( ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( sF6 = sK1 )
| ( $true = $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_62
| ~ spl23_63 ),
inference(constrained_superposition,[],[f552,f1331]) ).
thf(f1339,plain,
( ( sF6 = sK1 )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_62
| ~ spl23_63 ),
inference(trivial_inequality_removal,[],[f1336]) ).
thf(f1341,plain,
( ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_62
| ~ spl23_63 ),
inference(forward_subsumption_resolution,[],[f1339,f47]) ).
thf(f1343,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_62
| ~ spl23_63 ),
inference(forward_demodulation,[],[f1341,f41]) ).
thf(f1345,plain,
( ( ( in @ sF6 @ sF3 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_62
| ~ spl23_63 ),
inference(forward_demodulation,[],[f1343,f41]) ).
thf(f1348,plain,
( ( $true = $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ sK1 @ sF3 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63 ),
inference(forward_demodulation,[],[f1345,f384]) ).
thf(f1349,plain,
( ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ sK1 @ sF3 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63 ),
inference(trivial_inequality_removal,[],[f1348]) ).
thf(f1352,plain,
( ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( $true = $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63 ),
inference(forward_demodulation,[],[f1349,f218]) ).
thf(f1353,plain,
( ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63 ),
inference(trivial_inequality_removal,[],[f1352]) ).
thf(f1355,definition,
( spl23_73
<=> ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl23_73])],[avatar_definition]) ).
thf(f1357,plain,
( ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sF6 )
= $false )
| ~ spl23_73 ),
inference(avatar_component_clause,[],[f1355]) ).
thf(f1359,definition,
( spl23_74
<=> ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl23_74])],[avatar_definition]) ).
thf(f1361,plain,
( ( ( in @ ( sK19 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $false )
| ~ spl23_74 ),
inference(avatar_component_clause,[],[f1359]) ).
thf(f1363,plain,
( spl23_73
| spl23_74
| ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63 ),
inference(avatar_split_clause,[],[f1353,f1111,f1107,f382,f288,f249,f216,f175,f1359,f1355]) ).
thf(f1372,plain,
( ( sF6 = sK1 )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true = $false )
| ~ spl23_26
| ~ spl23_73 ),
inference(constrained_superposition,[],[f285,f1357]) ).
thf(f1379,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( sF6 = sK1 )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl23_26
| ~ spl23_73 ),
inference(trivial_inequality_removal,[],[f1372]) ).
thf(f1388,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ~ spl23_26
| ~ spl23_73 ),
inference(forward_subsumption_resolution,[],[f1379,f47]) ).
thf(f1391,plain,
( ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sF6 @ sF3 )
= $false )
| ~ spl23_26
| ~ spl23_73 ),
inference(forward_demodulation,[],[f1388,f41]) ).
thf(f1394,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sF6 @ sF3 )
= $false )
| ( $true = $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(forward_demodulation,[],[f1391,f1331]) ).
thf(f1395,plain,
( ( ( in @ sF6 @ sF3 )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(trivial_inequality_removal,[],[f1394]) ).
thf(f1398,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true = $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(forward_demodulation,[],[f1395,f384]) ).
thf(f1399,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(trivial_inequality_removal,[],[f1398]) ).
thf(f1401,plain,
( ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(forward_demodulation,[],[f1399,f41]) ).
thf(f1405,plain,
( ( $true = $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(forward_demodulation,[],[f1401,f218]) ).
thf(f1406,plain,
( $false
| ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(trivial_inequality_removal,[],[f1405]) ).
thf(f1407,plain,
( ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(avatar_contradiction_clause,[],[f1406]) ).
thf(f1423,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( $true = $false )
| ( sF6 = sK1 )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ~ spl23_25
| ~ spl23_74 ),
inference(constrained_superposition,[],[f281,f1361]) ).
thf(f1427,plain,
( ( sF6 = sK1 )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ~ spl23_25
| ~ spl23_74 ),
inference(trivial_inequality_removal,[],[f1423]) ).
thf(f1432,plain,
( ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ~ spl23_25
| ~ spl23_74 ),
inference(forward_subsumption_resolution,[],[f1427,f47]) ).
thf(f1434,plain,
( ( ( in @ ( sK18 @ sF6 @ sK0 @ sK1 ) @ sK0 )
= $true )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sF6 @ sF3 )
= $false )
| ~ spl23_25
| ~ spl23_74 ),
inference(forward_demodulation,[],[f1432,f41]) ).
thf(f1437,plain,
( ( ( in @ sF6 @ sF3 )
= $false )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true = $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(forward_demodulation,[],[f1434,f1331]) ).
thf(f1438,plain,
( ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( ( in @ sF6 @ sF3 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(trivial_inequality_removal,[],[f1437]) ).
thf(f1440,plain,
( ( ( in @ sF6 @ sF3 )
= $false )
| ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(forward_demodulation,[],[f1438,f41]) ).
thf(f1443,plain,
( ( $true = $false )
| ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(forward_demodulation,[],[f1440,f384]) ).
thf(f1444,plain,
( ( ( in @ sK1 @ sF3 )
= $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(trivial_inequality_removal,[],[f1443]) ).
thf(f1448,plain,
( ( $true = $false )
| ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(forward_demodulation,[],[f1444,f218]) ).
thf(f1449,plain,
( $false
| ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(trivial_inequality_removal,[],[f1448]) ).
thf(f1450,plain,
( ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(avatar_contradiction_clause,[],[f1449]) ).
cnf(s1,plain,
( spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f177]) ).
cnf(s7,plain,
( spl23_10
| spl23_11 ),
inference(sat_conversion,[],[f219]) ).
cnf(s12,plain,
( spl23_17
| spl23_18 ),
inference(sat_conversion,[],[f251]) ).
cnf(s13,plain,
spl23_3,
inference(sat_conversion,[],[f252]) ).
cnf(s14,plain,
( spl23_19
| spl23_20 ),
inference(sat_conversion,[],[f260]) ).
cnf(s17,plain,
( spl23_24
| spl23_25 ),
inference(sat_conversion,[],[f282]) ).
cnf(s18,plain,
( spl23_24
| spl23_26 ),
inference(sat_conversion,[],[f286]) ).
cnf(s19,plain,
( spl23_24
| spl23_27 ),
inference(sat_conversion,[],[f290]) ).
cnf(s20,plain,
( spl23_24
| spl23_28 ),
inference(sat_conversion,[],[f294]) ).
cnf(s21,plain,
( spl23_24
| spl23_29 ),
inference(sat_conversion,[],[f298]) ).
cnf(s22,plain,
( spl23_24
| spl23_30 ),
inference(sat_conversion,[],[f302]) ).
cnf(s23,plain,
( spl23_24
| spl23_31 ),
inference(sat_conversion,[],[f306]) ).
cnf(s24,plain,
( spl23_24
| spl23_32 ),
inference(sat_conversion,[],[f310]) ).
cnf(s25,plain,
( spl23_24
| spl23_33 ),
inference(sat_conversion,[],[f314]) ).
cnf(s31,plain,
spl23_13,
inference(sat_conversion,[],[f342]) ).
cnf(s32,plain,
spl23_8,
inference(sat_conversion,[],[f343]) ).
cnf(s33,plain,
spl23_22,
inference(sat_conversion,[],[f344]) ).
cnf(s34,plain,
spl23_34,
inference(sat_conversion,[],[f345]) ).
cnf(s35,plain,
( ~ spl23_8
| ~ spl23_10 ),
inference(sat_conversion,[],[f348]) ).
cnf(s36,plain,
( ~ spl23_13
| ~ spl23_17 ),
inference(sat_conversion,[],[f361]) ).
cnf(s37,plain,
( ~ spl23_24
| ~ spl23_34 ),
inference(sat_conversion,[],[f366]) ).
cnf(s39,plain,
( ~ spl23_20
| ~ spl23_22 ),
inference(sat_conversion,[],[f388]) ).
cnf(s40,plain,
( ~ spl23_11
| ~ spl23_19
| ~ spl23_40 ),
inference(sat_conversion,[],[f403]) ).
cnf(s41,plain,
( ~ spl23_19
| spl23_40
| spl23_41 ),
inference(sat_conversion,[],[f406]) ).
cnf(s44,plain,
( ~ spl23_1
| ~ spl23_3 ),
inference(sat_conversion,[],[f516]) ).
cnf(s73,plain,
( ~ spl23_2
| ~ spl23_11
| ~ spl23_28
| ~ spl23_30
| ~ spl23_32
| ~ spl23_41
| spl23_62 ),
inference(sat_conversion,[],[f1120]) ).
cnf(s90,plain,
( ~ spl23_2
| ~ spl23_11
| ~ spl23_29
| ~ spl23_31
| ~ spl23_33
| ~ spl23_41
| spl23_63 ),
inference(sat_conversion,[],[f1322]) ).
cnf(s94,plain,
( ~ spl23_2
| ~ spl23_11
| ~ spl23_18
| ~ spl23_27
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| spl23_73
| spl23_74 ),
inference(sat_conversion,[],[f1363]) ).
cnf(s98,plain,
( ~ spl23_11
| ~ spl23_18
| ~ spl23_26
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_73 ),
inference(sat_conversion,[],[f1407]) ).
cnf(s100,plain,
( ~ spl23_11
| ~ spl23_18
| ~ spl23_25
| ~ spl23_41
| ~ spl23_62
| ~ spl23_63
| ~ spl23_74 ),
inference(sat_conversion,[],[f1450]) ).
cnf(s101,plain,
~ spl23_24,
inference(rat,[],[s37,s34]) ).
cnf(s102,plain,
~ spl23_20,
inference(rat,[],[s39,s33]) ).
cnf(s103,plain,
~ spl23_10,
inference(rat,[],[s35,s32]) ).
cnf(s104,plain,
~ spl23_17,
inference(rat,[],[s36,s31]) ).
cnf(s105,plain,
spl23_33,
inference(rat,[],[s25,s101]) ).
cnf(s106,plain,
spl23_32,
inference(rat,[],[s24,s101]) ).
cnf(s107,plain,
spl23_31,
inference(rat,[],[s23,s101]) ).
cnf(s108,plain,
spl23_30,
inference(rat,[],[s22,s101]) ).
cnf(s109,plain,
spl23_29,
inference(rat,[],[s21,s101]) ).
cnf(s110,plain,
spl23_28,
inference(rat,[],[s20,s101]) ).
cnf(s111,plain,
spl23_27,
inference(rat,[],[s19,s101]) ).
cnf(s112,plain,
spl23_26,
inference(rat,[],[s18,s101]) ).
cnf(s113,plain,
spl23_25,
inference(rat,[],[s17,s101]) ).
cnf(s114,plain,
spl23_19,
inference(rat,[],[s14,s102]) ).
cnf(s115,plain,
~ spl23_1,
inference(rat,[],[s44,s13]) ).
cnf(s116,plain,
spl23_18,
inference(rat,[],[s12,s104]) ).
cnf(s117,plain,
spl23_11,
inference(rat,[],[s7,s103]) ).
cnf(s118,plain,
~ spl23_40,
inference(rat,[],[s40,s114,s117]) ).
cnf(s119,plain,
spl23_41,
inference(rat,[],[s41,s114,s118]) ).
cnf(s121,plain,
spl23_2,
inference(rat,[],[s1,s115]) ).
cnf(s122,plain,
spl23_63,
inference(rat,[],[s90,s119,s117,s105,s107,s109,s121]) ).
cnf(s123,plain,
spl23_62,
inference(rat,[],[s73,s119,s117,s106,s108,s110,s121]) ).
cnf(s124,plain,
~ spl23_74,
inference(rat,[],[s100,s122,s119,s117,s116,s113,s123]) ).
cnf(s125,plain,
~ spl23_73,
inference(rat,[],[s98,s122,s119,s117,s116,s112,s123]) ).
cnf(s126,plain,
$false,
inference(rat,[],[s94,s124,s122,s121,s119,s117,s111,s116,s125,s123]) ).
thf(f1451,plain,
$false,
inference(avatar_sat_refutation,[],[s126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU731^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:18:03 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.74/0.38 % (843206)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.38 % (843215)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2630487186:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.38 % (843212)lrs+10_16_si=on:nwc=1.5:random_seed=1755533231:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.38 % (843211)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1401522705:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.38 % (843214)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=1552758251: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)
% 0.74/0.38 % (843213)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2779027414:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.38 % (843213)Instruction limit reached!
% 0.74/0.38 % (843213)------------------------------
% 0.74/0.38 % (843213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843213)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843213)Termination reason: Instruction limit
% 0.74/0.38 % (843213)Termination phase: Saturation
% 0.74/0.38 % (843213)Time elapsed: 0.002 s
% 0.74/0.38 % (843213)Peak memory usage: 11 MB
% 0.74/0.38 % (843213)Instructions burned: 3 (million)
% 0.74/0.38 % (843215)Instruction limit reached!
% 0.74/0.38 % (843215)------------------------------
% 0.74/0.38 % (843215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843215)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843215)Termination reason: Instruction limit
% 0.74/0.38 % (843215)Termination phase: Saturation
% 0.74/0.38 % (843215)Time elapsed: 0.013 s
% 0.74/0.38 % (843215)Peak memory usage: 12 MB
% 0.74/0.38 % (843215)Instructions burned: 25 (million)
% 0.74/0.38 % (843212)Instruction limit reached!
% 0.74/0.38 % (843212)------------------------------
% 0.74/0.38 % (843212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843212)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843212)Termination reason: Instruction limit
% 0.74/0.38 % (843212)Termination phase: Saturation
% 0.74/0.38 % (843212)Time elapsed: 0.011 s
% 0.74/0.38 % (843212)Peak memory usage: 12 MB
% 0.74/0.38 % (843212)Instructions burned: 20 (million)
% 0.74/0.38 % (843216)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=723847306:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.38 % (843217)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.38 % (843217)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
% 0.74/0.38 % (843217)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=1477875749:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.38 % (843223)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3631653835:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.38 % (843223)Instruction limit reached!
% 0.74/0.38 % (843223)------------------------------
% 0.74/0.38 % (843223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843223)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843223)Termination reason: Instruction limit
% 0.74/0.38 % (843223)Termination phase: Property scanning
% 0.74/0.38 % (843223)Time elapsed: 0.001 s
% 0.74/0.38 % (843223)Peak memory usage: 10 MB
% 0.74/0.38 % (843223)Instructions burned: 2 (million)
% 0.74/0.38 % (843226)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.38 % (843226)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=641791167:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.38 % (843224)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3528452952:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.38 % (843216)Instruction limit reached!
% 0.74/0.38 % (843216)------------------------------
% 0.74/0.38 % (843216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843216)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843216)Termination reason: Instruction limit
% 0.74/0.38 % (843216)Termination phase: Saturation
% 0.74/0.38 % (843216)Time elapsed: 0.021 s
% 0.74/0.38 % (843216)Peak memory usage: 12 MB
% 0.74/0.38 % (843216)Instructions burned: 78 (million)
% 0.74/0.38 % (843226)Instruction limit reached!
% 0.74/0.38 % (843226)------------------------------
% 0.74/0.38 % (843226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843226)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843226)Termination reason: Instruction limit
% 0.74/0.38 % (843226)Termination phase: Saturation
% 0.74/0.38 % (843226)Time elapsed: 0.005 s
% 0.74/0.38 % (843226)Peak memory usage: 12 MB
% 0.74/0.38 % (843226)Instructions burned: 8 (million)
% 0.74/0.38 % (843224)Instruction limit reached!
% 0.74/0.38 % (843224)------------------------------
% 0.74/0.38 % (843224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843224)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843224)Termination reason: Instruction limit
% 0.74/0.38 % (843224)Termination phase: Saturation
% 0.74/0.38 % (843224)Time elapsed: 0.004 s
% 0.74/0.38 % (843224)Peak memory usage: 12 MB
% 0.74/0.38 % (843224)Instructions burned: 5 (million)
% 0.74/0.38 % (843211)Instruction limit reached!
% 0.74/0.38 % (843211)------------------------------
% 0.74/0.38 % (843211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843211)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843211)Termination reason: Instruction limit
% 0.74/0.38 % (843211)Termination phase: Saturation
% 0.74/0.38 % (843211)Time elapsed: 0.040 s
% 0.74/0.38 % (843211)Peak memory usage: 12 MB
% 0.74/0.38 % (843211)Instructions burned: 87 (million)
% 0.74/0.38 % (843232)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
% 0.74/0.38 % (843232)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.38 % (843229)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3692700818:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.38 % (843232)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=428505841:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.38 % (843229)Instruction limit reached!
% 0.74/0.38 % (843229)------------------------------
% 0.74/0.38 % (843229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843229)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843229)Termination reason: Instruction limit
% 0.74/0.38 % (843229)Termination phase: Saturation
% 0.74/0.38 % (843229)Time elapsed: 0.007 s
% 0.74/0.38 % (843229)Peak memory usage: 12 MB
% 0.74/0.38 % (843229)Instructions burned: 12 (million)
% 0.74/0.38 % (843232)Instruction limit reached!
% 0.74/0.38 % (843232)------------------------------
% 0.74/0.38 % (843232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843232)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843232)Termination reason: Instruction limit
% 0.74/0.38 % (843232)Termination phase: Saturation
% 0.74/0.38 % (843232)Time elapsed: 0.010 s
% 0.74/0.38 % (843232)Peak memory usage: 12 MB
% 0.74/0.38 % (843232)Instructions burned: 29 (million)
% 0.74/0.38 % (843234)lrs+10_1_si=on:cs=on:random_seed=3120437543:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.38 % (843235)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.38 % (843235)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=977190810:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.38 % (843234)Instruction limit reached!
% 0.74/0.38 % (843234)------------------------------
% 0.74/0.38 % (843234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843234)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843234)Termination reason: Instruction limit
% 0.74/0.38 % (843234)Termination phase: Saturation
% 0.74/0.38 % (843234)Time elapsed: 0.005 s
% 0.74/0.38 % (843234)Peak memory usage: 11 MB
% 0.74/0.38 % (843234)Instructions burned: 10 (million)
% 0.74/0.38 % (843235)Instruction limit reached!
% 0.74/0.38 % (843235)------------------------------
% 0.74/0.38 % (843235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843235)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843235)Termination reason: Instruction limit
% 0.74/0.38 % (843235)Termination phase: Saturation
% 0.74/0.38 % (843235)Time elapsed: 0.003 s
% 0.74/0.38 % (843235)Peak memory usage: 12 MB
% 0.74/0.38 % (843235)Instructions burned: 6 (million)
% 0.74/0.38 % (843233)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3203407980:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.38 % (843238)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4019226527:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.38 % (843217) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-843206-843217"...
% 0.74/0.38 % (843243)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3867869481:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.74/0.38 % (843240)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=785516823:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.74/0.38 % (843242)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=69808763:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.74/0.38 % (843243)Instruction limit reached!
% 0.74/0.38 % (843243)------------------------------
% 0.74/0.38 % (843243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843243)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843243)Termination reason: Instruction limit
% 0.74/0.38 % (843243)Termination phase: Saturation
% 0.74/0.38 % (843243)Time elapsed: 0.005 s
% 0.74/0.38 % (843243)Peak memory usage: 12 MB
% 0.74/0.38 % (843243)Instructions burned: 15 (million)
% 0.74/0.38 % (843217)...printing done.
% 0.74/0.38 % (843217)Refutation found. Thanks to Tanya!
% 0.74/0.38 % SZS status Theorem for theBenchmark
% 0.74/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.74/0.38 % (843217)------------------------------
% 0.74/0.38 % (843217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.38 % (843217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.38 % (843217)CaDiCaL version: 2.1.3
% 0.74/0.38 % (843217)Termination reason: Refutation
% 0.74/0.38 % (843217)Time elapsed: 0.067 s
% 0.74/0.38 % (843217)Peak memory usage: 14 MB
% 0.74/0.38 % (843217)Instructions burned: 135 (million)
% 0.74/0.38 % (843206)Success in time 0.122 s
% 0.74/0.38 % Vampire exiting
%------------------------------------------------------------------------------