%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU731^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:33:09 AM UTC 2026
% Result : Theorem 6.32s 1.16s
% Output : Refutation 6.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 13
% Syntax : Number of formulae : 213 ( 57 unt; 0 typ; 8 def)
% Number of atoms : 2900 ( 722 equ; 0 cnn)
% Maximal formula atoms : 10 ( 13 avg)
% Number of connectives : 3671 ( 8 ~; 470 |; 15 &;2778 @)
% ( 0 <=>; 279 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 17 con; 0-4 aty)
% ( 121 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 411 ( 138 ^; 269 !; 4 ?; 411 :)
% 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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
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_21,type,
sF3: $o ).
thf(func_def_22,type,
sF4: $o ).
thf(func_def_23,type,
sF5: $o ).
thf(func_def_27,type,
sF9: $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_34,type,
sK15: $i > $i > $i > $i ).
thf(func_def_35,type,
sK16: $i > $i > $i > $i ).
thf(f1,axiom,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(f2,axiom,
( setextT
= ( ! [X0: $i,X1: $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/sandbox/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/sandbox/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(f4,axiom,
( doubleComplementE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(f5,conjecture,
( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(f6,negated_conjecture,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( setextT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ X4 @ X2 )
=> ( in @ X4 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,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(f12,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,[],[f11]) ).
thf(f13,plain,
( doubleComplementE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( complementT_lem
=> ( setextT
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( X1
= ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
~ ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
= X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( setextT = $true )
& ( complementT_lem = $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( setextT = $true )
& ( complementT_lem = $true ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( sK1
!= ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( setextT = $true )
& ( complementT_lem = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18]) ).
thf(f20,plain,
( complementT_lem
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
( setextT
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f22,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,[],[f12]) ).
thf(f23,plain,
( doubleComplementE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
complementT_lem = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f25,plain,
setextT = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
doubleComplementI1 = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
doubleComplementE1 = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f28,plain,
( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
( sK1
!= ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f20,f24]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f21,f25]) ).
thf(f34,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,[],[f22,f26]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f23,f27]) ).
thf(f36,definition,
( sF2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f37,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) )
= sF2 ),
inference(reorient_equations,[],[f36]) ).
thf(f38,plain,
$true = sF2,
inference(definition_folding,[],[f32,f37]) ).
thf(f39,definition,
( sF3
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f40,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) )
= sF3 ),
inference(reorient_equations,[],[f39]) ).
thf(f41,plain,
$true = sF3,
inference(definition_folding,[],[f33,f40]) ).
thf(f42,definition,
( sF4
= ( !! @ $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,[sF4])],[function_definition]) ).
thf(f43,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 ) ) ) ) ) ) ) ) )
= sF4 ),
inference(reorient_equations,[],[f42]) ).
thf(f44,plain,
$true = sF4,
inference(definition_folding,[],[f34,f43]) ).
thf(f45,definition,
( sF5
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f46,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= sF5 ),
inference(reorient_equations,[],[f45]) ).
thf(f47,plain,
$true = sF5,
inference(definition_folding,[],[f35,f46]) ).
thf(f48,definition,
( sF6
= ( setminus @ sK0 @ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f49,plain,
( ( setminus @ sK0 @ sK1 )
= sF6 ),
inference(reorient_equations,[],[f48]) ).
thf(f50,definition,
( sF7
= ( setminus @ sK0 @ sF6 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f51,plain,
( ( setminus @ sK0 @ sF6 )
= sF7 ),
inference(reorient_equations,[],[f50]) ).
thf(f52,plain,
sK1 != sF7,
inference(definition_folding,[],[f29,f51,f49]) ).
thf(f53,definition,
( sF8
= ( powerset @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f54,plain,
( ( powerset @ sK0 )
= sF8 ),
inference(reorient_equations,[],[f53]) ).
thf(f55,definition,
( sF9
= ( in @ sK1 @ sF8 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f56,plain,
( ( in @ sK1 @ sF8 )
= sF9 ),
inference(reorient_equations,[],[f55]) ).
thf(f57,plain,
$true = sF9,
inference(definition_folding,[],[f28,f56,f54]) ).
thf(f58,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) ) )
= $true )
| ( $false = sF2 ) ),
inference(iff_proxy_clausification,[],[f37]) ).
thf(f66,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( in @ ( setminus @ Y1 @ Y0 ) @ ( powerset @ Y1 ) ) ) )
@ X1 ) )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f67,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ X1 ) @ ( powerset @ Y0 ) ) ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ X1 ) @ ( powerset @ Y0 ) ) )
@ X2 ) )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF2 )
| ( $true
= ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false = sF3 ) ),
inference(iff_proxy_clausification,[],[f40]) ).
thf(f96,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y1 ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y0 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y0 ) ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) )
@ X1 ) )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f97,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ X1 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ X1 ) ) ) )
=> ( X1 = Y1 ) ) ) ) ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ X1 )
=> ( in @ Y2 @ Y1 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ X1 ) ) ) )
=> ( X1 = Y1 ) ) ) ) ) )
@ X2 ) )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
=> ( X1 = Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
=> ( X1 = Y0 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $true
= ( ( in @ X3 @ ( powerset @ X2 ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) ) )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK15 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) )
=> ( X1 = X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK15 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) ) ) )
| ( $true
= ( X1 = X3 ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK15 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) )
@ ( sK16 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( X1 = X3 ) ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X3 ) ) )
@ ( sK15 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X3 )
=> ( in @ Y0 @ X1 ) ) )
@ ( sK16 @ X3 @ X1 @ X2 ) ) )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) ) ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f112,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f114,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f115,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f117,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 )
=> ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f118]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f118]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 )
=> ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF3 )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( X1 = X3 ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f126,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 )
| ( $false = sF4 ) ),
inference(iff_proxy_clausification,[],[f43]) ).
thf(f140,plain,
! [X1: $i] :
( ( $true
= ( ^ [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 ) )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f141,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) ) ) ) ) ) )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) ) ) ) ) )
@ X2 ) )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ) ) ) )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( $true
= ( ( in @ X3 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( ( in @ X3 @ X2 )
= $false )
| ( $true
= ( ( in @ X3 @ X1 )
=> ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF4 )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( in @ X3 @ X1 )
= $false )
| ( $true
= ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
= $true )
| ( $false = sF5 ) ),
inference(iff_proxy_clausification,[],[f46]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( in @ Y2 @ ( setminus @ Y1 @ ( setminus @ Y1 @ Y0 ) ) )
=> ( in @ Y2 @ Y0 ) ) ) ) ) )
@ X1 ) )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) )
=> ( in @ Y1 @ X1 ) ) ) ) ) ) )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y1 @ ( setminus @ Y0 @ ( setminus @ Y0 @ X1 ) ) )
=> ( in @ Y1 @ X1 ) ) ) ) )
@ X2 ) )
| ( $false = sF5 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ Y0 @ X1 ) ) ) ) ) )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF5 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ Y0 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF5 )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ Y0 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF5 )
| ( $true
= ( ( in @ X3 @ X2 )
=> ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ X3 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF5 )
| ( ( in @ X3 @ X2 )
= $false )
| ( $true
= ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
=> ( in @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false = sF5 )
| ( ( in @ X3 @ X2 )
= $false )
| ( $false
= ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true
= ( in @ sK1 @ sF8 ) )
| ( $false = sF9 ) ),
inference(iff_proxy_clausification,[],[f56]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) ) ),
inference(forward_demodulation,[],[f70,f38]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f113,f41]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f115,f41]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f114,f41]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f119,f41]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f121,f41]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f120,f41]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f123,f41]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f125,f41]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( X1 = X3 ) ),
inference(forward_demodulation,[],[f124,f41]) ).
thf(f193,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ ( sK16 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( in @ ( sK15 @ X3 @ X1 @ X2 ) @ X3 ) )
| ( $false
= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( X1 = X3 ) ),
inference(trivial_inequality_removal,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( in @ X3 @ X1 )
= $false )
| ( $true
= ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ) ),
inference(forward_demodulation,[],[f148,f44]) ).
thf(f195,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( ( in @ X3 @ X1 )
= $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( $false
= ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(forward_demodulation,[],[f171,f47]) ).
thf(f197,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( in @ X3 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f198,plain,
( ( $true = $false )
| ( $true
= ( in @ sK1 @ sF8 ) ) ),
inference(forward_demodulation,[],[f172,f57]) ).
thf(f199,plain,
( $true
= ( in @ sK1 @ sF8 ) ),
inference(trivial_inequality_removal,[],[f198]) ).
thf(f208,plain,
( ( $true
= ( in @ sF6 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f175,f49]) ).
thf(f209,plain,
( ( $true
= ( in @ sF6 @ sF8 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f208,f54]) ).
thf(f210,plain,
( ( $false
= ( in @ sK1 @ sF8 ) )
| ( $true
= ( in @ sF6 @ sF8 ) ) ),
inference(forward_demodulation,[],[f209,f54]) ).
thf(f211,plain,
( ( $true = $false )
| ( $true
= ( in @ sF6 @ sF8 ) ) ),
inference(forward_demodulation,[],[f210,f199]) ).
thf(f212,plain,
( $true
= ( in @ sF6 @ sF8 ) ),
inference(trivial_inequality_removal,[],[f211]) ).
thf(f213,plain,
( ( $true
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f175,f51]) ).
thf(f214,plain,
( ( $true
= ( in @ sF7 @ sF8 ) )
| ( $false
= ( in @ sF6 @ ( powerset @ sK0 ) ) ) ),
inference(forward_demodulation,[],[f213,f54]) ).
thf(f215,plain,
( ( $false
= ( in @ sF6 @ sF8 ) )
| ( $true
= ( in @ sF7 @ sF8 ) ) ),
inference(forward_demodulation,[],[f214,f54]) ).
thf(f216,plain,
( ( $true = $false )
| ( $true
= ( in @ sF7 @ sF8 ) ) ),
inference(forward_demodulation,[],[f215,f212]) ).
thf(f217,plain,
( $true
= ( in @ sF7 @ sF8 ) ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f218,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ sK0 @ sF6 ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(constrained_superposition,[],[f195,f49]) ).
thf(f221,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f218,f51]) ).
thf(f224,plain,
! [X0: $i] :
( ( $false
= ( in @ sK1 @ sF8 ) )
| ( $true
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f221,f54]) ).
thf(f225,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f224,f199]) ).
thf(f226,plain,
! [X0: $i] :
( ( $true
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f229,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ ( setminus @ sK0 @ sF6 ) ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f197,f49]) ).
thf(f240,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $true
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f229,f51]) ).
thf(f243,plain,
! [X0: $i] :
( ( $false
= ( in @ sK1 @ sF8 ) )
| ( $false
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f240,f54]) ).
thf(f244,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ X0 @ sK1 ) ) ),
inference(forward_demodulation,[],[f243,f199]) ).
thf(f245,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sF7 ) )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
= ( in @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f281,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK0 ) )
| ( $true
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK1 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ X0 @ X1 ) @ X1 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( sF7 = X0 ) ),
inference(constrained_superposition,[],[f245,f179]) ).
thf(f286,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK1 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ X0 @ X1 ) @ X1 ) )
| ( $false
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( sF7 = X0 ) ),
inference(trivial_inequality_removal,[],[f281]) ).
thf(f395,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK0 ) )
| ( $true
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK1 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ X0 @ X1 ) @ X0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( sF7 = X0 ) ),
inference(constrained_superposition,[],[f245,f185]) ).
thf(f400,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK1 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ X0 @ X1 ) @ X0 ) )
| ( $false
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( sF7 = X0 ) ),
inference(trivial_inequality_removal,[],[f395]) ).
thf(f461,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK0 ) )
| ( $true
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ X0 @ X1 ) @ sF7 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( sF7 = X0 ) ),
inference(constrained_superposition,[],[f245,f191]) ).
thf(f462,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ ( sK16 @ sF7 @ X0 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ X0 @ X1 ) @ sF7 ) )
| ( $false
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( sF7 = X0 ) ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f599,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ X0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 ) ),
inference(constrained_superposition,[],[f181,f286]) ).
thf(f604,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ X0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f599]) ).
thf(f605,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ X0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f622,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ X0 ) )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) ) ),
inference(forward_subsumption_resolution,[],[f605,f52]) ).
thf(f758,plain,
( ( $true = $false )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f177,f622]) ).
thf(f759,plain,
( ( $true = $false )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 ) ),
inference(duplicate_literal_removal,[],[f758]) ).
thf(f760,plain,
( ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 ) ),
inference(trivial_inequality_removal,[],[f759]) ).
thf(f776,plain,
( ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_subsumption_resolution,[],[f760,f52]) ).
thf(f782,plain,
( ( $false
= ( in @ sF7 @ sF8 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f776,f54]) ).
thf(f788,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f782,f217]) ).
thf(f789,plain,
( ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f788]) ).
thf(f800,plain,
( ( $false
= ( in @ sK1 @ sF8 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) ) ),
inference(forward_demodulation,[],[f789,f54]) ).
thf(f806,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) ) ),
inference(forward_demodulation,[],[f800,f199]) ).
thf(f807,plain,
( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) ),
inference(trivial_inequality_removal,[],[f806]) ).
thf(f2487,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 ) ),
inference(constrained_superposition,[],[f187,f400]) ).
thf(f2510,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f2487]) ).
thf(f2511,plain,
! [X0: $i] :
( ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f2510]) ).
thf(f2536,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) ) ),
inference(forward_subsumption_resolution,[],[f2511,f52]) ).
thf(f2651,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f183,f2536]) ).
thf(f2664,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 ) ),
inference(duplicate_literal_removal,[],[f2651]) ).
thf(f2665,plain,
( ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 ) ),
inference(trivial_inequality_removal,[],[f2664]) ).
thf(f2684,plain,
( ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_subsumption_resolution,[],[f2665,f52]) ).
thf(f2691,plain,
( ( $false
= ( in @ sF7 @ sF8 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f2684,f54]) ).
thf(f2695,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f2691,f217]) ).
thf(f2696,plain,
( ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f2695]) ).
thf(f2703,plain,
( ( $false
= ( in @ sK1 @ sF8 ) )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) ) ),
inference(forward_demodulation,[],[f2696,f54]) ).
thf(f2707,plain,
( ( $true = $false )
| ( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) ) ),
inference(forward_demodulation,[],[f2703,f199]) ).
thf(f2708,plain,
( $true
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) ),
inference(trivial_inequality_removal,[],[f2707]) ).
thf(f2835,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sF7 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sF7 ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 ) ),
inference(constrained_superposition,[],[f193,f462]) ).
thf(f2863,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sF7 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f2835]) ).
thf(f2864,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sF7 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( sK1 = sF7 )
| ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f2863]) ).
thf(f2889,plain,
! [X0: $i] :
( ( $false
= ( in @ ( sK16 @ sF7 @ sK1 @ X0 ) @ sK0 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ sK1 @ ( powerset @ X0 ) ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ X0 ) @ sF7 ) ) ),
inference(forward_subsumption_resolution,[],[f2864,f52]) ).
thf(f3276,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) ) ),
inference(constrained_superposition,[],[f189,f2889]) ).
thf(f3292,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 ) ),
inference(duplicate_literal_removal,[],[f3276]) ).
thf(f3293,plain,
( ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false )
| ( sK1 = sF7 ) ),
inference(trivial_inequality_removal,[],[f3292]) ).
thf(f3309,plain,
( ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) )
| ( $false
= ( in @ sF7 @ ( powerset @ sK0 ) ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_subsumption_resolution,[],[f3293,f52]) ).
thf(f3313,plain,
( ( $false
= ( in @ sF7 @ sF8 ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f3309,f54]) ).
thf(f3315,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f3313,f217]) ).
thf(f3316,plain,
( ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) )
| ( ( in @ sK1 @ ( powerset @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f3315]) ).
thf(f3319,plain,
( ( $false
= ( in @ sK1 @ sF8 ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) ) ),
inference(forward_demodulation,[],[f3316,f54]) ).
thf(f3321,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) ) ),
inference(forward_demodulation,[],[f3319,f199]) ).
thf(f3322,plain,
( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sF7 ) ),
inference(trivial_inequality_removal,[],[f3321]) ).
thf(f3405,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f226,f3322]) ).
thf(f3406,plain,
( ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK0 ) )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f3405]) ).
thf(f3409,plain,
( ( $true = $false )
| ( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) ) ),
inference(forward_demodulation,[],[f3406,f807]) ).
thf(f3410,plain,
( $false
= ( in @ ( sK15 @ sF7 @ sK1 @ sK0 ) @ sK1 ) ),
inference(trivial_inequality_removal,[],[f3409]) ).
thf(f3493,plain,
$true = $false,
inference(constrained_superposition,[],[f2708,f3410]) ).
thf(f3494,plain,
$false,
inference(trivial_inequality_removal,[],[f3493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU731^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:17:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.46/1.02 % (842243)Will run a generic schedule for satisfiability detection.
% 4.46/1.02 % (842252)dis+10_1_sil=32000:sp=arity:random_seed=3181377523:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.46/1.02 % (842250)% WARNING: option uhcvi not known.
% 4.46/1.02 % (842249)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1595746148_2999 on theBenchmark for (2999ds/0Mi)
% 4.46/1.02 % (842250)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1216746050:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.46/1.02 % (842253)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=418216126:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.46/1.02 % (842251)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3411301977:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.46/1.02 % (842250)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.46/1.02 % (842253)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.46/1.02 % Exception at run slice level
% 4.46/1.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.46/1.02 % (842250)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.46/1.02 % (842255)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2305804122:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.46/1.02 % (842254)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2462089579:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.46/1.02 % (842252)Instruction limit reached!
% 4.46/1.02 % (842252)------------------------------
% 4.46/1.02 % (842252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.02 % (842252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.02 % (842252)CaDiCaL version: 2.1.3
% 4.46/1.02 % (842252)Termination reason: Instruction limit
% 4.46/1.02 % (842252)Termination phase: Saturation
% 4.46/1.02 % (842252)Time elapsed: 0.040 s
% 4.46/1.02 % (842252)Peak memory usage: 12 MB
% 4.46/1.02 % (842252)Instructions burned: 105 (million)
% 4.46/1.02 % (842268)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3659887439:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.46/1.02 % Exception at run slice level
% 4.46/1.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.46/1.02 % (842278)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1088440094:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.46/1.02 % (842282)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2351192943:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.46/1.02 % (842282)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.46/1.02 % (842282)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.46/1.02 % (842253)Instruction limit reached!
% 4.46/1.02 % (842253)------------------------------
% 4.46/1.02 % (842253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.02 % (842253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.02 % (842253)CaDiCaL version: 2.1.3
% 4.46/1.02 % (842253)Termination reason: Instruction limit
% 4.46/1.02 % (842253)Termination phase: Saturation
% 4.46/1.02 % (842253)Time elapsed: 0.096 s
% 4.46/1.02 % (842253)Peak memory usage: 12 MB
% 4.46/1.02 % (842253)Instructions burned: 116 (million)
% 4.46/1.02 % (842254)Instruction limit reached!
% 4.46/1.02 % (842254)------------------------------
% 4.46/1.02 % (842254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.02 % (842254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/1.02 % (842254)CaDiCaL version: 2.1.3
% 4.46/1.02 % (842254)Termination reason: Instruction limit
% 4.46/1.02 % (842254)Termination phase: Saturation
% 4.46/1.02 % (842254)Time elapsed: 0.078 s
% 4.46/1.02 % (842254)Peak memory usage: 13 MB
% 4.46/1.02 % (842254)Instructions burned: 132 (million)
% 4.46/1.02 % (842278)Instruction limit reached!
% 4.46/1.02 % (842278)------------------------------
% 4.46/1.02 % (842278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.46/1.02 % (842278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842278)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842278)Termination reason: Instruction limit
% 6.32/1.16 % (842278)Termination phase: Saturation
% 6.32/1.16 % (842278)Time elapsed: 0.057 s
% 6.32/1.16 % (842278)Peak memory usage: 12 MB
% 6.32/1.16 % (842278)Instructions burned: 132 (million)
% 6.32/1.16 % (842296)ott-21_1_sil=16000:fs=off:random_seed=2881897350:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.32/1.16 % (842300)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3136385722:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842298)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4006954512:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.32/1.16 % (842255)Instruction limit reached!
% 6.32/1.16 % (842255)------------------------------
% 6.32/1.16 % (842255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842255)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842255)Termination reason: Instruction limit
% 6.32/1.16 % (842255)Termination phase: Saturation
% 6.32/1.16 % (842255)Time elapsed: 0.128 s
% 6.32/1.16 % (842255)Peak memory usage: 13 MB
% 6.32/1.16 % (842255)Instructions burned: 159 (million)
% 6.32/1.16 % (842305)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2840935744:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.32/1.16 % (842312)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=999035450:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842321)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1709721579:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 6.32/1.16 % (842321)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.32/1.16 % (842296)Instruction limit reached!
% 6.32/1.16 % (842296)------------------------------
% 6.32/1.16 % (842296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842296)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842296)Termination reason: Instruction limit
% 6.32/1.16 % (842296)Termination phase: Saturation
% 6.32/1.16 % (842296)Time elapsed: 0.135 s
% 6.32/1.16 % (842296)Peak memory usage: 12 MB
% 6.32/1.16 % (842296)Instructions burned: 180 (million)
% 6.32/1.16 % (842335)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2315979110:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.32/1.16 % (842335)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.32/1.16 % (842298)Instruction limit reached!
% 6.32/1.16 % (842298)------------------------------
% 6.32/1.16 % (842298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842298)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842298)Termination reason: Instruction limit
% 6.32/1.16 % (842298)Termination phase: Saturation
% 6.32/1.16 % (842298)Time elapsed: 0.350 s
% 6.32/1.16 % (842298)Peak memory usage: 13 MB
% 6.32/1.16 % (842298)Instructions burned: 477 (million)
% 6.32/1.16 % (842282)Instruction limit reached!
% 6.32/1.16 % (842282)------------------------------
% 6.32/1.16 % (842282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842282)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842282)Termination reason: Instruction limit
% 6.32/1.16 % (842282)Termination phase: Saturation
% 6.32/1.16 % (842282)Time elapsed: 0.421 s
% 6.32/1.16 % (842282)Peak memory usage: 14 MB
% 6.32/1.16 % (842282)Instructions burned: 684 (million)
% 6.32/1.16 % (842358)fmb+10_1_sil=64000:random_seed=3682515623:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 6.32/1.16 % (842358)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842359)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=485935062:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842305)Instruction limit reached!
% 6.32/1.16 % (842305)------------------------------
% 6.32/1.16 % (842305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842305)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842305)Termination reason: Instruction limit
% 6.32/1.16 % (842305)Termination phase: Saturation
% 6.32/1.16 % (842305)Time elapsed: 0.373 s
% 6.32/1.16 % (842305)Peak memory usage: 17 MB
% 6.32/1.16 % (842305)Instructions burned: 1181 (million)
% 6.32/1.16 % (842361)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1524648335:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842364)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1585424916:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 6.32/1.16 % (842364)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.32/1.16 % (842364)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.32/1.16 % (842363)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1528005804:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 6.32/1.16 % (842363)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.32/1.16 % (842366)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1435723632:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842370)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3083794446:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842380)ott-2_1_sil=16000:newcnf=on:random_seed=2880916806:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 6.32/1.16 % (842380)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.32/1.16 % (842321)Instruction limit reached!
% 6.32/1.16 % (842321)------------------------------
% 6.32/1.16 % (842321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842321)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842321)Termination reason: Instruction limit
% 6.32/1.16 % (842321)Termination phase: Saturation
% 6.32/1.16 % (842321)Time elapsed: 0.394 s
% 6.32/1.16 % (842321)Peak memory usage: 14 MB
% 6.32/1.16 % (842321)Instructions burned: 692 (million)
% 6.32/1.16 % (842399)ott+10_1_sil=32000:tgt=ground:random_seed=1251790014:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.32/1.16 % (842335)Instruction limit reached!
% 6.32/1.16 % (842335)------------------------------
% 6.32/1.16 % (842335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842335)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842335)Termination reason: Instruction limit
% 6.32/1.16 % (842335)Termination phase: Saturation
% 6.32/1.16 % (842335)Time elapsed: 0.424 s
% 6.32/1.16 % (842335)Peak memory usage: 13 MB
% 6.32/1.16 % (842335)Instructions burned: 881 (million)
% 6.32/1.16 % (842445)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3895591897:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 6.32/1.16 % Exception at run slice level
% 6.32/1.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.32/1.16 % (842454)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3145122377:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 6.32/1.16 % (842454)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.32/1.16 % (842399) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-842243-842399"...
% 6.32/1.16 % (842399)...printing done.
% 6.32/1.16 % (842399)Refutation found. Thanks to Tanya!
% 6.32/1.16 % SZS status Theorem for theBenchmark
% 6.32/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 6.32/1.16 % (842399)------------------------------
% 6.32/1.16 % (842399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.32/1.16 % (842399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.16 % (842399)CaDiCaL version: 2.1.3
% 6.32/1.16 % (842399)Termination reason: Refutation
% 6.32/1.16 % (842399)Time elapsed: 0.260 s
% 6.32/1.16 % (842399)Peak memory usage: 14 MB
% 6.32/1.16 % (842399)Instructions burned: 570 (million)
% 6.32/1.16 % (842243)Success in time 0.922 s
% 6.32/1.16 % Vampire exiting
%------------------------------------------------------------------------------