%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP266^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:16:32 AM UTC 2026
% Result : Theorem 0.53s 0.38s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 14
% Syntax : Number of formulae : 194 ( 70 unt; 0 typ; 2 def)
% Number of atoms : 2171 ( 453 equ; 0 cnn)
% Maximal formula atoms : 20 ( 11 avg)
% Number of connectives : 3815 ( 36 ~; 296 |; 96 &;3060 @)
% ( 2 <=>; 148 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 93 ( 93 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 47 usr; 11 con; 0-4 aty)
% ( 124 !!; 53 ??; 0 @@+; 0 @@-)
% Number of variables : 709 ( 0 sgn 313 !; 2 ?; 709 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_15,type,
number: $i > $i > mworld > $o ).
thf(func_def_16,type,
string: $i > mworld > $o ).
thf(func_def_17,type,
in: $i > $i > $i > mworld > $o ).
thf(func_def_18,type,
do: $i > $i > $i > mworld > $o ).
thf(func_def_19,type,
entry_box: $i > mworld > $o ).
thf(func_def_20,type,
userid: $i > $i > mworld > $o ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vAND: $o > $o > $o ).
thf(func_def_34,type,
vIFF: $o > $o > $o ).
thf(func_def_35,type,
vOR: $o > $o > $o ).
thf(func_def_36,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
sK0: mworld ).
thf(func_def_40,type,
sK1: $i > $i > mworld ).
thf(func_def_41,type,
sK2: $i > $i > $i > $i > mworld ).
thf(func_def_42,type,
sK3: $i > $i > $i > $i > $i ).
thf(func_def_43,type,
sK4: $i > $i > $i > $i > $i ).
thf(func_def_45,type,
sK6: mworld > $i ).
thf(func_def_46,type,
sK7: mworld > $i > $i > $i > $i ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
! [X0: mworld,X2: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
& ( mrel @ X0 @ X1 ) )
=> ( mrel @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f12,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) )
= mexists_di ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f13,axiom,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f14,axiom,
( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f15,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] :
( mimplies @ ( mand @ ( string @ X1 ) @ ( entry_box @ X2 ) )
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X0 @ X3 @ X4 ) @ ( in @ X1 @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f16,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f17,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f20,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f21,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] :
( mimplies @ ( mand @ ( string @ X1 ) @ ( entry_box @ X2 ) )
@ ( mexists_di
@ ^ [X3: $i] :
( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X0 @ X3 @ X4 ) @ ( in @ X1 @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f23,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_di
@ ^ [Y3: $i] :
( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f27,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f29,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f31,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) )
= mexists_di ),
inference(rectify,[],[f12]) ).
thf(f32,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f36,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f38,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f40,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f42,plain,
( ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X4: $i] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f44,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X2 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X0 @ X1 ) ),
inference(rectify,[],[f10]) ).
thf(f46,plain,
! [X1: mworld,X0: mworld,X2: mworld] :
( ( ( ( mrel @ X0 @ X2 )
= $true )
& ( ( mrel @ X2 @ X1 )
= $true ) )
=> ( ( mrel @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f44]) ).
thf(f50,plain,
! [X1: mworld,X0: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X1 )
= $true )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X2 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f46]) ).
thf(f51,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X2 @ X1 )
!= $true )
| ( ( mrel @ X0 @ X1 )
= $true ) ),
inference(flattening,[],[f50]) ).
thf(f52,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X0 )
!= $true )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X1 @ X2 )
= $true ) ),
inference(rectify,[],[f51]) ).
thf(f53,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f54,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f55,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f56,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f36]) ).
thf(f57,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f59,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] :
( mexists_di
@ ^ [Y3: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f60,plain,
( ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f61,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_di
@ ^ [Y3: $i] :
( mbox
@ ( mforall_di
@ ^ [Y4: $i] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f62,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X0 )
!= $true )
| ( ( mrel @ X1 @ X2 )
= $true )
| ( ( mrel @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f63,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f66,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f40]) ).
thf(f71,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) )
@ ( userid @ u @ Y0 )
@ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f56,f53,f57,f54,f57,f55]) ).
thf(f72,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ ( userid @ u @ Y0 )
@ ( ^ [Y4: mworld > $o,Y5: mworld > $o,Y6: mworld] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ ( entry_box @ Y1 )
@ ( number @ Y1 @ one ) ) ) )
@ ( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: $i > mworld > $o,Y5: mworld] :
( !! @ $i
@ ^ [Y6: $i] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: $i] :
( ^ [Y5: mworld > $o,Y6: mworld > $o,Y7: mworld] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( do @ Y3 @ Y2 @ Y4 )
@ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f59,f53,f57,f54,f54,f54,f54,f55,f57,f55,f55,f57,f63,f64]) ).
thf(f73,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) )
@ ( entry_box @ Y0 )
@ ( number @ Y0 @ one ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f60,f53,f54,f57,f55]) ).
thf(f74,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( string @ Y1 )
@ ( entry_box @ Y2 ) )
@ ( ^ [Y3: $i > mworld > $o,Y4: mworld] :
( ?? @ $i
@ ^ [Y5: $i] : ( Y3 @ Y5 @ Y4 ) )
@ ^ [Y3: $i] :
( ^ [Y4: mworld > $o,Y5: mworld] :
( !! @ mworld
@ ^ [Y6: mworld] :
( ( mrel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ ( ^ [Y4: $i > mworld > $o,Y5: mworld] :
( !! @ $i
@ ^ [Y6: $i] : ( Y4 @ Y6 @ Y5 ) )
@ ^ [Y4: $i] :
( ^ [Y5: mworld > $o,Y6: mworld > $o,Y7: mworld] :
( ( Y5 @ Y7 )
=> ( Y6 @ Y7 ) )
@ ( do @ Y0 @ Y3 @ Y4 )
@ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f61,f53,f57,f63,f63,f63,f64,f55,f54,f57,f63,f64]) ).
thf(f75,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( number @ Y2 @ one @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( userid @ u @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f76,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y4 @ Y3 @ Y6 @ Y5 )
=> ( in @ Y1 @ Y2 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( ( number @ Y2 @ one @ Y5 )
& ( entry_box @ Y2 @ Y5 )
& ( userid @ u @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f75]) ).
thf(f77,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( ( number @ Y1 @ one @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f78,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( ( number @ Y1 @ one @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( mrel @ mactual @ sK0 )
= $true ),
inference(imp_proxy_clausification,[],[f77]) ).
thf(f80,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y3 @ Y2 @ Y5 @ Y4 )
=> ( in @ Y0 @ Y1 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ sK0 @ Y4 )
=> ( ( number @ Y1 @ one @ Y4 )
& ( entry_box @ Y1 @ Y4 )
& ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f81,plain,
! [X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( ( number @ Y0 @ one @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( userid @ u @ X1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ Y2 @ Y1 @ Y4 @ Y3 )
=> ( in @ X1 @ Y0 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ sK0 @ Y3 )
=> ( ( number @ Y0 @ one @ Y3 )
& ( entry_box @ Y0 @ Y3 )
& ( userid @ u @ X1 @ Y3 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( ( number @ X2 @ one @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( userid @ u @ X1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ Y1 @ Y0 @ Y3 @ Y2 )
=> ( in @ X1 @ X2 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK0 @ Y2 )
=> ( ( number @ X2 @ one @ Y2 )
& ( entry_box @ X2 @ Y2 )
& ( userid @ u @ X1 @ Y2 ) ) ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i] :
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( ( number @ X2 @ one @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( userid @ u @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $false
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ Y0 @ X3 @ Y2 @ Y1 )
=> ( in @ X1 @ X2 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK0 @ Y1 )
=> ( ( number @ X2 @ one @ Y1 )
& ( entry_box @ X2 @ Y1 )
& ( userid @ u @ X1 @ Y1 ) ) ) ) )
@ X4 ) ),
inference(pi_proxy_clausification,[],[f85]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f88,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) )
@ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f88]) ).
thf(f90,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X4 @ X3 @ Y1 @ Y0 )
=> ( in @ X1 @ X2 @ Y1 @ Y0 ) ) ) )
@ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ( number @ X2 @ one @ Y0 )
& ( entry_box @ X2 @ Y0 )
& ( userid @ u @ X1 @ Y0 ) ) )
@ ( sK1 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( mrel @ sK0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) )
| ( $false
= ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
=> ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
=> ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( mrel @ sK0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
=> ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f91]) ).
thf(f94,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( mrel @ sK0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( mrel @ sK0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f96,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) ) ) )
| ( ( mrel @ sK0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f97,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( mrel @ sK0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) ) ) )
| ( $false
= ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK3 @ X1 @ X2 @ X3 @ X4 ) ) )
| ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( do @ X4 @ X3 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
= $false )
| ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( do @ X4 @ X3 @ ( sK3 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( ( mrel @ sK0 @ ( sK1 @ X1 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) )
& ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK4 @ X1 @ X3 @ X4 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f98]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK4 @ X1 @ X3 @ X4 @ X2 ) )
= $false )
| ( $false
= ( ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) )
& ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
@ ( sK4 @ X1 @ X3 @ X4 @ X2 ) )
= $false )
| ( $false
= ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( ( do @ X4 @ X3 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
=> ( in @ X1 @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X1 @ X2 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( do @ X4 @ X3 @ ( sK4 @ X1 @ X3 @ X4 @ X2 ) @ ( sK2 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( userid @ u @ X1 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( number @ X2 @ one @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( entry_box @ X2 @ ( sK1 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( number @ Y0 @ one @ Y1 )
& ( entry_box @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f111,plain,
( ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( ( number @ Y0 @ one @ Y1 )
& ( entry_box @ Y0 @ Y1 ) ) ) )
@ sK5 )
= $true ),
inference(sigma_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( number @ sK5 @ one @ Y0 )
& ( entry_box @ sK5 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( number @ sK5 @ one @ Y0 )
& ( entry_box @ sK5 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( number @ sK5 @ one @ X1 )
& ( entry_box @ sK5 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( number @ sK5 @ one @ X1 )
& ( entry_box @ sK5 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( entry_box @ sK5 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X1: mworld] :
( ( ( number @ sK5 @ one @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f118,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( string @ Y1 @ Y2 )
& ( userid @ u @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f119,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( ( string @ Y1 @ Y2 )
& ( userid @ u @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( string @ Y0 @ Y1 )
& ( userid @ u @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X1: mworld] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( string @ Y0 @ Y1 )
& ( userid @ u @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X1: mworld] :
( ( ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( string @ Y0 @ Y1 )
& ( userid @ u @ Y0 @ Y1 ) ) ) )
@ ( sK6 @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( string @ ( sK6 @ X1 ) @ Y0 )
& ( userid @ u @ ( sK6 @ X1 ) @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f124,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( string @ ( sK6 @ X1 ) @ Y0 )
& ( userid @ u @ ( sK6 @ X1 ) @ Y0 ) ) )
@ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ X2 )
=> ( ( string @ ( sK6 @ X1 ) @ X2 )
& ( userid @ u @ ( sK6 @ X1 ) @ X2 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( string @ ( sK6 @ X1 ) @ X2 )
& ( userid @ u @ ( sK6 @ X1 ) @ X2 ) )
= $true )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: mworld,X1: mworld] :
( ( ( userid @ u @ ( sK6 @ X1 ) @ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: mworld,X1: mworld] :
( ( ( string @ ( sK6 @ X1 ) @ X2 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( entry_box @ Y3 @ Y0 )
& ( string @ Y2 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f130,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( entry_box @ Y3 @ Y0 )
& ( string @ Y2 @ Y0 ) )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y0 @ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( ( do @ Y1 @ Y4 @ Y6 @ Y5 )
=> ( in @ Y2 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( entry_box @ Y2 @ X1 )
& ( string @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( entry_box @ Y2 @ X1 )
& ( string @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( entry_box @ Y2 @ X1 )
& ( string @ Y1 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ X1 @ Y4 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ( do @ Y0 @ Y3 @ Y5 @ Y4 )
=> ( in @ Y1 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( entry_box @ Y1 @ X1 )
& ( string @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( entry_box @ Y1 @ X1 )
& ( string @ Y0 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( do @ X2 @ Y2 @ Y4 @ Y3 )
=> ( in @ Y0 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( entry_box @ Y0 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( ( entry_box @ Y0 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( do @ X2 @ Y1 @ Y3 @ Y2 )
=> ( in @ X3 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( entry_box @ X4 @ X1 )
& ( string @ X3 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) )
@ ( sK7 @ X1 @ X3 @ X4 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( $false
= ( entry_box @ X4 @ X1 ) )
| ( ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( do @ X2 @ Y0 @ Y2 @ Y1 )
=> ( in @ X3 @ X4 @ Y2 @ Y1 ) ) ) ) )
@ ( sK7 @ X1 @ X3 @ X4 @ X2 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( string @ X3 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i] :
( ( ( string @ X3 @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X2 @ ( sK7 @ X1 @ X3 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( ( string @ X3 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( do @ X2 @ ( sK7 @ X1 @ X3 @ X4 @ X2 ) @ Y1 @ Y0 )
=> ( in @ X3 @ X4 @ Y1 @ Y0 ) ) ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( string @ X3 @ X1 )
= $false )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( ( ( mrel @ X1 @ X5 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X2 @ ( sK7 @ X1 @ X3 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: mworld,X4: $i,X5: mworld] :
( ( ( string @ X3 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( do @ X2 @ ( sK7 @ X1 @ X3 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( entry_box @ X4 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( do @ X2 @ ( sK7 @ X1 @ X3 @ X4 @ X2 ) @ Y0 @ X5 )
=> ( in @ X3 @ X4 @ Y0 @ X5 ) )
@ X6 )
= $true )
| ( ( string @ X3 @ X1 )
= $false )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( string @ X3 @ X1 )
= $false )
| ( ( ( do @ X2 @ ( sK7 @ X1 @ X3 @ X4 @ X2 ) @ X6 @ X5 )
=> ( in @ X3 @ X4 @ X6 @ X5 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: mworld,X6: $i,X4: $i,X5: mworld] :
( ( $false
= ( do @ X2 @ ( sK7 @ X1 @ X3 @ X4 @ X2 ) @ X6 @ X5 ) )
| ( $false
= ( entry_box @ X4 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X5 ) )
| ( ( string @ X3 @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( in @ X3 @ X4 @ X6 @ X5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( ( mrel @ sK0 @ ( sK1 @ X4 @ X5 ) )
= $true )
| ( ( in @ X2 @ X3 @ ( sK3 @ X4 @ X5 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( string @ X2 @ X1 ) )
| ( $false
= ( entry_box @ X3 @ X1 ) )
| ( $false
= ( mrel @ X1 @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) ) ),
inference(constrained_superposition,[],[f103,f148]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( ( in @ X2 @ X3 @ ( sK3 @ X4 @ X5 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true )
| ( $false
= ( entry_box @ X3 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( mrel @ sK0 @ ( sK1 @ X4 @ X5 ) )
= $true )
| ( $false
= ( mrel @ X1 @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( string @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( $false
= ( entry_box @ X3 @ X1 ) )
| ( $false
= ( userid @ u @ X4 @ ( sK1 @ X4 @ X5 ) ) )
| ( ( entry_box @ X5 @ ( sK1 @ X4 @ X5 ) )
= $false )
| ( ( in @ X2 @ X3 @ ( sK4 @ X4 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true )
| ( $false
= ( mrel @ X1 @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false = $true )
| ( $false
= ( string @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( number @ X5 @ one @ ( sK1 @ X4 @ X5 ) ) ) ),
inference(constrained_superposition,[],[f109,f148]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X0: $i,X1: mworld,X4: $i,X5: $i] :
( ( ( in @ X2 @ X3 @ ( sK4 @ X4 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X0 @ X5 ) @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) )
= $true )
| ( $false
= ( string @ X2 @ X1 ) )
| ( $false
= ( mrel @ X1 @ ( sK2 @ ( sK7 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X0 @ X5 ) ) )
| ( $false
= ( number @ X5 @ one @ ( sK1 @ X4 @ X5 ) ) )
| ( $false
= ( entry_box @ X3 @ X1 ) )
| ( ( entry_box @ X5 @ ( sK1 @ X4 @ X5 ) )
= $false )
| ( $false
= ( userid @ u @ X4 @ ( sK1 @ X4 @ X5 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f153]) ).
thf(f157,plain,
( ( $false = $true )
| ( ( entry_box @ sK5 @ sK0 )
= $true ) ),
inference(constrained_superposition,[],[f116,f79]) ).
thf(f162,plain,
( ( entry_box @ sK5 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f157]) ).
thf(f166,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false = $true )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ ( sK2 @ ( sK7 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(constrained_superposition,[],[f102,f151]) ).
thf(f167,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ ( sK2 @ ( sK7 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false = $true )
| ( $false
= ( entry_box @ X1 @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f166]) ).
thf(f168,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( mrel @ X2 @ ( sK2 @ ( sK7 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( entry_box @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f167]) ).
thf(f172,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( string @ X0 @ sK0 ) )
| ( $false = $true )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ sK0 ) ) ),
inference(constrained_superposition,[],[f168,f95]) ).
thf(f176,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( string @ X0 @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f172]) ).
thf(f177,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f183,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( string @ X0 @ sK0 ) ) ),
inference(forward_demodulation,[],[f177,f79]) ).
thf(f184,plain,
! [X0: $i,X1: $i] :
( ( ( mrel @ sK0 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false
= ( string @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f190,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( mrel @ X2 @ ( sK2 @ ( sK7 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) )
| ( $false = $true )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ X2 ) ) ),
inference(constrained_superposition,[],[f108,f155]) ).
thf(f191,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) )
| ( $false = $true )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( mrel @ X2 @ ( sK2 @ ( sK7 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[],[f190]) ).
thf(f192,plain,
! [X2: mworld,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( mrel @ X2 @ ( sK2 @ ( sK7 @ X2 @ X0 @ X1 @ X3 ) @ X0 @ X3 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f197,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false = $true )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f97,f192]) ).
thf(f200,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) ) ),
inference(duplicate_literal_removal,[],[f197]) ).
thf(f201,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f205,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false = $true )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) ) ),
inference(forward_demodulation,[],[f201,f79]) ).
thf(f206,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( userid @ u @ X0 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( number @ X1 @ one @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ X0 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false
= ( string @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f209,plain,
! [X0: mworld] :
( ( $true != $true )
| ( ( mrel @ mactual @ X0 )
= $true )
| ( ( mrel @ sK0 @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f62,f79]) ).
thf(f219,plain,
! [X0: mworld] :
( ( ( mrel @ sK0 @ X0 )
!= $true )
| ( ( mrel @ mactual @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f223,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( string @ X0 @ sK0 ) )
| ( $true != $true )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( ( mrel @ mactual @ ( sK1 @ X0 @ X1 ) )
= $true ) ),
inference(constrained_superposition,[],[f219,f184]) ).
thf(f227,plain,
! [X0: $i,X1: $i] :
( ( ( mrel @ mactual @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f232,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( ( entry_box @ sK5 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( string @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f116,f227]) ).
thf(f234,plain,
! [X0: $i,X1: $i] :
( ( ( entry_box @ sK5 @ ( sK1 @ X0 @ X1 ) )
= $true )
| ( $false
= ( string @ X0 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f326,plain,
! [X0: mworld,X1: $i] :
( ( $false
= ( number @ X1 @ one @ ( sK1 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( mrel @ X0 @ ( sK1 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(constrained_superposition,[],[f127,f206]) ).
thf(f339,plain,
! [X0: mworld,X1: $i] :
( ( $false
= ( number @ X1 @ one @ ( sK1 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK1 @ ( sK6 @ X0 ) @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ sK0 ) )
| ( $false
= ( entry_box @ X1 @ ( sK1 @ ( sK6 @ X0 ) @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f326]) ).
thf(f371,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false = $true )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(constrained_superposition,[],[f117,f339]) ).
thf(f381,plain,
! [X0: mworld] :
( ( $false
= ( entry_box @ sK5 @ sK0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f371]) ).
thf(f383,plain,
! [X0: mworld] :
( ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( mrel @ mactual @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f381,f162]) ).
thf(f384,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( mrel @ X0 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ X0 ) @ sK0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ X0 ) @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f383]) ).
thf(f390,plain,
( ( $false = $true )
| ( $false = $true )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(constrained_superposition,[],[f384,f227]) ).
thf(f415,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ( $false = $true )
| ( $false
= ( entry_box @ sK5 @ sK0 ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f390]) ).
thf(f416,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f415]) ).
thf(f436,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ( $false = $true )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) ) ),
inference(forward_demodulation,[],[f416,f66]) ).
thf(f437,plain,
( ( $false
= ( entry_box @ sK5 @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f436]) ).
thf(f455,definition,
( spl8_1
<=> ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f457,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f455]) ).
thf(f463,definition,
( spl8_3
<=> ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f465,plain,
( ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f463]) ).
thf(f468,plain,
( ( $false = $true )
| ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) ) ),
inference(forward_demodulation,[],[f437,f162]) ).
thf(f469,plain,
( ( $false
= ( entry_box @ sK5 @ ( sK1 @ ( sK6 @ mactual ) @ sK5 ) ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f468]) ).
thf(f495,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f469,f463,f455]) ).
thf(f505,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ( $false
= ( entry_box @ sK5 @ sK0 ) )
| ( $false = $true )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f465,f234]) ).
thf(f508,plain,
( ( $false
= ( entry_box @ sK5 @ sK0 ) )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f505]) ).
thf(f512,plain,
( ( $false = $true )
| ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl8_3 ),
inference(forward_demodulation,[],[f508,f162]) ).
thf(f513,plain,
( ( $false
= ( string @ ( sK6 @ mactual ) @ sK0 ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f520,plain,
( spl8_1
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f513,f463,f455]) ).
thf(f522,plain,
( ( $false
= ( mrel @ mactual @ sK0 ) )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f457,f128]) ).
thf(f525,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f522]) ).
thf(f528,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ sK0 ) )
| ~ spl8_1 ),
inference(forward_demodulation,[],[f525,f66]) ).
thf(f529,plain,
( ( $false
= ( mrel @ mactual @ sK0 ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f528]) ).
thf(f533,plain,
( ( $false = $true )
| ~ spl8_1 ),
inference(forward_demodulation,[],[f529,f79]) ).
thf(f534,plain,
( $false
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f535,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f534]) ).
cnf(s4,plain,
( spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f495]) ).
cnf(s9,plain,
( spl8_1
| ~ spl8_3 ),
inference(sat_conversion,[],[f520]) ).
cnf(s14,plain,
~ spl8_1,
inference(sat_conversion,[],[f535]) ).
cnf(s15,plain,
~ spl8_3,
inference(rat,[],[s9,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s4,s15,s14]) ).
thf(f536,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP266^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n010.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 11:47:27 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running higher-order theorem proving
% 0.10/0.27 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
% 0.53/0.38 % (2755361)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.53/0.38 % (2755367)lrs+10_16_si=on:nwc=1.5:random_seed=2447623332:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.53/0.38 % (2755370)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2591338876:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.53/0.38 % (2755366)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3008432611:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.53/0.38 % (2755369)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=2898221464: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)
% 0.53/0.38 % (2755368)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1796373909:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.53/0.38 % (2755372)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.53/0.38 % (2755372)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
% 0.53/0.38 % (2755368)Instruction limit reached!
% 0.53/0.38 % (2755368)------------------------------
% 0.53/0.38 % (2755368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.38 % (2755368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.38 % (2755368)CaDiCaL version: 2.1.3
% 0.53/0.38 % (2755368)Termination reason: Instruction limit
% 0.53/0.38 % (2755368)Termination phase: Saturation
% 0.53/0.38 % (2755368)Time elapsed: 0.002 s
% 0.53/0.38 % (2755368)Peak memory usage: 10 MB
% 0.53/0.38 % (2755368)Instructions burned: 4 (million)
% 0.53/0.38 % (2755371)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3680891565:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.53/0.38 % (2755372)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=1327226965:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.53/0.38 % (2755370)Instruction limit reached!
% 0.53/0.38 % (2755370)------------------------------
% 0.53/0.38 % (2755370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.38 % (2755370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.38 % (2755370)CaDiCaL version: 2.1.3
% 0.53/0.38 % (2755370)Termination reason: Instruction limit
% 0.53/0.38 % (2755370)Termination phase: Saturation
% 0.53/0.38 % (2755370)Time elapsed: 0.013 s
% 0.53/0.38 % (2755370)Peak memory usage: 11 MB
% 0.53/0.38 % (2755370)Instructions burned: 24 (million)
% 0.53/0.38 % (2755367)Instruction limit reached!
% 0.53/0.38 % (2755367)------------------------------
% 0.53/0.38 % (2755367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.38 % (2755367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.38 % (2755367)CaDiCaL version: 2.1.3
% 0.53/0.38 % (2755367)Termination reason: Instruction limit
% 0.53/0.38 % (2755367)Termination phase: Saturation
% 0.53/0.38 % (2755367)Time elapsed: 0.014 s
% 0.53/0.38 % (2755367)Peak memory usage: 12 MB
% 0.53/0.38 % (2755367)Instructions burned: 19 (million)
% 0.53/0.38 % (2755366) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2755361-2755366"...
% 0.53/0.38 % (2755381)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3220638249:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.53/0.38 % (2755379)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=798141255:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.53/0.38 % (2755381)Instruction limit reached!
% 0.53/0.38 % (2755381)------------------------------
% 0.53/0.38 % (2755381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.38 % (2755381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.38 % (2755381)CaDiCaL version: 2.1.3
% 0.53/0.38 % (2755381)Termination reason: Instruction limit
% 0.53/0.38 % (2755381)Termination phase: Saturation
% 0.53/0.38 % (2755381)Time elapsed: 0.003 s
% 0.53/0.38 % (2755381)Peak memory usage: 11 MB
% 0.53/0.38 % (2755381)Instructions burned: 5 (million)
% 0.53/0.38 % (2755379)Instruction limit reached!
% 0.53/0.38 % (2755379)------------------------------
% 0.53/0.38 % (2755379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.38 % (2755379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.38 % (2755379)CaDiCaL version: 2.1.3
% 0.53/0.38 % (2755379)Termination reason: Instruction limit
% 0.53/0.38 % (2755379)Termination phase: Property scanning
% 0.53/0.38 % (2755379)Time elapsed: 0.005 s
% 0.53/0.38 % (2755379)Peak memory usage: 10 MB
% 0.53/0.38 % (2755379)Instructions burned: 3 (million)
% 0.53/0.38 % (2755382)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.38 % (2755371)Instruction limit reached!
% 0.53/0.38 % (2755371)------------------------------
% 0.53/0.38 % (2755371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.38 % (2755371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.38 % (2755371)CaDiCaL version: 2.1.3
% 0.53/0.38 % (2755371)Termination reason: Instruction limit
% 0.53/0.38 % (2755371)Termination phase: Saturation
% 0.53/0.38 % (2755371)Time elapsed: 0.040 s
% 0.53/0.38 % (2755371)Peak memory usage: 12 MB
% 0.53/0.38 % (2755371)Instructions burned: 82 (million)
% 0.53/0.38 % (2755382)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4202639592:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.53/0.38 % (2755366)...printing done.
% 0.53/0.38 % (2755366)Refutation found. Thanks to Tanya!
% 0.53/0.38 % SZS status Theorem for theBenchmark
% 0.53/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.53/0.38 % (2755366)------------------------------
% 0.53/0.38 % (2755366)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.38 % (2755366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.38 % (2755366)CaDiCaL version: 2.1.3
% 0.53/0.38 % (2755366)Termination reason: Refutation
% 0.53/0.38 % (2755366)Time elapsed: 0.049 s
% 0.53/0.38 % (2755366)Peak memory usage: 13 MB
% 0.53/0.38 % (2755366)Instructions burned: 78 (million)
% 0.53/0.38 % (2755361)Success in time 0.101 s
% 0.53/0.38 % Vampire exiting
%------------------------------------------------------------------------------