%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS272^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:11:54 AM UTC 2026
% Result : Theorem 1.30s 0.56s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 24
% Syntax : Number of formulae : 339 ( 114 unt; 0 typ; 9 def)
% Number of atoms : 6140 (1331 equ; 0 cnn)
% Maximal formula atoms : 23 ( 18 avg)
% Number of connectives : 10514 ( 930 ~;1578 |; 0 &;7381 @)
% ( 9 <=>; 239 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 197 ( 197 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 78 usr; 16 con; 0-4 aty)
% ( 377 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1439 ( 0 sgn 706 !; 0 ?;1439 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
string: mu > $i > $o ).
thf(func_def_37,type,
in: mu > mu > mu > $i > $o ).
thf(func_def_38,type,
do: mu > mu > mu > $i > $o ).
thf(func_def_39,type,
number: mu > mu > $i > $o ).
thf(func_def_40,type,
entry_box: mu > $i > $o ).
thf(func_def_41,type,
userid: mu > mu > $i > $o ).
thf(func_def_42,type,
one: mu ).
thf(func_def_43,type,
u: mu ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_58,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_64,type,
sK2: mu > mu > mu > mu > $i ).
thf(func_def_65,type,
sK3: mu > mu > $i ).
thf(func_def_66,type,
sK4: mu > mu > mu > mu > mu ).
thf(func_def_67,type,
sK5: $i > mu ).
thf(func_def_68,type,
sK6: $i > mu ).
thf(func_def_69,type,
sK7: $i > mu ).
thf(func_def_70,type,
sK8: $i > mu > mu > mu > mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f16,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mexists_ind) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f37,axiom,
! [X0: $i] : ( exists_in_world @ one @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_one_ax) ).
thf(f39,axiom,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f40,axiom,
( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f41,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] :
( mimplies @ ( mand @ ( string @ X1 ) @ ( entry_box @ X2 ) )
@ ( mexists_ind
@ ^ [X3: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X4: mu] : ( mimplies @ ( do @ X0 @ X3 @ X4 ) @ ( in @ X1 @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(f42,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] :
( mexists_ind
@ ^ [X3: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X4: mu] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f43,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] :
( mexists_ind
@ ^ [X3: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X4: mu] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
thf(f46,plain,
! [X0: $i] : ( exists_in_world @ one @ X0 ),
inference(rectify,[],[f37]) ).
thf(f47,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( exists_in_world @ one @ Y0 ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f49,plain,
( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ X0 ) @ ( number @ X0 @ one ) ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f50,plain,
( $true
= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f56,plain,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ X0 ) @ ( string @ X0 ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f57,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f59,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f62,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f63,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f70,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] :
( mexists_ind
@ ^ [X3: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ X0 ) @ ( mand @ ( entry_box @ X1 ) @ ( number @ X1 @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X4: mu] : ( mimplies @ ( do @ X3 @ X2 @ X4 ) @ ( in @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f71,plain,
( $true
= ( ~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] :
( mexists_ind
@ ^ [Y2: mu] :
( mexists_ind
@ ^ [Y3: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y4: mu] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f78,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f79,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f78]) ).
thf(f92,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f93,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f94,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f99,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f100,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f104,plain,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mforall_ind
@ ^ [X2: mu] :
( mimplies @ ( mand @ ( string @ X1 ) @ ( entry_box @ X2 ) )
@ ( mexists_ind
@ ^ [X3: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X4: mu] : ( mimplies @ ( do @ X0 @ X3 @ X4 ) @ ( in @ X1 @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f105,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_ind
@ ^ [Y3: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y4: mu] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f104]) ).
thf(f107,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f108,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f107]) ).
thf(f109,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f110,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f112,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f111]) ).
thf(f118,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f112]) ).
thf(f119,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ Y0 ) @ ( string @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f122,plain,
( $true
= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ Y0 ) @ ( number @ Y0 @ one ) ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f123,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f125,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f136,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f79]) ).
thf(f138,plain,
( $true
= ( ~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] :
( mexists_ind
@ ^ [Y2: mu] :
( mexists_ind
@ ^ [Y3: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ Y0 ) @ ( mand @ ( entry_box @ Y1 ) @ ( number @ Y1 @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y4: mu] : ( mimplies @ ( do @ Y3 @ Y2 @ Y4 ) @ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f139,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mforall_ind
@ ^ [Y2: mu] :
( mimplies @ ( mand @ ( string @ Y1 ) @ ( entry_box @ Y2 ) )
@ ( mexists_ind
@ ^ [Y3: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y4: mu] : ( mimplies @ ( do @ Y0 @ Y3 @ Y4 ) @ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f142,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f143,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f144,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( exists_in_world @ one @ Y0 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f147,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f149,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f153,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f158,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f163,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f147,f153,f143,f153,f153]) ).
thf(f164,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f125,f143,f153]) ).
thf(f169,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f123,f153,f158,f153]) ).
thf(f172,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ ( userid @ u @ Y0 )
@ ( string @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f119,f118,f142,f169,f142,f163]) ).
thf(f173,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ ( entry_box @ Y0 )
@ ( number @ Y0 @ one ) ) ) ) ) ),
inference(definition_unfolding,[],[f122,f118,f169,f142,f163]) ).
thf(f175,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f136,f149]) ).
thf(f176,plain,
( $true
= ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mu > $i > $o,Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) )
@ ^ [Y3: mu] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( Y2 @ Y3 ) ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: mu > $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: mu > $i > $o,Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) )
@ ^ [Y4: mu] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( Y3 @ Y4 ) ) ) )
@ ^ [Y3: mu] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( userid @ u @ Y0 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y7 @ Y8 )
| ( Y6 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( entry_box @ Y1 )
@ ( number @ Y1 @ one ) ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
@ ( ^ [Y4: mu > $i > $o,Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) )
@ ^ [Y4: mu] :
( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $o,Y8: $i > $o,Y9: $i] :
( ( Y8 @ Y9 )
| ( Y7 @ Y9 ) )
@ ( ^ [Y7: $i > $o,Y8: $i] :
~ ( Y7 @ Y8 )
@ Y5 )
@ Y6 )
@ ( do @ Y3 @ Y2 @ Y4 )
@ ( in @ Y0 @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f118,f142,f169,f169,f169,f169,f163,f142,f163,f163,f142,f158,f164]) ).
thf(f177,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y6 @ Y7 )
| ( Y5 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y6 @ Y7 )
| ( Y5 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( string @ Y1 )
@ ( entry_box @ Y2 ) )
@ ( ^ [Y3: mu > $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: mu > $i > $o,Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) )
@ ^ [Y4: mu] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( Y3 @ Y4 ) ) ) )
@ ^ [Y3: mu] :
( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
@ ( ^ [Y4: mu > $i > $o,Y5: $i] :
( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) )
@ ^ [Y4: mu] :
( ^ [Y5: $i > $o,Y6: $i > $o] :
( ^ [Y7: $i > $o,Y8: $i > $o,Y9: $i] :
( ( Y8 @ Y9 )
| ( Y7 @ Y9 ) )
@ ( ^ [Y7: $i > $o,Y8: $i] :
~ ( Y7 @ Y8 )
@ Y5 )
@ Y6 )
@ ( do @ Y0 @ Y3 @ Y4 )
@ ( in @ Y1 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f139,f118,f142,f158,f158,f158,f164,f163,f169,f142,f158,f164]) ).
thf(f179,plain,
( $true
= ( !! @ $i @ ( exists_in_world @ one ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f180,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y3 @ Y4 @ Y7 @ Y6 )
| ~ ( do @ Y2 @ Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) )
| ~ ~ ( ~ ( entry_box @ Y4 @ Y1 )
| ~ ( string @ Y3 @ Y1 ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f181,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y3 @ Y4 @ Y7 @ Y6 )
| ~ ( do @ Y2 @ Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) )
| ~ ( entry_box @ Y4 @ Y1 )
| ~ ( string @ Y3 @ Y1 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(boolean_simplification,[],[f180]) ).
thf(f182,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f183,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ~ ( string @ Y2 @ Y3 )
| ~ ( userid @ u @ Y2 @ Y3 ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f184,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 ) )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f185,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 ) )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f184]) ).
thf(f186,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 ) )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f185]) ).
thf(f187,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 ) )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f186]) ).
thf(f188,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 ) )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(boolean_simplification,[],[f187]) ).
thf(f189,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f188]) ).
thf(f191,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( number @ Y1 @ one @ Y2 )
| ~ ( entry_box @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f192,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f193,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ~ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( ~ ( number @ Y3 @ one @ Y6 )
| ~ ( entry_box @ Y3 @ Y6 )
| ~ ( userid @ u @ Y2 @ Y6 ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ( in @ Y1 @ Y2 @ Y6 @ Y5 )
| ~ ( do @ Y4 @ Y3 @ Y6 @ Y5 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( ~ ( number @ Y2 @ one @ Y5 )
| ~ ( entry_box @ Y2 @ Y5 )
| ~ ( userid @ u @ Y1 @ Y5 ) )
| ~ ( rel_s4 @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ( in @ Y1 @ Y2 @ Y6 @ Y5 )
| ~ ( do @ Y4 @ Y3 @ Y6 @ Y5 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( ~ ( number @ Y2 @ one @ Y5 )
| ~ ( entry_box @ Y2 @ Y5 )
| ~ ( userid @ u @ Y1 @ Y5 ) )
| ~ ( rel_s4 @ Y0 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y0 @ Y1 @ Y5 @ Y4 )
| ~ ( do @ Y3 @ Y2 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ~ ( number @ Y1 @ one @ Y4 )
| ~ ( entry_box @ Y1 @ Y4 )
| ~ ( userid @ u @ Y0 @ Y4 ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
( ( ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y0 @ Y1 @ Y5 @ Y4 )
| ~ ( do @ Y3 @ Y2 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ~ ( number @ Y1 @ one @ Y4 )
| ~ ( entry_box @ Y1 @ Y4 )
| ~ ( userid @ u @ Y0 @ Y4 ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f199,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f200,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y0 @ Y1 @ Y5 @ Y4 )
| ~ ( do @ Y3 @ Y2 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ~ ( number @ Y1 @ one @ Y4 )
| ~ ( entry_box @ Y1 @ Y4 )
| ~ ( userid @ u @ Y0 @ Y4 ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f201,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y0 @ Y1 @ Y5 @ Y4 )
| ~ ( do @ Y3 @ Y2 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ~ ( number @ Y1 @ one @ Y4 )
| ~ ( entry_box @ Y1 @ Y4 )
| ~ ( userid @ u @ Y0 @ Y4 ) )
| ~ ( rel_s4 @ sK1 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ X1 @ Y0 @ Y4 @ Y3 )
| ~ ( do @ Y2 @ Y1 @ Y4 @ Y3 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ~ ( number @ Y0 @ one @ Y3 )
| ~ ( entry_box @ Y0 @ Y3 )
| ~ ( userid @ u @ X1 @ Y3 ) )
| ~ ( rel_s4 @ sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X1: mu] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ X1 @ Y0 @ Y4 @ Y3 )
| ~ ( do @ Y2 @ Y1 @ Y4 @ Y3 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ~ ( number @ Y0 @ one @ Y3 )
| ~ ( entry_box @ Y0 @ Y3 )
| ~ ( userid @ u @ X1 @ Y3 ) )
| ~ ( rel_s4 @ sK1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f215,plain,
! [X2: mu,X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ X1 @ Y0 @ Y4 @ Y3 )
| ~ ( do @ Y2 @ Y1 @ Y4 @ Y3 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ~ ( number @ Y0 @ one @ Y3 )
| ~ ( entry_box @ Y0 @ Y3 )
| ~ ( userid @ u @ X1 @ Y3 ) )
| ~ ( rel_s4 @ sK1 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f216,plain,
! [X2: mu,X1: mu] :
( ( $true
= ( ( exists_in_world @ X2 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X1 @ X2 @ Y3 @ Y2 )
| ~ ( do @ Y1 @ Y0 @ Y3 @ Y2 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y2 )
| ~ ( entry_box @ X2 @ Y2 )
| ~ ( userid @ u @ X1 @ Y2 ) )
| ~ ( rel_s4 @ sK1 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X2: mu,X1: mu] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X1 @ X2 @ Y3 @ Y2 )
| ~ ( do @ Y1 @ Y0 @ Y3 @ Y2 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y2 )
| ~ ( entry_box @ X2 @ Y2 )
| ~ ( userid @ u @ X1 @ Y2 ) )
| ~ ( rel_s4 @ sK1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f219,plain,
! [X2: mu,X3: mu,X1: mu] :
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X1 @ X2 @ Y3 @ Y2 )
| ~ ( do @ Y1 @ Y0 @ Y3 @ Y2 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y2 )
| ~ ( entry_box @ X2 @ Y2 )
| ~ ( userid @ u @ X1 @ Y2 ) )
| ~ ( rel_s4 @ sK1 @ Y2 ) ) ) ) ) ) )
@ X3 )
= $true )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f220,plain,
! [X2: mu,X3: mu,X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ( exists_in_world @ X3 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X1 @ X2 @ Y2 @ Y1 )
| ~ ( do @ Y0 @ X3 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y1 )
| ~ ( entry_box @ X2 @ Y1 )
| ~ ( userid @ u @ X1 @ Y1 ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
! [X2: mu,X3: mu,X1: mu] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X1 @ X2 @ Y2 @ Y1 )
| ~ ( do @ Y0 @ X3 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y1 )
| ~ ( entry_box @ X2 @ Y1 )
| ~ ( userid @ u @ X1 @ Y1 ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X1 @ X2 @ Y2 @ Y1 )
| ~ ( do @ Y0 @ X3 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y1 )
| ~ ( entry_box @ X2 @ Y1 )
| ~ ( userid @ u @ X1 @ Y1 ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) )
@ X4 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ( exists_in_world @ X4 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X1 @ X2 @ Y1 @ Y0 )
| ~ ( do @ X4 @ X3 @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X1 @ X2 @ Y1 @ Y0 )
| ~ ( do @ X4 @ X3 @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X1 @ X2 @ Y1 @ Y0 )
| ~ ( do @ X4 @ X3 @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X1 @ X2 @ Y1 @ Y0 )
| ~ ( do @ X4 @ X3 @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X1 @ X2 @ Y1 @ Y0 )
| ~ ( do @ X4 @ X3 @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( $true
= ( exists_in_world @ one @ X1 ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f229,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X1 @ X2 @ Y1 @ Y0 )
| ~ ( do @ X4 @ X3 @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f232,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
=> ( ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
| ~ ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f233,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
=> ( ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
| ~ ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f235,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f236,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f238,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
| ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f240,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f241,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f242,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f243,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f244,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( rel_s4 @ sK1 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
=> ( ( in @ X1 @ X2 @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
| ~ ( do @ X4 @ X3 @ Y0 @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) )
@ ( sK4 @ X1 @ X2 @ X3 @ X4 ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f234]) ).
thf(f252,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
=> ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
| ~ ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f253,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
| ~ ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f252]) ).
thf(f255,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( ~ ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f253]) ).
thf(f256,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f253]) ).
thf(f257,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f258,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f259,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f254]) ).
thf(f263,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
| ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f264,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f266,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f268,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f269,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f275,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f256]) ).
thf(f278,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
| ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f279,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f281,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f282,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f283,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $true
= ( ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( $false
= ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( in @ X1 @ X2 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f286]) ).
thf(f292,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( ~ ( number @ X2 @ one @ Y0 )
| ~ ( entry_box @ X2 @ Y0 )
| ~ ( userid @ u @ X1 @ Y0 ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f257]) ).
thf(f294,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
| ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f296,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f297,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( ~ ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) ) )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f298,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
| ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f300,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( ~ ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) ) )
= $true )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f298]) ).
thf(f301,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) )
| ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $true
= ( ~ ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: mu,X3: mu,X1: mu,X4: mu] :
( ( $true
= ( do @ X4 @ X3 @ ( sK4 @ X1 @ X2 @ X3 @ X4 ) @ ( sK2 @ X4 @ X3 @ X1 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( entry_box @ X2 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X2 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( number @ X2 @ one @ ( sK3 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f349,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( number @ Y1 @ one @ Y2 )
| ~ ( entry_box @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f350,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( number @ Y0 @ one @ Y1 )
| ~ ( entry_box @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f349]) ).
thf(f351,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( number @ Y0 @ one @ Y1 )
| ~ ( entry_box @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( number @ Y0 @ one @ Y1 )
| ~ ( entry_box @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) )
@ ( sK6 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f351]) ).
thf(f355,plain,
! [X1: $i] :
( ( ( exists_in_world @ ( sK6 @ X1 ) @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ ( sK6 @ X1 ) @ one @ Y0 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ Y0 ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f356,plain,
! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ ( sK6 @ X1 ) @ one @ Y0 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ Y0 ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X1: $i] :
( $true
= ( exists_in_world @ ( sK6 @ X1 ) @ X1 ) ),
inference(imp_proxy_clausification,[],[f355]) ).
thf(f358,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( number @ ( sK6 @ X1 ) @ one @ Y0 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ Y0 ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f356]) ).
thf(f381,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ~ ( string @ Y2 @ Y3 )
| ~ ( userid @ u @ Y2 @ Y3 ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f382,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( string @ Y1 @ Y2 )
| ~ ( userid @ u @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f383,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( string @ Y1 @ Y2 )
| ~ ( userid @ u @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f382]) ).
thf(f384,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( string @ Y0 @ Y1 )
| ~ ( userid @ u @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f383]) ).
thf(f385,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( string @ Y0 @ Y1 )
| ~ ( userid @ u @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f384]) ).
thf(f386,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( string @ Y0 @ Y1 )
| ~ ( userid @ u @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( string @ Y0 @ Y1 )
| ~ ( userid @ u @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f386]) ).
thf(f398,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( string @ Y0 @ Y1 )
| ~ ( userid @ u @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) )
@ ( sK7 @ X2 ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f387]) ).
thf(f401,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ( exists_in_world @ ( sK7 @ X2 ) @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( string @ ( sK7 @ X2 ) @ Y0 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ Y0 ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f398]) ).
thf(f402,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( string @ ( sK7 @ X2 ) @ Y0 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ Y0 ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f401]) ).
thf(f403,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( exists_in_world @ ( sK7 @ X2 ) @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f401]) ).
thf(f404,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( string @ ( sK7 @ X2 ) @ Y0 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ Y0 ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f402]) ).
thf(f411,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( !! @ mu
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y3 @ Y4 @ Y7 @ Y6 )
| ~ ( do @ Y2 @ Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y6 ) ) ) ) )
| ~ ( entry_box @ Y4 @ Y1 )
| ~ ( string @ Y3 @ Y1 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f412,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ( in @ Y2 @ Y3 @ Y6 @ Y5 )
| ~ ( do @ Y1 @ Y4 @ Y6 @ Y5 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y5 ) ) ) ) )
| ~ ( entry_box @ Y3 @ Y0 )
| ~ ( string @ Y2 @ Y0 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f411]) ).
thf(f413,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ( in @ Y2 @ Y3 @ Y6 @ Y5 )
| ~ ( do @ Y1 @ Y4 @ Y6 @ Y5 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y5 ) ) ) ) )
| ~ ( entry_box @ Y3 @ Y0 )
| ~ ( string @ Y2 @ Y0 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f412]) ).
thf(f414,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y1 @ Y2 @ Y5 @ Y4 )
| ~ ( do @ Y0 @ Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y4 ) ) ) ) )
| ~ ( entry_box @ Y2 @ X2 )
| ~ ( string @ Y1 @ X2 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f413]) ).
thf(f415,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y1 @ Y2 @ Y5 @ Y4 )
| ~ ( do @ Y0 @ Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y4 ) ) ) ) )
| ~ ( entry_box @ Y2 @ X2 )
| ~ ( string @ Y1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f414]) ).
thf(f416,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y1 @ Y2 @ Y5 @ Y4 )
| ~ ( do @ Y0 @ Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y4 ) ) ) ) )
| ~ ( entry_box @ Y2 @ X2 )
| ~ ( string @ Y1 @ X2 ) ) ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f415]) ).
thf(f423,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y1 @ Y2 @ Y5 @ Y4 )
| ~ ( do @ Y0 @ Y3 @ Y5 @ Y4 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y4 ) ) ) ) )
| ~ ( entry_box @ Y2 @ X2 )
| ~ ( string @ Y1 @ X2 ) ) ) ) ) ) )
@ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f416]) ).
thf(f424,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $true
= ( ( exists_in_world @ X3 @ X2 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ Y0 @ Y1 @ Y4 @ Y3 )
| ~ ( do @ X3 @ Y2 @ Y4 @ Y3 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) ) ) )
| ~ ( entry_box @ Y1 @ X2 )
| ~ ( string @ Y0 @ X2 ) ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f423]) ).
thf(f425,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ Y0 @ Y1 @ Y4 @ Y3 )
| ~ ( do @ X3 @ Y2 @ Y4 @ Y3 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) ) ) )
| ~ ( entry_box @ Y1 @ X2 )
| ~ ( string @ Y0 @ X2 ) ) ) ) ) ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f424]) ).
thf(f430,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ Y0 @ Y1 @ Y4 @ Y3 )
| ~ ( do @ X3 @ Y2 @ Y4 @ Y3 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) ) ) )
| ~ ( entry_box @ Y1 @ X2 )
| ~ ( string @ Y0 @ X2 ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f425]) ).
thf(f431,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ( exists_in_world @ X4 @ X2 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X4 @ Y0 @ Y3 @ Y2 )
| ~ ( do @ X3 @ Y1 @ Y3 @ Y2 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) ) ) )
| ~ ( entry_box @ Y0 @ X2 )
| ~ ( string @ X4 @ X2 ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f430]) ).
thf(f432,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X4 @ Y0 @ Y3 @ Y2 )
| ~ ( do @ X3 @ Y1 @ Y3 @ Y2 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) ) ) )
| ~ ( entry_box @ Y0 @ X2 )
| ~ ( string @ X4 @ X2 ) ) ) ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f431]) ).
thf(f433,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X4 @ Y0 @ Y3 @ Y2 )
| ~ ( do @ X3 @ Y1 @ Y3 @ Y2 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) ) ) )
| ~ ( entry_box @ Y0 @ X2 )
| ~ ( string @ X4 @ X2 ) ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f432]) ).
thf(f434,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ( exists_in_world @ X5 @ X2 )
=> ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) )
| ~ ( entry_box @ X5 @ X2 )
| ~ ( string @ X4 @ X2 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f433]) ).
thf(f435,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) )
| ~ ( entry_box @ X5 @ X2 )
| ~ ( string @ X4 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f434]) ).
thf(f436,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( entry_box @ X5 @ X2 )
| ~ ( string @ X4 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f435]) ).
thf(f437,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( entry_box @ X5 @ X2 )
| ~ ( string @ X4 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f436]) ).
thf(f438,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( ~ ( entry_box @ X5 @ X2 ) )
= $true )
| ( $true
= ( ~ ( string @ X4 @ X2 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f437]) ).
thf(f439,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( string @ X4 @ X2 ) ) )
| ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f438]) ).
thf(f440,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f439]) ).
thf(f441,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X4 @ X5 @ Y2 @ Y1 )
| ~ ( do @ X3 @ Y0 @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) )
@ ( sK8 @ X2 @ X5 @ X4 @ X3 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f440]) ).
thf(f444,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( ( exists_in_world @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X4 @ X5 @ Y1 @ Y0 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f441]) ).
thf(f445,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X4 @ X5 @ Y1 @ Y0 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f444]) ).
thf(f446,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f444]) ).
thf(f447,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: mu] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X4 @ X5 @ Y1 @ Y0 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f445]) ).
thf(f448,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( number @ ( sK6 @ X1 ) @ one @ Y0 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ Y0 ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f449,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( ~ ( number @ ( sK6 @ X1 ) @ one @ X2 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ X2 ) )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f448]) ).
thf(f450,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( $true
= ( ~ ( ~ ( number @ ( sK6 @ X1 ) @ one @ X2 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f449]) ).
thf(f451,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ~ ( number @ ( sK6 @ X1 ) @ one @ X2 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ X2 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f450]) ).
thf(f452,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( number @ ( sK6 @ X1 ) @ one @ X2 )
| ~ ( entry_box @ ( sK6 @ X1 ) @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f451]) ).
thf(f453,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( entry_box @ ( sK6 @ X1 ) @ X2 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f452]) ).
thf(f454,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( number @ ( sK6 @ X1 ) @ one @ X2 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f452]) ).
thf(f455,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( number @ ( sK6 @ X1 ) @ one @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f454]) ).
thf(f456,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( entry_box @ ( sK6 @ X1 ) @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f453]) ).
thf(f457,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( string @ ( sK7 @ X2 ) @ Y0 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ Y0 ) )
| ~ ( rel_s4 @ X2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f404]) ).
thf(f458,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( ~ ( string @ ( sK7 @ X2 ) @ X3 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ X3 ) )
| ~ ( rel_s4 @ X2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f457]) ).
thf(f459,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X3 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( ~ ( string @ ( sK7 @ X2 ) @ X3 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ X3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f458]) ).
thf(f460,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( $true
= ( ~ ( ~ ( string @ ( sK7 @ X2 ) @ X3 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ X3 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f459]) ).
thf(f461,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( ~ ( string @ ( sK7 @ X2 ) @ X3 )
| ~ ( userid @ u @ ( sK7 @ X2 ) @ X3 ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f460]) ).
thf(f462,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( userid @ u @ ( sK7 @ X2 ) @ X3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f461]) ).
thf(f463,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( string @ ( sK7 @ X2 ) @ X3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f461]) ).
thf(f464,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( userid @ u @ ( sK7 @ X2 ) @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f462]) ).
thf(f465,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( string @ ( sK7 @ X2 ) @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f463]) ).
thf(f466,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X4 @ X5 @ Y1 @ Y0 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) )
@ X6 ) )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f447]) ).
thf(f467,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( ( in @ X4 @ X5 @ Y0 @ X6 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y0 @ X6 ) ) ) )
| ~ ( rel_s4 @ X2 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f466]) ).
thf(f468,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( ( in @ X4 @ X5 @ Y0 @ X6 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y0 @ X6 ) ) ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f467]) ).
thf(f469,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( ( in @ X4 @ X5 @ Y0 @ X6 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y0 @ X6 ) ) ) ) )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X6 )
= $false ) ),
inference(not_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X7: mu,X4: mu,X5: mu] :
( ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( ( in @ X4 @ X5 @ Y0 @ X6 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ Y0 @ X6 ) ) )
@ X7 ) )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X6 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f469]) ).
thf(f471,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X7: mu,X4: mu,X5: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( $true
= ( ( exists_in_world @ X7 @ X6 )
=> ( ( in @ X4 @ X5 @ X7 @ X6 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ X7 @ X6 ) ) ) )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X6 )
= $false ) ),
inference(beta-eta_normalization,[],[f470]) ).
thf(f472,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X7: mu,X4: mu,X5: mu] :
( ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X6 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( $true
= ( ( in @ X4 @ X5 @ X7 @ X6 )
| ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ X7 @ X6 ) ) )
| ( ( exists_in_world @ X7 @ X6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f471]) ).
thf(f473,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X7: mu,X4: mu,X5: mu] :
( ( ( ~ ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ X7 @ X6 ) )
= $true )
| ( ( exists_in_world @ X7 @ X6 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X6 )
= $false )
| ( $true
= ( in @ X4 @ X5 @ X7 @ X6 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f472]) ).
thf(f474,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X7: mu,X4: mu,X5: mu] :
( ( ( do @ X3 @ ( sK8 @ X2 @ X5 @ X4 @ X3 ) @ X7 @ X6 )
= $false )
| ( ( exists_in_world @ X5 @ X2 )
= $false )
| ( ( entry_box @ X5 @ X2 )
= $false )
| ( ( exists_in_world @ X7 @ X6 )
= $false )
| ( ( string @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X2 @ X6 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( in @ X4 @ X5 @ X7 @ X6 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f473]) ).
thf(f475,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( ( userid @ u @ X4 @ ( sK3 @ X4 @ X5 ) )
= $false )
| ( ( string @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( rel_s4 @ X6 @ X1 )
= $false )
| ( ( entry_box @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $false
= ( number @ X5 @ one @ ( sK3 @ X4 @ X5 ) ) )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( $false
= ( entry_box @ X5 @ ( sK3 @ X4 @ X5 ) ) )
| ( $true = $false )
| ( ( exists_in_world @ X5 @ sK1 )
= $false )
| ( $true
= ( in @ X3 @ X2 @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) ) ) ),
inference(superposition,[],[f474,f304]) ).
thf(f476,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( rel_s4 @ X6 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( entry_box @ X2 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X4 @ X5 ) ) )
| ( ( exists_in_world @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ sK1 )
= $false )
| ( $true
= ( in @ X3 @ X2 @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) ) )
| ( $true = $false )
| ( ( string @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X5 @ sK1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(superposition,[],[f474,f299]) ).
thf(f480,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( $true
= ( in @ X3 @ X2 @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( number @ X5 @ one @ ( sK3 @ X4 @ X5 ) ) )
| ( ( userid @ u @ X4 @ ( sK3 @ X4 @ X5 ) )
= $false )
| ( ( entry_box @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X5 @ ( sK3 @ X4 @ X5 ) ) )
| ( ( string @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X5 @ sK1 )
= $false )
| ( ( rel_s4 @ X6 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f475]) ).
thf(f481,plain,
! [X2: mu,X3: mu,X0: mu,X1: $i,X6: $i,X4: mu,X5: mu] :
( ( $true
= ( in @ X3 @ X2 @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) ) )
| ( ( string @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X4 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( entry_box @ X2 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X4 @ X5 ) ) )
| ( ( exists_in_world @ ( sK4 @ X4 @ X5 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X0 ) @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ X5 @ sK1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( rel_s4 @ X6 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ ( sK2 @ X0 @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ X4 @ X5 ) )
= $false )
| ( ( exists_in_world @ ( sK8 @ X1 @ X2 @ X3 @ X0 ) @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f476]) ).
thf(f486,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true = $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X3 ) @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( string @ X0 @ X2 )
= $false ) ),
inference(superposition,[],[f481,f281]) ).
thf(f491,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true = $false )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X3 ) @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false ) ),
inference(duplicate_literal_removal,[],[f486]) ).
thf(f492,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X3 ) @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f502,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $true = $false )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(superposition,[],[f267,f492]) ).
thf(f510,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $true = $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( entry_box @ X1 @ X2 )
= $false ) ),
inference(duplicate_literal_removal,[],[f502]) ).
thf(f511,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f510]) ).
thf(f522,plain,
! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( string @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X2 @ X1 ) ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X2 @ X1 ) ) ) ),
inference(superposition,[],[f242,f511]) ).
thf(f536,plain,
! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X2 @ X1 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( string @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[],[f522]) ).
thf(f537,plain,
! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( string @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X2 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f536]) ).
thf(f553,definition,
( spl9_3
<=> ! [X2: mu,X0: mu,X1: mu] :
( ( ( string @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X2 @ X1 ) ) )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f554,plain,
( ! [X2: mu,X0: mu,X1: mu] :
( ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X2 @ X1 ) ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( string @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f553]) ).
thf(f556,definition,
( spl9_4
<=> ! [X3: $i] :
( ( rel_s4 @ X3 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f557,plain,
( ! [X3: $i] :
( ( rel_s4 @ X3 @ sK1 )
= $false )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f556]) ).
thf(f568,plain,
( spl9_4
| spl9_3 ),
inference(avatar_split_clause,[],[f537,f553,f556]) ).
thf(f576,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X3 ) @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( $true = $false )
| ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false ) ),
inference(superposition,[],[f480,f287]) ).
thf(f580,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X3 ) @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( $true = $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f576]) ).
thf(f581,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( exists_in_world @ ( sK4 @ X0 @ X1 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X3 ) @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f580]) ).
thf(f600,plain,
( ( $true = $false )
| ~ spl9_4 ),
inference(superposition,[],[f557,f199]) ).
thf(f616,plain,
( $false
| ~ spl9_4 ),
inference(trivial_inequality_removal,[],[f600]) ).
thf(f617,plain,
~ spl9_4,
inference(avatar_contradiction_clause,[],[f616]) ).
thf(f618,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false ) ),
inference(superposition,[],[f581,f272]) ).
thf(f628,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f618]) ).
thf(f629,plain,
! [X2: $i,X3: mu,X0: mu,X1: mu,X4: $i] :
( ( $false
= ( rel_s4 @ X2 @ ( sK2 @ X3 @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ X0 @ X1 ) ) )
| ( ( entry_box @ X1 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( exists_in_world @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X3 @ sK1 ) )
| ( ( userid @ u @ X0 @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( rel_s4 @ X4 @ X2 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X0 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ X2 )
= $false )
| ( ( string @ X0 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( exists_in_world @ ( sK8 @ X2 @ X1 @ X0 @ X3 ) @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f628]) ).
thf(f636,plain,
( ! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X0 ) ) )
| ( $true = $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) )
| ~ spl9_3 ),
inference(superposition,[],[f554,f446]) ).
thf(f646,plain,
( ! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X0 ) ) )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( $true = $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( string @ X1 @ sK1 ) ) )
| ~ spl9_3 ),
inference(duplicate_literal_removal,[],[f636]) ).
thf(f647,plain,
( ! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X0 ) ) )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false ) )
| ~ spl9_3 ),
inference(trivial_inequality_removal,[],[f646]) ).
thf(f649,definition,
( spl9_8
<=> ! [X0: mu,X1: mu] :
( ( $false
= ( string @ X1 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f650,plain,
( ! [X0: mu,X1: mu] :
( ( $true
= ( rel_s4 @ sK1 @ ( sK3 @ X1 @ X0 ) ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( string @ X1 @ sK1 ) ) )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f649]) ).
thf(f652,definition,
( spl9_9
<=> ! [X2: mu] :
( ( exists_in_world @ X2 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
thf(f653,plain,
( ! [X2: mu] :
( ( exists_in_world @ X2 @ sK1 )
= $false )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f652]) ).
thf(f655,plain,
( spl9_8
| spl9_4
| spl9_9
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f647,f553,f652,f556,f649]) ).
thf(f657,plain,
( ( $true = $false )
| ~ spl9_9 ),
inference(superposition,[],[f653,f228]) ).
thf(f692,plain,
( $false
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f657]) ).
thf(f693,plain,
~ spl9_9,
inference(avatar_contradiction_clause,[],[f692]) ).
thf(f695,plain,
! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( ( userid @ u @ X2 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( string @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( $true = $false )
| ( ( userid @ u @ X2 @ ( sK3 @ X2 @ X1 ) )
= $false ) ),
inference(superposition,[],[f629,f248]) ).
thf(f723,plain,
! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( string @ X2 @ sK1 )
= $false )
| ( ( userid @ u @ X2 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( $true = $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( number @ X1 @ one @ ( sK3 @ X2 @ X1 ) )
= $false ) ),
inference(duplicate_literal_removal,[],[f695]) ).
thf(f724,plain,
! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( userid @ u @ X2 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( ( entry_box @ X1 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( string @ X2 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X2 @ X1 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f723]) ).
thf(f737,definition,
( spl9_12
<=> ! [X2: mu,X0: mu,X1: mu] :
( ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( string @ X2 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( userid @ u @ X2 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ X2 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
thf(f738,plain,
( ! [X2: mu,X0: mu,X1: mu] :
( ( $false
= ( exists_in_world @ ( sK8 @ sK1 @ X1 @ X2 @ X0 ) @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( string @ X2 @ sK1 )
= $false )
| ( ( userid @ u @ X2 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( entry_box @ X1 @ ( sK3 @ X2 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( number @ X1 @ one @ ( sK3 @ X2 @ X1 ) )
= $false ) )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f737]) ).
thf(f741,plain,
( spl9_4
| spl9_12 ),
inference(avatar_split_clause,[],[f724,f737,f556]) ).
thf(f775,plain,
( ! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( number @ X0 @ one @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( entry_box @ X0 @ ( sK3 @ X1 @ X0 ) )
= $false ) )
| ~ spl9_12 ),
inference(superposition,[],[f446,f738]) ).
thf(f782,plain,
( ! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( entry_box @ X0 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( $true = $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( number @ X0 @ one @ ( sK3 @ X1 @ X0 ) )
= $false ) )
| ~ spl9_12 ),
inference(duplicate_literal_removal,[],[f775]) ).
thf(f783,plain,
( ! [X2: mu,X3: $i,X0: mu,X1: mu] :
( ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( rel_s4 @ X3 @ sK1 )
= $false )
| ( ( exists_in_world @ X2 @ sK1 )
= $false )
| ( ( number @ X0 @ one @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( entry_box @ X0 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X0 ) )
= $false ) )
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f782]) ).
thf(f785,definition,
( spl9_13
<=> ! [X0: mu,X1: mu] :
( ( ( number @ X0 @ one @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( ( entry_box @ X0 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( entry_box @ X0 @ sK1 ) )
| ( ( exists_in_world @ X0 @ sK1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
thf(f786,plain,
( ! [X0: mu,X1: mu] :
( ( ( userid @ u @ X1 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( entry_box @ X0 @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( string @ X1 @ sK1 ) )
| ( ( number @ X0 @ one @ ( sK3 @ X1 @ X0 ) )
= $false )
| ( $false
= ( entry_box @ X0 @ sK1 ) ) )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f785]) ).
thf(f788,plain,
( spl9_4
| spl9_9
| spl9_13
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f783,f737,f785,f652,f556]) ).
thf(f797,plain,
( ! [X2: $i,X0: $i,X1: mu] :
( ( ( entry_box @ X1 @ ( sK3 @ ( sK7 @ X0 ) @ X1 ) )
= $false )
| ( $true = $false )
| ( ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X0 ) @ X1 ) )
= $false )
| ( ( rel_s4 @ X2 @ X0 )
= $false )
| ( ( number @ X1 @ one @ ( sK3 @ ( sK7 @ X0 ) @ X1 ) )
= $false )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( exists_in_world @ ( sK7 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( string @ ( sK7 @ X0 ) @ sK1 )
= $false ) )
| ~ spl9_13 ),
inference(superposition,[],[f464,f786]) ).
thf(f798,plain,
( ! [X2: $i,X0: $i,X1: mu] :
( ( ( number @ X1 @ one @ ( sK3 @ ( sK7 @ X0 ) @ X1 ) )
= $false )
| ( ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X0 ) @ X1 ) )
= $false )
| ( ( rel_s4 @ X2 @ X0 )
= $false )
| ( ( entry_box @ X1 @ ( sK3 @ ( sK7 @ X0 ) @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( entry_box @ X1 @ sK1 ) )
| ( ( string @ ( sK7 @ X0 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK7 @ X0 ) @ sK1 )
= $false ) )
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f797]) ).
thf(f921,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( string @ ( sK7 @ X1 ) @ sK1 ) )
| ( ( exists_in_world @ ( sK7 @ X1 ) @ sK1 )
= $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X2 @ X1 )
= $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X1 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) ) )
| ( $true = $false ) )
| ~ spl9_13 ),
inference(superposition,[],[f455,f798]) ).
thf(f923,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( entry_box @ ( sK6 @ X0 ) @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) ) )
| ( ( rel_s4 @ X1 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( string @ ( sK7 @ X1 ) @ sK1 ) )
| ( ( exists_in_world @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ ( sK7 @ X1 ) @ sK1 )
= $false ) )
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f921]) ).
thf(f935,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( rel_s4 @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) ) )
| ( $false
= ( string @ ( sK7 @ X1 ) @ sK1 ) )
| ( ( rel_s4 @ X1 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( $true = $false )
| ( ( exists_in_world @ ( sK7 @ X1 ) @ sK1 )
= $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) ) ) )
| ~ spl9_13 ),
inference(superposition,[],[f923,f456]) ).
thf(f939,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( $false
= ( string @ ( sK7 @ X1 ) @ sK1 ) )
| ( ( exists_in_world @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( $true = $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) ) )
| ( ( exists_in_world @ ( sK7 @ X1 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X2 @ X1 )
= $false ) )
| ~ spl9_13 ),
inference(duplicate_literal_removal,[],[f935]) ).
thf(f940,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) ) )
| ( ( exists_in_world @ ( sK7 @ X1 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X1 @ ( sK3 @ ( sK7 @ X1 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( $false
= ( string @ ( sK7 @ X1 ) @ sK1 ) )
| ( ( rel_s4 @ X2 @ X1 )
= $false ) )
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f939]) ).
thf(f960,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X1 @ X0 )
= $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK7 @ X0 ) @ sK1 )
= $false )
| ( $false != $false )
| ( ( string @ ( sK7 @ X0 ) @ sK1 )
= $false ) )
| ~ spl9_13 ),
inference(equality_factoring,[],[f940]) ).
thf(f970,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s4 @ X0 @ ( sK3 @ ( sK7 @ X0 ) @ ( sK6 @ X0 ) ) )
= $false )
| ( ( exists_in_world @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK7 @ X0 ) @ sK1 )
= $false )
| ( ( entry_box @ ( sK6 @ X0 ) @ sK1 )
= $false )
| ( ( string @ ( sK7 @ X0 ) @ sK1 )
= $false )
| ( ( rel_s4 @ X1 @ X0 )
= $false ) )
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f960]) ).
thf(f1023,definition,
( spl9_26
<=> ( ( entry_box @ ( sK6 @ sK1 ) @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_26])],[avatar_definition]) ).
thf(f1024,plain,
( ( ( entry_box @ ( sK6 @ sK1 ) @ sK1 )
!= $false )
| spl9_26 ),
inference(avatar_component_clause,[],[f1023]) ).
thf(f1025,plain,
( ( ( entry_box @ ( sK6 @ sK1 ) @ sK1 )
= $false )
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f1023]) ).
thf(f1082,plain,
( ( ( rel_s4 @ sK1 @ sK1 )
= $false )
| ( $true = $false )
| ~ spl9_26 ),
inference(superposition,[],[f1025,f456]) ).
thf(f1086,plain,
( ( ( rel_s4 @ sK1 @ sK1 )
= $false )
| ~ spl9_26 ),
inference(trivial_inequality_removal,[],[f1082]) ).
thf(f1091,plain,
( ( $true = $false )
| ~ spl9_26 ),
inference(forward_demodulation,[],[f1086,f259]) ).
thf(f1092,plain,
( $false
| ~ spl9_26 ),
inference(trivial_inequality_removal,[],[f1091]) ).
thf(f1093,plain,
~ spl9_26,
inference(avatar_contradiction_clause,[],[f1092]) ).
thf(f1160,definition,
( spl9_33
<=> ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_33])],[avatar_definition]) ).
thf(f1162,plain,
( ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false )
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f1160]) ).
thf(f1164,definition,
( spl9_34
<=> ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_34])],[avatar_definition]) ).
thf(f1166,plain,
( ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) )
| ~ spl9_34 ),
inference(avatar_component_clause,[],[f1164]) ).
thf(f1171,plain,
( ! [X0: $i] :
( ( ( entry_box @ ( sK6 @ sK1 ) @ sK1 )
= $false )
| ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) )
| ( $true = $false )
| ( $false
= ( exists_in_world @ ( sK6 @ sK1 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK6 @ sK1 ) @ sK1 ) )
| ( ( entry_box @ ( sK6 @ sK1 ) @ sK1 )
= $false )
| ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) )
| ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false ) )
| ~ spl9_8
| ~ spl9_13 ),
inference(superposition,[],[f970,f650]) ).
thf(f1191,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false )
| ( ( entry_box @ ( sK6 @ sK1 ) @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ ( sK6 @ sK1 ) @ sK1 ) )
| ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) )
| ( $true = $false ) )
| ~ spl9_8
| ~ spl9_13 ),
inference(duplicate_literal_removal,[],[f1171]) ).
thf(f1192,plain,
( ! [X0: $i] :
( ( $false
= ( exists_in_world @ ( sK6 @ sK1 ) @ sK1 ) )
| ( ( entry_box @ ( sK6 @ sK1 ) @ sK1 )
= $false )
| ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) )
| ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl9_8
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f1191]) ).
thf(f1201,plain,
( ! [X0: $i] :
( ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false )
| ( $false
= ( exists_in_world @ ( sK6 @ sK1 ) @ sK1 ) ) )
| ~ spl9_8
| ~ spl9_13
| spl9_26 ),
inference(forward_subsumption_resolution,[],[f1192,f1024]) ).
thf(f1204,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) )
| ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false ) )
| ~ spl9_8
| ~ spl9_13
| spl9_26 ),
inference(forward_demodulation,[],[f1201,f357]) ).
thf(f1205,plain,
( ! [X0: $i] :
( ( ( exists_in_world @ ( sK7 @ sK1 ) @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $false
= ( string @ ( sK7 @ sK1 ) @ sK1 ) ) )
| ~ spl9_8
| ~ spl9_13
| spl9_26 ),
inference(trivial_inequality_removal,[],[f1204]) ).
thf(f1207,plain,
( spl9_4
| spl9_34
| spl9_33
| ~ spl9_8
| ~ spl9_13
| spl9_26 ),
inference(avatar_split_clause,[],[f1205,f1023,f785,f649,f1160,f1164,f556]) ).
thf(f1251,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $true = $false ) )
| ~ spl9_33 ),
inference(superposition,[],[f403,f1162]) ).
thf(f1253,plain,
( ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ~ spl9_33 ),
inference(trivial_inequality_removal,[],[f1251]) ).
thf(f1258,plain,
( spl9_4
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f1253,f1160,f556]) ).
thf(f1262,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( ( rel_s4 @ sK1 @ sK1 )
= $false ) )
| ~ spl9_34 ),
inference(superposition,[],[f1166,f465]) ).
thf(f1266,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( ( rel_s4 @ sK1 @ sK1 )
= $false ) )
| ~ spl9_34 ),
inference(trivial_inequality_removal,[],[f1262]) ).
thf(f1268,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $true = $false ) )
| ~ spl9_34 ),
inference(forward_demodulation,[],[f1266,f259]) ).
thf(f1269,plain,
( ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ~ spl9_34 ),
inference(trivial_inequality_removal,[],[f1268]) ).
thf(f1272,plain,
( spl9_4
| ~ spl9_34 ),
inference(avatar_split_clause,[],[f1269,f1164,f556]) ).
cnf(s6,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f568]) ).
cnf(s16,plain,
~ spl9_4,
inference(sat_conversion,[],[f617]) ).
cnf(s18,plain,
( ~ spl9_3
| spl9_4
| spl9_8
| spl9_9 ),
inference(sat_conversion,[],[f655]) ).
cnf(s26,plain,
~ spl9_9,
inference(sat_conversion,[],[f693]) ).
cnf(s36,plain,
( spl9_4
| spl9_12 ),
inference(sat_conversion,[],[f741]) ).
cnf(s38,plain,
( spl9_4
| spl9_9
| ~ spl9_12
| spl9_13 ),
inference(sat_conversion,[],[f788]) ).
cnf(s66,plain,
~ spl9_26,
inference(sat_conversion,[],[f1093]) ).
cnf(s74,plain,
( spl9_4
| ~ spl9_8
| ~ spl9_13
| spl9_26
| spl9_33
| spl9_34 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s75,plain,
( spl9_4
| ~ spl9_33 ),
inference(sat_conversion,[],[f1258]) ).
cnf(s77,plain,
( spl9_4
| ~ spl9_34 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s91,plain,
( ~ spl9_3
| spl9_4
| spl9_8 ),
inference(rat,[],[s18,s26]) ).
cnf(s93,plain,
~ spl9_34,
inference(rat,[],[s77,s16]) ).
cnf(s94,plain,
~ spl9_33,
inference(rat,[],[s75,s16]) ).
cnf(s95,plain,
spl9_12,
inference(rat,[],[s36,s16]) ).
cnf(s96,plain,
spl9_13,
inference(rat,[],[s38,s16,s26,s95]) ).
cnf(s97,plain,
~ spl9_8,
inference(rat,[],[s74,s93,s94,s66,s16,s96]) ).
cnf(s98,plain,
~ spl9_3,
inference(rat,[],[s91,s16,s97]) ).
cnf(s105,plain,
$false,
inference(rat,[],[s6,s16,s98]) ).
thf(f1273,plain,
$false,
inference(avatar_sat_refutation,[],[s105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS272^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 08:36:56 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.60/0.40 % (3068827)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.60/0.40 % (3068833)lrs+10_16_si=on:nwc=1.5:random_seed=82177365:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.60/0.40 % (3068833)Instruction limit reached!
% 0.60/0.40 % (3068833)------------------------------
% 0.60/0.40 % (3068833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (3068833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (3068833)CaDiCaL version: 2.1.3
% 0.60/0.40 % (3068833)Termination reason: Instruction limit
% 0.60/0.40 % (3068833)Termination phase: Saturation
% 0.60/0.40 % (3068833)Time elapsed: 0.005 s
% 0.60/0.40 % (3068833)Peak memory usage: 11 MB
% 0.60/0.40 % (3068833)Instructions burned: 22 (million)
% 0.60/0.40 % (3068832)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=224443190:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.60/0.40 % (3068834)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4213943565:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.60/0.40 % (3068834)Instruction limit reached!
% 0.60/0.40 % (3068834)------------------------------
% 0.60/0.40 % (3068834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (3068834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (3068834)CaDiCaL version: 2.1.3
% 0.60/0.40 % (3068834)Termination reason: Instruction limit
% 0.60/0.40 % (3068834)Termination phase: shuffling
% 0.60/0.40 % (3068834)Time elapsed: 0.003 s
% 0.60/0.40 % (3068834)Peak memory usage: 9 MB
% 0.60/0.40 % (3068834)Instructions burned: 3 (million)
% 0.60/0.40 % (3068840)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2629308270:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.60/0.40 % (3068840)Instruction limit reached!
% 0.60/0.40 % (3068840)------------------------------
% 0.60/0.40 % (3068840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (3068840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (3068840)CaDiCaL version: 2.1.3
% 0.60/0.40 % (3068840)Termination reason: Instruction limit
% 0.60/0.40 % (3068840)Termination phase: shuffling
% 0.60/0.40 % (3068840)Time elapsed: 0.003 s
% 0.60/0.40 % (3068840)Peak memory usage: 9 MB
% 0.60/0.40 % (3068840)Instructions burned: 3 (million)
% 0.60/0.40 % (3068843)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=945061756:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.60/0.40 % (3068843)Instruction limit reached!
% 0.60/0.40 % (3068843)------------------------------
% 0.60/0.40 % (3068843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (3068843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (3068843)CaDiCaL version: 2.1.3
% 0.60/0.40 % (3068843)Termination reason: Instruction limit
% 0.60/0.40 % (3068843)Termination phase: Function definition elimination
% 0.60/0.40 % (3068843)Time elapsed: 0.002 s
% 0.60/0.40 % (3068843)Peak memory usage: 10 MB
% 0.60/0.40 % (3068843)Instructions burned: 8 (million)
% 0.60/0.40 % (3068836)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3121837939:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.60/0.40 % (3068832)Instruction limit reached!
% 0.60/0.40 % (3068832)------------------------------
% 0.60/0.40 % (3068832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.40 % (3068832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.40 % (3068832)CaDiCaL version: 2.1.3
% 0.60/0.40 % (3068832)Termination reason: Instruction limit
% 0.60/0.40 % (3068832)Termination phase: Saturation
% 0.60/0.40 % (3068832)Time elapsed: 0.044 s
% 0.60/0.40 % (3068832)Peak memory usage: 12 MB
% 0.60/0.40 % (3068832)Instructions burned: 89 (million)
% 0.60/0.40 % (3068838)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.60/0.40 % (3068838)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
% 0.60/0.40 % (3068845)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.40 % (3068849)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
% 0.60/0.44 % (3068849)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.44 % (3068845)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3444526627:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.60/0.44 % (3068835)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=2030483935: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)
% 0.60/0.44 % (3068849)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3796948915:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.60/0.44 % (3068837)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2356252830:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.60/0.44 % (3068845)Instruction limit reached!
% 0.60/0.44 % (3068845)------------------------------
% 0.60/0.44 % (3068845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (3068845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (3068845)CaDiCaL version: 2.1.3
% 0.60/0.44 % (3068845)Termination reason: Instruction limit
% 0.60/0.44 % (3068845)Termination phase: Clausification
% 0.60/0.44 % (3068845)Time elapsed: 0.006 s
% 0.60/0.44 % (3068845)Peak memory usage: 10 MB
% 0.60/0.44 % (3068845)Instructions burned: 7 (million)
% 0.60/0.44 % (3068838)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=1141014784:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.60/0.44 % (3068849)Instruction limit reached!
% 0.60/0.44 % (3068849)------------------------------
% 0.60/0.44 % (3068849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (3068849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (3068849)CaDiCaL version: 2.1.3
% 0.60/0.44 % (3068849)Termination reason: Instruction limit
% 0.60/0.44 % (3068849)Termination phase: Saturation
% 0.60/0.44 % (3068849)Time elapsed: 0.011 s
% 0.60/0.44 % (3068849)Peak memory usage: 12 MB
% 0.60/0.44 % (3068849)Instructions burned: 42 (million)
% 0.60/0.44 % (3068836)Instruction limit reached!
% 0.60/0.44 % (3068836)------------------------------
% 0.60/0.44 % (3068836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (3068836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (3068836)CaDiCaL version: 2.1.3
% 0.60/0.44 % (3068836)Termination reason: Instruction limit
% 0.60/0.44 % (3068836)Termination phase: Saturation
% 0.60/0.44 % (3068836)Time elapsed: 0.025 s
% 0.60/0.44 % (3068836)Peak memory usage: 12 MB
% 0.60/0.44 % (3068836)Instructions burned: 26 (million)
% 0.60/0.44 % (3068856)lrs+10_1_si=on:cs=on:random_seed=2730852267:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.60/0.44 % (3068856)Instruction limit reached!
% 0.60/0.44 % (3068856)------------------------------
% 0.60/0.44 % (3068856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.44 % (3068856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.44 % (3068856)CaDiCaL version: 2.1.3
% 0.60/0.44 % (3068856)Termination reason: Instruction limit
% 0.60/0.44 % (3068856)Termination phase: Property scanning
% 0.60/0.44 % (3068856)Time elapsed: 0.003 s
% 0.60/0.44 % (3068856)Peak memory usage: 10 MB
% 0.60/0.44 % (3068856)Instructions burned: 11 (million)
% 0.60/0.44 % (3068857)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.60/0.44 % (3068847)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3774888793:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.60/0.44 % (3068857)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2731990783:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.30/0.48 % (3068857)Instruction limit reached!
% 1.30/0.48 % (3068857)------------------------------
% 1.30/0.48 % (3068857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.48 % (3068857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.48 % (3068857)CaDiCaL version: 2.1.3
% 1.30/0.48 % (3068857)Termination reason: Instruction limit
% 1.30/0.48 % (3068857)Termination phase: Property scanning
% 1.30/0.48 % (3068857)Time elapsed: 0.002 s
% 1.30/0.48 % (3068857)Peak memory usage: 9 MB
% 1.30/0.48 % (3068857)Instructions burned: 4 (million)
% 1.30/0.48 % (3068859)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2061345244:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.30/0.48 % (3068854)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2861388419:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.30/0.48 % (3068847)Instruction limit reached!
% 1.30/0.48 % (3068847)------------------------------
% 1.30/0.48 % (3068847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.48 % (3068847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.48 % (3068847)CaDiCaL version: 2.1.3
% 1.30/0.48 % (3068847)Termination reason: Instruction limit
% 1.30/0.48 % (3068847)Termination phase: Property scanning
% 1.30/0.48 % (3068847)Time elapsed: 0.011 s
% 1.30/0.48 % (3068847)Peak memory usage: 11 MB
% 1.30/0.48 % (3068847)Instructions burned: 13 (million)
% 1.30/0.48 % (3068859)Refutation not found, incomplete strategy
% 1.30/0.48 % (3068859)------------------------------
% 1.30/0.48 % (3068859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.48 % (3068859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.48 % (3068859)CaDiCaL version: 2.1.3
% 1.30/0.48 % (3068859)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.48 % (3068859)Time elapsed: 0.009 s
% 1.30/0.48 % (3068859)Peak memory usage: 12 MB
% 1.30/0.48 % (3068859)Instructions burned: 37 (million)
% 1.30/0.48 % (3068859)------------------------------
% 1.30/0.48 % (3068859)------------------------------
% 1.30/0.48 % (3068837)Instruction limit reached!
% 1.30/0.48 % (3068837)------------------------------
% 1.30/0.48 % (3068837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.48 % (3068837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.48 % (3068837)CaDiCaL version: 2.1.3
% 1.30/0.48 % (3068837)Termination reason: Instruction limit
% 1.30/0.48 % (3068837)Termination phase: Saturation
% 1.30/0.48 % (3068837)Time elapsed: 0.047 s
% 1.30/0.48 % (3068837)Peak memory usage: 13 MB
% 1.30/0.48 % (3068837)Instructions burned: 75 (million)
% 1.30/0.48 % (3068862)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1128645801:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.30/0.48 % (3068866)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=358691324:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.30/0.48 % (3068865)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1590715909:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.30/0.48 % (3068866)Instruction limit reached!
% 1.30/0.48 % (3068866)------------------------------
% 1.30/0.48 % (3068866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.48 % (3068866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.48 % (3068866)CaDiCaL version: 2.1.3
% 1.30/0.48 % (3068866)Termination reason: Instruction limit
% 1.30/0.48 % (3068866)Termination phase: Saturation
% 1.30/0.48 % (3068866)Time elapsed: 0.004 s
% 1.30/0.48 % (3068866)Peak memory usage: 11 MB
% 1.30/0.48 % (3068866)Instructions burned: 19 (million)
% 1.30/0.48 % (3068862)Refutation not found, incomplete strategy
% 1.30/0.48 % (3068862)------------------------------
% 1.30/0.48 % (3068862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.48 % (3068862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.48 % (3068862)CaDiCaL version: 2.1.3
% 1.30/0.52 % (3068862)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.52 % (3068862)Time elapsed: 0.010 s
% 1.30/0.52 % (3068862)Peak memory usage: 12 MB
% 1.30/0.52 % (3068862)Instructions burned: 20 (million)
% 1.30/0.52 % (3068862)------------------------------
% 1.30/0.52 % (3068862)------------------------------
% 1.30/0.52 % (3068867)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2562194812:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.30/0.52 % (3068871)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3744826013:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.30/0.52 % (3068871)Instruction limit reached!
% 1.30/0.52 % (3068871)------------------------------
% 1.30/0.52 % (3068871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (3068871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (3068871)CaDiCaL version: 2.1.3
% 1.30/0.52 % (3068871)Termination reason: Instruction limit
% 1.30/0.52 % (3068871)Termination phase: Saturation
% 1.30/0.52 % (3068871)Time elapsed: 0.004 s
% 1.30/0.52 % (3068871)Peak memory usage: 11 MB
% 1.30/0.52 % (3068871)Instructions burned: 17 (million)
% 1.30/0.52 % (3068865)Instruction limit reached!
% 1.30/0.52 % (3068865)------------------------------
% 1.30/0.52 % (3068865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (3068865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (3068865)CaDiCaL version: 2.1.3
% 1.30/0.52 % (3068865)Termination reason: Instruction limit
% 1.30/0.52 % (3068865)Termination phase: Saturation
% 1.30/0.52 % (3068865)Time elapsed: 0.015 s
% 1.30/0.52 % (3068865)Peak memory usage: 12 MB
% 1.30/0.52 % (3068865)Instructions burned: 26 (million)
% 1.30/0.52 % (3068872)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3481662444:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.30/0.52 % (3068875)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4175438374:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.30/0.52 % (3068872)Instruction limit reached!
% 1.30/0.52 % (3068872)------------------------------
% 1.30/0.52 % (3068872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (3068872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (3068872)CaDiCaL version: 2.1.3
% 1.30/0.52 % (3068872)Termination reason: Instruction limit
% 1.30/0.52 % (3068872)Termination phase: Preprocessing 3
% 1.30/0.52 % (3068872)Time elapsed: 0.003 s
% 1.30/0.52 % (3068872)Peak memory usage: 10 MB
% 1.30/0.52 % (3068872)Instructions burned: 7 (million)
% 1.30/0.52 % (3068875)Instruction limit reached!
% 1.30/0.52 % (3068875)------------------------------
% 1.30/0.52 % (3068875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (3068875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (3068875)CaDiCaL version: 2.1.3
% 1.30/0.52 % (3068875)Termination reason: Instruction limit
% 1.30/0.52 % (3068875)Termination phase: Saturation
% 1.30/0.52 % (3068875)Time elapsed: 0.006 s
% 1.30/0.52 % (3068875)Peak memory usage: 12 MB
% 1.30/0.52 % (3068875)Instructions burned: 28 (million)
% 1.30/0.52 % (3068876)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2555985646:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.30/0.52 % (3068880)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.30/0.52 % (3068880)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.30/0.52 % (3068880)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2614831314:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.30/0.52 % (3068879)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4129417546:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.30/0.52 % (3068880)Instruction limit reached!
% 1.30/0.52 % (3068880)------------------------------
% 1.30/0.56 % (3068880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068880)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068880)Termination reason: Instruction limit
% 1.30/0.56 % (3068880)Termination phase: Saturation
% 1.30/0.56 % (3068880)Time elapsed: 0.004 s
% 1.30/0.56 % (3068880)Peak memory usage: 11 MB
% 1.30/0.56 % (3068880)Instructions burned: 17 (million)
% 1.30/0.56 % (3068854)Instruction limit reached!
% 1.30/0.56 % (3068854)------------------------------
% 1.30/0.56 % (3068854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068854)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068854)Termination reason: Instruction limit
% 1.30/0.56 % (3068854)Termination phase: Saturation
% 1.30/0.56 % (3068854)Time elapsed: 0.072 s
% 1.30/0.56 % (3068854)Peak memory usage: 12 MB
% 1.30/0.56 % (3068854)Instructions burned: 87 (million)
% 1.30/0.56 % (3068838)Instruction limit reached!
% 1.30/0.56 % (3068838)------------------------------
% 1.30/0.56 % (3068838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068838)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068838)Termination reason: Instruction limit
% 1.30/0.56 % (3068838)Termination phase: Saturation
% 1.30/0.56 % (3068838)Time elapsed: 0.106 s
% 1.30/0.56 % (3068838)Peak memory usage: 13 MB
% 1.30/0.56 % (3068838)Instructions burned: 159 (million)
% 1.30/0.56 % (3068876)Instruction limit reached!
% 1.30/0.56 % (3068876)------------------------------
% 1.30/0.56 % (3068876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068884)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.30/0.56 % (3068876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068876)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068876)Termination reason: Instruction limit
% 1.30/0.56 % (3068876)Termination phase: Saturation
% 1.30/0.56 % (3068876)Time elapsed: 0.020 s
% 1.30/0.56 % (3068876)Peak memory usage: 11 MB
% 1.30/0.56 % (3068876)Instructions burned: 23 (million)
% 1.30/0.56 % (3068884)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1859610904:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.30/0.56 % (3068884)Instruction limit reached!
% 1.30/0.56 % (3068884)------------------------------
% 1.30/0.56 % (3068884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068884)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068884)Termination reason: Instruction limit
% 1.30/0.56 % (3068884)Termination phase: Property scanning
% 1.30/0.56 % (3068884)Time elapsed: 0.002 s
% 1.30/0.56 % (3068884)Peak memory usage: 11 MB
% 1.30/0.56 % (3068884)Instructions burned: 8 (million)
% 1.30/0.56 % (3068889)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=301770101:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.30/0.56 % (3068887)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3307035133:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.30/0.56 % (3068889)Instruction limit reached!
% 1.30/0.56 % (3068889)------------------------------
% 1.30/0.56 % (3068889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068889)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068889)Termination reason: Instruction limit
% 1.30/0.56 % (3068889)Termination phase: Saturation
% 1.30/0.56 % (3068889)Time elapsed: 0.006 s
% 1.30/0.56 % (3068889)Peak memory usage: 12 MB
% 1.30/0.56 % (3068889)Instructions burned: 20 (million)
% 1.30/0.56 % (3068886)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2249749203:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.30/0.56 % (3068892)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1789248519:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.30/0.56 % (3068886)Instruction limit reached!
% 1.30/0.56 % (3068886)------------------------------
% 1.30/0.56 % (3068886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068886)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068886)Termination reason: Instruction limit
% 1.30/0.56 % (3068886)Termination phase: Function definition elimination
% 1.30/0.56 % (3068886)Time elapsed: 0.004 s
% 1.30/0.56 % (3068886)Peak memory usage: 10 MB
% 1.30/0.56 % (3068886)Instructions burned: 9 (million)
% 1.30/0.56 % (3068887)Instruction limit reached!
% 1.30/0.56 % (3068887)------------------------------
% 1.30/0.56 % (3068887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068887)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068887)Termination reason: Instruction limit
% 1.30/0.56 % (3068887)Termination phase: Saturation
% 1.30/0.56 % (3068887)Time elapsed: 0.011 s
% 1.30/0.56 % (3068887)Peak memory usage: 11 MB
% 1.30/0.56 % (3068887)Instructions burned: 25 (million)
% 1.30/0.56 % (3068885)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2597635150:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.30/0.56 % (3068879)Instruction limit reached!
% 1.30/0.56 % (3068879)------------------------------
% 1.30/0.56 % (3068879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068879)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068879)Termination reason: Instruction limit
% 1.30/0.56 % (3068879)Termination phase: Saturation
% 1.30/0.56 % (3068879)Time elapsed: 0.057 s
% 1.30/0.56 % (3068879)Peak memory usage: 12 MB
% 1.30/0.56 % (3068879)Instructions burned: 61 (million)
% 1.30/0.56 % (3068885)Instruction limit reached!
% 1.30/0.56 % (3068885)------------------------------
% 1.30/0.56 % (3068885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068885)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068885)Termination reason: Instruction limit
% 1.30/0.56 % (3068885)Termination phase: Saturation
% 1.30/0.56 % (3068885)Time elapsed: 0.016 s
% 1.30/0.56 % (3068885)Peak memory usage: 12 MB
% 1.30/0.56 % (3068885)Instructions burned: 31 (million)
% 1.30/0.56 % (3068895)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=516114725:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.30/0.56 % (3068896)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1212596467:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.30/0.56 % (3068896)Refutation not found, incomplete strategy
% 1.30/0.56 % (3068896)------------------------------
% 1.30/0.56 % (3068896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068896)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068896)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.56 % (3068896)Time elapsed: 0.014 s
% 1.30/0.56 % (3068896)Peak memory usage: 12 MB
% 1.30/0.56 % (3068896)Instructions burned: 28 (million)
% 1.30/0.56 % (3068901)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.30/0.56 % (3068896)------------------------------
% 1.30/0.56 % (3068896)------------------------------
% 1.30/0.56 % (3068901)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2251840448:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.30/0.56 % (3068901)Instruction limit reached!
% 1.30/0.56 % (3068901)------------------------------
% 1.30/0.56 % (3068901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068901)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068901)Termination reason: Instruction limit
% 1.30/0.56 % (3068901)Termination phase: Property scanning
% 1.30/0.56 % (3068901)Time elapsed: 0.004 s
% 1.30/0.56 % (3068901)Peak memory usage: 10 MB
% 1.30/0.56 % (3068901)Instructions burned: 9 (million)
% 1.30/0.56 % (3068902)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=958288798:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.30/0.56 % (3068898)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3950720303:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.30/0.56 % (3068904)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1077067919:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.30/0.56 % (3068892) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3068827-3068892"...
% 1.30/0.56 % (3068902)Refutation not found, incomplete strategy
% 1.30/0.56 % (3068902)------------------------------
% 1.30/0.56 % (3068902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.56 % (3068902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.56 % (3068902)CaDiCaL version: 2.1.3
% 1.30/0.56 % (3068902)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.56 % (3068902)Time elapsed: 0.010 s
% 1.30/0.56 % (3068902)Peak memory usage: 12 MB
% 1.30/0.56 % (3068902)Instructions burned: 20 (million)
% 1.30/0.56 % (3068902)------------------------------
% 1.30/0.56 % (3068902)------------------------------
% 1.30/0.56 % (3068867) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3068827-3068867"...
% 1.30/0.56 % (3068892)...printing done.
% 1.30/0.56 % (3068892)Refutation found. Thanks to Tanya!
% 1.30/0.56 % SZS status Theorem for theBenchmark
% 1.30/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.30/0.57 % (3068892)------------------------------
% 1.30/0.57 % (3068892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.57 % (3068892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.57 % (3068892)CaDiCaL version: 2.1.3
% 1.30/0.57 % (3068892)Termination reason: Refutation
% 1.30/0.57 % (3068892)Time elapsed: 0.076 s
% 1.30/0.57 % (3068892)Peak memory usage: 14 MB
% 1.30/0.57 % (3068892)Instructions burned: 293 (million)
% 1.30/0.57 % (3068827)Success in time 0.316 s
% 1.30/0.57 % Vampire exiting
%------------------------------------------------------------------------------