%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA033^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:20:25 AM UTC 2026
% Result : Theorem 0.20s 0.33s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 24
% Syntax : Number of formulae : 221 ( 84 unt; 0 typ; 10 def)
% Number of atoms : 2755 ( 523 equ; 0 cnn)
% Maximal formula atoms : 25 ( 12 avg)
% Number of connectives : 5115 ( 898 ~; 831 |; 0 &;3071 @)
% ( 9 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 76 usr; 19 con; 0-4 aty)
% ( 230 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 971 ( 0 sgn 331 !; 0 ?; 971 :)
% 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,
closed: mu > $i > $o ).
thf(func_def_37,type,
open: mu > $i > $o ).
thf(func_def_38,type,
h: mu > $i > $o ).
thf(func_def_39,type,
combo: mu > mu > $i > $o ).
thf(func_def_40,type,
o: mu ).
thf(func_def_41,type,
n: mu ).
thf(func_def_42,type,
d: mu ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_53,type,
vIMP: $o > $o > $o ).
thf(func_def_54,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_57,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
sK0: $i > mu ).
thf(func_def_59,type,
sF1: $o ).
thf(func_def_60,type,
sK2: $i > mu ).
thf(func_def_61,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_62,type,
sK3: mu > mu > $i > mu ).
thf(func_def_66,type,
sK7: $i > mu ).
thf(func_def_67,type,
sK8: $i > mu ).
thf(func_def_68,type,
sK9: $i > $i ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f15,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL015^0.ax',mexists_ind) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f39,axiom,
! [X0: $i] : ( exists_in_world @ d @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_d_ax) ).
thf(f40,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( combo @ X0 @ X1 ) @ ( h @ X2 ) ) ) @ ( mbox_s4 @ ( open @ X0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( mnot @ ( combo @ X0 @ X1 ) ) @ ( h @ o ) ) ) @ ( mbox_s4 @ ( closed @ X0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f41,axiom,
mvalid @ ( mbox_s4 @ ( closed @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(f45,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ X0 ) @ ( h @ X1 ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f46,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ X0 ) @ ( h @ X1 ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
thf(f53,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f54,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f58,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f61,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f62,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f72,plain,
! [X0: $i] : ( exists_in_world @ d @ X0 ),
inference(rectify,[],[f39]) ).
thf(f73,plain,
! [X0: $i] :
( ( exists_in_world @ d @ X0 )
= $true ),
inference(fool_elimination,[],[f72]) ).
thf(f80,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f89,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f90,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f92,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f95,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f96,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
mvalid @ ( mbox_s4 @ ( closed @ d ) ),
inference(rectify,[],[f41]) ).
thf(f98,plain,
( ( mvalid @ ( mbox_s4 @ ( closed @ d ) ) )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f103,plain,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( combo @ X0 @ X1 ) @ ( h @ X2 ) ) ) @ ( mbox_s4 @ ( open @ X0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( mnot @ ( combo @ X0 @ X1 ) ) @ ( h @ o ) ) ) @ ( mbox_s4 @ ( closed @ X0 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f104,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( combo @ Y0 @ Y1 ) @ ( h @ Y2 ) ) ) @ ( mbox_s4 @ ( open @ Y0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( mnot @ ( combo @ Y0 @ Y1 ) ) @ ( h @ o ) ) ) @ ( mbox_s4 @ ( closed @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f108,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f109,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ X0 ) @ ( h @ X1 ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f110,plain,
( ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f112,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f111]) ).
thf(f116,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f117,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f116]) ).
thf(f126,plain,
( ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f110]) ).
thf(f131,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f140,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f144,plain,
( ( mvalid @ ( mbox_s4 @ ( closed @ d ) ) )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f148,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f149,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f151,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f112]) ).
thf(f156,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f159,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f162,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( combo @ Y0 @ Y1 ) @ ( h @ Y2 ) ) ) @ ( mbox_s4 @ ( open @ Y0 ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( mnot @ ( combo @ Y0 @ Y1 ) ) @ ( h @ o ) ) ) @ ( mbox_s4 @ ( closed @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f165,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f90]) ).
thf(f166,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f167,plain,
! [X0: $i] :
( ( exists_in_world @ d @ X0 )
= $true ),
inference(cnf_transformation,[],[f73]) ).
thf(f172,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f117]) ).
thf(f174,plain,
( ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f126]) ).
thf(f179,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f159,f172,f148,f172,f172]) ).
thf(f180,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f131,f148,f172]) ).
thf(f185,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,[],[f140,f172,f151,f172]) ).
thf(f189,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( closed @ d ) ) ) ),
inference(definition_unfolding,[],[f144,f166,f149]) ).
thf(f193,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 > $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: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ 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] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( closed @ Y0 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( combo @ Y0 @ Y1 )
@ ( h @ Y2 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( open @ Y0 ) ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ 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] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( closed @ Y0 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( combo @ Y0 @ Y1 ) )
@ ( h @ o ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( closed @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f162,f166,f149,f151,f151,f185,f179,f149,f180,f179,f179,f149,f149,f180,f179,f179,f172,f149]) ).
thf(f194,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f165,f156]) ).
thf(f195,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: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f174,f166,f149,f185,f185,f180,f149,f179,f149]) ).
thf(f196,definition,
( sF1
= ( ^ [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: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f197,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: 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: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f196]) ).
thf(f198,plain,
$true != sF1,
inference(definition_folding,[],[f195,f197]) ).
thf(f212,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( closed @ d @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f213,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( closed @ d @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( closed @ d @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( closed @ d @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( closed @ d @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( closed @ d @ X2 ) )
| ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( closed @ d @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f228,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 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ~ ( ~ ( closed @ Y2 @ Y5 )
| ~ ~ ( ~ ( combo @ Y2 @ Y3 @ Y5 )
| ~ ( h @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( open @ Y2 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y1 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ~ ( ~ ( closed @ Y2 @ Y5 )
| ~ ~ ( ~ ~ ( combo @ Y2 @ Y3 @ Y5 )
| ~ ( h @ o @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( closed @ Y2 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f229,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 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ~ ( ~ ( closed @ Y2 @ Y5 )
| ~ ~ ( ~ ( combo @ Y2 @ Y3 @ Y5 )
| ~ ( h @ Y4 @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( open @ Y2 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y1 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ~ ( ~ ( closed @ Y2 @ Y5 )
| ~ ~ ( ~ ~ ( combo @ Y2 @ Y3 @ Y5 )
| ~ ( h @ o @ Y5 ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( closed @ Y2 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,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 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ~ ( ~ ( closed @ Y1 @ Y4 )
| ~ ~ ( ~ ( combo @ Y1 @ Y2 @ Y4 )
| ~ ( h @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( open @ Y1 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y0 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ~ ( ~ ( closed @ Y1 @ Y4 )
| ~ ~ ( ~ ~ ( combo @ Y1 @ Y2 @ Y4 )
| ~ ( h @ o @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( closed @ Y1 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,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 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ~ ( ~ ( closed @ Y1 @ Y4 )
| ~ ~ ( ~ ( combo @ Y1 @ Y2 @ Y4 )
| ~ ( h @ Y3 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( open @ Y1 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y0 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ~ ( ~ ( closed @ Y1 @ Y4 )
| ~ ~ ( ~ ~ ( combo @ Y1 @ Y2 @ Y4 )
| ~ ( h @ o @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( closed @ Y1 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,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 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( open @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ o @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( closed @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,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 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( open @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ o @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( closed @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $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] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( open @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ o @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( closed @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ^ [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] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ Y2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( open @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ~ ( ~ ( closed @ Y0 @ Y3 )
| ~ ~ ( ~ ~ ( combo @ Y0 @ Y1 @ Y3 )
| ~ ( h @ o @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( closed @ Y0 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ X2 @ Y3 ) ) ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X2 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y2 )
| ~ ~ ( ~ ( combo @ X3 @ Y0 @ Y2 )
| ~ ( h @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( open @ X3 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y2 )
| ~ ~ ( ~ ~ ( combo @ X3 @ Y0 @ Y2 )
| ~ ( h @ o @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( closed @ X3 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y2 )
| ~ ~ ( ~ ( combo @ X3 @ Y0 @ Y2 )
| ~ ( h @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( open @ X3 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y2 )
| ~ ~ ( ~ ~ ( combo @ X3 @ Y0 @ Y2 )
| ~ ( h @ o @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( closed @ X3 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y2 )
| ~ ~ ( ~ ( combo @ X3 @ Y0 @ Y2 )
| ~ ( h @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( open @ X3 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y2 )
| ~ ~ ( ~ ~ ( combo @ X3 @ Y0 @ Y2 )
| ~ ( h @ o @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( closed @ X3 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ X2 @ Y2 ) ) ) ) ) ) )
@ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $true
= ( ( exists_in_world @ X4 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ o @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( closed @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ o @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( closed @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ o @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( closed @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y1 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y1 )
| ~ ( h @ o @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( closed @ X3 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) )
@ ( sK3 @ X3 @ X4 @ X2 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( ( exists_in_world @ ( sK3 @ X3 @ X4 @ X2 ) @ X2 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ o @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( closed @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ o @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( closed @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( $true
= ( exists_in_world @ ( sK3 @ X3 @ X4 @ X2 ) @ X2 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f246,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ o @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( closed @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) ) ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f247,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ o @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( closed @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f249,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f250,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu] :
( ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ~ ( ~ ( closed @ X3 @ Y0 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ Y0 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ X3 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X2 @ Y0 ) )
@ X5 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ~ ( ~ ( closed @ X3 @ X5 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) ) )
| ~ ( rel_s4 @ X2 @ X5 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: $i] :
( ( $true
= ( ~ ~ ( ~ ( closed @ X3 @ X5 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: $i] :
( ( ( ~ ~ ( ~ ( closed @ X3 @ X5 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) ) )
= $true )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: $i] :
( ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( ~ ( ~ ( closed @ X3 @ X5 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) ) )
= $true )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $true
= ( ~ ( closed @ X3 @ X5 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) ) ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: mu,X1: $i,X4: mu,X5: $i] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( closed @ X3 @ X5 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) ) ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $true
= ( ~ ( closed @ X3 @ X5 )
| ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $true
= ( ~ ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $true
= ( ~ ( closed @ X3 @ X5 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( ~ ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $true
= ( ~ ( closed @ X3 @ X5 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) )
| ( $true
= ( ~ ( closed @ X3 @ X5 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $true
= ( ~ ( combo @ X3 @ X4 @ X5 )
| ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( closed @ X3 @ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $false
= ( closed @ X3 @ X5 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( combo @ X3 @ X4 @ X5 ) ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) )
| ( $true
= ( ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $false
= ( combo @ X3 @ X4 @ X5 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( closed @ X3 @ X5 ) )
| ( $true
= ( ~ ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $false
= ( combo @ X3 @ X4 @ X5 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( open @ X3 @ Y0 )
| ~ ( rel_s4 @ X5 @ Y0 ) )
@ X6 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) )
| ( $false
= ( closed @ X3 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( closed @ X3 @ X5 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $false
= ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) )
| ( $true
= ( ( open @ X3 @ X6 )
| ~ ( rel_s4 @ X5 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( combo @ X3 @ X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $true
= ( open @ X3 @ X6 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ~ ( rel_s4 @ X5 @ X6 ) ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) )
| ( $false
= ( closed @ X3 @ X5 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $false
= ( combo @ X3 @ X4 @ X5 ) ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X3: mu,X1: $i,X6: $i,X4: mu,X5: $i] :
( ( $false
= ( h @ ( sK3 @ X3 @ X4 @ X2 ) @ X5 ) )
| ( $false
= ( closed @ X3 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( open @ X3 @ X6 ) )
| ( ( exists_in_world @ X4 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( exists_in_world @ X3 @ X2 ) )
| ( $false
= ( rel_s4 @ X5 @ X6 ) )
| ( $false
= ( combo @ X3 @ X4 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f305,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [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: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f197]) ).
thf(f306,plain,
( ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ~ ( combo @ d @ Y2 @ Y4 )
| ~ ( h @ Y3 @ Y4 ) )
| ~ ( rel_s4 @ Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( open @ d @ Y4 )
| ~ ( rel_s4 @ Y1 @ Y4 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f307,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ~ ( combo @ d @ Y2 @ Y4 )
| ~ ( h @ Y3 @ Y4 ) )
| ~ ( rel_s4 @ Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( open @ d @ Y4 )
| ~ ( rel_s4 @ Y1 @ Y4 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ sK4 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f306]) ).
thf(f308,plain,
( ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ~ ( combo @ d @ Y1 @ Y3 )
| ~ ( h @ Y2 @ Y3 ) )
| ~ ( rel_s4 @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( open @ d @ Y3 )
| ~ ( rel_s4 @ Y0 @ Y3 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f307]) ).
thf(f309,plain,
( ( ( ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ~ ( combo @ d @ Y1 @ Y3 )
| ~ ( h @ Y2 @ Y3 ) )
| ~ ( rel_s4 @ Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( open @ d @ Y3 )
| ~ ( rel_s4 @ Y0 @ Y3 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) )
@ sK5 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( combo @ d @ Y0 @ Y2 )
| ~ ( h @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ d @ Y2 )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ sK5 ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f312,plain,
( ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( combo @ d @ Y0 @ Y2 )
| ~ ( h @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ d @ Y2 )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f310]) ).
thf(f313,plain,
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( combo @ d @ Y0 @ Y2 )
| ~ ( h @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ d @ Y2 )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ~ ( combo @ d @ Y0 @ Y2 )
| ~ ( h @ Y1 @ Y2 ) )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( open @ d @ Y2 )
| ~ ( rel_s4 @ sK5 @ Y2 ) ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X1: mu] :
( ( $true
= ( ( exists_in_world @ X1 @ sK5 )
=> ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ d @ Y1 )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f316,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ d @ Y1 )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(imp_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ d @ Y1 )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X1: mu] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ d @ Y1 )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) ) ) ) ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: mu,X1: mu] :
( ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y1 )
| ~ ( h @ Y0 @ Y1 ) )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( open @ d @ Y1 )
| ~ ( rel_s4 @ sK5 @ Y1 ) ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: mu,X1: mu] :
( ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true
= ( ( exists_in_world @ X2 @ sK5 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y0 )
| ~ ( h @ X2 @ Y0 ) )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ d @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f319]) ).
thf(f321,plain,
! [X2: mu,X1: mu] :
( ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y0 )
| ~ ( h @ X2 @ Y0 ) )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ d @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X2: mu,X1: mu] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y0 )
| ~ ( h @ X2 @ Y0 ) )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ d @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) )
= $false )
| ( $true = sF1 )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: mu,X1: mu] :
( ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( open @ d @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f324,plain,
! [X2: mu,X1: mu] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y0 )
| ~ ( h @ X2 @ Y0 ) )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f325,plain,
! [X2: mu,X1: mu] :
( ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y0 )
| ~ ( h @ X2 @ Y0 ) )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f324]) ).
thf(f326,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true = sF1 )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( combo @ d @ X1 @ Y0 )
| ~ ( h @ X2 @ Y0 ) )
| ~ ( rel_s4 @ sK5 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( $true
= ( ~ ( ~ ( combo @ d @ X1 @ X3 )
| ~ ( h @ X2 @ X3 ) )
| ~ ( rel_s4 @ sK5 @ X3 ) ) )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true = sF1 )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f328,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true
= ( ~ ( ~ ( combo @ d @ X1 @ X3 )
| ~ ( h @ X2 @ X3 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK5 @ X3 ) ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( $true
= ( ~ ( rel_s4 @ sK5 @ X3 ) ) )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( ( ~ ( combo @ d @ X1 @ X3 )
| ~ ( h @ X2 @ X3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true = sF1 )
| ( ( ~ ( combo @ d @ X1 @ X3 )
| ~ ( h @ X2 @ X3 ) )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $true = sF1 )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $false
= ( ~ ( h @ X2 @ X3 ) ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(or_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true = sF1 )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $false
= ( ~ ( combo @ d @ X1 @ X3 ) ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(or_proxy_clausification,[],[f330]) ).
thf(f333,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( ( combo @ d @ X1 @ X3 )
= $true )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $true = sF1 )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(not_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: mu,X3: $i,X1: mu] :
( ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $true
= ( h @ X2 @ X3 ) )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f335,plain,
! [X2: mu,X1: mu] :
( ( $false
= ( ^ [Y0: $i] :
( ( open @ d @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) )
@ sK6 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true = sF1 )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f323]) ).
thf(f336,plain,
! [X2: mu,X1: mu] :
( ( $true = sF1 )
| ( $false
= ( ( open @ d @ sK6 )
| ~ ( rel_s4 @ sK5 @ sK6 ) ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f335]) ).
thf(f337,plain,
! [X2: mu,X1: mu] :
( ( $true = sF1 )
| ( ( ~ ( rel_s4 @ sK5 @ sK6 ) )
= $false )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) ),
inference(or_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: mu,X1: mu] :
( ( $true = sF1 )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $false
= ( open @ d @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f336]) ).
thf(f339,plain,
! [X2: mu,X1: mu] :
( ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true = sF1 )
| ( $true
= ( rel_s4 @ sK5 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f337]) ).
thf(f376,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f377,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f376]) ).
thf(f378,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f377]) ).
thf(f389,definition,
( spl10_1
<=> ! [X1: mu,X3: $i] :
( ( ( combo @ d @ X1 @ X3 )
= $true )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f390,plain,
( ! [X3: $i,X1: mu] :
( ( ( combo @ d @ X1 @ X3 )
= $true )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f389]) ).
thf(f392,definition,
( spl10_2
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f396,definition,
( spl10_3
<=> ! [X2: mu] :
( $false
= ( exists_in_world @ X2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f397,plain,
( ! [X2: mu] :
( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f396]) ).
thf(f398,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f333,f396,f392,f389]) ).
thf(f400,definition,
( spl10_4
<=> ! [X2: mu,X3: $i] :
( ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) )
| ( $true
= ( h @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f401,plain,
( ! [X2: mu,X3: $i] :
( ( $true
= ( h @ X2 @ X3 ) )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $false
= ( exists_in_world @ X2 @ sK5 ) ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f402,plain,
( spl10_3
| spl10_2
| spl10_4 ),
inference(avatar_split_clause,[],[f334,f400,f392,f396]) ).
thf(f404,definition,
( spl10_5
<=> ( $false
= ( open @ d @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f406,plain,
( ( $false
= ( open @ d @ sK6 ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f404]) ).
thf(f407,plain,
( spl10_3
| spl10_2
| spl10_5
| spl10_3 ),
inference(avatar_split_clause,[],[f338,f396,f404,f392,f396]) ).
thf(f409,definition,
( spl10_6
<=> ( $true
= ( rel_s4 @ sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f411,plain,
( ( $true
= ( rel_s4 @ sK5 @ sK6 ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f409]) ).
thf(f412,plain,
( spl10_3
| spl10_3
| spl10_2
| spl10_6 ),
inference(avatar_split_clause,[],[f339,f409,f392,f396,f396]) ).
thf(f438,plain,
~ spl10_2,
inference(avatar_split_clause,[],[f198,f392]) ).
thf(f455,plain,
( ! [X2: $i,X3: $i,X0: mu,X1: mu,X4: $i,X5: $i] :
( ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $false
= ( rel_s4 @ X4 @ X2 ) )
| ( $false
= ( exists_in_world @ ( sK3 @ X0 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( closed @ X0 @ X3 ) )
| ( $true
= ( open @ X0 @ X5 ) )
| ( $false
= ( combo @ X0 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $false
= ( exists_in_world @ X1 @ X2 ) )
| ( $false
= ( rel_s4 @ X3 @ X5 ) )
| ( $true = $false ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f268,f401]) ).
thf(f458,plain,
( ! [X2: $i,X3: $i,X0: mu,X1: mu,X4: $i,X5: $i] :
( ( $false
= ( exists_in_world @ ( sK3 @ X0 @ X1 @ X2 ) @ sK5 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $false
= ( exists_in_world @ X1 @ X2 ) )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $false
= ( combo @ X0 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X3 @ X5 ) )
| ( $false
= ( rel_s4 @ X4 @ X2 ) )
| ( $true
= ( open @ X0 @ X5 ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $false
= ( closed @ X0 @ X3 ) ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f455]) ).
thf(f462,plain,
( ! [X2: $i,X3: $i,X0: mu,X1: mu,X4: $i,X5: $i] :
( ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X2 ) )
| ( $false
= ( rel_s4 @ sK5 @ X2 ) )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( $true = $false )
| ( $false
= ( combo @ X0 @ X1 @ X2 ) )
| ( $false
= ( closed @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $false
= ( rel_s4 @ X5 @ sK5 ) )
| ( $false
= ( rel_s4 @ X4 @ sK5 ) )
| ( $true
= ( open @ X0 @ X3 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f458,f245]) ).
thf(f470,plain,
( ! [X2: $i,X3: $i,X0: mu,X1: mu,X4: $i,X5: $i] :
( ( $true
= ( open @ X0 @ X3 ) )
| ( $false
= ( closed @ X0 @ X2 ) )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( $false
= ( rel_s4 @ X4 @ sK5 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ sK5 @ X2 ) )
| ( $false
= ( rel_s4 @ X5 @ sK5 ) )
| ( $false
= ( combo @ X0 @ X1 @ X2 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) )
| ~ spl10_4 ),
inference(duplicate_literal_removal,[],[f462]) ).
thf(f471,plain,
( ! [X2: $i,X3: $i,X0: mu,X1: mu,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X5 @ sK5 ) )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( $false
= ( rel_s4 @ sK5 @ X2 ) )
| ( $false
= ( closed @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( open @ X0 @ X3 ) )
| ( $false
= ( rel_s4 @ X4 @ sK5 ) )
| ( $false
= ( combo @ X0 @ X1 @ X2 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f470]) ).
thf(f474,definition,
( spl10_13
<=> ! [X5: $i] :
( $false
= ( rel_s4 @ X5 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f475,plain,
( ! [X5: $i] :
( $false
= ( rel_s4 @ X5 @ sK5 ) )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f474]) ).
thf(f477,definition,
( spl10_14
<=> ! [X4: $i,X0: mu,X3: $i,X1: mu] :
( ( $false
= ( rel_s4 @ X3 @ X4 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) )
| ( $false
= ( closed @ X0 @ X3 ) )
| ( $false
= ( combo @ X0 @ X1 @ X3 ) )
| ( $true
= ( open @ X0 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
thf(f478,plain,
( ! [X3: $i,X0: mu,X1: mu,X4: $i] :
( ( $false
= ( combo @ X0 @ X1 @ X3 ) )
| ( $false
= ( closed @ X0 @ X3 ) )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( ( exists_in_world @ X1 @ sK5 )
= $false )
| ( $true
= ( open @ X0 @ X4 ) )
| ( $false
= ( rel_s4 @ X3 @ X4 ) )
| ( $false
= ( rel_s4 @ sK5 @ X3 ) ) )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f477]) ).
thf(f480,plain,
( spl10_13
| spl10_13
| spl10_14
| ~ spl10_4 ),
inference(avatar_split_clause,[],[f471,f400,f477,f474,f474]) ).
thf(f485,plain,
( ( $true = $false )
| ~ spl10_3 ),
inference(constrained_superposition,[],[f397,f167]) ).
thf(f519,plain,
( $false
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f520,plain,
~ spl10_3,
inference(avatar_contradiction_clause,[],[f519]) ).
thf(f526,plain,
( ( $true = $false )
| ~ spl10_13 ),
inference(constrained_superposition,[],[f378,f475]) ).
thf(f532,plain,
( $false
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f526]) ).
thf(f533,plain,
~ spl10_13,
inference(avatar_contradiction_clause,[],[f532]) ).
thf(f548,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $false
= ( exists_in_world @ d @ sK5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( open @ d @ X2 )
= $true )
| ( $false
= ( closed @ d @ X1 ) )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) ) )
| ~ spl10_1
| ~ spl10_14 ),
inference(constrained_superposition,[],[f390,f478]) ).
thf(f558,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $false
= ( closed @ d @ X1 ) )
| ( $false
= ( exists_in_world @ d @ sK5 ) )
| ( $true = $false )
| ( ( open @ d @ X2 )
= $true )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) ) )
| ~ spl10_1
| ~ spl10_14 ),
inference(duplicate_literal_removal,[],[f548]) ).
thf(f559,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $false
= ( exists_in_world @ d @ sK5 ) )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( closed @ d @ X1 ) )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( ( open @ d @ X2 )
= $true ) )
| ~ spl10_1
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f565,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( ( open @ d @ X2 )
= $true )
| ( $false
= ( closed @ d @ X1 ) )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) ) )
| ~ spl10_1
| ~ spl10_14 ),
inference(forward_demodulation,[],[f559,f167]) ).
thf(f566,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( ( open @ d @ X2 )
= $true )
| ( $false
= ( exists_in_world @ X0 @ sK5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $false
= ( closed @ d @ X1 ) ) )
| ~ spl10_1
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f565]) ).
thf(f570,definition,
( spl10_15
<=> ! [X2: $i,X1: $i] :
( ( ( open @ d @ X2 )
= $true )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( closed @ d @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition]) ).
thf(f571,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( closed @ d @ X1 ) )
| ( ( open @ d @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) ) )
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f570]) ).
thf(f573,plain,
( spl10_15
| spl10_3
| ~ spl10_1
| ~ spl10_14 ),
inference(avatar_split_clause,[],[f566,f477,f389,f396,f570]) ).
thf(f574,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK5 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $true
= ( open @ d @ X1 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) ) )
| ~ spl10_15 ),
inference(constrained_superposition,[],[f571,f218]) ).
thf(f578,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( open @ d @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ sK5 @ X0 ) ) )
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f574]) ).
thf(f583,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ sK6 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true = $false ) )
| ~ spl10_5
| ~ spl10_15 ),
inference(constrained_superposition,[],[f406,f578]) ).
thf(f585,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ sK6 ) ) )
| ~ spl10_5
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f583]) ).
thf(f596,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ X0 @ sK5 )
= $false )
| ( $true = $false )
| ( $false
= ( rel_s4 @ sK5 @ sK6 ) ) )
| ~ spl10_5
| ~ spl10_15 ),
inference(constrained_superposition,[],[f378,f585]) ).
thf(f604,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ sK5 @ sK6 ) )
| ( ( rel_s4 @ X0 @ sK5 )
= $false ) )
| ~ spl10_5
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f610,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ X0 @ sK5 )
= $false )
| ( $true = $false ) )
| ~ spl10_5
| ~ spl10_6
| ~ spl10_15 ),
inference(forward_demodulation,[],[f604,f411]) ).
thf(f611,plain,
( ! [X0: $i] :
( ( rel_s4 @ X0 @ sK5 )
= $false )
| ~ spl10_5
| ~ spl10_6
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f610]) ).
thf(f616,plain,
( spl10_13
| ~ spl10_5
| ~ spl10_6
| ~ spl10_15 ),
inference(avatar_split_clause,[],[f611,f570,f409,f404,f474]) ).
cnf(s1,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f398]) ).
cnf(s2,plain,
( spl10_2
| spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f402]) ).
cnf(s3,plain,
( spl10_3
| spl10_2
| spl10_3
| spl10_5 ),
inference(sat_conversion,[],[f407]) ).
cnf(s4,plain,
( spl10_2
| spl10_3
| spl10_5 ),
inference(rat,[],[s3]) ).
cnf(s5,plain,
( spl10_3
| spl10_2
| spl10_3
| spl10_6 ),
inference(sat_conversion,[],[f412]) ).
cnf(s6,plain,
( spl10_2
| spl10_3
| spl10_6 ),
inference(rat,[],[s5]) ).
cnf(s12,plain,
~ spl10_2,
inference(sat_conversion,[],[f438]) ).
cnf(s15,plain,
( spl10_13
| ~ spl10_4
| spl10_13
| spl10_14 ),
inference(sat_conversion,[],[f480]) ).
cnf(s16,plain,
( ~ spl10_4
| spl10_13
| spl10_14 ),
inference(rat,[],[s15]) ).
cnf(s26,plain,
~ spl10_3,
inference(sat_conversion,[],[f520]) ).
cnf(s29,plain,
~ spl10_13,
inference(sat_conversion,[],[f533]) ).
cnf(s32,plain,
( ~ spl10_1
| spl10_3
| ~ spl10_14
| spl10_15 ),
inference(sat_conversion,[],[f573]) ).
cnf(s33,plain,
( ~ spl10_5
| ~ spl10_6
| spl10_13
| ~ spl10_15 ),
inference(sat_conversion,[],[f616]) ).
cnf(s35,plain,
( ~ spl10_4
| spl10_14 ),
inference(rat,[],[s16,s29]) ).
cnf(s38,plain,
spl10_6,
inference(rat,[],[s6,s26,s12]) ).
cnf(s39,plain,
spl10_5,
inference(rat,[],[s4,s26,s12]) ).
cnf(s40,plain,
~ spl10_15,
inference(rat,[],[s33,s38,s29,s39]) ).
cnf(s41,plain,
spl10_4,
inference(rat,[],[s2,s26,s12]) ).
cnf(s42,plain,
spl10_14,
inference(rat,[],[s35,s41]) ).
cnf(s43,plain,
~ spl10_1,
inference(rat,[],[s32,s40,s26,s42]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s1,s26,s12,s43]) ).
thf(f617,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA033^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:23:07 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.32 % (1260089)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (1260098)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1789668147:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (1260100)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (1260100)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
% 0.20/0.32 % (1260094)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3783328231:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (1260095)lrs+10_16_si=on:nwc=1.5:random_seed=494179569:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (1260096)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1917217078:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (1260097)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=1442341364: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)
% 0.20/0.32 % (1260099)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1016344902:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (1260100)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=2362174821:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (1260098)Instruction limit reached!
% 0.20/0.32 % (1260098)------------------------------
% 0.20/0.32 % (1260098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (1260098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (1260098)CaDiCaL version: 2.1.3
% 0.20/0.32 % (1260098)Termination reason: Instruction limit
% 0.20/0.32 % (1260098)Termination phase: Saturation
% 0.20/0.32 % (1260098)Time elapsed: 0.008 s
% 0.20/0.32 % (1260098)Peak memory usage: 12 MB
% 0.20/0.32 % (1260098)Instructions burned: 25 (million)
% 0.20/0.32 % (1260096)Instruction limit reached!
% 0.20/0.32 % (1260096)------------------------------
% 0.20/0.32 % (1260096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (1260096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (1260096)CaDiCaL version: 2.1.3
% 0.20/0.32 % (1260096)Termination reason: Instruction limit
% 0.20/0.32 % (1260096)Termination phase: Property scanning
% 0.20/0.32 % (1260096)Time elapsed: 0.002 s
% 0.20/0.32 % (1260096)Peak memory usage: 10 MB
% 0.20/0.32 % (1260096)Instructions burned: 4 (million)
% 0.20/0.32 % (1260095)Instruction limit reached!
% 0.20/0.32 % (1260095)------------------------------
% 0.20/0.32 % (1260095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (1260095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (1260095)CaDiCaL version: 2.1.3
% 0.20/0.33 % (1260095)Termination reason: Instruction limit
% 0.20/0.33 % (1260095)Termination phase: Saturation
% 0.20/0.33 % (1260095)Time elapsed: 0.009 s
% 0.20/0.33 % (1260095)Peak memory usage: 11 MB
% 0.20/0.33 % (1260095)Instructions burned: 19 (million)
% 0.20/0.33 % (1260108)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3481342117:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.33 % (1260108)Instruction limit reached!
% 0.20/0.33 % (1260108)------------------------------
% 0.20/0.33 % (1260108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (1260108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (1260108)CaDiCaL version: 2.1.3
% 0.20/0.33 % (1260108)Termination reason: Instruction limit
% 0.20/0.33 % (1260108)Termination phase: Property scanning
% 0.20/0.33 % (1260108)Time elapsed: 0.002 s
% 0.20/0.33 % (1260108)Peak memory usage: 10 MB
% 0.20/0.33 % (1260108)Instructions burned: 11 (million)
% 0.20/0.33 % (1260109)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2144636472:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.33 % (1260110)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.33 % (1260100) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1260089-1260100"...
% 0.20/0.33 % (1260109)Instruction limit reached!
% 0.20/0.33 % (1260109)------------------------------
% 0.20/0.33 % (1260109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (1260109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (1260109)CaDiCaL version: 2.1.3
% 0.20/0.33 % (1260109)Termination reason: Instruction limit
% 0.20/0.33 % (1260109)Termination phase: Property scanning
% 0.20/0.33 % (1260109)Time elapsed: 0.003 s
% 0.20/0.33 % (1260109)Peak memory usage: 10 MB
% 0.20/0.33 % (1260109)Instructions burned: 6 (million)
% 0.20/0.33 % (1260112)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=198192593:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.33 % (1260110)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3274776985:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.33 % (1260112)Instruction limit reached!
% 0.20/0.33 % (1260112)------------------------------
% 0.20/0.33 % (1260112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (1260112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (1260112)CaDiCaL version: 2.1.3
% 0.20/0.33 % (1260112)Termination reason: Instruction limit
% 0.20/0.33 % (1260112)Termination phase: Saturation
% 0.20/0.33 % (1260112)Time elapsed: 0.003 s
% 0.20/0.33 % (1260112)Peak memory usage: 11 MB
% 0.20/0.33 % (1260112)Instructions burned: 14 (million)
% 0.20/0.33 % (1260110)Instruction limit reached!
% 0.20/0.33 % (1260110)------------------------------
% 0.20/0.33 % (1260110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (1260110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (1260110)CaDiCaL version: 2.1.3
% 0.20/0.33 % (1260110)Termination reason: Instruction limit
% 0.20/0.33 % (1260110)Termination phase: Function definition elimination
% 0.20/0.33 % (1260110)Time elapsed: 0.004 s
% 0.20/0.33 % (1260110)Peak memory usage: 10 MB
% 0.20/0.33 % (1260110)Instructions burned: 9 (million)
% 0.20/0.33 % (1260099)Instruction limit reached!
% 0.20/0.33 % (1260099)------------------------------
% 0.20/0.33 % (1260099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (1260099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (1260099)CaDiCaL version: 2.1.3
% 0.20/0.33 % (1260099)Termination reason: Instruction limit
% 0.20/0.33 % (1260099)Termination phase: Saturation
% 0.20/0.33 % (1260099)Time elapsed: 0.037 s
% 0.20/0.33 % (1260099)Peak memory usage: 12 MB
% 0.20/0.33 % (1260099)Instructions burned: 75 (million)
% 0.20/0.33 % (1260100)...printing done.
% 0.20/0.33 % (1260100)Refutation found. Thanks to Tanya!
% 0.20/0.33 % SZS status Theorem for theBenchmark
% 0.20/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.33 % (1260100)------------------------------
% 0.20/0.33 % (1260100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (1260100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (1260100)CaDiCaL version: 2.1.3
% 0.20/0.33 % (1260100)Termination reason: Refutation
% 0.20/0.33 % (1260100)Time elapsed: 0.036 s
% 0.20/0.33 % (1260100)Peak memory usage: 13 MB
% 0.20/0.33 % (1260100)Instructions burned: 76 (million)
% 0.20/0.33 % (1260089)Success in time 0.084 s
% 0.20/0.33 % Vampire exiting
%------------------------------------------------------------------------------