%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA054^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:20:26 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 20
% Syntax : Number of formulae : 157 ( 61 unt; 0 typ; 9 def)
% Number of atoms : 1432 ( 244 equ; 0 cnn)
% Maximal formula atoms : 26 ( 9 avg)
% Number of connectives : 2232 ( 91 ~; 198 |; 86 &;1570 @)
% ( 8 <=>; 147 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 48 usr; 18 con; 0-4 aty)
% ( 103 !!; 29 ??; 0 @@+; 0 @@-)
% Number of variables : 481 ( 0 sgn 130 !; 2 ?; 481 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_16,type,
h: $i > mworld > $o ).
thf(func_def_17,type,
closed: $i > mworld > $o ).
thf(func_def_18,type,
combo: $i > $i > mworld > $o ).
thf(func_def_19,type,
open: $i > mworld > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_26,type,
vIFF: $o > $o > $o ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vAND: $o > $o > $o ).
thf(func_def_30,type,
vIMP: $o > $o > $o ).
thf(func_def_31,type,
vNOT: $o > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
sF0: $o ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
sK2: mworld ).
thf(func_def_38,type,
sK3: mworld ).
thf(func_def_39,type,
sK4: mworld > $i ).
thf(func_def_40,type,
sK5: mworld > $i ).
thf(func_def_41,type,
sK6: mworld > mworld ).
thf(func_def_42,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
sK7: $i > mworld > $i > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f12,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f13,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( combo @ X0 @ X1 ) @ ( h @ X2 ) ) ) @ ( mbox @ ( open @ X0 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( mnot @ ( combo @ X0 @ X1 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ X0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(f14,axiom,
mlocal @ ( mbox @ ( closed @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(f18,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ X0 ) @ ( h @ X1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f19,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ X0 ) @ ( h @ X1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
thf(f20,plain,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( combo @ X0 @ X1 ) @ ( h @ X2 ) ) ) @ ( mbox @ ( open @ X0 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ X0 ) @ ( mand @ ( mnot @ ( combo @ X0 @ X1 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ X0 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f21,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( combo @ Y0 @ Y1 ) @ ( h @ Y2 ) ) ) @ ( mbox @ ( open @ Y0 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( mnot @ ( combo @ Y0 @ Y1 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f20]) ).
thf(f28,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f29,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f31,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f33,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f35,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f36,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f43,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f44,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f46,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] :
( mexists_di
@ ^ [X1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ X0 ) @ ( h @ X1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f48,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
mlocal @ ( mbox @ ( closed @ d ) ),
inference(rectify,[],[f14]) ).
thf(f50,plain,
( ( mlocal @ ( mbox @ ( closed @ d ) ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f53,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f54,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ),
inference(flattening,[],[f48]) ).
thf(f60,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f61,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f65,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f66,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f68,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f69,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f70,plain,
( ( mlocal @ ( mbox @ ( closed @ d ) ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f71,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] :
( mexists_di
@ ^ [Y1: $i] : ( mimplies @ ( mbox @ ( mand @ ( combo @ d @ Y0 ) @ ( h @ Y1 ) ) ) @ ( mbox @ ( open @ d ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f73,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f74,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f76,plain,
( ( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mexists_di
@ ^ [Y2: $i] : ( mand @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( combo @ Y0 @ Y1 ) @ ( h @ Y2 ) ) ) @ ( mbox @ ( open @ Y0 ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( closed @ Y0 ) @ ( mand @ ( mnot @ ( combo @ Y0 @ Y1 ) ) @ ( h @ o ) ) ) @ ( mbox @ ( closed @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f81,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( closed @ d ) ) ) ),
inference(definition_unfolding,[],[f70,f66,f69]) ).
thf(f82,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f71,f66,f69,f60,f60,f61,f69,f74,f69]) ).
thf(f84,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( ?? @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( closed @ Y0 )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( combo @ Y0 @ Y1 )
@ ( h @ Y2 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( open @ Y0 ) ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( closed @ Y0 )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
~ ( Y3 @ Y4 )
@ ( combo @ Y0 @ Y1 ) )
@ ( h @ o ) ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld] :
( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ ( closed @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f76,f66,f69,f73,f73,f60,f74,f69,f61,f74,f74,f69,f69,f61,f74,f74,f68,f69]) ).
thf(f85,definition,
( sF0
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f86,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f85]) ).
thf(f87,plain,
$true != sF0,
inference(definition_folding,[],[f82,f86]) ).
thf(f94,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( closed @ d @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f95,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( closed @ d @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( closed @ d @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
! [X1: mworld] :
( ( $true
= ( closed @ d @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f107,plain,
( ( $false
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( ?? @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( combo @ d @ Y0 )
@ ( h @ Y1 ) ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ ( open @ d ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f86]) ).
thf(f108,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( h @ Y2 @ Y3 )
& ( combo @ d @ Y1 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( open @ d @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( ( h @ Y2 @ Y3 )
& ( combo @ d @ Y1 @ Y3 ) ) ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y3 )
=> ( open @ d @ Y3 ) ) ) ) ) ) )
@ sK2 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( ( h @ Y1 @ Y2 )
& ( combo @ d @ Y0 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( open @ d @ Y2 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( ( h @ Y1 @ Y2 )
& ( combo @ d @ Y0 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( open @ d @ Y2 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ( $true = sF0 )
| ( $true
= ( mrel @ mactual @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f113,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( ( h @ Y1 @ Y2 )
& ( combo @ d @ Y0 @ Y2 ) ) ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ sK2 @ Y2 )
=> ( open @ d @ Y2 ) ) ) ) )
@ X1 )
= $false )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f111]) ).
thf(f114,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( ( h @ Y0 @ Y1 )
& ( combo @ d @ X1 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( open @ d @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( ( h @ Y0 @ Y1 )
& ( combo @ d @ X1 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( open @ d @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( ( h @ X2 @ Y0 )
& ( combo @ d @ X1 @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( open @ d @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( open @ d @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( ( h @ X2 @ Y0 )
& ( combo @ d @ X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f119,plain,
! [X2: $i,X3: mworld,X1: $i] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( ( h @ X2 @ Y0 )
& ( combo @ d @ X1 @ Y0 ) ) )
@ X3 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X3: mworld,X1: $i] :
( ( $true
= ( ( mrel @ sK2 @ X3 )
=> ( ( h @ X2 @ X3 )
& ( combo @ d @ X1 @ X3 ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: mworld,X1: $i] :
( ( $false
= ( mrel @ sK2 @ X3 ) )
| ( $true = sF0 )
| ( $true
= ( ( h @ X2 @ X3 )
& ( combo @ d @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X3: mworld,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( combo @ d @ X1 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: mworld] :
( ( $true
= ( h @ X2 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) )
| ( $true = sF0 ) ),
inference(and_proxy_clausification,[],[f121]) ).
thf(f124,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( open @ d @ Y0 ) )
@ sK3 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f125,plain,
( ( $false
= ( ( mrel @ sK2 @ sK3 )
=> ( open @ d @ sK3 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
( ( ( open @ d @ sK3 )
= $false )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f127,plain,
( ( $true
= ( mrel @ sK2 @ sK3 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f125]) ).
thf(f151,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( h @ o @ Y4 )
& ~ ( combo @ Y1 @ Y2 @ Y4 )
& ( closed @ Y1 @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( closed @ Y1 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( h @ Y3 @ Y4 )
& ( combo @ Y1 @ Y2 @ Y4 )
& ( closed @ Y1 @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( open @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f84]) ).
thf(f152,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( h @ o @ Y4 )
& ~ ( combo @ Y1 @ Y2 @ Y4 )
& ( closed @ Y1 @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( closed @ Y1 @ Y5 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y0 @ Y4 )
=> ( ( ( h @ Y3 @ Y4 )
& ( combo @ Y1 @ Y2 @ Y4 )
& ( closed @ Y1 @ Y4 ) )
=> ( !! @ mworld
@ ^ [Y5: mworld] :
( ( mrel @ Y4 @ Y5 )
=> ( open @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( h @ o @ Y3 )
& ~ ( combo @ Y0 @ Y1 @ Y3 )
& ( closed @ Y0 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( closed @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( h @ Y2 @ Y3 )
& ( combo @ Y0 @ Y1 @ Y3 )
& ( closed @ Y0 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( open @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( h @ o @ Y3 )
& ~ ( combo @ Y0 @ Y1 @ Y3 )
& ( closed @ Y0 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( closed @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( h @ Y2 @ Y3 )
& ( combo @ Y0 @ Y1 @ Y3 )
& ( closed @ Y0 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( open @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( h @ o @ Y3 )
& ~ ( combo @ Y0 @ Y1 @ Y3 )
& ( closed @ Y0 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( closed @ Y0 @ Y4 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ X1 @ Y3 )
=> ( ( ( h @ Y2 @ Y3 )
& ( combo @ Y0 @ Y1 @ Y3 )
& ( closed @ Y0 @ Y3 ) )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y3 @ Y4 )
=> ( open @ Y0 @ Y4 ) ) ) ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ o @ Y2 )
& ~ ( combo @ X2 @ Y0 @ Y2 )
& ( closed @ X2 @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( closed @ X2 @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( combo @ X2 @ Y0 @ Y2 )
& ( closed @ X2 @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( open @ X2 @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ o @ Y2 )
& ~ ( combo @ X2 @ Y0 @ Y2 )
& ( closed @ X2 @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( closed @ X2 @ Y3 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ X1 @ Y2 )
=> ( ( ( h @ Y1 @ Y2 )
& ( combo @ X2 @ Y0 @ Y2 )
& ( closed @ X2 @ Y2 ) )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( open @ X2 @ Y3 ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ o @ Y1 )
& ~ ( combo @ X2 @ X3 @ Y1 )
& ( closed @ X2 @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( closed @ X2 @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ Y0 @ Y1 )
& ( combo @ X2 @ X3 @ Y1 )
& ( closed @ X2 @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( open @ X2 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ o @ Y1 )
& ~ ( combo @ X2 @ X3 @ Y1 )
& ( closed @ X2 @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( closed @ X2 @ Y2 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
=> ( ( ( h @ Y0 @ Y1 )
& ( combo @ X2 @ X3 @ Y1 )
& ( closed @ X2 @ Y1 ) )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( open @ X2 @ Y2 ) ) ) ) ) ) )
@ ( sK7 @ X3 @ X1 @ X2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ o @ Y0 )
& ~ ( combo @ X2 @ X3 @ Y0 )
& ( closed @ X2 @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( closed @ X2 @ Y1 ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 )
& ( combo @ X2 @ X3 @ Y0 )
& ( closed @ X2 @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( open @ X2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 )
& ( combo @ X2 @ X3 @ Y0 )
& ( closed @ X2 @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( open @ X2 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f160]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( ( ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ Y0 )
& ( combo @ X2 @ X3 @ Y0 )
& ( closed @ X2 @ Y0 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( open @ X2 @ Y1 ) ) ) ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ X4 )
=> ( ( ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 )
& ( combo @ X2 @ X3 @ X4 )
& ( closed @ X2 @ X4 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $true
= ( ( ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 )
& ( combo @ X2 @ X3 @ X4 )
& ( closed @ X2 @ X4 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 )
& ( combo @ X2 @ X3 @ X4 )
& ( closed @ X2 @ X4 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 )
& ( combo @ X2 @ X3 @ X4 ) ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( closed @ X2 @ X4 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld] :
( ( $false
= ( combo @ X2 @ X3 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) ) ) )
| ( $false
= ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 ) )
| ( $false
= ( closed @ X2 @ X4 ) )
| ( $false
= ( mrel @ X1 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( combo @ X2 @ X3 @ X4 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X4 @ Y0 )
=> ( open @ X2 @ Y0 ) )
@ X5 ) )
| ( $false
= ( closed @ X2 @ X4 ) )
| ( $false
= ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 ) )
| ( $false
= ( combo @ X2 @ X3 @ X4 ) )
| ( $true
= ( ( mrel @ X4 @ X5 )
=> ( open @ X2 @ X5 ) ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( closed @ X2 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: mworld,X4: mworld,X5: mworld] :
( ( $false
= ( h @ ( sK7 @ X3 @ X1 @ X2 ) @ X4 ) )
| ( $false
= ( mrel @ X1 @ X4 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X4 @ X5 ) )
| ( $true
= ( open @ X2 @ X5 ) )
| ( $false
= ( closed @ X2 @ X4 ) )
| ( $false
= ( combo @ X2 @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f183,definition,
( spl8_1
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f187,definition,
( spl8_2
<=> ( $true
= ( mrel @ mactual @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f189,plain,
( ( $true
= ( mrel @ mactual @ sK2 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f190,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f112,f187,f183]) ).
thf(f192,definition,
( spl8_3
<=> ! [X2: $i,X3: mworld] :
( ( $true
= ( h @ X2 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f193,plain,
( ! [X2: $i,X3: mworld] :
( ( $true
= ( h @ X2 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f192]) ).
thf(f194,plain,
( spl8_3
| spl8_1 ),
inference(avatar_split_clause,[],[f123,f183,f192]) ).
thf(f196,definition,
( spl8_4
<=> ! [X1: $i,X3: mworld] :
( ( $true
= ( combo @ d @ X1 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f197,plain,
( ! [X3: mworld,X1: $i] :
( ( $true
= ( combo @ d @ X1 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f198,plain,
( spl8_4
| spl8_1 ),
inference(avatar_split_clause,[],[f122,f183,f196]) ).
thf(f200,definition,
( spl8_5
<=> ( $true
= ( mrel @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f202,plain,
( ( $true
= ( mrel @ sK2 @ sK3 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f203,plain,
( spl8_5
| spl8_1 ),
inference(avatar_split_clause,[],[f127,f183,f200]) ).
thf(f205,definition,
( spl8_6
<=> ( ( open @ d @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f207,plain,
( ( ( open @ d @ sK3 )
= $false )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f208,plain,
( spl8_1
| spl8_6 ),
inference(avatar_split_clause,[],[f126,f205,f183]) ).
thf(f221,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f87,f183]) ).
thf(f267,plain,
( ! [X2: $i,X3: mworld,X0: $i,X1: mworld,X4: mworld] :
( ( $false
= ( combo @ X2 @ X0 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true = $false )
| ( $false
= ( closed @ X2 @ X3 ) )
| ( $true
= ( open @ X2 @ X4 ) )
| ( $false
= ( mrel @ X3 @ X4 ) ) )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f181,f193]) ).
thf(f270,plain,
( ! [X2: $i,X3: mworld,X0: $i,X1: mworld,X4: mworld] :
( ( $false
= ( combo @ X2 @ X0 @ X3 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( mrel @ sK2 @ X3 ) )
| ( $true
= ( open @ X2 @ X4 ) )
| ( $false
= ( mrel @ X3 @ X4 ) )
| ( $false
= ( closed @ X2 @ X3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f273,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ X1 @ X3 ) )
| ( $true
= ( open @ d @ X3 ) )
| ( $true = $false )
| ( $false
= ( mrel @ X2 @ X1 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $false
= ( closed @ d @ X1 ) ) )
| ~ spl8_3
| ~ spl8_4 ),
inference(constrained_superposition,[],[f270,f197]) ).
thf(f284,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( $true = $false )
| ( $false
= ( closed @ d @ X1 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( open @ d @ X3 ) )
| ( $false
= ( mrel @ X2 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) ) )
| ~ spl8_3
| ~ spl8_4 ),
inference(duplicate_literal_removal,[],[f273]) ).
thf(f285,plain,
( ! [X2: mworld,X3: mworld,X1: mworld] :
( ( $true
= ( open @ d @ X3 ) )
| ( $false
= ( closed @ d @ X1 ) )
| ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( mrel @ X2 @ X1 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) ) )
| ~ spl8_3
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f291,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false
= ( mrel @ X0 @ sK3 ) )
| ( $false
= ( closed @ d @ X0 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( mrel @ X1 @ X0 ) )
| ( $true = $false )
| ( $false
= ( mrel @ sK2 @ X0 ) ) )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_6 ),
inference(constrained_superposition,[],[f285,f207]) ).
thf(f300,plain,
( ! [X0: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X0 ) )
| ( $false
= ( mrel @ X0 @ sK3 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( closed @ d @ X0 ) )
| ( $false
= ( mrel @ X1 @ X0 ) ) )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f291]) ).
thf(f321,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ sK2 @ sK3 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ sK2 )
= $false )
| ( $false
= ( closed @ d @ sK2 ) )
| ( $true = $false ) )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_6 ),
inference(constrained_superposition,[],[f65,f300]) ).
thf(f328,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ sK2 )
= $false )
| ( $false
= ( closed @ d @ sK2 ) )
| ( $false
= ( mrel @ sK2 @ sK3 ) ) )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f338,plain,
( ! [X0: mworld] :
( ( ( mrel @ X0 @ sK2 )
= $false )
| ( $false
= ( closed @ d @ sK2 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true = $false ) )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6 ),
inference(forward_demodulation,[],[f328,f202]) ).
thf(f339,plain,
( ! [X0: mworld] :
( ( ( mrel @ X0 @ sK2 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( closed @ d @ sK2 ) ) )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6 ),
inference(trivial_inequality_removal,[],[f338]) ).
thf(f343,definition,
( spl8_12
<=> ( $false
= ( closed @ d @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition]) ).
thf(f345,plain,
( ( $false
= ( closed @ d @ sK2 ) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f343]) ).
thf(f347,definition,
( spl8_13
<=> ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ sK2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_13])],[avatar_definition]) ).
thf(f348,plain,
( ! [X0: mworld] :
( ( $false
= ( mrel @ mactual @ X0 ) )
| ( ( mrel @ X0 @ sK2 )
= $false ) )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f347]) ).
thf(f359,plain,
( spl8_12
| spl8_13
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6 ),
inference(avatar_split_clause,[],[f339,f205,f200,f196,f192,f347,f343]) ).
thf(f362,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ( $true = $false )
| ~ spl8_12 ),
inference(constrained_superposition,[],[f97,f345]) ).
thf(f364,plain,
( ( $false
= ( mrel @ mactual @ sK2 ) )
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f369,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_12 ),
inference(forward_demodulation,[],[f364,f189]) ).
thf(f370,plain,
( $false
| ~ spl8_2
| ~ spl8_12 ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f371,plain,
( ~ spl8_2
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f370]) ).
thf(f392,plain,
( ( $false
= ( mrel @ sK2 @ sK2 ) )
| ( $true = $false )
| ~ spl8_2
| ~ spl8_13 ),
inference(constrained_superposition,[],[f189,f348]) ).
thf(f400,plain,
( ( $false
= ( mrel @ sK2 @ sK2 ) )
| ~ spl8_2
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f392]) ).
thf(f411,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_13 ),
inference(forward_demodulation,[],[f400,f65]) ).
thf(f412,plain,
( $false
| ~ spl8_2
| ~ spl8_13 ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f413,plain,
( ~ spl8_2
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[],[f412]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f190]) ).
cnf(s2,plain,
( spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f194]) ).
cnf(s3,plain,
( spl8_1
| spl8_4 ),
inference(sat_conversion,[],[f198]) ).
cnf(s4,plain,
( spl8_1
| spl8_5 ),
inference(sat_conversion,[],[f203]) ).
cnf(s5,plain,
( spl8_1
| spl8_6 ),
inference(sat_conversion,[],[f208]) ).
cnf(s8,plain,
~ spl8_1,
inference(sat_conversion,[],[f221]) ).
cnf(s15,plain,
( ~ spl8_3
| ~ spl8_4
| ~ spl8_5
| ~ spl8_6
| spl8_12
| spl8_13 ),
inference(sat_conversion,[],[f359]) ).
cnf(s17,plain,
( ~ spl8_2
| ~ spl8_12 ),
inference(sat_conversion,[],[f371]) ).
cnf(s21,plain,
( ~ spl8_2
| ~ spl8_13 ),
inference(sat_conversion,[],[f413]) ).
cnf(s23,plain,
spl8_6,
inference(rat,[],[s5,s8]) ).
cnf(s24,plain,
spl8_5,
inference(rat,[],[s4,s8]) ).
cnf(s25,plain,
spl8_4,
inference(rat,[],[s3,s8]) ).
cnf(s26,plain,
spl8_3,
inference(rat,[],[s2,s8]) ).
cnf(s27,plain,
spl8_2,
inference(rat,[],[s1,s8]) ).
cnf(s28,plain,
~ spl8_13,
inference(rat,[],[s21,s27]) ).
cnf(s29,plain,
~ spl8_12,
inference(rat,[],[s17,s27]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s15,s26,s25,s23,s24,s28,s29]) ).
thf(f414,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA054^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:24:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 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
% 0.22/0.30 % (3501001)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (3501011)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1724030837:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (3501012)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (3501012)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
% 0.22/0.30 % (3501006)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3671754675:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (3501007)lrs+10_16_si=on:nwc=1.5:random_seed=1726908143:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (3501010)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2790641679:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (3501008)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2630747126:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (3501009)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=424905724: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)
% 0.22/0.30 % (3501012)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=2528998229:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (3501008)Instruction limit reached!
% 0.22/0.30 % (3501008)------------------------------
% 0.22/0.30 % (3501008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3501008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3501008)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3501008)Termination reason: Instruction limit
% 0.22/0.30 % (3501008)Termination phase: Property scanning
% 0.22/0.30 % (3501008)Time elapsed: 0.002 s
% 0.22/0.30 % (3501008)Peak memory usage: 10 MB
% 0.22/0.30 % (3501008)Instructions burned: 4 (million)
% 0.22/0.30 % (3501007)Instruction limit reached!
% 0.22/0.30 % (3501007)------------------------------
% 0.22/0.30 % (3501007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3501007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3501007)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3501007)Termination reason: Instruction limit
% 0.22/0.30 % (3501007)Termination phase: Saturation
% 0.22/0.30 % (3501007)Time elapsed: 0.009 s
% 0.22/0.30 % (3501007)Peak memory usage: 12 MB
% 0.22/0.30 % (3501007)Instructions burned: 19 (million)
% 0.22/0.30 % (3501011)Instruction limit reached!
% 0.22/0.30 % (3501011)------------------------------
% 0.22/0.30 % (3501011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3501011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3501011)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3501011)Termination reason: Instruction limit
% 0.22/0.31 % (3501011)Termination phase: Saturation
% 0.22/0.31 % (3501011)Time elapsed: 0.020 s
% 0.22/0.31 % (3501011)Peak memory usage: 12 MB
% 0.22/0.31 % (3501011)Instructions burned: 77 (million)
% 0.22/0.31 % (3501010)Instruction limit reached!
% 0.22/0.31 % (3501010)------------------------------
% 0.22/0.31 % (3501010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3501010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3501010)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3501010)Termination reason: Instruction limit
% 0.22/0.31 % (3501010)Termination phase: Saturation
% 0.22/0.31 % (3501010)Time elapsed: 0.013 s
% 0.22/0.31 % (3501010)Peak memory usage: 11 MB
% 0.22/0.31 % (3501010)Instructions burned: 24 (million)
% 0.22/0.31 % (3501012) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3501001-3501012"...
% 0.22/0.31 % (3501020)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3929491933:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (3501006) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3501001-3501006"...
% 0.22/0.31 % (3501012)...printing done.
% 0.22/0.31 % (3501020)Instruction limit reached!
% 0.22/0.31 % (3501020)------------------------------
% 0.22/0.31 % (3501020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3501020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3501020)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3501020)Termination reason: Instruction limit
% 0.22/0.31 % (3501020)Termination phase: Function definition elimination
% 0.22/0.31 % (3501020)Time elapsed: 0.002 s
% 0.22/0.31 % (3501020)Peak memory usage: 10 MB
% 0.22/0.31 % (3501020)Instructions burned: 4 (million)
% 0.22/0.31 % (3501012)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (3501012)------------------------------
% 0.22/0.31 % (3501012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3501012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3501012)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3501012)Termination reason: Refutation
% 0.22/0.31 % (3501012)Time elapsed: 0.021 s
% 0.22/0.31 % (3501012)Peak memory usage: 13 MB
% 0.22/0.31 % (3501012)Instructions burned: 41 (million)
% 0.22/0.31 % (3501001)Success in time 0.053 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------