%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL956^18 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:15:28 AM UTC 2026
% Result : Theorem 0.23s 0.34s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 23
% Syntax : Number of formulae : 262 ( 40 unt; 0 typ; 15 def)
% Number of atoms : 2533 ( 410 equ; 0 cnn)
% Maximal formula atoms : 30 ( 9 avg)
% Number of connectives : 3869 ( 187 ~; 387 |; 186 &;2497 @)
% ( 15 <=>; 327 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 67 usr; 36 con; 0-4 aty)
% ( 212 !!; 58 ??; 0 @@+; 0 @@-)
% Number of variables : 616 ( 0 sgn 166 !; 2 ?; 616 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
p: mworld > $o ).
thf(func_def_15,type,
big_q: $i > mworld > $o ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vIFF: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
sK0: mworld > $i ).
thf(func_def_30,type,
sK1: mworld ).
thf(func_def_31,type,
sK2: mworld ).
thf(func_def_33,type,
sK4: mworld ).
thf(func_def_34,type,
sK5: $i > mworld ).
thf(func_def_36,type,
sK7: mworld ).
thf(func_def_37,type,
sK8: $i > mworld ).
thf(func_def_40,type,
sK11: mworld ).
thf(func_def_41,type,
sK12: $i > mworld ).
thf(func_def_42,type,
sK13: $i > mworld ).
thf(func_def_43,type,
sK14: $i > mworld ).
thf(func_def_44,type,
sK15: mworld ).
thf(func_def_46,type,
sK17: $i > mworld ).
thf(func_def_47,type,
sK18: mworld ).
thf(func_def_48,type,
sK19: mworld ).
thf(func_def_49,type,
sK20: mworld ).
thf(func_def_50,type,
sK21: mworld ).
thf(func_def_51,type,
sK22: $i > mworld ).
thf(func_def_52,type,
sK23: $i > mworld ).
thf(func_def_53,type,
sK24: mworld ).
thf(func_def_54,type,
sK25: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
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,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f11,axiom,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( mrel @ X0 @ X1 )
& ( eiw_di @ X2 @ X0 ) )
=> ( eiw_di @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(f13,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f14,conjecture,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X0 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( big_q @ X0 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( big_q @ X0 ) ) ) )
@ ( mexists_di
@ ^ [X0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2109) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X0 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( big_q @ X0 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( big_q @ X0 ) ) ) )
@ ( mexists_di
@ ^ [X0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X0 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f16,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f19,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f20,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f23,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f24,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f27,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f28,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f31,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f32,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( mrel @ X0 @ X1 )
& ( eiw_di @ X2 @ X0 ) )
=> ( eiw_di @ X2 @ X1 ) ),
inference(rectify,[],[f11]) ).
thf(f36,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( ( mrel @ X0 @ X1 )
= $true )
& ( ( eiw_di @ X2 @ X0 )
= $true ) )
=> ( ( eiw_di @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f35]) ).
thf(f39,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f40,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
~ ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X0 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X1: $i] : ( mbox @ ( big_q @ X1 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [X2: $i] : ( mbox @ ( big_q @ X2 ) ) ) )
@ ( mexists_di
@ ^ [X3: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f42,plain,
( $true
!= ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ Y0 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_q @ Y0 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_q @ Y0 ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( $true
!= ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ Y0 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_q @ Y0 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_q @ Y0 ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ Y0 ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f42]) ).
thf(f44,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f36]) ).
thf(f45,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(flattening,[],[f44]) ).
thf(f47,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f55,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f32]) ).
thf(f57,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f59,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f60,plain,
( $true
!= ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ Y0 ) ) ) )
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_q @ Y0 ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mand @ ( mbox @ p )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( big_q @ Y0 ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mand @ ( mbox @ p ) @ ( mbox @ ( big_q @ Y0 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f63,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ p )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( big_q @ Y0 ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( big_q @ Y0 ) ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( big_q @ Y0 ) ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y1 @ Y3 )
& ( Y2 @ Y3 ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ p )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( big_q @ Y0 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f60,f47,f49,f53,f51,f59,f49,f53,f53,f49,f53,f59,f53,f53,f51,f49,f53,f59,f53,f59,f49,f53,f53]) ).
thf(f64,plain,
( $true
!= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( p @ Y2 ) ) )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( $false
= ( ( mrel @ mactual @ sK1 )
=> ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( $false
= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f101,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f102,plain,
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f103,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f104,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f105,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f111,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f112,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ( p @ X1 ) ) )
| ( $true
= ( ( eiw_di @ sK6 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK6 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ( eiw_di @ sK6 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK6 @ Y0 ) ) ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK6 @ Y0 ) ) ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f118,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f119,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ( mrel @ sK2 @ X2 )
=> ( p @ X2 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $false
= ( mrel @ sK2 @ X2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f140,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK9 ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f103]) ).
thf(f141,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK9 ) )
| ( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f150,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK9 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f141]) ).
thf(f151,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK9 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $true
= ( ( eiw_di @ sK9 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) ) ) ) )
| ( $true
= ( ( eiw_di @ sK10 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) ) ) )
| ( $true
= ( ( eiw_di @ sK10 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( ( eiw_di @ sK10 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( eiw_di @ sK10 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f157,plain,
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f159,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( ( mrel @ sK2 @ X1 )
=> ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f163,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $true
= ( ( mrel @ sK2 @ X1 )
=> ( big_q @ sK10 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( big_q @ sK10 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( eiw_di @ sK10 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f166,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) )
@ X1 ) )
| ( $true
= ( eiw_di @ sK10 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f165]) ).
thf(f168,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ( big_q @ sK9 @ X1 ) ) )
| ( $true
= ( eiw_di @ sK10 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( eiw_di @ sK10 @ sK2 ) )
| ( $true
= ( big_q @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f171,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f172,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ( big_q @ sK9 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK2 @ X2 )
=> ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ( mrel @ sK2 @ X2 )
=> ( p @ X2 ) ) )
| ( $true
= ( big_q @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $false
= ( mrel @ sK2 @ X2 ) )
| ( $true
= ( big_q @ sK9 @ X1 ) )
| ( $true
= ( p @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK9 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f177,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ( big_q @ sK9 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK2 @ X2 )
=> ( big_q @ sK10 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( ( mrel @ sK2 @ X2 )
=> ( big_q @ sK10 @ X2 ) ) )
| ( $true
= ( big_q @ sK9 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $false
= ( mrel @ sK2 @ X2 ) )
| ( $true
= ( big_q @ sK9 @ X1 ) )
| ( $true
= ( big_q @ sK10 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f209,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f224,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f225,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f226,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK16 ) ) ),
inference(sigma_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( $false
= ( ( eiw_di @ X1 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) )
| ( $true
= ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( $true
= ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( $true
= ( eiw_di @ sK16 @ sK2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f230]) ).
thf(f233,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( $true
= ( eiw_di @ sK16 @ sK2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK18 ) ) ),
inference(sigma_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $false
= ( ( mrel @ sK1 @ ( sK17 @ X1 ) )
=> ( big_q @ X1 @ ( sK17 @ X1 ) ) ) )
| ( $true
= ( eiw_di @ sK16 @ sK2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK18 )
=> ( p @ sK18 ) ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK17 @ X1 ) ) )
| ( $true
= ( eiw_di @ sK16 @ sK2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK18 )
=> ( p @ sK18 ) ) ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f239,plain,
! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK17 @ X1 ) ) )
| ( $true
= ( eiw_di @ sK16 @ sK2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( p @ sK18 ) ) ),
inference(imp_proxy_clausification,[],[f235]) ).
thf(f241,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f231]) ).
thf(f254,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) )
@ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f241]) ).
thf(f255,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK17 @ X1 ) ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) )
@ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK20 ) ) ),
inference(sigma_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( ( mrel @ sK1 @ ( sK17 @ X1 ) )
=> ( big_q @ X1 @ ( sK17 @ X1 ) ) ) )
| ( $true
= ( ( mrel @ sK2 @ X2 )
=> ( big_q @ sK16 @ X2 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK20 )
=> ( p @ sK20 ) ) ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK17 @ X1 ) ) )
| ( $true
= ( ( mrel @ sK2 @ X2 )
=> ( big_q @ sK16 @ X2 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK20 )
=> ( p @ sK20 ) ) ) ),
inference(imp_proxy_clausification,[],[f256]) ).
thf(f262,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK17 @ X1 ) ) )
| ( $false
= ( mrel @ sK2 @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK20 )
=> ( p @ sK20 ) ) )
| ( $true
= ( big_q @ sK16 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f257]) ).
thf(f263,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK17 @ X1 ) ) )
| ( $false
= ( mrel @ sK2 @ X2 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( p @ sK20 ) )
| ( $true
= ( big_q @ sK16 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f265,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK21 ) ) ),
inference(sigma_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( eiw_di @ X1 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( $false
= ( ( eiw_di @ X2 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) ) ),
inference(beta-eta_normalization,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( $false
= ( ( eiw_di @ X2 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) )
| ( $false
= ( ( eiw_di @ X2 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK22 @ X1 ) ) )
| ( $false
= ( ( eiw_di @ X2 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK22 @ X1 ) ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) ) )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK22 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK23 @ X2 ) ) )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK22 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK23 @ X2 ) ) )
| ( $false
= ( p @ sK21 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f273]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK22 @ X1 ) ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK23 @ X2 ) ) )
| ( $false
= ( p @ sK21 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK25 ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f274]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( mrel @ sK1 @ ( sK22 @ X1 ) )
=> ( big_q @ X1 @ ( sK22 @ X1 ) ) ) )
| ( $false
= ( ( mrel @ sK2 @ ( sK23 @ X2 ) )
=> ( big_q @ X2 @ ( sK23 @ X2 ) ) ) )
| ( $false
= ( p @ sK21 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK25 )
=> ( p @ sK25 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f294,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( $false
= ( ( mrel @ sK2 @ ( sK23 @ X2 ) )
=> ( big_q @ X2 @ ( sK23 @ X2 ) ) ) )
| ( $false
= ( p @ sK21 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK25 )
=> ( p @ sK25 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f302,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( $false
= ( big_q @ X2 @ ( sK23 @ X2 ) ) )
| ( $false
= ( p @ sK21 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( ( mrel @ sK1 @ sK25 )
=> ( p @ sK25 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f294]) ).
thf(f306,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( $false
= ( big_q @ X2 @ ( sK23 @ X2 ) ) )
| ( $false
= ( p @ sK21 ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) )
| ( $false
= ( p @ sK25 ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f302]) ).
thf(f323,definition,
( spl26_4
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_4])],[avatar_definition]) ).
thf(f324,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl26_4 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f349,definition,
( spl26_10
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_10])],[avatar_definition]) ).
thf(f350,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f349]) ).
thf(f357,plain,
( spl26_4
| spl26_10 ),
inference(avatar_split_clause,[],[f121,f349,f323]) ).
thf(f381,definition,
( spl26_17
<=> ( $true
= ( eiw_di @ sK9 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_17])],[avatar_definition]) ).
thf(f383,plain,
( ( $true
= ( eiw_di @ sK9 @ sK1 ) )
| ~ spl26_17 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f386,definition,
( spl26_18
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( big_q @ sK9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_18])],[avatar_definition]) ).
thf(f387,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK1 @ X1 ) )
| ( $true
= ( big_q @ sK9 @ X1 ) ) )
| ~ spl26_18 ),
inference(avatar_component_clause,[],[f386]) ).
thf(f390,definition,
( spl26_19
<=> ( $true
= ( eiw_di @ sK10 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_19])],[avatar_definition]) ).
thf(f392,plain,
( ( $true
= ( eiw_di @ sK10 @ sK2 ) )
| ~ spl26_19 ),
inference(avatar_component_clause,[],[f390]) ).
thf(f393,plain,
( spl26_19
| spl26_17 ),
inference(avatar_split_clause,[],[f156,f381,f390]) ).
thf(f394,plain,
( spl26_4
| spl26_17 ),
inference(avatar_split_clause,[],[f161,f381,f323]) ).
thf(f396,definition,
( spl26_20
<=> ! [X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( big_q @ sK10 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_20])],[avatar_definition]) ).
thf(f397,plain,
( ! [X1: mworld] :
( ( $false
= ( mrel @ sK2 @ X1 ) )
| ( $true
= ( big_q @ sK10 @ X1 ) ) )
| ~ spl26_20 ),
inference(avatar_component_clause,[],[f396]) ).
thf(f398,plain,
( spl26_20
| spl26_17 ),
inference(avatar_split_clause,[],[f164,f381,f396]) ).
thf(f399,plain,
( spl26_19
| spl26_18 ),
inference(avatar_split_clause,[],[f169,f386,f390]) ).
thf(f400,plain,
( spl26_4
| spl26_18 ),
inference(avatar_split_clause,[],[f175,f386,f323]) ).
thf(f401,plain,
( spl26_20
| spl26_18 ),
inference(avatar_split_clause,[],[f179,f386,f396]) ).
thf(f453,definition,
( spl26_32
<=> ( $true
= ( eiw_di @ sK16 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_32])],[avatar_definition]) ).
thf(f455,plain,
( ( $true
= ( eiw_di @ sK16 @ sK2 ) )
| ~ spl26_32 ),
inference(avatar_component_clause,[],[f453]) ).
thf(f461,definition,
( spl26_34
<=> ( $false
= ( p @ sK18 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_34])],[avatar_definition]) ).
thf(f463,plain,
( ( $false
= ( p @ sK18 ) )
| ~ spl26_34 ),
inference(avatar_component_clause,[],[f461]) ).
thf(f466,definition,
( spl26_35
<=> ! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK17 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_35])],[avatar_definition]) ).
thf(f467,plain,
( ! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK17 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) ) )
| ~ spl26_35 ),
inference(avatar_component_clause,[],[f466]) ).
thf(f469,plain,
( spl26_34
| spl26_32
| spl26_35 ),
inference(avatar_split_clause,[],[f239,f466,f453,f461]) ).
thf(f487,definition,
( spl26_39
<=> ! [X2: mworld] :
( ( $false
= ( mrel @ sK2 @ X2 ) )
| ( $true
= ( big_q @ sK16 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_39])],[avatar_definition]) ).
thf(f488,plain,
( ! [X2: mworld] :
( ( $false
= ( mrel @ sK2 @ X2 ) )
| ( $true
= ( big_q @ sK16 @ X2 ) ) )
| ~ spl26_39 ),
inference(avatar_component_clause,[],[f487]) ).
thf(f491,definition,
( spl26_40
<=> ( $false
= ( p @ sK20 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_40])],[avatar_definition]) ).
thf(f493,plain,
( ( $false
= ( p @ sK20 ) )
| ~ spl26_40 ),
inference(avatar_component_clause,[],[f491]) ).
thf(f496,plain,
( spl26_40
| spl26_39
| spl26_35 ),
inference(avatar_split_clause,[],[f263,f466,f487,f491]) ).
thf(f518,definition,
( spl26_46
<=> ! [X2: $i] :
( ( $false
= ( big_q @ X2 @ ( sK23 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_46])],[avatar_definition]) ).
thf(f519,plain,
( ! [X2: $i] :
( ( $false
= ( big_q @ X2 @ ( sK23 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ sK2 ) ) )
| ~ spl26_46 ),
inference(avatar_component_clause,[],[f518]) ).
thf(f523,definition,
( spl26_47
<=> ! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl26_47])],[avatar_definition]) ).
thf(f524,plain,
( ! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK1 ) ) )
| ~ spl26_47 ),
inference(avatar_component_clause,[],[f523]) ).
thf(f534,definition,
( spl26_49
<=> ( $false
= ( p @ sK21 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_49])],[avatar_definition]) ).
thf(f536,plain,
( ( $false
= ( p @ sK21 ) )
| ~ spl26_49 ),
inference(avatar_component_clause,[],[f534]) ).
thf(f539,definition,
( spl26_50
<=> ( $false
= ( p @ sK25 ) ) ),
introduced(definition,[new_symbols(definition,[spl26_50])],[avatar_definition]) ).
thf(f541,plain,
( ( $false
= ( p @ sK25 ) )
| ~ spl26_50 ),
inference(avatar_component_clause,[],[f539]) ).
thf(f548,plain,
( spl26_50
| spl26_49
| spl26_46
| spl26_47 ),
inference(avatar_split_clause,[],[f306,f523,f518,f534,f539]) ).
thf(f549,plain,
( ! [X1: mworld] :
( ( $true = $false )
| ( $true
= ( p @ X1 ) ) )
| ~ spl26_10 ),
inference(forward_demodulation,[],[f350,f55]) ).
thf(f550,plain,
( ! [X1: mworld] :
( $true
= ( p @ X1 ) )
| ~ spl26_10 ),
inference(trivial_inequality_removal,[],[f549]) ).
thf(f551,plain,
( ! [X1: mworld] :
( ( $true = $false )
| ( $true
= ( big_q @ sK9 @ X1 ) ) )
| ~ spl26_18 ),
inference(forward_demodulation,[],[f387,f55]) ).
thf(f552,plain,
( ! [X1: mworld] :
( $true
= ( big_q @ sK9 @ X1 ) )
| ~ spl26_18 ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f573,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( $true != $true )
| ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f57,f55]) ).
thf(f582,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f573]) ).
thf(f608,plain,
( ! [X0: mworld] :
( ( $true != $true )
| ( $true
= ( eiw_di @ sK9 @ X0 ) ) )
| ~ spl26_17 ),
inference(constrained_superposition,[],[f582,f383]) ).
thf(f613,plain,
( ! [X0: mworld] :
( $true
= ( eiw_di @ sK9 @ X0 ) )
| ~ spl26_17 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f687,plain,
( ! [X2: mworld] :
( ( $true = $false )
| ( $true
= ( big_q @ sK16 @ X2 ) ) )
| ~ spl26_39 ),
inference(forward_demodulation,[],[f488,f55]) ).
thf(f688,plain,
( ! [X2: mworld] :
( $true
= ( big_q @ sK16 @ X2 ) )
| ~ spl26_39 ),
inference(trivial_inequality_removal,[],[f687]) ).
thf(f692,plain,
( ! [X0: mworld] :
( ( $true != $true )
| ( $true
= ( eiw_di @ sK16 @ X0 ) ) )
| ~ spl26_32 ),
inference(constrained_superposition,[],[f582,f455]) ).
thf(f693,plain,
( ! [X0: mworld] :
( $true
= ( eiw_di @ sK16 @ X0 ) )
| ~ spl26_32 ),
inference(trivial_inequality_removal,[],[f692]) ).
thf(f702,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ sK2 ) )
| ~ spl26_18
| ~ spl26_46 ),
inference(constrained_superposition,[],[f519,f552]) ).
thf(f703,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK16 @ sK2 ) )
| ~ spl26_39
| ~ spl26_46 ),
inference(constrained_superposition,[],[f519,f688]) ).
thf(f710,plain,
( ( $false
= ( eiw_di @ sK16 @ sK2 ) )
| ~ spl26_39
| ~ spl26_46 ),
inference(trivial_inequality_removal,[],[f703]) ).
thf(f711,plain,
( ( $false
= ( eiw_di @ sK9 @ sK2 ) )
| ~ spl26_18
| ~ spl26_46 ),
inference(trivial_inequality_removal,[],[f702]) ).
thf(f718,plain,
( ( $true = $false )
| ~ spl26_32
| ~ spl26_39
| ~ spl26_46 ),
inference(forward_demodulation,[],[f710,f693]) ).
thf(f719,plain,
( $false
| ~ spl26_32
| ~ spl26_39
| ~ spl26_46 ),
inference(trivial_inequality_removal,[],[f718]) ).
thf(f720,plain,
( ~ spl26_32
| ~ spl26_39
| ~ spl26_46 ),
inference(avatar_contradiction_clause,[],[f719]) ).
thf(f721,plain,
( ( $true = $false )
| ~ spl26_17
| ~ spl26_18
| ~ spl26_46 ),
inference(forward_demodulation,[],[f711,f613]) ).
thf(f722,plain,
( $false
| ~ spl26_17
| ~ spl26_18
| ~ spl26_46 ),
inference(trivial_inequality_removal,[],[f721]) ).
thf(f723,plain,
( ~ spl26_17
| ~ spl26_18
| ~ spl26_46 ),
inference(avatar_contradiction_clause,[],[f722]) ).
thf(f724,plain,
( ( $true = $false )
| ~ spl26_10
| ~ spl26_49 ),
inference(forward_demodulation,[],[f536,f550]) ).
thf(f725,plain,
( $false
| ~ spl26_10
| ~ spl26_49 ),
inference(trivial_inequality_removal,[],[f724]) ).
thf(f726,plain,
( ~ spl26_10
| ~ spl26_49 ),
inference(avatar_contradiction_clause,[],[f725]) ).
thf(f728,plain,
( ( $true = $false )
| ~ spl26_10
| ~ spl26_50 ),
inference(forward_demodulation,[],[f541,f550]) ).
thf(f729,plain,
( $false
| ~ spl26_10
| ~ spl26_50 ),
inference(trivial_inequality_removal,[],[f728]) ).
thf(f730,plain,
( ~ spl26_10
| ~ spl26_50 ),
inference(avatar_contradiction_clause,[],[f729]) ).
thf(f732,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK9 @ sK1 ) )
| ~ spl26_18
| ~ spl26_47 ),
inference(constrained_superposition,[],[f524,f552]) ).
thf(f733,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK16 @ sK1 ) )
| ~ spl26_39
| ~ spl26_47 ),
inference(constrained_superposition,[],[f524,f688]) ).
thf(f740,plain,
( ( $false
= ( eiw_di @ sK16 @ sK1 ) )
| ~ spl26_39
| ~ spl26_47 ),
inference(trivial_inequality_removal,[],[f733]) ).
thf(f741,plain,
( ( $false
= ( eiw_di @ sK9 @ sK1 ) )
| ~ spl26_18
| ~ spl26_47 ),
inference(trivial_inequality_removal,[],[f732]) ).
thf(f748,plain,
( ( $true = $false )
| ~ spl26_32
| ~ spl26_39
| ~ spl26_47 ),
inference(forward_demodulation,[],[f740,f693]) ).
thf(f749,plain,
( $false
| ~ spl26_32
| ~ spl26_39
| ~ spl26_47 ),
inference(trivial_inequality_removal,[],[f748]) ).
thf(f750,plain,
( ~ spl26_32
| ~ spl26_39
| ~ spl26_47 ),
inference(avatar_contradiction_clause,[],[f749]) ).
thf(f751,plain,
( ( $true = $false )
| ~ spl26_17
| ~ spl26_18
| ~ spl26_47 ),
inference(forward_demodulation,[],[f741,f613]) ).
thf(f752,plain,
( $false
| ~ spl26_17
| ~ spl26_18
| ~ spl26_47 ),
inference(trivial_inequality_removal,[],[f751]) ).
thf(f753,plain,
( ~ spl26_17
| ~ spl26_18
| ~ spl26_47 ),
inference(avatar_contradiction_clause,[],[f752]) ).
thf(f756,plain,
( ! [X1: mworld] :
( ( $true = $false )
| ( $true
= ( p @ X1 ) ) )
| ~ spl26_4 ),
inference(forward_demodulation,[],[f324,f55]) ).
thf(f757,plain,
( ! [X1: mworld] :
( $true
= ( p @ X1 ) )
| ~ spl26_4 ),
inference(trivial_inequality_removal,[],[f756]) ).
thf(f768,plain,
( ( $true = $false )
| ~ spl26_4
| ~ spl26_49 ),
inference(constrained_superposition,[],[f536,f757]) ).
thf(f774,plain,
( $false
| ~ spl26_4
| ~ spl26_49 ),
inference(trivial_inequality_removal,[],[f768]) ).
thf(f775,plain,
( ~ spl26_4
| ~ spl26_49 ),
inference(avatar_contradiction_clause,[],[f774]) ).
thf(f777,plain,
( ( $true = $false )
| ~ spl26_4
| ~ spl26_50 ),
inference(forward_demodulation,[],[f541,f757]) ).
thf(f778,plain,
( $false
| ~ spl26_4
| ~ spl26_50 ),
inference(trivial_inequality_removal,[],[f777]) ).
thf(f779,plain,
( ~ spl26_4
| ~ spl26_50 ),
inference(avatar_contradiction_clause,[],[f778]) ).
thf(f784,plain,
( ! [X1: mworld] :
( ( $true = $false )
| ( $true
= ( big_q @ sK10 @ X1 ) ) )
| ~ spl26_20 ),
inference(forward_demodulation,[],[f397,f55]) ).
thf(f785,plain,
( ! [X1: mworld] :
( $true
= ( big_q @ sK10 @ X1 ) )
| ~ spl26_20 ),
inference(trivial_inequality_removal,[],[f784]) ).
thf(f786,plain,
( ( $true = $false )
| ~ spl26_4
| ~ spl26_34 ),
inference(forward_demodulation,[],[f463,f757]) ).
thf(f787,plain,
( $false
| ~ spl26_4
| ~ spl26_34 ),
inference(trivial_inequality_removal,[],[f786]) ).
thf(f788,plain,
( ~ spl26_4
| ~ spl26_34 ),
inference(avatar_contradiction_clause,[],[f787]) ).
thf(f791,plain,
( ( $true = $false )
| ~ spl26_4
| ~ spl26_40 ),
inference(forward_demodulation,[],[f493,f757]) ).
thf(f792,plain,
( $false
| ~ spl26_4
| ~ spl26_40 ),
inference(trivial_inequality_removal,[],[f791]) ).
thf(f793,plain,
( ~ spl26_4
| ~ spl26_40 ),
inference(avatar_contradiction_clause,[],[f792]) ).
thf(f811,plain,
( ! [X0: mworld] :
( ( $true != $true )
| ( $true
= ( eiw_di @ sK10 @ X0 ) ) )
| ~ spl26_19 ),
inference(constrained_superposition,[],[f582,f392]) ).
thf(f812,plain,
( ! [X0: mworld] :
( $true
= ( eiw_di @ sK10 @ X0 ) )
| ~ spl26_19 ),
inference(trivial_inequality_removal,[],[f811]) ).
thf(f873,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK10 @ sK1 ) )
| ~ spl26_20
| ~ spl26_35 ),
inference(constrained_superposition,[],[f467,f785]) ).
thf(f882,plain,
( ( $false
= ( eiw_di @ sK10 @ sK1 ) )
| ~ spl26_20
| ~ spl26_35 ),
inference(trivial_inequality_removal,[],[f873]) ).
thf(f891,plain,
( ( $true = $false )
| ~ spl26_19
| ~ spl26_20
| ~ spl26_35 ),
inference(forward_demodulation,[],[f882,f812]) ).
thf(f892,plain,
( $false
| ~ spl26_19
| ~ spl26_20
| ~ spl26_35 ),
inference(trivial_inequality_removal,[],[f891]) ).
thf(f893,plain,
( ~ spl26_19
| ~ spl26_20
| ~ spl26_35 ),
inference(avatar_contradiction_clause,[],[f892]) ).
cnf(s11,plain,
( spl26_4
| spl26_10 ),
inference(sat_conversion,[],[f357]) ).
cnf(s19,plain,
( spl26_17
| spl26_19 ),
inference(sat_conversion,[],[f393]) ).
cnf(s20,plain,
( spl26_4
| spl26_17 ),
inference(sat_conversion,[],[f394]) ).
cnf(s21,plain,
( spl26_17
| spl26_20 ),
inference(sat_conversion,[],[f398]) ).
cnf(s22,plain,
( spl26_18
| spl26_19 ),
inference(sat_conversion,[],[f399]) ).
cnf(s23,plain,
( spl26_4
| spl26_18 ),
inference(sat_conversion,[],[f400]) ).
cnf(s24,plain,
( spl26_18
| spl26_20 ),
inference(sat_conversion,[],[f401]) ).
cnf(s40,plain,
( spl26_32
| spl26_34
| spl26_35 ),
inference(sat_conversion,[],[f469]) ).
cnf(s48,plain,
( spl26_35
| spl26_39
| spl26_40 ),
inference(sat_conversion,[],[f496]) ).
cnf(s64,plain,
( spl26_46
| spl26_47
| spl26_49
| spl26_50 ),
inference(sat_conversion,[],[f548]) ).
cnf(s78,plain,
( ~ spl26_32
| ~ spl26_39
| ~ spl26_46 ),
inference(sat_conversion,[],[f720]) ).
cnf(s79,plain,
( ~ spl26_17
| ~ spl26_18
| ~ spl26_46 ),
inference(sat_conversion,[],[f723]) ).
cnf(s80,plain,
( ~ spl26_10
| ~ spl26_49 ),
inference(sat_conversion,[],[f726]) ).
cnf(s81,plain,
( ~ spl26_10
| ~ spl26_50 ),
inference(sat_conversion,[],[f730]) ).
cnf(s84,plain,
( ~ spl26_32
| ~ spl26_39
| ~ spl26_47 ),
inference(sat_conversion,[],[f750]) ).
cnf(s85,plain,
( ~ spl26_17
| ~ spl26_18
| ~ spl26_47 ),
inference(sat_conversion,[],[f753]) ).
cnf(s87,plain,
( ~ spl26_4
| ~ spl26_49 ),
inference(sat_conversion,[],[f775]) ).
cnf(s88,plain,
( ~ spl26_4
| ~ spl26_50 ),
inference(sat_conversion,[],[f779]) ).
cnf(s89,plain,
( ~ spl26_4
| ~ spl26_34 ),
inference(sat_conversion,[],[f788]) ).
cnf(s90,plain,
( ~ spl26_4
| ~ spl26_40 ),
inference(sat_conversion,[],[f793]) ).
cnf(s98,plain,
( ~ spl26_19
| ~ spl26_20
| ~ spl26_35 ),
inference(sat_conversion,[],[f893]) ).
cnf(s101,plain,
spl26_4,
inference(rat,[],[s64,s80,s81,s79,s85,s11,s20,s23]) ).
cnf(s103,plain,
~ spl26_40,
inference(rat,[],[s90,s101]) ).
cnf(s104,plain,
~ spl26_34,
inference(rat,[],[s89,s101]) ).
cnf(s105,plain,
~ spl26_50,
inference(rat,[],[s88,s101]) ).
cnf(s106,plain,
~ spl26_49,
inference(rat,[],[s87,s101]) ).
cnf(s107,plain,
( ~ spl26_18
| ~ spl26_17 ),
inference(rat,[],[s64,s79,s85,s105,s106]) ).
cnf(s108,plain,
( ~ spl26_32
| ~ spl26_39 ),
inference(rat,[],[s64,s78,s84,s105,s106]) ).
cnf(s109,plain,
spl26_35,
inference(rat,[],[s108,s40,s48,s104,s103]) ).
cnf(s110,plain,
spl26_18,
inference(rat,[],[s98,s22,s24,s109]) ).
cnf(s111,plain,
~ spl26_17,
inference(rat,[],[s107,s110]) ).
cnf(s112,plain,
spl26_20,
inference(rat,[],[s21,s111]) ).
cnf(s113,plain,
spl26_19,
inference(rat,[],[s19,s111]) ).
cnf(s114,plain,
$false,
inference(rat,[],[s98,s109,s112,s113]) ).
thf(f897,plain,
$false,
inference(avatar_sat_refutation,[],[s114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL956^18 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n013.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 10:56:51 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.34 % (1947436)Will run a generic schedule for satisfiability detection.
% 0.23/0.34 % (1947442)% WARNING: option uhcvi not known.
% 0.23/0.34 % (1947443)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2999197396:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.34 % (1947441)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3006877158_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.34 % (1947442)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=38640277:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.34 % (1947442)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.34 % (1947442)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.34 % Exception at run slice level
% 0.23/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.34 % (1947444)dis+10_1_sil=32000:sp=arity:random_seed=1963785468:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.34 % (1947446)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3795836119:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.34 % (1947445)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=388893214:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.34 % (1947447)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3303539007:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.34 % (1947445)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.34 % (1947446) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1947436-1947446"...
% 0.23/0.34 % (1947445) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1947436-1947445"...
% 0.23/0.34 % (1947442) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1947436-1947442"...
% 0.23/0.34 % (1947451)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3877606921:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.23/0.34 % Exception at run slice level
% 0.23/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.34 % (1947445)...printing done.
% 0.23/0.34 % (1947446)...printing done.
% 0.23/0.34 % (1947445)Refutation found. Thanks to Tanya!
% 0.23/0.34 % SZS status Theorem for theBenchmark
% 0.23/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.34 % (1947445)------------------------------
% 0.23/0.34 % (1947445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.34 % (1947445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.34 % (1947445)CaDiCaL version: 2.1.3
% 0.23/0.34 % (1947445)Termination reason: Refutation
% 0.23/0.34 % (1947445)Time elapsed: 0.024 s
% 0.23/0.34 % (1947445)Peak memory usage: 13 MB
% 0.23/0.34 % (1947445)Instructions burned: 51 (million)
% 0.23/0.34 % (1947436)Success in time 0.076 s
% 0.23/0.34 % Vampire exiting
%------------------------------------------------------------------------------