%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL956^18 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:14:55 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 26
% Syntax : Number of formulae : 284 ( 40 unt; 0 typ; 19 def)
% Number of atoms : 2754 ( 463 equ; 0 cnn)
% Maximal formula atoms : 30 ( 9 avg)
% Number of connectives : 4061 ( 188 ~; 445 |; 189 &;2619 @)
% ( 19 <=>; 319 =>; 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 : 83 ( 78 usr; 40 con; 0-4 aty)
% ( 224 !!; 58 ??; 0 @@+; 0 @@-)
% Number of variables : 623 ( 0 sgn 162 !; 2 ?; 623 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
vIFF: $o > $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_35,type,
sK6: $i > mworld ).
thf(func_def_37,type,
sK8: $i > mworld ).
thf(func_def_38,type,
sK9: mworld ).
thf(func_def_41,type,
sK12: 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: $i > mworld ).
thf(func_def_48,type,
sK19: $i > mworld ).
thf(func_def_50,type,
sK21: mworld ).
thf(func_def_51,type,
sK22: $i > mworld ).
thf(func_def_52,type,
sK23: mworld ).
thf(func_def_53,type,
sK24: $i > mworld ).
thf(func_def_54,type,
sK25: mworld ).
thf(func_def_55,type,
sK26: $i > mworld ).
thf(func_def_56,type,
sK27: mworld ).
thf(func_def_57,type,
sK28: $i > mworld ).
thf(func_def_58,type,
sK29: $i > mworld ).
thf(func_def_59,type,
sK30: mworld ).
thf(func_def_60,type,
sK31: $i > mworld ).
thf(func_def_61,type,
sK32: $i > mworld ).
thf(func_def_62,type,
sK33: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(f13,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
file('/export/starexec/sandbox/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/sandbox/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(f24,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[],[f13]) ).
thf(f25,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f27,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f28,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f30,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
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(f33,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f37,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(f38,plain,
( ( 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 ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f37]) ).
thf(f43,plain,
( ( 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 ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f38]) ).
thf(f47,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f48,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f51,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f53,plain,
( ( 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 ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f56,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f58,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f32]) ).
thf(f60,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f63,plain,
( ( ^ [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 ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f53,f56,f48,f51,f60,f47,f48,f51,f51,f48,f51,f47,f51,f51,f60,f48,f51,f47,f51,f47,f48,f51,f51]) ).
thf(f64,plain,
( ( ( !! @ 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 ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
( ( $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 ) ) ) ) ) ) ) ) ) )
| ( $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 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f66,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 ) ) ) ) ) ) ) ) )
| ( ( ^ [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 ) ) ) ) ) ) ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( ( ^ [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 ) ) ) ) ) ) ) )
@ sK1 )
= $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 ) ) ) ) ) ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( ( !! @ 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 ) ) ) ) ) )
=> ( ?? @ $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 ) ) ) ) ) ) ) )
| ( $false
= ( ( mrel @ mactual @ sK1 )
=> ( ( ?? @ $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 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( $false
= ( ( mrel @ mactual @ sK1 )
=> ( ( ?? @ $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 ) ) ) ) )
=> ( ( !! @ 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
= ( ( ( !! @ 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 ) ) ) ) ) )
=> ( ?? @ $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,[],[f68]) ).
thf(f103,plain,
( ( $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 ) ) ) ) ) )
=> ( ?? @ $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 ) ) ) ) ) ) )
| ( $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 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f132,plain,
( ( ( ?? @ $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 ) ) ) ) )
= $false )
| ( $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 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f133,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 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) ) ) ) )
| ( ( ( !! @ 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 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f134,plain,
( ( ( ( !! @ 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 ) ) ) ) ) )
= $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 ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( ( ( ?? @ $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 ) ) ) ) )
= $true )
| ( ( ( !! @ 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 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f133]) ).
thf(f136,plain,
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK10 )
= $true )
| ( ( ( !! @ 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 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK10 )
= $true ) ),
inference(and_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK10 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f136]) ).
thf(f139,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK10 )
= $true ) ),
inference(pi_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X1: mworld] :
( ( ( ( eiw_di @ sK10 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK2 @ X1 )
=> ( p @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true )
| ( ( ( mrel @ sK2 @ X1 )
=> ( p @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f145,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK2 @ X1 )
=> ( p @ X1 ) )
= $true )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f141]) ).
thf(f146,plain,
! [X1: mworld] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( ( p @ X1 )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: mworld,X1: mworld] :
( ( ( p @ X1 )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X2 )
=> ( p @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK1 @ X2 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false )
| ( ( p @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f154,plain,
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK10 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f155,plain,
( ( $true
= ( ( eiw_di @ sK11 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) ) ) ) )
| ( ( ( eiw_di @ sK10 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( ( ( eiw_di @ sK10 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( eiw_di @ sK11 @ sK2 )
= $true )
| ( ( ( eiw_di @ sK10 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ( eiw_di @ sK11 @ sK2 )
= $true )
| ( $true
= ( eiw_di @ sK10 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) )
= $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f165,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK11 @ sK2 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f166,plain,
! [X1: mworld] :
( ( ( ( mrel @ sK1 @ X1 )
=> ( big_q @ sK10 @ X1 ) )
= $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $true ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( big_q @ sK10 @ X1 )
= $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) ) )
= $true )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f169,plain,
( ( $true
= ( eiw_di @ sK10 @ sK1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f170,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK10 @ sK1 ) )
| ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK10 @ sK1 ) )
| ( ( ( mrel @ sK2 @ X1 )
=> ( big_q @ sK11 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK10 @ sK1 ) )
| ( ( mrel @ sK2 @ X1 )
= $false )
| ( ( big_q @ sK11 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) )
@ X1 ) )
| ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f174,plain,
! [X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) )
@ X1 ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f173]) ).
thf(f180,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK11 @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK10 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f181,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK2 @ X1 )
=> ( big_q @ sK11 @ X1 ) )
= $true )
| ( ( ( mrel @ sK1 @ X2 )
=> ( big_q @ sK10 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X2: mworld,X1: mworld] :
( ( ( big_q @ sK11 @ X1 )
= $true )
| ( ( ( mrel @ sK1 @ X2 )
=> ( big_q @ sK10 @ X2 ) )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: mworld,X1: mworld] :
( ( ( big_q @ sK11 @ X1 )
= $true )
| ( ( mrel @ sK1 @ X2 )
= $false )
| ( ( mrel @ sK2 @ X1 )
= $false )
| ( ( big_q @ sK10 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( ( ( !! @ 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 )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f134]) ).
thf(f204,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 ) ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f184]) ).
thf(f205,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK15 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK15 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK16 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ sK16 )
= $true )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK15 )
= $false ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( ( mrel @ sK1 @ sK15 )
=> ( p @ sK15 ) ) )
| ( ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) )
= $true )
| ( ( ( eiw_di @ X1 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( ( ( eiw_di @ X1 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) )
= $false )
| ( ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) )
= $true )
| ( ( p @ sK15 )
= $false ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f225,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) )
= $false )
| ( ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) )
= $true )
| ( ( p @ sK15 )
= $false ) ),
inference(and_proxy_clausification,[],[f209]) ).
thf(f226,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK19 @ X1 ) ) )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( p @ sK15 )
= $false )
| ( ( ( eiw_di @ sK16 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( ( p @ sK15 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK19 @ X1 ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK19 @ X1 ) ) )
| ( ( eiw_di @ sK16 @ sK2 )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( p @ sK15 )
= $false ) ),
inference(and_proxy_clausification,[],[f226]) ).
thf(f229,plain,
! [X1: $i] :
( ( ( ( mrel @ sK1 @ ( sK19 @ X1 ) )
=> ( big_q @ X1 @ ( sK19 @ X1 ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( p @ sK15 )
= $false )
| ( ( eiw_di @ sK16 @ sK2 )
= $true ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( eiw_di @ sK16 @ sK2 )
= $true )
| ( ( big_q @ X1 @ ( sK19 @ X1 ) )
= $false )
| ( ( p @ sK15 )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f232,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK19 @ X1 ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ sK16 @ Y0 ) )
@ X2 )
= $true )
| ( ( p @ sK15 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f233,plain,
! [X2: mworld,X1: $i] :
( ( ( ( mrel @ sK1 @ ( sK19 @ X1 ) )
=> ( big_q @ X1 @ ( sK19 @ X1 ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( ( mrel @ sK2 @ X2 )
=> ( big_q @ sK16 @ X2 ) )
= $true )
| ( ( p @ sK15 )
= $false ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X2: mworld,X1: $i] :
( ( ( big_q @ X1 @ ( sK19 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( p @ sK15 )
= $false )
| ( ( ( mrel @ sK2 @ X2 )
=> ( big_q @ sK16 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f237,plain,
! [X2: mworld,X1: $i] :
( ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( p @ sK15 )
= $false )
| ( ( big_q @ sK16 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( big_q @ X1 @ ( sK19 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f238,plain,
! [X1: $i] :
( ( $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 ) ) ) ) )
=> ( ( !! @ 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 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f239,plain,
! [X1: $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 ) ) ) )
@ X1 )
= $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 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( ( ?? @ $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 ) ) ) ) )
= $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 ) ) ) )
@ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f241,plain,
! [X1: $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 ) ) ) )
@ X1 )
= $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 ) ) ) )
@ sK20 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X1: $i] :
( ( ( ( eiw_di @ sK20 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) ) ) ) )
| ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X1: $i] :
( ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( ( eiw_di @ sK20 @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f245,plain,
! [X1: $i] :
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( ( eiw_di @ sK20 @ sK1 )
= $true )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( ( eiw_di @ sK20 @ sK1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK21 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) )
= $false )
| ( ( eiw_di @ sK20 @ sK1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X1: $i] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK21 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK22 @ X1 ) )
= $false )
| ( ( eiw_di @ sK20 @ sK1 )
= $true )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X1: $i] :
( ( ( eiw_di @ sK20 @ sK1 )
= $true )
| ( ( ( mrel @ sK2 @ ( sK22 @ X1 ) )
=> ( big_q @ X1 @ ( sK22 @ X1 ) ) )
= $false )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
! [X1: $i] :
( ( ( eiw_di @ sK20 @ sK1 )
= $true )
| ( $false
= ( ( mrel @ sK2 @ sK21 )
=> ( p @ sK21 ) ) )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f249]) ).
thf(f254,plain,
! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( ( p @ sK21 )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( eiw_di @ sK20 @ sK1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f256,plain,
! [X1: $i] :
( ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f243]) ).
thf(f271,plain,
! [X1: $i] :
( ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) ) )
= $true )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f256]) ).
thf(f272,plain,
! [X1: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) ) )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: mworld,X1: $i] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) )
@ X2 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK25 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ sK20 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK26 @ X1 ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK25 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: mworld,X1: $i] :
( ( ( ( mrel @ sK2 @ ( sK26 @ X1 ) )
=> ( big_q @ X1 @ ( sK26 @ X1 ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ( mrel @ sK1 @ X2 )
=> ( big_q @ sK20 @ X2 ) )
= $true )
| ( $false
= ( ( mrel @ sK2 @ sK25 )
=> ( p @ sK25 ) ) ) ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f277,plain,
! [X2: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( big_q @ X1 @ ( sK26 @ X1 ) )
= $false )
| ( $false
= ( ( mrel @ sK2 @ sK25 )
=> ( p @ sK25 ) ) )
| ( ( ( mrel @ sK1 @ X2 )
=> ( big_q @ sK20 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f276]) ).
thf(f282,plain,
! [X2: mworld,X1: $i] :
( ( ( p @ sK25 )
= $false )
| ( ( big_q @ X1 @ ( sK26 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ( mrel @ sK1 @ X2 )
=> ( big_q @ sK20 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f277]) ).
thf(f285,plain,
! [X2: mworld,X1: $i] :
( ( ( p @ sK25 )
= $false )
| ( ( big_q @ sK20 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( mrel @ sK1 @ X2 )
= $false )
| ( ( big_q @ X1 @ ( sK26 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f282]) ).
thf(f286,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false )
| ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f239]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( p @ Y0 ) )
@ sK27 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK1 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( p @ Y1 ) ) )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ( big_q @ Y0 @ Y1 ) ) ) )
@ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( ( ( mrel @ sK1 @ sK27 )
=> ( p @ sK27 ) )
= $false )
| ( ( ( eiw_di @ X2 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK27 )
= $false )
| ( ( ( eiw_di @ X2 @ sK1 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f289]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) ) )
= $false )
| ( ( p @ sK27 )
= $false )
| ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f290]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( eiw_di @ X1 @ sK2 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK31 @ X2 ) )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( p @ sK27 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) ) ) )
| ( ( p @ sK27 )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK31 @ X2 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) ) )
= $false )
| ( ( p @ sK27 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK31 @ X2 ) )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( ( p @ sK27 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK32 @ X1 ) )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK31 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK33 )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( p @ sK27 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( big_q @ X1 @ Y0 ) )
@ ( sK32 @ X1 ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ( big_q @ X2 @ Y0 ) )
@ ( sK31 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK27 )
= $false )
| ( ( ( mrel @ sK2 @ sK33 )
=> ( p @ sK33 ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ( mrel @ sK2 @ ( sK32 @ X1 ) )
=> ( big_q @ X1 @ ( sK32 @ X1 ) ) )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( ( mrel @ sK1 @ ( sK31 @ X2 ) )
=> ( big_q @ X2 @ ( sK31 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK33 )
= $false )
| ( ( ( mrel @ sK1 @ ( sK31 @ X2 ) )
=> ( big_q @ X2 @ ( sK31 @ X2 ) ) )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( ( mrel @ sK2 @ ( sK32 @ X1 ) )
=> ( big_q @ X1 @ ( sK32 @ X1 ) ) )
= $false )
| ( ( p @ sK27 )
= $false ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK33 )
= $false )
| ( ( p @ sK27 )
= $false )
| ( ( ( mrel @ sK2 @ ( sK32 @ X1 ) )
=> ( big_q @ X1 @ ( sK32 @ X1 ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false )
| ( ( big_q @ X2 @ ( sK31 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f320]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( ( ( big_q @ X1 @ ( sK32 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( big_q @ X2 @ ( sK31 @ X2 ) )
= $false )
| ( ( p @ sK33 )
= $false )
| ( ( p @ sK27 )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f336,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( $false = $true )
| ( ( p @ X2 )
= $true ) ),
inference(forward_demodulation,[],[f149,f58]) ).
thf(f337,plain,
! [X2: mworld,X1: mworld] :
( ( ( p @ X1 )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f341,definition,
( spl34_1
<=> ( $true
= ( eiw_di @ sK10 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl34_1])],[avatar_definition]) ).
thf(f343,plain,
( ( $true
= ( eiw_di @ sK10 @ sK1 ) )
| ~ spl34_1 ),
inference(avatar_component_clause,[],[f341]) ).
thf(f345,definition,
( spl34_2
<=> ( ( eiw_di @ sK11 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_2])],[avatar_definition]) ).
thf(f347,plain,
( ( ( eiw_di @ sK11 @ sK2 )
= $true )
| ~ spl34_2 ),
inference(avatar_component_clause,[],[f345]) ).
thf(f348,plain,
( spl34_1
| spl34_2 ),
inference(avatar_split_clause,[],[f159,f345,f341]) ).
thf(f351,plain,
! [X1: mworld] :
( ( $false = $true )
| ( ( big_q @ sK10 @ X1 )
= $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $true ) ),
inference(forward_demodulation,[],[f167,f58]) ).
thf(f352,plain,
! [X1: mworld] :
( ( ( big_q @ sK10 @ X1 )
= $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f351]) ).
thf(f353,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ sK10 @ sK1 ) )
| ( $false = $true )
| ( ( big_q @ sK11 @ X1 )
= $true ) ),
inference(forward_demodulation,[],[f172,f58]) ).
thf(f354,plain,
! [X1: mworld] :
( ( ( big_q @ sK11 @ X1 )
= $true )
| ( $true
= ( eiw_di @ sK10 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f357,plain,
! [X2: mworld,X1: mworld] :
( ( $false = $true )
| ( ( big_q @ sK11 @ X1 )
= $true )
| ( ( big_q @ sK10 @ X2 )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false ) ),
inference(forward_demodulation,[],[f183,f58]) ).
thf(f358,plain,
! [X2: mworld,X1: mworld] :
( ( ( big_q @ sK11 @ X1 )
= $true )
| ( ( mrel @ sK2 @ X1 )
= $false )
| ( ( big_q @ sK10 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f357]) ).
thf(f362,definition,
( spl34_3
<=> ( ( eiw_di @ sK16 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_3])],[avatar_definition]) ).
thf(f364,plain,
( ( ( eiw_di @ sK16 @ sK2 )
= $true )
| ~ spl34_3 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f366,definition,
( spl34_4
<=> ( ( p @ sK15 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl34_4])],[avatar_definition]) ).
thf(f368,plain,
( ( ( p @ sK15 )
= $false )
| ~ spl34_4 ),
inference(avatar_component_clause,[],[f366]) ).
thf(f370,definition,
( spl34_5
<=> ! [X1: $i] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( big_q @ X1 @ ( sK19 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl34_5])],[avatar_definition]) ).
thf(f371,plain,
( ! [X1: $i] :
( ( ( big_q @ X1 @ ( sK19 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) )
| ~ spl34_5 ),
inference(avatar_component_clause,[],[f370]) ).
thf(f372,plain,
( spl34_3
| spl34_4
| spl34_5 ),
inference(avatar_split_clause,[],[f230,f370,f366,f362]) ).
thf(f373,plain,
! [X2: mworld,X1: $i] :
( ( ( p @ sK15 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( big_q @ sK16 @ X2 )
= $true )
| ( $false = $true )
| ( ( big_q @ X1 @ ( sK19 @ X1 ) )
= $false ) ),
inference(forward_demodulation,[],[f237,f58]) ).
thf(f374,plain,
! [X2: mworld,X1: $i] :
( ( ( big_q @ sK16 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( big_q @ X1 @ ( sK19 @ X1 ) )
= $false )
| ( ( p @ sK15 )
= $false ) ),
inference(trivial_inequality_removal,[],[f373]) ).
thf(f376,definition,
( spl34_6
<=> ( ( eiw_di @ sK20 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_6])],[avatar_definition]) ).
thf(f378,plain,
( ( ( eiw_di @ sK20 @ sK1 )
= $true )
| ~ spl34_6 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f380,definition,
( spl34_7
<=> ! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl34_7])],[avatar_definition]) ).
thf(f381,plain,
( ! [X1: $i] :
( ( $false
= ( big_q @ X1 @ ( sK22 @ X1 ) ) )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) )
| ~ spl34_7 ),
inference(avatar_component_clause,[],[f380]) ).
thf(f383,definition,
( spl34_8
<=> ( ( p @ sK21 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl34_8])],[avatar_definition]) ).
thf(f385,plain,
( ( ( p @ sK21 )
= $false )
| ~ spl34_8 ),
inference(avatar_component_clause,[],[f383]) ).
thf(f386,plain,
( spl34_6
| spl34_7
| spl34_8 ),
inference(avatar_split_clause,[],[f254,f383,f380,f376]) ).
thf(f389,plain,
! [X2: mworld,X1: $i] :
( ( $false = $true )
| ( ( big_q @ sK20 @ X2 )
= $true )
| ( ( big_q @ X1 @ ( sK26 @ X1 ) )
= $false )
| ( ( p @ sK25 )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(forward_demodulation,[],[f285,f58]) ).
thf(f390,plain,
! [X2: mworld,X1: $i] :
( ( ( big_q @ sK20 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( big_q @ X1 @ ( sK26 @ X1 ) )
= $false )
| ( ( p @ sK25 )
= $false ) ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f392,definition,
( spl34_9
<=> ! [X2: $i] :
( ( ( big_q @ X2 @ ( sK31 @ X2 ) )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl34_9])],[avatar_definition]) ).
thf(f393,plain,
( ! [X2: $i] :
( ( ( big_q @ X2 @ ( sK31 @ X2 ) )
= $false )
| ( ( eiw_di @ X2 @ sK1 )
= $false ) )
| ~ spl34_9 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f395,definition,
( spl34_10
<=> ! [X1: $i] :
( ( ( big_q @ X1 @ ( sK32 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl34_10])],[avatar_definition]) ).
thf(f396,plain,
( ! [X1: $i] :
( ( ( big_q @ X1 @ ( sK32 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) )
| ~ spl34_10 ),
inference(avatar_component_clause,[],[f395]) ).
thf(f398,definition,
( spl34_11
<=> ( ( p @ sK33 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl34_11])],[avatar_definition]) ).
thf(f400,plain,
( ( ( p @ sK33 )
= $false )
| ~ spl34_11 ),
inference(avatar_component_clause,[],[f398]) ).
thf(f402,definition,
( spl34_12
<=> ( ( p @ sK27 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl34_12])],[avatar_definition]) ).
thf(f404,plain,
( ( ( p @ sK27 )
= $false )
| ~ spl34_12 ),
inference(avatar_component_clause,[],[f402]) ).
thf(f405,plain,
( spl34_9
| spl34_10
| spl34_11
| spl34_12 ),
inference(avatar_split_clause,[],[f332,f402,f398,f395,f392]) ).
thf(f407,definition,
( spl34_13
<=> ! [X1: mworld] :
( ( p @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_13])],[avatar_definition]) ).
thf(f408,plain,
( ! [X1: mworld] :
( ( p @ X1 )
= $true )
| ~ spl34_13 ),
inference(avatar_component_clause,[],[f407]) ).
thf(f410,plain,
! [X2: mworld,X1: mworld] :
( ( $false = $true )
| ( ( p @ X2 )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(forward_demodulation,[],[f337,f58]) ).
thf(f411,plain,
! [X2: mworld,X1: mworld] :
( ( ( p @ X1 )
= $true )
| ( ( p @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f410]) ).
thf(f416,definition,
( spl34_14
<=> ! [X1: mworld] :
( ( big_q @ sK10 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_14])],[avatar_definition]) ).
thf(f417,plain,
( ! [X1: mworld] :
( ( big_q @ sK10 @ X1 )
= $true )
| ~ spl34_14 ),
inference(avatar_component_clause,[],[f416]) ).
thf(f418,plain,
( spl34_14
| spl34_2 ),
inference(avatar_split_clause,[],[f352,f345,f416]) ).
thf(f420,definition,
( spl34_15
<=> ! [X1: mworld] :
( ( big_q @ sK11 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_15])],[avatar_definition]) ).
thf(f421,plain,
( ! [X1: mworld] :
( ( big_q @ sK11 @ X1 )
= $true )
| ~ spl34_15 ),
inference(avatar_component_clause,[],[f420]) ).
thf(f422,plain,
( spl34_1
| spl34_15 ),
inference(avatar_split_clause,[],[f354,f420,f341]) ).
thf(f425,plain,
! [X2: mworld,X1: mworld] :
( ( ( big_q @ sK10 @ X2 )
= $true )
| ( $false = $true )
| ( ( big_q @ sK11 @ X1 )
= $true ) ),
inference(forward_demodulation,[],[f358,f58]) ).
thf(f426,plain,
! [X2: mworld,X1: mworld] :
( ( ( big_q @ sK10 @ X2 )
= $true )
| ( ( big_q @ sK11 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f425]) ).
thf(f436,definition,
( spl34_18
<=> ! [X2: mworld] :
( ( big_q @ sK16 @ X2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_18])],[avatar_definition]) ).
thf(f437,plain,
( ! [X2: mworld] :
( ( big_q @ sK16 @ X2 )
= $true )
| ~ spl34_18 ),
inference(avatar_component_clause,[],[f436]) ).
thf(f438,plain,
( spl34_5
| spl34_18
| spl34_4 ),
inference(avatar_split_clause,[],[f374,f366,f436,f370]) ).
thf(f448,definition,
( spl34_21
<=> ! [X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
= $false )
| ( ( big_q @ X1 @ ( sK26 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl34_21])],[avatar_definition]) ).
thf(f449,plain,
( ! [X1: $i] :
( ( ( big_q @ X1 @ ( sK26 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) )
| ~ spl34_21 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f451,definition,
( spl34_22
<=> ( ( p @ sK25 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl34_22])],[avatar_definition]) ).
thf(f453,plain,
( ( ( p @ sK25 )
= $false )
| ~ spl34_22 ),
inference(avatar_component_clause,[],[f451]) ).
thf(f455,definition,
( spl34_23
<=> ! [X2: mworld] :
( ( big_q @ sK20 @ X2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl34_23])],[avatar_definition]) ).
thf(f456,plain,
( ! [X2: mworld] :
( ( big_q @ sK20 @ X2 )
= $true )
| ~ spl34_23 ),
inference(avatar_component_clause,[],[f455]) ).
thf(f457,plain,
( spl34_21
| spl34_22
| spl34_23 ),
inference(avatar_split_clause,[],[f390,f455,f451,f448]) ).
thf(f458,plain,
( spl34_13
| spl34_13 ),
inference(avatar_split_clause,[],[f411,f407,f407]) ).
thf(f461,plain,
( spl34_14
| spl34_15 ),
inference(avatar_split_clause,[],[f426,f420,f416]) ).
thf(f463,plain,
( ( $false = $true )
| ~ spl34_4
| ~ spl34_13 ),
inference(constrained_superposition,[],[f408,f368]) ).
thf(f466,plain,
( $false
| ~ spl34_4
| ~ spl34_13 ),
inference(trivial_inequality_removal,[],[f463]) ).
thf(f467,plain,
( ~ spl34_4
| ~ spl34_13 ),
inference(avatar_contradiction_clause,[],[f466]) ).
thf(f477,plain,
( ( $false = $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $false )
| ~ spl34_15
| ~ spl34_21 ),
inference(constrained_superposition,[],[f449,f421]) ).
thf(f480,plain,
( ( ( eiw_di @ sK11 @ sK2 )
= $false )
| ~ spl34_15
| ~ spl34_21 ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f484,plain,
( ( $false = $true )
| ~ spl34_2
| ~ spl34_15
| ~ spl34_21 ),
inference(forward_demodulation,[],[f480,f347]) ).
thf(f485,plain,
( $false
| ~ spl34_2
| ~ spl34_15
| ~ spl34_21 ),
inference(trivial_inequality_removal,[],[f484]) ).
thf(f486,plain,
( ~ spl34_2
| ~ spl34_15
| ~ spl34_21 ),
inference(avatar_contradiction_clause,[],[f485]) ).
thf(f487,plain,
( ( $false = $true )
| ~ spl34_13
| ~ spl34_22 ),
inference(forward_demodulation,[],[f453,f408]) ).
thf(f488,plain,
( $false
| ~ spl34_13
| ~ spl34_22 ),
inference(trivial_inequality_removal,[],[f487]) ).
thf(f489,plain,
( ~ spl34_13
| ~ spl34_22 ),
inference(avatar_contradiction_clause,[],[f488]) ).
thf(f491,plain,
( ( $false = $true )
| ( ( eiw_di @ sK20 @ sK1 )
= $false )
| ~ spl34_5
| ~ spl34_23 ),
inference(constrained_superposition,[],[f456,f371]) ).
thf(f494,plain,
( ( $false = $true )
| ( ( eiw_di @ sK20 @ sK1 )
= $false )
| ~ spl34_9
| ~ spl34_23 ),
inference(constrained_superposition,[],[f393,f456]) ).
thf(f496,plain,
( ( ( eiw_di @ sK20 @ sK1 )
= $false )
| ~ spl34_5
| ~ spl34_23 ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f498,plain,
( ( ( eiw_di @ sK20 @ sK1 )
= $false )
| ~ spl34_9
| ~ spl34_23 ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f502,plain,
( ( $false = $true )
| ~ spl34_5
| ~ spl34_6
| ~ spl34_23 ),
inference(forward_demodulation,[],[f496,f378]) ).
thf(f503,plain,
( $false
| ~ spl34_5
| ~ spl34_6
| ~ spl34_23 ),
inference(trivial_inequality_removal,[],[f502]) ).
thf(f504,plain,
( ~ spl34_5
| ~ spl34_6
| ~ spl34_23 ),
inference(avatar_contradiction_clause,[],[f503]) ).
thf(f508,plain,
( ( $false = $true )
| ~ spl34_6
| ~ spl34_9
| ~ spl34_23 ),
inference(forward_demodulation,[],[f498,f378]) ).
thf(f509,plain,
( $false
| ~ spl34_6
| ~ spl34_9
| ~ spl34_23 ),
inference(trivial_inequality_removal,[],[f508]) ).
thf(f510,plain,
( ~ spl34_6
| ~ spl34_9
| ~ spl34_23 ),
inference(avatar_contradiction_clause,[],[f509]) ).
thf(f512,plain,
( ( $false = $true )
| ( ( eiw_di @ sK11 @ sK2 )
= $false )
| ~ spl34_7
| ~ spl34_15 ),
inference(constrained_superposition,[],[f381,f421]) ).
thf(f517,plain,
( ( ( eiw_di @ sK11 @ sK2 )
= $false )
| ~ spl34_7
| ~ spl34_15 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f523,plain,
( ( $false = $true )
| ~ spl34_2
| ~ spl34_7
| ~ spl34_15 ),
inference(forward_demodulation,[],[f517,f347]) ).
thf(f524,plain,
( $false
| ~ spl34_2
| ~ spl34_7
| ~ spl34_15 ),
inference(trivial_inequality_removal,[],[f523]) ).
thf(f525,plain,
( ~ spl34_2
| ~ spl34_7
| ~ spl34_15 ),
inference(avatar_contradiction_clause,[],[f524]) ).
thf(f526,plain,
( ( $false = $true )
| ~ spl34_8
| ~ spl34_13 ),
inference(forward_demodulation,[],[f385,f408]) ).
thf(f527,plain,
( $false
| ~ spl34_8
| ~ spl34_13 ),
inference(trivial_inequality_removal,[],[f526]) ).
thf(f528,plain,
( ~ spl34_8
| ~ spl34_13 ),
inference(avatar_contradiction_clause,[],[f527]) ).
thf(f533,plain,
( ( $false = $true )
| ( $false
= ( eiw_di @ sK10 @ sK1 ) )
| ~ spl34_5
| ~ spl34_14 ),
inference(constrained_superposition,[],[f417,f371]) ).
thf(f534,plain,
( ( $false
= ( eiw_di @ sK10 @ sK1 ) )
| ( $false = $true )
| ~ spl34_9
| ~ spl34_14 ),
inference(constrained_superposition,[],[f417,f393]) ).
thf(f538,plain,
( ( $false
= ( eiw_di @ sK10 @ sK1 ) )
| ~ spl34_9
| ~ spl34_14 ),
inference(trivial_inequality_removal,[],[f534]) ).
thf(f540,plain,
( ( $false
= ( eiw_di @ sK10 @ sK1 ) )
| ~ spl34_5
| ~ spl34_14 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f544,plain,
( ( $false = $true )
| ~ spl34_1
| ~ spl34_9
| ~ spl34_14 ),
inference(forward_demodulation,[],[f538,f343]) ).
thf(f545,plain,
( $false
| ~ spl34_1
| ~ spl34_9
| ~ spl34_14 ),
inference(trivial_inequality_removal,[],[f544]) ).
thf(f546,plain,
( ~ spl34_1
| ~ spl34_9
| ~ spl34_14 ),
inference(avatar_contradiction_clause,[],[f545]) ).
thf(f550,plain,
( ( $false = $true )
| ~ spl34_1
| ~ spl34_5
| ~ spl34_14 ),
inference(forward_demodulation,[],[f540,f343]) ).
thf(f551,plain,
( $false
| ~ spl34_1
| ~ spl34_5
| ~ spl34_14 ),
inference(trivial_inequality_removal,[],[f550]) ).
thf(f552,plain,
( ~ spl34_1
| ~ spl34_5
| ~ spl34_14 ),
inference(avatar_contradiction_clause,[],[f551]) ).
thf(f558,plain,
( ( ( eiw_di @ sK16 @ sK2 )
= $false )
| ( $false = $true )
| ~ spl34_10
| ~ spl34_18 ),
inference(constrained_superposition,[],[f437,f396]) ).
thf(f562,plain,
( ( ( eiw_di @ sK16 @ sK2 )
= $false )
| ~ spl34_10
| ~ spl34_18 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f568,plain,
( ( $false = $true )
| ~ spl34_3
| ~ spl34_10
| ~ spl34_18 ),
inference(forward_demodulation,[],[f562,f364]) ).
thf(f569,plain,
( $false
| ~ spl34_3
| ~ spl34_10
| ~ spl34_18 ),
inference(trivial_inequality_removal,[],[f568]) ).
thf(f570,plain,
( ~ spl34_3
| ~ spl34_10
| ~ spl34_18 ),
inference(avatar_contradiction_clause,[],[f569]) ).
thf(f571,plain,
( ( $false = $true )
| ~ spl34_11
| ~ spl34_13 ),
inference(forward_demodulation,[],[f400,f408]) ).
thf(f572,plain,
( $false
| ~ spl34_11
| ~ spl34_13 ),
inference(trivial_inequality_removal,[],[f571]) ).
thf(f573,plain,
( ~ spl34_11
| ~ spl34_13 ),
inference(avatar_contradiction_clause,[],[f572]) ).
thf(f575,plain,
( ( $false = $true )
| ~ spl34_12
| ~ spl34_13 ),
inference(forward_demodulation,[],[f404,f408]) ).
thf(f576,plain,
( $false
| ~ spl34_12
| ~ spl34_13 ),
inference(trivial_inequality_removal,[],[f575]) ).
thf(f577,plain,
( ~ spl34_12
| ~ spl34_13 ),
inference(avatar_contradiction_clause,[],[f576]) ).
cnf(s1,plain,
( spl34_1
| spl34_2 ),
inference(sat_conversion,[],[f348]) ).
cnf(s2,plain,
( spl34_3
| spl34_4
| spl34_5 ),
inference(sat_conversion,[],[f372]) ).
cnf(s3,plain,
( spl34_6
| spl34_7
| spl34_8 ),
inference(sat_conversion,[],[f386]) ).
cnf(s4,plain,
( spl34_9
| spl34_10
| spl34_11
| spl34_12 ),
inference(sat_conversion,[],[f405]) ).
cnf(s7,plain,
( spl34_2
| spl34_14 ),
inference(sat_conversion,[],[f418]) ).
cnf(s8,plain,
( spl34_1
| spl34_15 ),
inference(sat_conversion,[],[f422]) ).
cnf(s10,plain,
( spl34_4
| spl34_5
| spl34_18 ),
inference(sat_conversion,[],[f438]) ).
cnf(s12,plain,
( spl34_21
| spl34_22
| spl34_23 ),
inference(sat_conversion,[],[f457]) ).
cnf(s13,plain,
( spl34_13
| spl34_13 ),
inference(sat_conversion,[],[f458]) ).
cnf(s14,plain,
spl34_13,
inference(rat,[],[s13]) ).
cnf(s17,plain,
( spl34_14
| spl34_15 ),
inference(sat_conversion,[],[f461]) ).
cnf(s19,plain,
( ~ spl34_4
| ~ spl34_13 ),
inference(sat_conversion,[],[f467]) ).
cnf(s21,plain,
( ~ spl34_2
| ~ spl34_15
| ~ spl34_21 ),
inference(sat_conversion,[],[f486]) ).
cnf(s22,plain,
( ~ spl34_13
| ~ spl34_22 ),
inference(sat_conversion,[],[f489]) ).
cnf(s24,plain,
( ~ spl34_5
| ~ spl34_6
| ~ spl34_23 ),
inference(sat_conversion,[],[f504]) ).
cnf(s26,plain,
( ~ spl34_6
| ~ spl34_9
| ~ spl34_23 ),
inference(sat_conversion,[],[f510]) ).
cnf(s28,plain,
( ~ spl34_2
| ~ spl34_7
| ~ spl34_15 ),
inference(sat_conversion,[],[f525]) ).
cnf(s29,plain,
( ~ spl34_8
| ~ spl34_13 ),
inference(sat_conversion,[],[f528]) ).
cnf(s31,plain,
( ~ spl34_1
| ~ spl34_9
| ~ spl34_14 ),
inference(sat_conversion,[],[f546]) ).
cnf(s33,plain,
( ~ spl34_1
| ~ spl34_5
| ~ spl34_14 ),
inference(sat_conversion,[],[f552]) ).
cnf(s35,plain,
( ~ spl34_3
| ~ spl34_10
| ~ spl34_18 ),
inference(sat_conversion,[],[f570]) ).
cnf(s36,plain,
( ~ spl34_11
| ~ spl34_13 ),
inference(sat_conversion,[],[f573]) ).
cnf(s37,plain,
( ~ spl34_12
| ~ spl34_13 ),
inference(sat_conversion,[],[f577]) ).
cnf(s38,plain,
~ spl34_12,
inference(rat,[],[s37,s14]) ).
cnf(s39,plain,
~ spl34_11,
inference(rat,[],[s36,s14]) ).
cnf(s40,plain,
~ spl34_8,
inference(rat,[],[s29,s14]) ).
cnf(s41,plain,
~ spl34_22,
inference(rat,[],[s22,s14]) ).
cnf(s42,plain,
~ spl34_4,
inference(rat,[],[s19,s14]) ).
cnf(s43,plain,
( spl34_21
| spl34_23 ),
inference(rat,[],[s12,s41]) ).
cnf(s44,plain,
( spl34_5
| spl34_18 ),
inference(rat,[],[s10,s42]) ).
cnf(s45,plain,
( spl34_9
| spl34_10 ),
inference(rat,[],[s4,s38,s39]) ).
cnf(s46,plain,
( spl34_6
| spl34_7 ),
inference(rat,[],[s3,s40]) ).
cnf(s47,plain,
( spl34_3
| spl34_5 ),
inference(rat,[],[s2,s42]) ).
cnf(s48,plain,
( ~ spl34_6
| ~ spl34_23 ),
inference(rat,[],[s35,s45,s47,s44,s26,s24]) ).
cnf(s49,plain,
( ~ spl34_15
| ~ spl34_2 ),
inference(rat,[],[s48,s43,s46,s21,s28]) ).
cnf(s50,plain,
spl34_1,
inference(rat,[],[s49,s1,s8]) ).
cnf(s51,plain,
~ spl34_14,
inference(rat,[],[s35,s47,s44,s45,s33,s31,s50]) ).
cnf(s52,plain,
spl34_15,
inference(rat,[],[s17,s51]) ).
cnf(s53,plain,
spl34_2,
inference(rat,[],[s7,s51]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s49,s53,s52]) ).
thf(f578,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL956^18 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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 10:56:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.30 % (2513540)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (2513546)lrs+10_16_si=on:nwc=1.5:random_seed=1304790853:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (2513545)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2121167262:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (2513546)Instruction limit reached!
% 0.20/0.30 % (2513546)------------------------------
% 0.20/0.30 % (2513546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2513546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2513546)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2513546)Termination reason: Instruction limit
% 0.20/0.30 % (2513546)Termination phase: Saturation
% 0.20/0.30 % (2513547)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1590289624:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (2513546)Time elapsed: 0.006 s
% 0.20/0.30 % (2513546)Peak memory usage: 12 MB
% 0.20/0.30 % (2513546)Instructions burned: 21 (million)
% 0.20/0.30 % (2513549)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=629442853:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (2513548)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=20175865:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.30 % (2513547)Instruction limit reached!
% 0.20/0.30 % (2513547)------------------------------
% 0.20/0.30 % (2513547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2513547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2513547)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2513547)Termination reason: Instruction limit
% 0.20/0.30 % (2513547)Termination phase: Saturation
% 0.20/0.30 % (2513547)Time elapsed: 0.002 s
% 0.20/0.30 % (2513547)Peak memory usage: 11 MB
% 0.20/0.30 % (2513547)Instructions burned: 4 (million)
% 0.20/0.30 % (2513545) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2513540-2513545"...
% 0.20/0.30 % (2513557)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1438720927:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (2513551)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (2513551)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.30 % (2513557)Instruction limit reached!
% 0.20/0.30 % (2513557)------------------------------
% 0.20/0.30 % (2513557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2513557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2513557)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2513557)Termination reason: Instruction limit
% 0.20/0.30 % (2513557)Termination phase: Saturation
% 0.20/0.30 % (2513557)Time elapsed: 0.001 s
% 0.20/0.30 % (2513557)Peak memory usage: 10 MB
% 0.20/0.30 % (2513557)Instructions burned: 4 (million)
% 0.20/0.30 % (2513549)Instruction limit reached!
% 0.20/0.30 % (2513549)------------------------------
% 0.20/0.30 % (2513549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2513549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2513549)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2513549)Termination reason: Instruction limit
% 0.20/0.30 % (2513549)Termination phase: Saturation
% 0.20/0.30 % (2513549)Time elapsed: 0.014 s
% 0.20/0.30 % (2513549)Peak memory usage: 12 MB
% 0.20/0.30 % (2513549)Instructions burned: 24 (million)
% 0.20/0.30 % (2513550)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3566448325:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (2513551)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=1054272368:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (2513558)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1061033348:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.30 % (2513545)...printing done.
% 0.20/0.30 % (2513545)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (2513545)------------------------------
% 0.20/0.30 % (2513545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2513545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2513545)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2513545)Termination reason: Refutation
% 0.20/0.30 % (2513545)Time elapsed: 0.021 s
% 0.20/0.30 % (2513545)Peak memory usage: 13 MB
% 0.20/0.30 % (2513545)Instructions burned: 42 (million)
% 0.20/0.30 % (2513540)Success in time 0.059 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------