%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL959^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:14:56 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 20
% Syntax : Number of formulae : 238 ( 42 unt; 0 typ; 10 def)
% Number of atoms : 2783 ( 529 equ; 0 cnn)
% Maximal formula atoms : 28 ( 11 avg)
% Number of connectives : 4771 ( 196 ~; 416 |; 42 &;3268 @)
% ( 10 <=>; 468 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 67 usr; 21 con; 0-4 aty)
% ( 346 !!; 25 ??; 0 @@+; 0 @@-)
% Number of variables : 907 ( 0 sgn 349 !; 2 ?; 907 :)
% 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,
f: $i > mworld > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vIFF: $o > $o > $o ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vAND: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
sK0: mworld > $i ).
thf(func_def_29,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
sK1: mworld ).
thf(func_def_31,type,
sK2: mworld ).
thf(func_def_33,type,
sK4: mworld > mworld ).
thf(func_def_34,type,
sK5: mworld ).
thf(func_def_35,type,
sK6: mworld > mworld ).
thf(func_def_36,type,
sK7: mworld > $i ).
thf(func_def_37,type,
sK8: mworld > mworld ).
thf(func_def_39,type,
sK10: mworld > mworld ).
thf(func_def_40,type,
sK11: mworld > mworld ).
thf(func_def_41,type,
sK12: mworld > $i ).
thf(func_def_42,type,
sK13: mworld > mworld ).
thf(func_def_43,type,
sK14: mworld > mworld ).
thf(func_def_44,type,
sK15: mworld > $i ).
thf(func_def_45,type,
sK16: mworld > mworld ).
thf(func_def_46,type,
sK17: mworld ).
thf(func_def_47,type,
sK18: mworld > mworld ).
thf(func_def_48,type,
sK19: mworld > $i ).
thf(func_def_49,type,
sK20: mworld > mworld ).
thf(func_def_50,type,
sK21: mworld > mworld ).
thf(func_def_51,type,
sK22: mworld > $i ).
thf(func_def_52,type,
sK23: mworld > mworld ).
thf(func_def_53,type,
sK24: $i > mworld ).
thf(func_def_55,type,
sK26: $i > mworld ).
thf(func_def_56,type,
sK27: mworld > mworld ).
thf(func_def_57,type,
sK28: $i > mworld ).
thf(func_def_58,type,
sK29: mworld ).
thf(func_def_59,type,
sK30: $i > mworld ).
thf(func_def_60,type,
sK31: $i > mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
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,
! [X1: mworld,X0: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X0 )
& ( mrel @ X1 @ X0 ) )
=> ( eiw_di @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_decr) ).
thf(f12,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f13,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f14,conjecture,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X1 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X1 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish203) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X1 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X1 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f16,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f17,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [X1: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X1 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X2: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ X2 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [X3: $i] : ( mbox @ ( f @ X3 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f19,plain,
( ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y0 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y0 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f24,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
& ( mrel @ X0 @ X1 ) )
=> ( eiw_di @ X2 @ X0 ) ),
inference(rectify,[],[f11]) ).
thf(f25,plain,
! [X1: mworld,X2: $i,X0: mworld] :
( ( ( ( eiw_di @ X2 @ X1 )
= $true )
& ( ( mrel @ X0 @ X1 )
= $true ) )
=> ( ( eiw_di @ X2 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f27,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f30,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f31,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f33,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f38,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f40,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y0 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y0 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f19]) ).
thf(f44,plain,
! [X1: mworld,X2: $i,X0: mworld] :
( ( ( eiw_di @ X2 @ X0 )
= $true )
| ( ( eiw_di @ X2 @ X1 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f45,plain,
! [X1: mworld,X0: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X0 )
= $true )
| ( ( eiw_di @ X2 @ X1 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f44]) ).
thf(f46,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true )
| ( ( mrel @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f45]) ).
thf(f48,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f49,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f50,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( ( eiw_di @ X2 @ X0 )
!= $true )
| ( ( mrel @ X1 @ X0 )
!= $true )
| ( ( eiw_di @ X2 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f51,plain,
( ( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y0 ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( mnot @ ( mbox @ ( f @ Y0 ) ) ) ) )
@ ( mbox
@ ( mnot
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f43]) ).
thf(f52,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f56,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f57,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f59,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f60,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f61,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f64,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ 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: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( f @ Y0 ) ) ) ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( f @ 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: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( f @ Y0 ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f51,f61,f57,f52,f48,f52,f60,f52,f56,f52,f59,f52,f60,f52,f52,f48,f59,f52,f60,f52,f52,f60,f52,f56,f52]) ).
thf(f65,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) )
@ sK1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ~ ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( f @ Y1 @ Y3 ) ) ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( !! @ mworld
@ ^ [Y4: mworld] :
( ( mrel @ Y2 @ Y4 )
=> ( f @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( ( ( mrel @ mactual @ sK1 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK1 ) ) ) ) )
= $false )
| ( ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK1 ) ) ) )
= $false )
| ( ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f102,plain,
( ( ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f103,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f104,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( ( ( mrel @ mactual @ sK2 )
=> ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f122,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f123,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f124,plain,
! [X1: mworld] :
( ( ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) )
@ sK9 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X1: mworld] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ sK9 @ Y1 ) ) ) ) )
& ( eiw_di @ sK9 @ sK2 ) )
= $true )
| ( $true
= ( ( mrel @ sK1 @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f126,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( $true
= ( ( mrel @ sK1 @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ sK9 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f128,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ sK9 @ Y1 ) ) ) ) ) )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: mworld,X1: mworld] :
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ sK9 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ sK9 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) )
@ ( sK10 @ X1 ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ sK9 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ sK2 @ X2 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ sK9 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ X1 @ ( sK10 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK10 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ sK9 @ Y0 ) ) ) )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ X1 @ ( sK10 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK10 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ sK9 @ Y0 ) ) )
= $false )
| ( ( ( mrel @ X1 @ ( sK10 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK10 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ sK9 @ Y0 ) )
@ ( sK11 @ X2 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ X1 @ ( sK10 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK10 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK10 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ sK9 @ Y0 ) )
@ ( sK11 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f141,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK10 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ ( sK12 @ X1 ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ sK9 @ Y0 ) )
@ ( sK11 @ X2 ) )
= $false )
| ( ( mrel @ sK2 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f142,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y0 )
=> ( f @ ( sK12 @ X1 ) @ Y0 ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( ( mrel @ X2 @ ( sK11 @ X2 ) )
=> ( f @ sK9 @ ( sK11 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X2: mworld,X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y0 )
=> ( f @ ( sK12 @ X1 ) @ Y0 ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ X2 @ ( sK11 @ X2 ) )
=> ( f @ sK9 @ ( sK11 @ X2 ) ) )
= $false )
| ( ( mrel @ sK2 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: mworld,X1: mworld] :
( ( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true )
| ( ( ( mrel @ X2 @ ( sK11 @ X2 ) )
=> ( f @ sK9 @ ( sK11 @ X2 ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK2 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X2: mworld,X1: mworld] :
( ( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK2 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f147,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X2 @ ( sK11 @ X2 ) )
=> ( f @ sK9 @ ( sK11 @ X2 ) ) )
= $false )
| ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y0 )
=> ( f @ ( sK12 @ X1 ) @ Y0 ) )
@ ( sK13 @ X1 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f148,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ ( sK10 @ X1 ) @ Y0 )
=> ( f @ ( sK12 @ X1 ) @ Y0 ) )
@ ( sK13 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f153,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( ( mrel @ ( sK10 @ X1 ) @ ( sK13 @ X1 ) )
=> ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f154,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) )
= $false )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f153]) ).
thf(f156,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f157,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) )
@ ( sK14 @ X1 ) )
= $false )
| ( ( eiw_di @ sK9 @ sK2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( ( mrel @ X1 @ ( sK14 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK14 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK14 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X1: mworld] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK14 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK14 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f162,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK14 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK14 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ ( sK15 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f163,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( eiw_di @ ( sK15 @ X1 ) @ ( sK14 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK14 @ X1 ) @ Y0 )
=> ( f @ ( sK15 @ X1 ) @ Y0 ) ) ) )
= $false )
| ( ( eiw_di @ sK9 @ sK2 )
= $true ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK14 @ X1 ) @ Y0 )
=> ( f @ ( sK15 @ X1 ) @ Y0 ) ) )
= $false )
| ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( eiw_di @ ( sK15 @ X1 ) @ ( sK14 @ X1 ) )
= $true )
| ( ( eiw_di @ sK9 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ ( sK14 @ X1 ) @ Y0 )
=> ( f @ ( sK15 @ X1 ) @ Y0 ) )
@ ( sK16 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f167,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ ( sK14 @ X1 ) @ ( sK16 @ X1 ) )
=> ( f @ ( sK15 @ X1 ) @ ( sK16 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X1: mworld] :
( ( ( f @ ( sK15 @ X1 ) @ ( sK16 @ X1 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( eiw_di @ sK9 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f170,plain,
! [X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK17 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f171,plain,
! [X1: mworld] :
( ( $true
= ( ( mrel @ sK1 @ X1 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( ( mrel @ sK2 @ sK17 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK17 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X1: mworld] :
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( ( ( mrel @ sK2 @ sK17 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK17 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ sK2 @ sK17 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK17 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: mworld] :
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK17 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f188,plain,
! [X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK17 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f189,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK17 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) )
@ ( sK21 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK17 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) )
@ ( sK21 @ X1 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ sK17 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ( ( ( mrel @ X1 @ ( sK21 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ X1 @ ( sK21 @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f201,plain,
! [X2: mworld,X3: $i,X1: mworld] :
( ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f202,plain,
! [X2: mworld,X3: $i,X1: mworld] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ ( sK22 @ X1 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: mworld,X3: $i,X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( ( eiw_di @ X3 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) ) ) )
= $true )
| ( ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y0 )
=> ( f @ ( sK22 @ X1 ) @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X2: mworld,X3: $i,X1: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) ) )
= $true )
| ( ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y0 )
=> ( f @ ( sK22 @ X1 ) @ Y0 ) ) ) )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y0 )
=> ( f @ ( sK22 @ X1 ) @ Y0 ) ) ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) )
@ X4 )
= $true )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y0 )
=> ( f @ ( sK22 @ X1 ) @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) )
@ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f205]) ).
thf(f208,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X4 ) )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( mrel @ X2 @ X4 )
= $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ ( sK21 @ X1 ) @ Y0 )
=> ( f @ ( sK22 @ X1 ) @ Y0 ) )
@ ( sK23 @ X1 ) )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) )
@ X4 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f211,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( ( mrel @ ( sK21 @ X1 ) @ ( sK23 @ X1 ) )
=> ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) ) )
= $false )
| ( ( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( ( mrel @ X2 @ X4 )
=> ( f @ X3 @ X4 ) )
= $true )
| ( ( mrel @ sK17 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f215,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f212]) ).
thf(f216,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK1 ) ) )
= $false )
| ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f229,plain,
! [X1: $i] :
( ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK2 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK2 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK1 ) )
@ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f230,plain,
! [X1: $i] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK1 ) )
@ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f263,plain,
! [X1: $i] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y1 @ Y3 )
=> ( f @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ sK29 )
= $false )
| ( ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK1 @ Y1 )
=> ~ ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( f @ Y0 @ Y2 ) ) ) ) )
& ( eiw_di @ Y0 @ sK1 ) )
@ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f264,plain,
! [X1: $i] :
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X1 @ Y1 ) ) ) ) )
& ( eiw_di @ X1 @ sK1 ) )
= $false )
| ( ( ( mrel @ sK2 @ sK29 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK29 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f263]) ).
thf(f265,plain,
! [X1: $i] :
( ( ( ( mrel @ sK2 @ sK29 )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK29 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X1 @ Y1 ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X1 @ Y1 ) ) ) ) )
= $false )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK29 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f276,plain,
! [X1: $i] :
( ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK29 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X1 @ Y1 ) ) ) )
@ ( sK31 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f266]) ).
thf(f277,plain,
! [X1: $i] :
( ( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK29 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X1 @ Y1 ) ) ) )
@ ( sK31 @ X1 ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK29 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( f @ Y1 @ Y2 ) ) ) ) ) )
@ X2 )
= $true )
| ( ( ^ [Y0: mworld] :
( ( mrel @ sK1 @ Y0 )
=> ~ ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( f @ X1 @ Y1 ) ) ) )
@ ( sK31 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: mworld,X1: $i] :
( ( ( ( mrel @ sK1 @ ( sK31 @ X1 ) )
=> ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK31 @ X1 ) @ Y0 )
=> ( f @ X1 @ Y0 ) ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( $true
= ( ( mrel @ sK29 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f280,plain,
! [X2: mworld,X1: $i] :
( ( $true
= ( ( mrel @ sK29 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK31 @ X1 ) @ Y0 )
=> ( f @ X1 @ Y0 ) ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f279]) ).
thf(f289,plain,
! [X2: mworld,X1: $i] :
( ( ( mrel @ sK29 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ) )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK31 @ X1 ) @ Y0 )
=> ( f @ X1 @ Y0 ) ) ) )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f280]) ).
thf(f290,plain,
! [X2: mworld,X3: $i,X1: $i] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( ~ ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK31 @ X1 ) @ Y0 )
=> ( f @ X1 @ Y0 ) ) ) )
= $false )
| ( ( mrel @ sK29 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: mworld,X3: $i,X1: $i] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ ( sK31 @ X1 ) @ Y0 )
=> ( f @ X1 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X2 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X2 @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ ( sK31 @ X1 ) @ Y0 )
=> ( f @ X1 @ Y0 ) )
@ X4 )
= $true )
| ( ( mrel @ sK29 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld] :
( ( ( mrel @ sK29 @ X2 )
= $false )
| ( $true
= ( ( mrel @ ( sK31 @ X1 ) @ X4 )
=> ( f @ X1 @ X4 ) ) )
| ( ( ( eiw_di @ X3 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) ) ) )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f292]) ).
thf(f294,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld] :
( ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( f @ X1 @ X4 )
= $true )
| ( ( ( eiw_di @ X3 @ X2 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) ) )
= $true )
| ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ X1 @ X4 )
= $true )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( f @ X1 @ X4 )
= $true )
| ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X2 @ Y0 )
=> ( f @ X3 @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( ( mrel @ X2 @ X5 )
=> ( f @ X3 @ X5 ) )
= $true )
| ( ( f @ X1 @ X4 )
= $true ) ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f298,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( f @ X3 @ X5 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ X2 @ X5 )
= $false )
| ( ( f @ X1 @ X4 )
= $true )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: mworld,X1: mworld] :
( ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( $true = $false )
| ( ( mrel @ sK2 @ X2 )
= $false )
| ( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true ) ),
inference(forward_demodulation,[],[f145,f49]) ).
thf(f300,plain,
! [X2: mworld,X1: mworld] :
( ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true )
| ( ( mrel @ sK2 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f301,plain,
! [X2: mworld,X1: mworld] :
( ( ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) )
= $false )
| ( $true = $false )
| ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false ) ),
inference(forward_demodulation,[],[f154,f49]) ).
thf(f302,plain,
! [X2: mworld,X1: mworld] :
( ( ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) )
= $false )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f301]) ).
thf(f303,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( $true = $false )
| ( ( eiw_di @ ( sK15 @ X1 ) @ ( sK14 @ X1 ) )
= $true ) ),
inference(forward_demodulation,[],[f165,f49]) ).
thf(f304,plain,
! [X1: mworld] :
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( eiw_di @ ( sK15 @ X1 ) @ ( sK14 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f305,plain,
! [X1: mworld] :
( ( $true = $false )
| ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ( ( f @ ( sK15 @ X1 ) @ ( sK16 @ X1 ) )
= $false ) ),
inference(forward_demodulation,[],[f168,f49]) ).
thf(f306,plain,
! [X1: mworld] :
( ( ( f @ ( sK15 @ X1 ) @ ( sK16 @ X1 ) )
= $false )
| ( ( eiw_di @ sK9 @ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f307,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( $true = $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( mrel @ sK1 @ X1 )
= $false ) ),
inference(forward_demodulation,[],[f209,f49]) ).
thf(f308,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( mrel @ sK1 @ X1 )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( f @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f307]) ).
thf(f309,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( mrel @ X2 @ X4 )
= $false )
| ( $true = $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f215,f49]) ).
thf(f310,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( f @ X3 @ X4 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( mrel @ X2 @ X4 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f315,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( f @ X1 @ X4 )
= $true )
| ( $true = $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( f @ X3 @ X5 )
= $true ) ),
inference(forward_demodulation,[],[f298,f49]) ).
thf(f316,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( f @ X3 @ X5 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ X1 @ X4 )
= $true )
| ( ( mrel @ sK29 @ X2 )
= $false )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( ( eiw_di @ X2 @ X0 )
!= $true )
| ( ( eiw_di @ X2 @ X1 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f50,f49]) ).
thf(f318,plain,
! [X2: mworld,X1: mworld] :
( ( $true = $false )
| ( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false ) ),
inference(forward_demodulation,[],[f300,f49]) ).
thf(f319,plain,
! [X2: mworld,X1: mworld] :
( ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f318]) ).
thf(f320,plain,
! [X2: mworld,X1: mworld] :
( ( $true = $false )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ( ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) )
= $false ) ),
inference(forward_demodulation,[],[f302,f49]) ).
thf(f321,plain,
! [X2: mworld,X1: mworld] :
( ( ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) )
= $false )
| ( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f323,definition,
( spl32_1
<=> ! [X1: mworld] :
( ( eiw_di @ ( sK15 @ X1 ) @ ( sK14 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
thf(f324,plain,
( ! [X1: mworld] :
( ( eiw_di @ ( sK15 @ X1 ) @ ( sK14 @ X1 ) )
= $true )
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f326,definition,
( spl32_2
<=> ( ( eiw_di @ sK9 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl32_2])],[avatar_definition]) ).
thf(f328,plain,
( ( ( eiw_di @ sK9 @ sK2 )
= $true )
| ~ spl32_2 ),
inference(avatar_component_clause,[],[f326]) ).
thf(f329,plain,
( spl32_1
| spl32_2 ),
inference(avatar_split_clause,[],[f304,f326,f323]) ).
thf(f331,definition,
( spl32_3
<=> ! [X1: mworld] :
( ( f @ ( sK15 @ X1 ) @ ( sK16 @ X1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl32_3])],[avatar_definition]) ).
thf(f332,plain,
( ! [X1: mworld] :
( ( f @ ( sK15 @ X1 ) @ ( sK16 @ X1 ) )
= $false )
| ~ spl32_3 ),
inference(avatar_component_clause,[],[f331]) ).
thf(f333,plain,
( spl32_2
| spl32_3 ),
inference(avatar_split_clause,[],[f306,f331,f326]) ).
thf(f334,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f308,f49]) ).
thf(f335,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( mrel @ sK17 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f336,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( $true = $false )
| ( ( mrel @ sK17 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f310,f49]) ).
thf(f337,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( mrel @ sK17 @ X2 )
= $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f345,definition,
( spl32_5
<=> ! [X2: mworld,X1: $i] :
( ( ( f @ X1 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl32_5])],[avatar_definition]) ).
thf(f346,plain,
( ! [X2: mworld,X1: $i] :
( ( ( f @ X1 @ X2 )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) )
| ~ spl32_5 ),
inference(avatar_component_clause,[],[f345]) ).
thf(f348,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( f @ X1 @ X4 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( $true = $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( f @ X3 @ X5 )
= $true ) ),
inference(forward_demodulation,[],[f316,f49]) ).
thf(f349,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( f @ X1 @ X4 )
= $true )
| ( ( mrel @ ( sK31 @ X1 ) @ X4 )
= $false )
| ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ X3 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f351,definition,
( spl32_6
<=> ! [X1: mworld] :
( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl32_6])],[avatar_definition]) ).
thf(f352,plain,
( ! [X1: mworld] :
( ( eiw_di @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
= $true )
| ~ spl32_6 ),
inference(avatar_component_clause,[],[f351]) ).
thf(f354,definition,
( spl32_7
<=> ! [X2: mworld] :
( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl32_7])],[avatar_definition]) ).
thf(f355,plain,
( ! [X2: mworld] :
( ( f @ sK9 @ ( sK11 @ X2 ) )
= $false )
| ~ spl32_7 ),
inference(avatar_component_clause,[],[f354]) ).
thf(f356,plain,
( spl32_6
| spl32_7 ),
inference(avatar_split_clause,[],[f319,f354,f351]) ).
thf(f358,definition,
( spl32_8
<=> ! [X1: mworld] :
( ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl32_8])],[avatar_definition]) ).
thf(f359,plain,
( ! [X1: mworld] :
( ( f @ ( sK12 @ X1 ) @ ( sK13 @ X1 ) )
= $false )
| ~ spl32_8 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f360,plain,
( spl32_8
| spl32_7 ),
inference(avatar_split_clause,[],[f321,f354,f358]) ).
thf(f361,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( $true = $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f335,f49]) ).
thf(f362,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( f @ X3 @ X4 )
= $true )
| ( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f363,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( f @ X3 @ X4 )
= $true )
| ( $true = $false )
| ( ( eiw_di @ X3 @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f337,f49]) ).
thf(f364,plain,
! [X2: mworld,X3: $i,X1: mworld,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ( ( f @ X3 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f363]) ).
thf(f369,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( eiw_di @ X1 @ sK1 )
= $false )
| ( $true = $false )
| ( ( f @ X3 @ X5 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ X1 @ X4 )
= $true ) ),
inference(forward_demodulation,[],[f349,f49]) ).
thf(f370,plain,
! [X2: mworld,X3: $i,X1: $i,X4: mworld,X5: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ X3 @ X5 )
= $true )
| ( ( f @ X1 @ X4 )
= $true )
| ( ( eiw_di @ X1 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f372,definition,
( spl32_10
<=> ! [X1: mworld] :
( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl32_10])],[avatar_definition]) ).
thf(f373,plain,
( ! [X1: mworld] :
( ( eiw_di @ ( sK22 @ X1 ) @ ( sK21 @ X1 ) )
= $true )
| ~ spl32_10 ),
inference(avatar_component_clause,[],[f372]) ).
thf(f375,definition,
( spl32_11
<=> ! [X4: mworld,X2: mworld,X3: $i] :
( ( ( f @ X3 @ X4 )
= $true )
| ( ( eiw_di @ X3 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl32_11])],[avatar_definition]) ).
thf(f376,plain,
( ! [X2: mworld,X3: $i,X4: mworld] :
( ( ( eiw_di @ X3 @ X2 )
= $false )
| ( ( f @ X3 @ X4 )
= $true ) )
| ~ spl32_11 ),
inference(avatar_component_clause,[],[f375]) ).
thf(f377,plain,
( spl32_10
| spl32_11 ),
inference(avatar_split_clause,[],[f362,f375,f372]) ).
thf(f379,definition,
( spl32_12
<=> ! [X1: mworld] :
( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl32_12])],[avatar_definition]) ).
thf(f380,plain,
( ! [X1: mworld] :
( ( f @ ( sK22 @ X1 ) @ ( sK23 @ X1 ) )
= $false )
| ~ spl32_12 ),
inference(avatar_component_clause,[],[f379]) ).
thf(f381,plain,
( spl32_11
| spl32_12 ),
inference(avatar_split_clause,[],[f364,f379,f375]) ).
thf(f382,plain,
( spl32_11
| spl32_5 ),
inference(avatar_split_clause,[],[f370,f345,f375]) ).
thf(f388,plain,
( ! [X1: mworld] :
( ( $true = $false )
| ( ( eiw_di @ sK9 @ X1 )
= $false ) )
| ~ spl32_7
| ~ spl32_11 ),
inference(constrained_superposition,[],[f355,f376]) ).
thf(f389,plain,
( ! [X1: mworld] :
( ( eiw_di @ sK9 @ X1 )
= $false )
| ~ spl32_7
| ~ spl32_11 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f392,plain,
( ( $true = $false )
| ~ spl32_2
| ~ spl32_7
| ~ spl32_11 ),
inference(constrained_superposition,[],[f328,f389]) ).
thf(f395,plain,
( $false
| ~ spl32_2
| ~ spl32_7
| ~ spl32_11 ),
inference(trivial_inequality_removal,[],[f392]) ).
thf(f396,plain,
( ~ spl32_2
| ~ spl32_7
| ~ spl32_11 ),
inference(avatar_contradiction_clause,[],[f395]) ).
thf(f398,plain,
( ! [X0: mworld,X1: mworld] :
( ( $true
= ( f @ ( sK12 @ X0 ) @ X1 ) )
| ( $true = $false ) )
| ~ spl32_6
| ~ spl32_11 ),
inference(constrained_superposition,[],[f376,f352]) ).
thf(f399,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( f @ ( sK12 @ X0 ) @ X1 ) )
| ~ spl32_6
| ~ spl32_11 ),
inference(trivial_inequality_removal,[],[f398]) ).
thf(f406,plain,
( ( $true = $false )
| ~ spl32_6
| ~ spl32_8
| ~ spl32_11 ),
inference(constrained_superposition,[],[f399,f359]) ).
thf(f410,plain,
( $false
| ~ spl32_6
| ~ spl32_8
| ~ spl32_11 ),
inference(trivial_inequality_removal,[],[f406]) ).
thf(f411,plain,
( ~ spl32_6
| ~ spl32_8
| ~ spl32_11 ),
inference(avatar_contradiction_clause,[],[f410]) ).
thf(f416,plain,
( ! [X0: mworld] :
( ( $false
= ( eiw_di @ ( sK22 @ X0 ) @ sK1 ) )
| ( $true = $false ) )
| ~ spl32_5
| ~ spl32_12 ),
inference(constrained_superposition,[],[f346,f380]) ).
thf(f417,plain,
( ! [X0: mworld] :
( $false
= ( eiw_di @ ( sK22 @ X0 ) @ sK1 ) )
| ~ spl32_5
| ~ spl32_12 ),
inference(trivial_inequality_removal,[],[f416]) ).
thf(f422,plain,
( ! [X0: mworld,X1: mworld] :
( ( $true != $true )
| ( ( eiw_di @ ( sK22 @ X0 ) @ X1 )
= $true ) )
| ~ spl32_10 ),
inference(constrained_superposition,[],[f317,f373]) ).
thf(f425,plain,
( ! [X0: mworld,X1: mworld] :
( ( eiw_di @ ( sK22 @ X0 ) @ X1 )
= $true )
| ~ spl32_10 ),
inference(trivial_inequality_removal,[],[f422]) ).
thf(f433,plain,
( ( $true = $false )
| ~ spl32_5
| ~ spl32_10
| ~ spl32_12 ),
inference(constrained_superposition,[],[f417,f425]) ).
thf(f437,plain,
( $false
| ~ spl32_5
| ~ spl32_10
| ~ spl32_12 ),
inference(trivial_inequality_removal,[],[f433]) ).
thf(f438,plain,
( ~ spl32_5
| ~ spl32_10
| ~ spl32_12 ),
inference(avatar_contradiction_clause,[],[f437]) ).
thf(f453,plain,
( ! [X0: mworld,X1: mworld] :
( ( $true != $true )
| ( $true
= ( eiw_di @ ( sK15 @ X0 ) @ X1 ) ) )
| ~ spl32_1 ),
inference(constrained_superposition,[],[f317,f324]) ).
thf(f454,plain,
( ! [X0: mworld,X1: mworld] :
( $true
= ( eiw_di @ ( sK15 @ X0 ) @ X1 ) )
| ~ spl32_1 ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f488,plain,
( ! [X0: mworld,X1: mworld] :
( ( ( eiw_di @ ( sK15 @ X0 ) @ X1 )
= $false )
| ( $true = $false ) )
| ~ spl32_3
| ~ spl32_11 ),
inference(constrained_superposition,[],[f332,f376]) ).
thf(f510,plain,
( ! [X0: mworld,X1: mworld] :
( ( eiw_di @ ( sK15 @ X0 ) @ X1 )
= $false )
| ~ spl32_3
| ~ spl32_11 ),
inference(trivial_inequality_removal,[],[f488]) ).
thf(f521,plain,
( ( $true = $false )
| ~ spl32_1
| ~ spl32_3
| ~ spl32_11 ),
inference(forward_demodulation,[],[f510,f454]) ).
thf(f522,plain,
( $false
| ~ spl32_1
| ~ spl32_3
| ~ spl32_11 ),
inference(trivial_inequality_removal,[],[f521]) ).
thf(f523,plain,
( ~ spl32_1
| ~ spl32_3
| ~ spl32_11 ),
inference(avatar_contradiction_clause,[],[f522]) ).
cnf(s1,plain,
( spl32_1
| spl32_2 ),
inference(sat_conversion,[],[f329]) ).
cnf(s2,plain,
( spl32_2
| spl32_3 ),
inference(sat_conversion,[],[f333]) ).
cnf(s4,plain,
( spl32_6
| spl32_7 ),
inference(sat_conversion,[],[f356]) ).
cnf(s5,plain,
( spl32_7
| spl32_8 ),
inference(sat_conversion,[],[f360]) ).
cnf(s7,plain,
( spl32_10
| spl32_11 ),
inference(sat_conversion,[],[f377]) ).
cnf(s8,plain,
( spl32_11
| spl32_12 ),
inference(sat_conversion,[],[f381]) ).
cnf(s9,plain,
( spl32_5
| spl32_11 ),
inference(sat_conversion,[],[f382]) ).
cnf(s11,plain,
( ~ spl32_2
| ~ spl32_7
| ~ spl32_11 ),
inference(sat_conversion,[],[f396]) ).
cnf(s13,plain,
( ~ spl32_6
| ~ spl32_8
| ~ spl32_11 ),
inference(sat_conversion,[],[f411]) ).
cnf(s15,plain,
( ~ spl32_5
| ~ spl32_10
| ~ spl32_12 ),
inference(sat_conversion,[],[f438]) ).
cnf(s21,plain,
( ~ spl32_1
| ~ spl32_3
| ~ spl32_11 ),
inference(sat_conversion,[],[f523]) ).
cnf(s22,plain,
( spl32_11
| ~ spl32_5 ),
inference(rat,[],[s15,s7,s8]) ).
cnf(s23,plain,
( ~ spl32_11
| ~ spl32_2 ),
inference(rat,[],[s13,s4,s5,s11]) ).
cnf(s24,plain,
spl32_11,
inference(rat,[],[s22,s9]) ).
cnf(s25,plain,
~ spl32_2,
inference(rat,[],[s23,s24]) ).
cnf(s26,plain,
spl32_3,
inference(rat,[],[s2,s25]) ).
cnf(s27,plain,
spl32_1,
inference(rat,[],[s1,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s21,s24,s27,s26]) ).
thf(f524,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL959^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n026.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 10:58:42 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.31 % (435134)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (435140)lrs+10_16_si=on:nwc=1.5:random_seed=519368681:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (435140)Instruction limit reached!
% 0.20/0.31 % (435140)------------------------------
% 0.20/0.31 % (435140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (435140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (435140)CaDiCaL version: 2.1.3
% 0.20/0.31 % (435140)Termination reason: Instruction limit
% 0.20/0.31 % (435140)Termination phase: Saturation
% 0.20/0.31 % (435140)Time elapsed: 0.005 s
% 0.20/0.31 % (435140)Peak memory usage: 12 MB
% 0.20/0.31 % (435140)Instructions burned: 19 (million)
% 0.20/0.31 % (435141)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1605584310:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (435139)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2124935559:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (435142)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=3503210907: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)
% 0.20/0.31 % (435141)Instruction limit reached!
% 0.20/0.31 % (435141)------------------------------
% 0.20/0.31 % (435141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (435141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (435141)CaDiCaL version: 2.1.3
% 0.20/0.31 % (435141)Termination reason: Instruction limit
% 0.20/0.31 % (435141)Termination phase: Saturation
% 0.20/0.31 % (435141)Time elapsed: 0.002 s
% 0.20/0.31 % (435141)Peak memory usage: 11 MB
% 0.20/0.31 % (435141)Instructions burned: 4 (million)
% 0.20/0.31 % (435147)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3941186296:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.31 % (435147)Instruction limit reached!
% 0.20/0.31 % (435147)------------------------------
% 0.20/0.31 % (435147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (435147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (435147)CaDiCaL version: 2.1.3
% 0.20/0.31 % (435147)Termination reason: Instruction limit
% 0.20/0.31 % (435147)Termination phase: Saturation
% 0.20/0.31 % (435147)Time elapsed: 0.001 s
% 0.20/0.31 % (435147)Peak memory usage: 11 MB
% 0.20/0.31 % (435147)Instructions burned: 4 (million)
% 0.20/0.31 % (435145)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.31 % (435145)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
% 0.20/0.31 % (435144)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1519893509:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.31 % (435139) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-435134-435139"...
% 0.20/0.31 % (435145)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=209593071:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.31 % (435143)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=405031874:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.31 % (435153)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.31 % (435151)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1675573721:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.31 % (435153)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1615483497:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.31 % (435151)Instruction limit reached!
% 0.20/0.31 % (435151)------------------------------
% 0.20/0.31 % (435151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (435151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (435151)CaDiCaL version: 2.1.3
% 0.20/0.31 % (435151)Termination reason: Instruction limit
% 0.20/0.31 % (435151)Termination phase: Saturation
% 0.20/0.31 % (435151)Time elapsed: 0.003 s
% 0.20/0.31 % (435151)Peak memory usage: 11 MB
% 0.20/0.31 % (435151)Instructions burned: 6 (million)
% 0.20/0.31 % (435139)...printing done.
% 0.20/0.31 % (435153)Instruction limit reached!
% 0.20/0.31 % (435153)------------------------------
% 0.20/0.31 % (435153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (435153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (435153)CaDiCaL version: 2.1.3
% 0.20/0.31 % (435153)Termination reason: Instruction limit
% 0.20/0.31 % (435153)Termination phase: Saturation
% 0.20/0.31 % (435153)Time elapsed: 0.002 s
% 0.20/0.31 % (435153)Peak memory usage: 12 MB
% 0.20/0.31 % (435153)Instructions burned: 9 (million)
% 0.20/0.31 % (435139)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.32 % (435139)------------------------------
% 0.20/0.32 % (435139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (435139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (435139)CaDiCaL version: 2.1.3
% 0.20/0.32 % (435139)Termination reason: Refutation
% 0.20/0.32 % (435139)Time elapsed: 0.024 s
% 0.20/0.32 % (435139)Peak memory usage: 13 MB
% 0.20/0.32 % (435139)Instructions burned: 48 (million)
% 0.20/0.32 % (435134)Success in time 0.071 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------