%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX184^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:40:40 AM UTC 2026
% Result : Theorem 63.71s 9.49s
% Output : Refutation 63.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 4
% Syntax : Number of formulae : 169 ( 96 unt; 0 typ; 2 def)
% Number of atoms : 7780 (1284 equ; 26 cnn)
% Maximal formula atoms : 33 ( 46 avg)
% Number of connectives : 37970 (5098 ~;4840 |; 913 &;21842 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 3 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 4599 (4599 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 79 usr; 11 con; 0-4 aty)
% (5203 !!; 33 ??; 0 @@+; 0 @@-)
% Number of variables : 6911 (6267 ^; 642 !; 2 ?;6911 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
unsorted: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
d_unsorted: $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_1,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_2,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_3,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_6,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_8,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_9,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_12,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_13,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_14,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_17,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_22,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_25,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
d2unsorted: d_unsorted > $i ).
thf(func_def_30,type,
d_unsorted_0: d_unsorted ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(func_def_33,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
vAND: $o > $o > $o ).
thf(func_def_36,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sF1: $o ).
thf(func_def_54,type,
sK2: $i > d_unsorted ).
thf(func_def_55,type,
sK3: $i > $i > $o ).
thf(func_def_59,type,
sK7: ( $i > $i > $o ) > $i ).
thf(func_def_60,type,
sK8: ( $i > $i > $o ) > $i ).
thf(func_def_61,type,
sK9: ( $i > $i > $o ) > $i ).
thf(func_def_62,type,
sK10: ( $i > $i > $o ) > $i ).
thf(func_def_63,type,
sK11: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_64,type,
sK12: ( $i > $i > $o ) > $i ).
thf(func_def_65,type,
sK13: ( $i > $i > $o ) > $i ).
thf(func_def_66,type,
sK14: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_67,type,
sK15: ( $i > $i > $o ) > $i ).
thf(func_def_68,type,
sK16: ( $i > $i > $o ) > $i ).
thf(func_def_69,type,
sK17: ( $i > $i > $o ) > $i ).
thf(func_def_70,type,
sK18: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_71,type,
sK19: ( $i > $i > $o ) > $i ).
thf(func_def_72,type,
sK20: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_73,type,
sK21: ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK22: ( $i > $i > $o ) > $i ).
thf(func_def_75,type,
sK23: ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK24: ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK25: ( $i > $i > $o ) > $i ).
thf(func_def_78,type,
sK26: ( ( $i > $i > $o ) > $i > $i > $o ) > $i > $i > $o ).
thf(func_def_79,type,
sK27: ( ( $i > $i > $o ) > $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK28: ( ( $i > $i > $o ) > $i > $i > $o ) > $i ).
thf(f1,axiom,
( ( ( ^ [X4: $i > $i > $o] :
! [X6: $i] : ( X4 @ X6 @ X6 ) )
= refl )
& ( total
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X4 @ X7 @ X6 )
| ( X4 @ X6 @ X7 )
| ( X6 = X7 ) ) ) )
& ( confl
= ( ^ [X4: $i > $i > $o] :
! [X33: $i > $i > $o,X6: $i,X7: $i,X34: $i > $i > $o,X11: $i] :
( ( ( X6 != X11 )
& ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X11 )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X26: $i,X12: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 ) ) ) )
| ( X34 @ X11 @ X7 )
| ( X33 @ X7 @ X11 )
| ~ ! [X13: $i,X25: $i,X12: $i] :
( ~ ( X33 @ X12 @ X13 )
| ( X33 @ X12 @ X25 )
| ~ ( X33 @ X13 @ X25 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X34 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X11 @ X27 )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 ) ) )
| ( X7 = X11 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X33 @ X14 @ X15 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X13: $i,X12: $i,X35: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X35 )
| ~ ( X5 @ X13 @ X35 ) ) )
& ( X6 != X7 ) )
| ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X34 @ X12 @ X13 )
| ~ ( X34 @ X13 @ X26 )
| ( X34 @ X12 @ X26 ) ) ) ) )
& ( asymm
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( sconfl
= ( ^ [X4: $i > $i > $o] :
! [X11: $i,X30: $i > $i > $o,X6: $i,X31: $i > $i > $o,X7: $i] :
( ~ ! [X14: $i,X15: $i] :
( ( X31 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X25: $i,X12: $i,X13: $i] :
( ( X30 @ X12 @ X25 )
| ~ ( X30 @ X12 @ X13 )
| ~ ( X30 @ X13 @ X25 ) )
| ~ ( X4 @ X6 @ X11 )
| ~ ! [X26: $i,X13: $i,X12: $i] :
( ~ ( X31 @ X13 @ X26 )
| ~ ( X31 @ X12 @ X13 )
| ( X31 @ X12 @ X26 ) )
| ( X7 = X11 )
| ( X31 @ X11 @ X7 )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X11 @ X27 )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X12 @ X13 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X25: $i,X12: $i] :
( ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X7 @ X27 ) ) )
| ( X30 @ X7 @ X11 )
| ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X7 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X32: $i,X12: $i,X13: $i] :
( ( X5 @ X12 @ X32 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X32 ) ) )
& ( X6 != X7 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X30 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ( X16 = X17 )
| ! [X5: $i > $i > $o] :
( ( X5 @ X16 @ X17 )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X11: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) ) )
| ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X17 @ X16 )
| ~ ! [X12: $i,X13: $i,X11: $i] :
( ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X11 ) ) ) ) )
= trsc )
& ( rc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X6 = X7 )
| ( X4 @ X6 @ X7 ) ) ) )
& ( irrefl
= ( ^ [X4: $i > $i > $o] :
! [X6: $i] :
~ ( X4 @ X6 @ X6 ) ) )
& ! [X3: d_unsorted,X2: d_unsorted] :
( ( ( d2unsorted @ X2 )
= ( d2unsorted @ X3 ) )
=> ( X2 = X3 ) )
& ! [X1: d_unsorted] : ( X1 = d_unsorted_0 )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
~ ( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 ) )
| ( X5 @ X6 @ X7 ) )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X12: $i,X25: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X13 @ X25 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X7 @ X6 ) )
& ( X6 != X7 )
& ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X7 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X26: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X26 )
| ( X5 @ X12 @ X26 ) )
| ( X5 @ X6 @ X27 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) ) ) )
= join )
& ( trans
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i,X11: $i] :
( ( X4 @ X6 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X11 ) ) ) )
& ( infl
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X7: $i,X6: $i,X4: $i > $i > $o] :
( ( X8 @ X4 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
! [X5: $i > $i > $o] :
( ( X5 @ X6 @ X7 )
| ~ ! [X12: $i,X13: $i,X11: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) ) )
= tc )
& ( ( ^ [X4: $i > $i > $o] :
( ! [X7: $i,X6: $i,X11: $i] :
( ~ ( X4 @ X7 @ X11 )
| ~ ( X4 @ X6 @ X7 )
| ( X4 @ X6 @ X11 ) )
& ! [X6: $i,X7: $i] :
( ( X6 = X7 )
| ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) )
& ! [X6: $i] : ( X4 @ X6 @ X6 ) ) )
= po )
& ( mono
= ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X5: $i > $i > $o,X10: $i,X4: $i > $i > $o,X9: $i] :
( ~ ! [X7: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ( X5 @ X6 @ X7 ) )
| ~ ( X8 @ X4 @ X9 @ X10 )
| ( X8 @ X5 @ X9 @ X10 ) ) ) )
& ( cr
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X37: $i > $i > $o,X36: $i > $i > $o,X7: $i] :
( ( X36 @ X7 @ X6 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X37 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X26: $i] :
( ~ ( X37 @ X12 @ X13 )
| ~ ( X37 @ X13 @ X26 )
| ( X37 @ X12 @ X26 ) )
| ( ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X6 )
| ~ ! [X13: $i,X12: $i,X11: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) )
& ( X6 != X7 )
& ~ ! [X5: $i > $i > $o] :
( ~ ! [X12: $i,X11: $i,X13: $i] :
( ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ( X5 @ X6 @ X7 ) ) )
| ~ ! [X13: $i,X12: $i,X25: $i] :
( ( X36 @ X12 @ X25 )
| ~ ( X36 @ X12 @ X13 )
| ~ ( X36 @ X13 @ X25 ) )
| ( X6 = X7 )
| ( X37 @ X6 @ X7 )
| ~ ! [X15: $i,X14: $i] :
( ( X36 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X26: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 )
| ~ ( X5 @ X13 @ X26 ) )
| ( X5 @ X6 @ X27 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) )
| ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X27 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) )
| ~ ! [X13: $i,X12: $i,X25: $i] :
( ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 ) ) ) ) ) ) )
& ( ( ^ [X8: ( $i > $i > $o ) > $i > $i > $o] :
! [X4: $i > $i > $o] :
( ( X8 @ X4 )
= ( X8 @ ( X8 @ X4 ) ) ) )
= idem )
& ( so
= ( ^ [X4: $i > $i > $o] :
( ! [X6: $i,X7: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X6 ) )
& ! [X7: $i,X11: $i,X6: $i] :
( ~ ( X4 @ X6 @ X7 )
| ~ ( X4 @ X7 @ X11 )
| ( X4 @ X6 @ X11 ) ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i] :
! [X7: $i] :
~ ( X4 @ X6 @ X7 ) )
= innf )
& ( trc
= ( ^ [X4: $i > $i > $o,X16: $i,X17: $i] :
( ! [X5: $i > $i > $o] :
( ~ ! [X13: $i,X11: $i,X12: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X13 @ X11 )
| ~ ( X5 @ X12 @ X13 ) )
| ( X5 @ X16 @ X17 )
| ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) ) )
| ( X16 = X17 ) ) ) )
& ( ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] : ( X4 @ X7 @ X6 ) )
= inv )
& ( ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 ) ) )
= symm )
& ( lconfl
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X11: $i,X28: $i > $i > $o,X6: $i,X29: $i > $i > $o] :
( ~ ( X4 @ X6 @ X7 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X29 @ X14 @ X15 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X28 @ X14 @ X15 ) )
| ~ ! [X27: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X14: $i,X15: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ~ ! [X12: $i,X13: $i,X26: $i] :
( ~ ( X5 @ X13 @ X26 )
| ~ ( X5 @ X12 @ X13 )
| ( X5 @ X12 @ X26 ) )
| ( X5 @ X11 @ X27 ) )
| ~ ! [X5: $i > $i > $o] :
( ( X5 @ X7 @ X27 )
| ~ ! [X25: $i,X12: $i,X13: $i] :
( ~ ( X5 @ X13 @ X25 )
| ( X5 @ X12 @ X25 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) ) )
| ( X29 @ X11 @ X7 )
| ( X28 @ X7 @ X11 )
| ~ ! [X25: $i,X13: $i,X12: $i] :
( ~ ( X28 @ X12 @ X13 )
| ( X28 @ X12 @ X25 )
| ~ ( X28 @ X13 @ X25 ) )
| ~ ( X4 @ X6 @ X11 )
| ~ ! [X13: $i,X12: $i,X26: $i] :
( ~ ( X29 @ X12 @ X13 )
| ( X29 @ X12 @ X26 )
| ~ ( X29 @ X13 @ X26 ) )
| ( X7 = X11 ) ) ) )
& ( norm
= ( ^ [X4: $i > $i > $o] :
! [X6: $i,X23: $i] :
( ~ ( X4 @ X6 @ X23 )
| ~ ! [X24: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X15: $i,X14: $i] :
( ( X5 @ X14 @ X15 )
| ~ ( X4 @ X14 @ X15 ) )
| ( X5 @ X6 @ X24 )
| ~ ! [X13: $i,X12: $i,X11: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) ) )
| ~ ! [X22: $i] :
~ ( X4 @ X24 @ X22 ) ) ) ) )
& ( ind
= ( ^ [X4: $i > $i > $o] :
! [X21: $i,X20: $i > $o] :
( ~ ! [X6: $i] :
( ( X20 @ X6 )
| ~ ! [X7: $i] :
( ~ ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X13: $i,X12: $i] :
( ( X5 @ X12 @ X11 )
| ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 ) )
| ( X5 @ X6 @ X7 )
| ~ ! [X14: $i,X15: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) )
| ( X20 @ X7 ) ) )
| ( X20 @ X21 ) ) ) )
& ( antisymm
= ( ^ [X4: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ~ ( X4 @ X7 @ X6 )
| ~ ( X4 @ X6 @ X7 )
| ( X6 = X7 ) ) ) )
& ! [X0: $i] :
? [X1: d_unsorted] :
( X0
= ( d2unsorted @ X1 ) )
& ( ( ^ [X4: $i > $i > $o,X5: $i > $i > $o] :
! [X7: $i,X6: $i] :
( ( X5 @ X6 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) )
= subrel )
& ( sc
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( X4 @ X7 @ X6 )
| ( X4 @ X6 @ X7 ) ) ) )
& ( ( ^ [X4: $i > $i > $o] :
! [X19: $i,X18: $i > $o] :
( ~ ! [X6: $i] :
( ~ ( X18 @ X6 )
| ~ ! [X7: $i] :
( ~ ( X18 @ X7 )
| ~ ( X4 @ X6 @ X7 ) ) )
| ~ ( X18 @ X19 ) ) )
= term )
& ( nfof
= ( ^ [X4: $i > $i > $o,X6: $i,X7: $i] :
( ( ! [X5: $i > $i > $o] :
( ~ ! [X11: $i,X13: $i,X12: $i] :
( ~ ( X5 @ X12 @ X13 )
| ~ ( X5 @ X13 @ X11 )
| ( X5 @ X12 @ X11 ) )
| ( X5 @ X7 @ X6 )
| ~ ! [X15: $i,X14: $i] :
( ~ ( X4 @ X14 @ X15 )
| ( X5 @ X14 @ X15 ) ) )
| ( X6 = X7 ) )
& ! [X22: $i] :
~ ( X4 @ X6 @ X22 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sev441_1) ).
thf(f2,conjecture,
( confl
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( trc @ X0 @ X1 @ X3 )
& ( trc @ X0 @ X1 @ X2 ) )
=> ( join @ X0 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',confluent) ).
thf(f3,negated_conjecture,
( confl
!= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( trc @ X0 @ X1 @ X3 )
& ( trc @ X0 @ X1 @ X2 ) )
=> ( join @ X0 @ X3 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( confl
!= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( trc @ X0 @ X3 @ X1 )
& ( trc @ X0 @ X3 @ X2 ) )
=> ( join @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
( ( confl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( ( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl )
& ( total
= ( ^ [X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X2 @ X3 @ X4 )
| ( X2 @ X4 @ X3 )
| ( X3 = X4 ) ) ) )
& ( confl
= ( ^ [X5: $i > $i > $o] :
! [X6: $i > $i > $o,X7: $i,X8: $i,X9: $i > $i > $o,X10: $i] :
( ( ( X7 != X10 )
& ~ ! [X11: $i > $i > $o] :
( ( X11 @ X7 @ X10 )
| ~ ! [X12: $i,X13: $i] :
( ( X11 @ X12 @ X13 )
| ~ ( X5 @ X12 @ X13 ) )
| ~ ! [X14: $i,X15: $i,X16: $i] :
( ~ ( X11 @ X16 @ X14 )
| ~ ( X11 @ X14 @ X15 )
| ( X11 @ X16 @ X15 ) ) ) )
| ( X9 @ X10 @ X8 )
| ( X6 @ X8 @ X10 )
| ~ ! [X17: $i,X18: $i,X19: $i] :
( ~ ( X6 @ X19 @ X17 )
| ( X6 @ X19 @ X18 )
| ~ ( X6 @ X17 @ X18 ) )
| ~ ! [X20: $i,X21: $i] :
( ( X9 @ X20 @ X21 )
| ~ ( X5 @ X20 @ X21 ) )
| ~ ! [X22: $i] :
( ~ ! [X23: $i > $i > $o] :
( ( X23 @ X10 @ X22 )
| ~ ! [X24: $i,X25: $i] :
( ( X23 @ X24 @ X25 )
| ~ ( X5 @ X24 @ X25 ) )
| ~ ! [X26: $i,X27: $i,X28: $i] :
( ~ ( X23 @ X26 @ X28 )
| ~ ( X23 @ X28 @ X27 )
| ( X23 @ X26 @ X27 ) ) )
| ~ ! [X29: $i > $i > $o] :
( ~ ! [X30: $i,X31: $i,X32: $i] :
( ~ ( X29 @ X31 @ X30 )
| ( X29 @ X32 @ X30 )
| ~ ( X29 @ X32 @ X31 ) )
| ~ ! [X33: $i,X34: $i] :
( ~ ( X5 @ X34 @ X33 )
| ( X29 @ X34 @ X33 ) )
| ( X29 @ X8 @ X22 ) ) )
| ( X8 = X10 )
| ~ ! [X35: $i,X36: $i] :
( ~ ( X5 @ X36 @ X35 )
| ( X6 @ X36 @ X35 ) )
| ( ~ ! [X37: $i > $i > $o] :
( ~ ! [X38: $i,X39: $i] :
( ( X37 @ X39 @ X38 )
| ~ ( X5 @ X39 @ X38 ) )
| ( X37 @ X7 @ X8 )
| ~ ! [X40: $i,X41: $i,X42: $i] :
( ~ ( X37 @ X41 @ X40 )
| ( X37 @ X41 @ X42 )
| ~ ( X37 @ X40 @ X42 ) ) )
& ( X7 != X8 ) )
| ~ ! [X43: $i,X44: $i,X45: $i] :
( ~ ( X9 @ X43 @ X45 )
| ~ ( X9 @ X45 @ X44 )
| ( X9 @ X43 @ X44 ) ) ) ) )
& ( asymm
= ( ^ [X46: $i > $i > $o] :
! [X47: $i,X48: $i] :
( ~ ( X46 @ X47 @ X48 )
| ~ ( X46 @ X48 @ X47 ) ) ) )
& ( sconfl
= ( ^ [X49: $i > $i > $o] :
! [X50: $i,X51: $i > $i > $o,X52: $i,X53: $i > $i > $o,X54: $i] :
( ~ ! [X55: $i,X56: $i] :
( ( X53 @ X55 @ X56 )
| ~ ( X49 @ X55 @ X56 ) )
| ~ ! [X57: $i,X58: $i,X59: $i] :
( ( X51 @ X58 @ X57 )
| ~ ( X51 @ X58 @ X59 )
| ~ ( X51 @ X59 @ X57 ) )
| ~ ( X49 @ X52 @ X50 )
| ~ ! [X60: $i,X61: $i,X62: $i] :
( ~ ( X53 @ X61 @ X60 )
| ~ ( X53 @ X62 @ X61 )
| ( X53 @ X62 @ X60 ) )
| ( X50 = X54 )
| ( X53 @ X50 @ X54 )
| ~ ! [X63: $i] :
( ~ ! [X64: $i > $i > $o] :
( ~ ! [X65: $i,X66: $i] :
( ( X64 @ X65 @ X66 )
| ~ ( X49 @ X65 @ X66 ) )
| ( X64 @ X50 @ X63 )
| ~ ! [X67: $i,X68: $i,X69: $i] :
( ~ ( X64 @ X68 @ X69 )
| ( X64 @ X67 @ X69 )
| ~ ( X64 @ X67 @ X68 ) ) )
| ~ ! [X70: $i > $i > $o] :
( ~ ! [X71: $i,X72: $i,X73: $i] :
( ( X70 @ X73 @ X72 )
| ~ ( X70 @ X71 @ X72 )
| ~ ( X70 @ X73 @ X71 ) )
| ~ ! [X74: $i,X75: $i] :
( ~ ( X49 @ X74 @ X75 )
| ( X70 @ X74 @ X75 ) )
| ( X70 @ X54 @ X63 ) ) )
| ( X51 @ X54 @ X50 )
| ( ~ ! [X76: $i > $i > $o] :
( ( X76 @ X52 @ X54 )
| ~ ! [X77: $i,X78: $i] :
( ( X76 @ X78 @ X77 )
| ~ ( X49 @ X78 @ X77 ) )
| ~ ! [X79: $i,X80: $i,X81: $i] :
( ( X76 @ X80 @ X79 )
| ~ ( X76 @ X80 @ X81 )
| ~ ( X76 @ X81 @ X79 ) ) )
& ( X52 != X54 ) )
| ~ ! [X82: $i,X83: $i] :
( ( X51 @ X83 @ X82 )
| ~ ( X49 @ X83 @ X82 ) ) ) ) )
& ( ( ^ [X84: $i > $i > $o,X85: $i,X86: $i] :
( ( X85 = X86 )
| ! [X87: $i > $i > $o] :
( ( X87 @ X85 @ X86 )
| ~ ! [X88: $i,X89: $i] :
( ( X87 @ X88 @ X89 )
| ~ ( X84 @ X88 @ X89 ) )
| ~ ! [X90: $i,X91: $i,X92: $i] :
( ( X87 @ X91 @ X92 )
| ~ ( X87 @ X91 @ X90 )
| ~ ( X87 @ X90 @ X92 ) ) )
| ! [X93: $i > $i > $o] :
( ~ ! [X94: $i,X95: $i] :
( ~ ( X84 @ X94 @ X95 )
| ( X93 @ X94 @ X95 ) )
| ( X93 @ X86 @ X85 )
| ~ ! [X96: $i,X97: $i,X98: $i] :
( ~ ( X93 @ X97 @ X98 )
| ~ ( X93 @ X96 @ X97 )
| ( X93 @ X96 @ X98 ) ) ) ) )
= trsc )
& ( rc
= ( ^ [X99: $i > $i > $o,X100: $i,X101: $i] :
( ( X100 = X101 )
| ( X99 @ X100 @ X101 ) ) ) )
& ( irrefl
= ( ^ [X102: $i > $i > $o] :
! [X103: $i] :
~ ( X102 @ X103 @ X103 ) ) )
& ! [X104: d_unsorted,X105: d_unsorted] :
( ( ( d2unsorted @ X104 )
= ( d2unsorted @ X105 ) )
=> ( X104 = X105 ) )
& ! [X106: d_unsorted] : ( d_unsorted_0 = X106 )
& ( ( ^ [X107: $i > $i > $o,X108: $i,X109: $i] :
~ ( ~ ! [X110: $i > $i > $o] :
( ~ ! [X111: $i,X112: $i] :
( ~ ( X107 @ X111 @ X112 )
| ( X110 @ X111 @ X112 ) )
| ~ ! [X113: $i,X114: $i,X115: $i] :
( ~ ( X110 @ X113 @ X114 )
| ~ ( X110 @ X114 @ X115 )
| ( X110 @ X113 @ X115 ) )
| ( X110 @ X108 @ X109 ) )
& ~ ! [X116: $i > $i > $o] :
( ~ ! [X117: $i,X118: $i,X119: $i] :
( ~ ( X116 @ X118 @ X117 )
| ( X116 @ X118 @ X119 )
| ~ ( X116 @ X117 @ X119 ) )
| ~ ! [X120: $i,X121: $i] :
( ( X116 @ X121 @ X120 )
| ~ ( X107 @ X121 @ X120 ) )
| ( X116 @ X109 @ X108 ) )
& ( X108 != X109 )
& ! [X122: $i] :
( ~ ! [X123: $i > $i > $o] :
( ~ ! [X124: $i,X125: $i,X126: $i] :
( ~ ( X123 @ X125 @ X124 )
| ( X123 @ X126 @ X124 )
| ~ ( X123 @ X126 @ X125 ) )
| ( X123 @ X109 @ X122 )
| ~ ! [X127: $i,X128: $i] :
( ~ ( X107 @ X128 @ X127 )
| ( X123 @ X128 @ X127 ) ) )
| ~ ! [X129: $i > $i > $o] :
( ~ ! [X130: $i,X131: $i,X132: $i] :
( ~ ( X129 @ X130 @ X132 )
| ~ ( X129 @ X132 @ X131 )
| ( X129 @ X130 @ X131 ) )
| ( X129 @ X108 @ X122 )
| ~ ! [X133: $i,X134: $i] :
( ~ ( X107 @ X133 @ X134 )
| ( X129 @ X133 @ X134 ) ) ) ) ) )
= join )
& ( trans
= ( ^ [X135: $i > $i > $o] :
! [X136: $i,X137: $i,X138: $i] :
( ( X135 @ X137 @ X138 )
| ~ ( X135 @ X137 @ X136 )
| ~ ( X135 @ X136 @ X138 ) ) ) )
& ( infl
= ( ^ [X139: ( $i > $i > $o ) > $i > $i > $o] :
! [X140: $i,X141: $i,X142: $i > $i > $o] :
( ( X139 @ X142 @ X141 @ X140 )
| ~ ( X142 @ X141 @ X140 ) ) ) )
& ( ( ^ [X143: $i > $i > $o,X144: $i,X145: $i] :
! [X146: $i > $i > $o] :
( ( X146 @ X144 @ X145 )
| ~ ! [X147: $i,X148: $i,X149: $i] :
( ~ ( X146 @ X147 @ X148 )
| ~ ( X146 @ X148 @ X149 )
| ( X146 @ X147 @ X149 ) )
| ~ ! [X150: $i,X151: $i] :
( ( X146 @ X151 @ X150 )
| ~ ( X143 @ X151 @ X150 ) ) ) )
= tc )
& ( ( ^ [X152: $i > $i > $o] :
( ! [X153: $i,X154: $i,X155: $i] :
( ~ ( X152 @ X153 @ X155 )
| ~ ( X152 @ X154 @ X153 )
| ( X152 @ X154 @ X155 ) )
& ! [X156: $i,X157: $i] :
( ( X156 = X157 )
| ~ ( X152 @ X156 @ X157 )
| ~ ( X152 @ X157 @ X156 ) )
& ! [X158: $i] : ( X152 @ X158 @ X158 ) ) )
= po )
& ( mono
= ( ^ [X159: ( $i > $i > $o ) > $i > $i > $o] :
! [X160: $i > $i > $o,X161: $i,X162: $i > $i > $o,X163: $i] :
( ~ ! [X164: $i,X165: $i] :
( ~ ( X162 @ X165 @ X164 )
| ( X160 @ X165 @ X164 ) )
| ~ ( X159 @ X162 @ X163 @ X161 )
| ( X159 @ X160 @ X163 @ X161 ) ) ) )
& ( cr
= ( ^ [X166: $i > $i > $o] :
! [X167: $i,X168: $i > $i > $o,X169: $i > $i > $o,X170: $i] :
( ( X169 @ X170 @ X167 )
| ~ ! [X171: $i,X172: $i] :
( ~ ( X166 @ X171 @ X172 )
| ( X168 @ X171 @ X172 ) )
| ~ ! [X173: $i,X174: $i,X175: $i] :
( ~ ( X168 @ X174 @ X173 )
| ~ ( X168 @ X173 @ X175 )
| ( X168 @ X174 @ X175 ) )
| ( ~ ! [X176: $i > $i > $o] :
( ( X176 @ X170 @ X167 )
| ~ ! [X177: $i,X178: $i,X179: $i] :
( ~ ( X176 @ X178 @ X177 )
| ~ ( X176 @ X177 @ X179 )
| ( X176 @ X178 @ X179 ) )
| ~ ! [X180: $i,X181: $i] :
( ( X176 @ X180 @ X181 )
| ~ ( X166 @ X180 @ X181 ) ) )
& ( X167 != X170 )
& ~ ! [X182: $i > $i > $o] :
( ~ ! [X183: $i,X184: $i,X185: $i] :
( ~ ( X182 @ X185 @ X184 )
| ( X182 @ X183 @ X184 )
| ~ ( X182 @ X183 @ X185 ) )
| ~ ! [X186: $i,X187: $i] :
( ~ ( X166 @ X186 @ X187 )
| ( X182 @ X186 @ X187 ) )
| ( X182 @ X167 @ X170 ) ) )
| ~ ! [X188: $i,X189: $i,X190: $i] :
( ( X169 @ X189 @ X190 )
| ~ ( X169 @ X189 @ X188 )
| ~ ( X169 @ X188 @ X190 ) )
| ( X167 = X170 )
| ( X168 @ X167 @ X170 )
| ~ ! [X191: $i,X192: $i] :
( ( X169 @ X192 @ X191 )
| ~ ( X166 @ X192 @ X191 ) )
| ~ ! [X193: $i] :
( ~ ! [X194: $i > $i > $o] :
( ~ ! [X195: $i,X196: $i,X197: $i] :
( ~ ( X194 @ X196 @ X197 )
| ( X194 @ X196 @ X195 )
| ~ ( X194 @ X197 @ X195 ) )
| ( X194 @ X167 @ X193 )
| ~ ! [X198: $i,X199: $i] :
( ( X194 @ X199 @ X198 )
| ~ ( X166 @ X199 @ X198 ) ) )
| ~ ! [X200: $i > $i > $o] :
( ( X200 @ X170 @ X193 )
| ~ ! [X201: $i,X202: $i] :
( ~ ( X166 @ X201 @ X202 )
| ( X200 @ X201 @ X202 ) )
| ~ ! [X203: $i,X204: $i,X205: $i] :
( ~ ( X200 @ X203 @ X205 )
| ( X200 @ X204 @ X205 )
| ~ ( X200 @ X204 @ X203 ) ) ) ) ) ) )
& ( ( ^ [X206: ( $i > $i > $o ) > $i > $i > $o] :
! [X207: $i > $i > $o] :
( ( X206 @ ( X206 @ X207 ) )
= ( X206 @ X207 ) ) )
= idem )
& ( so
= ( ^ [X208: $i > $i > $o] :
( ! [X209: $i,X210: $i] :
( ~ ( X208 @ X209 @ X210 )
| ~ ( X208 @ X210 @ X209 ) )
& ! [X211: $i,X212: $i,X213: $i] :
( ~ ( X208 @ X213 @ X211 )
| ~ ( X208 @ X211 @ X212 )
| ( X208 @ X213 @ X212 ) ) ) ) )
& ( ( ^ [X214: $i > $i > $o,X215: $i] :
! [X216: $i] :
~ ( X214 @ X215 @ X216 ) )
= innf )
& ( trc
= ( ^ [X217: $i > $i > $o,X218: $i,X219: $i] :
( ! [X220: $i > $i > $o] :
( ~ ! [X221: $i,X222: $i,X223: $i] :
( ( X220 @ X223 @ X222 )
| ~ ( X220 @ X221 @ X222 )
| ~ ( X220 @ X223 @ X221 ) )
| ( X220 @ X218 @ X219 )
| ~ ! [X224: $i,X225: $i] :
( ( X220 @ X225 @ X224 )
| ~ ( X217 @ X225 @ X224 ) ) )
| ( X218 = X219 ) ) ) )
& ( ( ^ [X226: $i > $i > $o,X227: $i,X228: $i] : ( X226 @ X228 @ X227 ) )
= inv )
& ( ( ^ [X229: $i > $i > $o] :
! [X230: $i,X231: $i] :
( ( X229 @ X230 @ X231 )
| ~ ( X229 @ X231 @ X230 ) ) )
= symm )
& ( lconfl
= ( ^ [X232: $i > $i > $o] :
! [X233: $i,X234: $i,X235: $i > $i > $o,X236: $i,X237: $i > $i > $o] :
( ~ ( X232 @ X236 @ X233 )
| ~ ! [X238: $i,X239: $i] :
( ~ ( X232 @ X238 @ X239 )
| ( X237 @ X238 @ X239 ) )
| ~ ! [X240: $i,X241: $i] :
( ~ ( X232 @ X240 @ X241 )
| ( X235 @ X240 @ X241 ) )
| ~ ! [X242: $i] :
( ~ ! [X243: $i > $i > $o] :
( ~ ! [X244: $i,X245: $i] :
( ( X243 @ X244 @ X245 )
| ~ ( X232 @ X244 @ X245 ) )
| ~ ! [X246: $i,X247: $i,X248: $i] :
( ~ ( X243 @ X247 @ X248 )
| ~ ( X243 @ X246 @ X247 )
| ( X243 @ X246 @ X248 ) )
| ( X243 @ X234 @ X242 ) )
| ~ ! [X249: $i > $i > $o] :
( ( X249 @ X233 @ X242 )
| ~ ! [X250: $i,X251: $i,X252: $i] :
( ~ ( X249 @ X252 @ X250 )
| ( X249 @ X251 @ X250 )
| ~ ( X249 @ X251 @ X252 ) )
| ~ ! [X253: $i,X254: $i] :
( ~ ( X232 @ X253 @ X254 )
| ( X249 @ X253 @ X254 ) ) ) )
| ( X237 @ X234 @ X233 )
| ( X235 @ X233 @ X234 )
| ~ ! [X255: $i,X256: $i,X257: $i] :
( ~ ( X235 @ X257 @ X256 )
| ( X235 @ X257 @ X255 )
| ~ ( X235 @ X256 @ X255 ) )
| ~ ( X232 @ X236 @ X234 )
| ~ ! [X258: $i,X259: $i,X260: $i] :
( ~ ( X237 @ X259 @ X258 )
| ( X237 @ X259 @ X260 )
| ~ ( X237 @ X258 @ X260 ) )
| ( X233 = X234 ) ) ) )
& ( norm
= ( ^ [X261: $i > $i > $o] :
! [X262: $i,X263: $i] :
( ~ ( X261 @ X262 @ X263 )
| ~ ! [X264: $i] :
( ~ ! [X265: $i > $i > $o] :
( ~ ! [X266: $i,X267: $i] :
( ( X265 @ X267 @ X266 )
| ~ ( X261 @ X267 @ X266 ) )
| ( X265 @ X262 @ X264 )
| ~ ! [X268: $i,X269: $i,X270: $i] :
( ( X265 @ X269 @ X270 )
| ~ ( X265 @ X269 @ X268 )
| ~ ( X265 @ X268 @ X270 ) ) )
| ~ ! [X271: $i] :
~ ( X261 @ X264 @ X271 ) ) ) ) )
& ( ind
= ( ^ [X272: $i > $i > $o] :
! [X273: $i,X274: $i > $o] :
( ~ ! [X275: $i] :
( ( X274 @ X275 )
| ~ ! [X276: $i] :
( ~ ! [X277: $i > $i > $o] :
( ~ ! [X278: $i,X279: $i,X280: $i] :
( ( X277 @ X280 @ X278 )
| ~ ( X277 @ X280 @ X279 )
| ~ ( X277 @ X279 @ X278 ) )
| ( X277 @ X275 @ X276 )
| ~ ! [X281: $i,X282: $i] :
( ~ ( X272 @ X281 @ X282 )
| ( X277 @ X281 @ X282 ) ) )
| ( X274 @ X276 ) ) )
| ( X274 @ X273 ) ) ) )
& ( antisymm
= ( ^ [X283: $i > $i > $o] :
! [X284: $i,X285: $i] :
( ~ ( X283 @ X284 @ X285 )
| ~ ( X283 @ X285 @ X284 )
| ( X284 = X285 ) ) ) )
& ! [X286: $i] :
? [X287: d_unsorted] :
( ( d2unsorted @ X287 )
= X286 )
& ( ( ^ [X288: $i > $i > $o,X289: $i > $i > $o] :
! [X290: $i,X291: $i] :
( ( X289 @ X291 @ X290 )
| ~ ( X288 @ X291 @ X290 ) ) )
= subrel )
& ( sc
= ( ^ [X292: $i > $i > $o,X293: $i,X294: $i] :
( ( X292 @ X294 @ X293 )
| ( X292 @ X293 @ X294 ) ) ) )
& ( ( ^ [X295: $i > $i > $o] :
! [X296: $i,X297: $i > $o] :
( ~ ! [X298: $i] :
( ~ ( X297 @ X298 )
| ~ ! [X299: $i] :
( ~ ( X297 @ X299 )
| ~ ( X295 @ X298 @ X299 ) ) )
| ~ ( X297 @ X296 ) ) )
= term )
& ( nfof
= ( ^ [X300: $i > $i > $o,X301: $i,X302: $i] :
( ( ! [X303: $i > $i > $o] :
( ~ ! [X304: $i,X305: $i,X306: $i] :
( ~ ( X303 @ X306 @ X305 )
| ~ ( X303 @ X305 @ X304 )
| ( X303 @ X306 @ X304 ) )
| ( X303 @ X302 @ X301 )
| ~ ! [X307: $i,X308: $i] :
( ~ ( X300 @ X308 @ X307 )
| ( X303 @ X308 @ X307 ) ) )
| ( X301 = X302 ) )
& ! [X309: $i] :
~ ( X300 @ X301 @ X309 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] : ( d_unsorted_0 = Y0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ( ( Y3 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y3 @ Y1 ) ) ) )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y5 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl ) )
= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] : ( d_unsorted_0 = Y0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ( ( Y3 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y3 @ Y1 ) ) ) )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y5 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl ) )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( confl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,definition,
( sF0
= ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f12,plain,
( ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f11]) ).
thf(f13,definition,
( sF1 = ( ~ sF0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f14,plain,
$true = sF1,
inference(definition_folding,[],[f9,f13,f12]) ).
thf(f15,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ( ( Y3 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y3 @ Y1 ) ) ) )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y5 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl ) ) ),
inference(beta-eta_normalization,[],[f8]) ).
thf(f16,plain,
( $true
= ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
= refl ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ( ( Y3 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y3 @ Y1 ) ) ) )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y5 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) ) ) )
& ( total
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f18,plain,
( $true = ( ~ sF0 ) ),
inference(forward_demodulation,[],[f13,f14]) ).
thf(f20,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ( ( Y3 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y3 @ Y1 ) ) ) )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y5 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f21,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(equality_proxy_clausification,[],[f16]) ).
thf(f22,plain,
( $true
= ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ( ( Y3 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y3 @ Y1 ) ) ) )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y5 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) )
& ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f25,plain,
( $true
= ( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc )
& ( sconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y7 ) ) ) )
| ( ( Y3 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y3 @ Y1 ) ) ) )
| ( Y4 @ Y1 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y1 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y10 @ Y9 )
| ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ( Y2 @ Y5 @ Y1 )
| ( Y5 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y6 @ Y8 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y3 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y4 @ Y6 @ Y8 )
| ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y7 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f27,plain,
( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f22]) ).
thf(f28,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f25]) ).
thf(f30,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 )
| ( Y3 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) )
| ( Y1 = Y2 ) ) )
= trsc ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f33,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
& ( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f36,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
& ( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f38,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
& ( !! @ d_unsorted
@ ^ [Y0: d_unsorted] :
( !! @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( ( d2unsorted @ Y1 )
= ( d2unsorted @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f36]) ).
thf(f42,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
& ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f43,plain,
( ( !! @ d_unsorted @ ( (=) @ d_unsorted_0 ) )
= $true ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f47,plain,
! [X1: d_unsorted] :
( $true
= ( d_unsorted_0 = X1 ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f48,plain,
( ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) )
= join )
= $true ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f49,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
& ( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f52,plain,
! [X1: d_unsorted] : ( d_unsorted_0 = X1 ),
inference(equality_proxy_clausification,[],[f47]) ).
thf(f54,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc )
& ( infl
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f55,plain,
( join
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f58,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ( Y3 @ Y1 @ Y2 ) ) ) )
= tc ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f63,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 )
| ( Y2 = Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 )
| ~ ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
= po ) ) ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f67,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) )
& ( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y0 @ Y4 @ Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f70,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem )
& ( cr
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y8 @ Y9 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y8 @ Y7 )
| ~ ( Y0 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y1 @ Y5 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) )
| ( Y6 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y9 )
| ( Y6 @ Y8 @ Y9 )
| ~ ( Y6 @ Y8 @ Y7 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y2 @ Y5 @ Y6 ) ) ) )
| ( Y3 @ Y4 @ Y1 )
| ( Y4 = Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y2 @ Y7 @ Y5 )
| ~ ( Y2 @ Y6 @ Y7 )
| ( Y2 @ Y6 @ Y5 ) ) ) ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
& ( Y4 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y8 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y1 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y7 @ Y5 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y2 @ Y1 @ Y4 ) ) ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f72,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
& ( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y0 @ ( Y0 @ Y1 ) )
= ( Y0 @ Y1 ) ) ) )
= idem ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f75,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf )
& ( so
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f78,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y0 @ Y1 @ Y2 ) ) )
= innf ) )
= $true ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f81,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv )
& ( trc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f84,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
= inv ) )
= $true ),
inference(and_proxy_clausification,[],[f81]) ).
thf(f87,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ) )
= symm ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f90,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( lconfl
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y5 = Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y1 @ Y8 @ Y6 )
| ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y7 @ Y8 ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y3 @ Y7 @ Y8 )
| ( Y3 @ Y6 @ Y8 )
| ~ ( Y3 @ Y6 @ Y7 ) ) ) ) )
| ( Y3 @ Y5 @ Y4 )
| ( Y1 @ Y4 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y9 @ Y8 )
| ~ ( Y0 @ Y9 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y10 )
| ~ ( Y7 @ Y8 @ Y10 ) ) ) ) )
| ( Y7 @ Y5 @ Y6 ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y4 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y8 )
| ~ ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y9 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y3 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ~ ( Y0 @ Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f94,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) )
& ( norm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
~ ( Y0 @ Y3 @ Y4 ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 )
| ( Y4 @ Y6 @ Y5 ) ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y0 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) ) )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f97,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
& ( ind
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y7 @ Y6 )
| ~ ( Y0 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y7 @ Y8 )
| ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 ) ) ) ) ) ) ) ) )
| ( Y1 @ Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f99,plain,
( $true
= ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) )
& ( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y2 = Y1 )
| ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f97]) ).
thf(f102,plain,
( ( ( nfof
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
~ ( Y0 @ Y1 @ Y3 ) )
& ( ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 )
| ~ ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) )
& ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y0 @ Y3 @ Y4 )
| ~ ( Y1 @ Y4 ) ) )
| ~ ( Y1 @ Y3 ) ) ) ) ) ) )
= term )
& ( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
& ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) )
= subrel )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f99]) ).
thf(f105,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f107,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ d_unsorted
@ ^ [Y1: d_unsorted] :
( ( d2unsorted @ Y1 )
= Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f108,plain,
! [X1: $i] :
( $true
= ( ?? @ d_unsorted
@ ^ [Y0: d_unsorted] :
( ( d2unsorted @ Y0 )
= X1 ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f111,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: d_unsorted] :
( ( d2unsorted @ Y0 )
= X1 )
@ ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f108]) ).
thf(f112,plain,
! [X1: $i] :
( $true
= ( ( d2unsorted @ ( sK2 @ X1 ) )
= X1 ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f116,plain,
! [X1: $i] :
( ( d2unsorted @ ( sK2 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[],[f112]) ).
thf(f123,plain,
! [X0: d_unsorted,X1: d_unsorted] : ( X0 = X1 ),
inference(superposition,[],[f52,f52]) ).
thf(f125,plain,
( ( ( ~ $true ) = $true )
| ( $false = sF0 ) ),
inference(fool_paramodulation,[],[f18]) ).
thf(f126,plain,
( ( $false = sF0 )
| ( $true = $false ) ),
inference(boolean_simplification,[],[f125]) ).
thf(f127,plain,
$false = sF0,
inference(trivial_inequality_removal,[],[f126]) ).
thf(f129,plain,
( ( confl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[],[f12,f127]) ).
thf(f131,plain,
( confl
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( confl @ sK3 )
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( trc @ Y0 @ Y1 @ Y2 )
& ( trc @ Y0 @ Y1 @ Y3 ) )
=> ( join @ Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f131]) ).
thf(f133,plain,
( ( confl @ sK3 )
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK3 @ Y0 @ Y1 )
& ( trc @ sK3 @ Y0 @ Y2 ) )
=> ( join @ sK3 @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f135,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK3 @ Y0 @ Y1 )
& ( trc @ sK3 @ Y0 @ Y2 ) )
=> ( join @ sK3 @ Y2 @ Y1 ) ) ) ) ) )
| ( ( confl @ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f133]) ).
thf(f138,plain,
( ( ( confl @ sK3 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK3 @ Y0 @ Y1 )
& ( trc @ sK3 @ Y0 @ Y2 ) )
=> ( join @ sK3 @ Y2 @ Y1 ) ) ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f139,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( trc @ sK3 @ sK4 @ Y0 )
& ( trc @ sK3 @ sK4 @ Y1 ) )
=> ( join @ sK3 @ Y1 @ Y0 ) ) ) ) )
| ( ( confl @ sK3 )
= $false ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f142,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( trc @ sK3 @ sK4 @ Y0 )
& ( trc @ sK3 @ sK4 @ Y1 ) )
=> ( join @ sK3 @ Y1 @ Y0 ) ) )
@ sK5 )
= $false )
| ( ( confl @ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f143,plain,
( ( ( confl @ sK3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( trc @ sK3 @ sK4 @ sK5 )
& ( trc @ sK3 @ sK4 @ Y0 ) )
=> ( join @ sK3 @ Y0 @ sK5 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f146,plain,
( ( ( ^ [Y0: $i] :
( ( ( trc @ sK3 @ sK4 @ sK5 )
& ( trc @ sK3 @ sK4 @ Y0 ) )
=> ( join @ sK3 @ Y0 @ sK5 ) )
@ sK6 )
= $false )
| ( ( confl @ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f147,plain,
( ( ( ( ( trc @ sK3 @ sK4 @ sK5 )
& ( trc @ sK3 @ sK4 @ sK6 ) )
=> ( join @ sK3 @ sK6 @ sK5 ) )
= $false )
| ( ( confl @ sK3 )
= $false ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f150,plain,
( ( ( ( trc @ sK3 @ sK4 @ sK5 )
& ( trc @ sK3 @ sK4 @ sK6 ) )
= $true )
| ( ( confl @ sK3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f152,plain,
( ( ( trc @ sK3 @ sK4 @ sK6 )
= $true )
| ( ( confl @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( $true
= ( trc @ sK3 @ sK4 @ sK5 ) )
| ( ( confl @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f154,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ X1 )
= ( refl @ X1 ) ),
inference(argument_congruence,[],[f21]) ).
thf(f155,plain,
! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) )
= ( refl @ X1 ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f158,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( refl @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) ) ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f159,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) ) )
| ( $true
= ( refl @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f160,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( $false
= ( refl @ X1 ) )
| ( ( ^ [Y0: $i] : ( X1 @ Y0 @ Y0 )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f161,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( $true
= ( X1 @ X2 @ X2 ) )
| ( $false
= ( refl @ X1 ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( refl @ X1 ) )
| ( ( ^ [Y0: $i] : ( X1 @ Y0 @ Y0 )
@ ( sK7 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f163,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK7 @ X1 ) @ ( sK7 @ X1 ) ) )
| ( $true
= ( refl @ X1 ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f166,plain,
! [X0: d_unsorted,X1: $i] :
( ( d2unsorted @ X0 )
= X1 ),
inference(superposition,[],[f116,f123]) ).
thf(f184,plain,
( ( $true
= ( refl
@ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ ( sK7
@ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) )
@ ( sK7
@ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) )
= $false ) ),
inference(primitive_instantiation,[],[f163]) ).
thf(f200,plain,
( ( ( ( sK7 @ (=) )
= ( sK7 @ (=) ) )
= $false )
| ( $true
= ( refl @ (=) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f201,plain,
( ( $true = $false )
| ( $true
= ( refl @ (=) ) ) ),
inference(boolean_simplification,[],[f200]) ).
thf(f202,plain,
( $true
= ( refl @ (=) ) ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f214,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(superposition,[],[f166,f116]) ).
thf(f247,plain,
! [X1: $i > $i > $o] :
( ( confl @ X1 )
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y2 @ Y8 @ Y7 )
| ~ ( Y2 @ Y6 @ Y7 )
| ~ ( Y2 @ Y8 @ Y6 ) ) ) ) )
| ( ( Y4 != Y3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y9 @ Y7 )
| ( Y6 @ Y8 @ Y7 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) )
| ( Y6 @ Y4 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y0 @ Y6 @ Y7 ) ) ) )
| ( Y3 = Y1 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ( Y7 @ Y3 @ Y6 )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y7 @ Y8 @ Y9 )
| ~ ( Y0 @ Y8 @ Y9 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ~ ( Y7 @ Y8 @ Y9 )
| ( Y7 @ Y8 @ Y10 )
| ~ ( Y7 @ Y9 @ Y10 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y7: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( !! @ $i
@ ^ [Y10: $i] :
( ( Y7 @ Y10 @ Y9 )
| ~ ( Y7 @ Y8 @ Y9 )
| ~ ( Y7 @ Y10 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y0 @ Y9 @ Y8 )
| ( Y7 @ Y9 @ Y8 ) ) ) )
| ( Y7 @ Y1 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y0 @ Y7 @ Y6 )
| ( Y2 @ Y7 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y7 )
| ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y1 )
| ( Y2 @ Y1 @ Y3 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y9 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y0 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y4 @ Y1 ) ) )
& ( Y4 != Y1 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f27]) ).
thf(f248,plain,
! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( ( Y3 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ( Y2 = Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( X1 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y0 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y0 )
| ( Y1 @ Y0 @ Y2 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y0 ) ) )
& ( Y3 != Y0 ) ) ) ) ) ) ) )
= ( confl @ X1 ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f282,plain,
! [X0: $i] :
( ( ( confl @ sK3 )
= $false )
| ( ( trc @ sK3 @ sK4 @ X0 )
= $true ) ),
inference(superposition,[],[f152,f214]) ).
thf(f313,plain,
! [X1: $i > $i > $o] :
( ( asymm @ X1 )
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f28]) ).
thf(f314,plain,
! [X1: $i > $i > $o] :
( ( asymm @ X1 )
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f313]) ).
thf(f360,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( ( Y3 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ( Y2 = Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( X1 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y0 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y0 )
| ( Y1 @ Y0 @ Y2 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y0 ) ) )
& ( Y3 != Y0 ) ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f248]) ).
thf(f363,plain,
! [X1: $i > $i > $o] :
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y1 @ Y7 @ Y6 )
| ~ ( Y1 @ Y5 @ Y6 )
| ~ ( Y1 @ Y7 @ Y5 ) ) ) ) )
| ( ( Y3 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y8 @ Y6 )
| ( Y5 @ Y7 @ Y6 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) )
| ( Y5 @ Y3 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ( Y2 = Y0 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ( Y6 @ Y2 @ Y5 )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y6 @ Y7 @ Y8 )
| ~ ( X1 @ Y7 @ Y8 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ~ ( Y6 @ Y7 @ Y8 )
| ( Y6 @ Y7 @ Y9 )
| ~ ( Y6 @ Y8 @ Y9 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y6: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 @ Y8 )
| ~ ( Y6 @ Y7 @ Y8 )
| ~ ( Y6 @ Y9 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( X1 @ Y8 @ Y7 )
| ( Y6 @ Y8 @ Y7 ) ) ) )
| ( Y6 @ Y0 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y6 )
| ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y0 )
| ( Y1 @ Y0 @ Y2 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y8 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ Y3 @ Y0 ) ) )
& ( Y3 != Y0 ) ) ) ) ) ) )
@ ( sK10 @ X1 ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f360]) ).
thf(f364,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 )
| ~ ( Y0 @ Y6 @ Y4 ) ) ) ) )
| ( ( Y2 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y1
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( X1 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ ( sK10 @ X1 ) @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ( Y3 @ Y1 @ ( sK10 @ X1 ) )
| ( Y0 @ ( sK10 @ X1 ) @ Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y2 @ ( sK10 @ X1 ) ) ) )
& ( Y2
!= ( sK10 @ X1 ) ) ) ) ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f367,plain,
! [X1: $i > $i > $o] :
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
| ~ ( Y0 @ Y4 @ Y5 )
| ~ ( Y0 @ Y6 @ Y4 ) ) ) ) )
| ( ( Y2 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y7 @ Y5 )
| ( Y4 @ Y6 @ Y5 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) )
| ( Y4 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y6 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y1
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ( Y5 @ Y1 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y5 @ Y6 @ Y7 )
| ~ ( X1 @ Y6 @ Y7 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ~ ( Y5 @ Y6 @ Y7 )
| ( Y5 @ Y6 @ Y8 )
| ~ ( Y5 @ Y7 @ Y8 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y5: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
| ~ ( Y5 @ Y6 @ Y7 )
| ~ ( Y5 @ Y8 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( X1 @ Y7 @ Y6 )
| ( Y5 @ Y7 @ Y6 ) ) ) )
| ( Y5 @ ( sK10 @ X1 ) @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y5 )
| ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ( Y3 @ Y1 @ ( sK10 @ X1 ) )
| ( Y0 @ ( sK10 @ X1 ) @ Y1 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y7 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y2 @ ( sK10 @ X1 ) ) ) )
& ( Y2
!= ( sK10 @ X1 ) ) ) ) ) ) )
@ ( sK11 @ X1 ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f364]) ).
thf(f368,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK11 @ X1 @ Y5 @ Y4 )
| ~ ( sK11 @ X1 @ Y3 @ Y4 )
| ~ ( sK11 @ X1 @ Y5 @ Y3 ) ) ) ) )
| ( ( Y1 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y0
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ ( sK10 @ X1 ) @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( sK11 @ X1 @ Y4 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ( Y2 @ Y0 @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ Y0 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ ( sK10 @ X1 ) ) ) )
& ( Y1
!= ( sK10 @ X1 ) ) ) ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f367]) ).
thf(f371,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK11 @ X1 @ Y5 @ Y4 )
| ~ ( sK11 @ X1 @ Y3 @ Y4 )
| ~ ( sK11 @ X1 @ Y5 @ Y3 ) ) ) ) )
| ( ( Y1 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) )
| ( Y3 @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y0
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( Y4 @ Y0 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( X1 @ Y5 @ Y6 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( X1 @ Y6 @ Y5 )
| ( Y4 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ ( sK10 @ X1 ) @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( sK11 @ X1 @ Y4 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y4 )
| ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ( Y2 @ Y0 @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ Y0 )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y6 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y1 @ ( sK10 @ X1 ) ) ) )
& ( Y1
!= ( sK10 @ X1 ) ) ) ) ) )
@ ( sK12 @ X1 ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f368]) ).
thf(f372,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK11 @ X1 @ Y4 @ Y3 )
| ~ ( sK11 @ X1 @ Y2 @ Y3 )
| ~ ( sK11 @ X1 @ Y4 @ Y2 ) ) ) ) )
| ( ( Y0
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) )
| ( Y2 @ Y0 @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ ( sK12 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ ( sK10 @ X1 ) @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( sK11 @ X1 @ Y3 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ( Y1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ ( sK10 @ X1 ) ) ) )
& ( Y0
!= ( sK10 @ X1 ) ) ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f371]) ).
thf(f375,plain,
! [X1: $i > $i > $o] :
( ( ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK11 @ X1 @ Y4 @ Y3 )
| ~ ( sK11 @ X1 @ Y2 @ Y3 )
| ~ ( sK11 @ X1 @ Y4 @ Y2 ) ) ) ) )
| ( ( Y0
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) )
| ( Y2 @ Y0 @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ ( sK12 @ X1 ) @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( X1 @ Y5 @ Y4 )
| ( Y3 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ ( sK10 @ X1 ) @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( sK11 @ X1 @ Y3 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y3 )
| ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ( Y1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ Y0 @ ( sK10 @ X1 ) ) ) )
& ( Y0
!= ( sK10 @ X1 ) ) ) ) )
@ ( sK13 @ X1 ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f372]) ).
thf(f376,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK11 @ X1 @ Y3 @ Y2 )
| ~ ( sK11 @ X1 @ Y1 @ Y2 )
| ~ ( sK11 @ X1 @ Y3 @ Y1 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) )
| ( Y1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ ( sK12 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ ( sK10 @ X1 ) @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK11 @ X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) ) )
& ( ( sK13 @ X1 )
!= ( sK10 @ X1 ) ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f375]) ).
thf(f379,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK11 @ X1 @ Y3 @ Y2 )
| ~ ( sK11 @ X1 @ Y1 @ Y2 )
| ~ ( sK11 @ X1 @ Y3 @ Y1 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) )
| ( Y1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( X1 @ Y1 @ Y2 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ ( sK12 @ X1 ) @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y4 @ Y3 )
| ( Y2 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ ( sK10 @ X1 ) @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( sK11 @ X1 @ Y2 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y2 )
| ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) ) )
& ( ( sK13 @ X1 )
!= ( sK10 @ X1 ) ) ) )
@ ( sK14 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f376]) ).
thf(f380,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ X1 @ Y2 @ Y1 )
| ~ ( sK11 @ X1 @ Y0 @ Y1 )
| ~ ( sK11 @ X1 @ Y2 @ Y0 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ ( sK12 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y1 @ Y0 )
| ( sK11 @ X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK14 @ X1 @ Y2 @ Y1 )
| ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( sK14 @ X1 @ Y0 @ Y2 ) ) ) ) )
| ( sK14 @ X1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
| ( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y1 @ Y2 )
| ~ ( Y0 @ Y3 @ Y2 )
| ~ ( Y0 @ Y1 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y2 @ Y1 )
| ( Y0 @ Y2 @ Y1 ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) ) )
& ( ( sK13 @ X1 )
!= ( sK10 @ X1 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f383,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ X1 @ Y2 @ Y1 )
| ~ ( sK11 @ X1 @ Y0 @ Y1 )
| ~ ( sK11 @ X1 @ Y2 @ Y0 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ ( sK12 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y1 @ Y0 )
| ( sK11 @ X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK14 @ X1 @ Y2 @ Y1 )
| ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( sK14 @ X1 @ Y0 @ Y2 ) ) ) ) )
| ( sK14 @ X1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) )
| ( sK11 @ X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f380]) ).
thf(f387,plain,
! [X1: $i > $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ X1 @ Y2 @ Y1 )
| ~ ( sK11 @ X1 @ Y0 @ Y1 )
| ~ ( sK11 @ X1 @ Y2 @ Y0 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ ( sK12 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y1 @ Y0 )
| ( sK11 @ X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK14 @ X1 @ Y2 @ Y1 )
| ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( sK14 @ X1 @ Y0 @ Y2 ) ) ) ) )
| ( sK14 @ X1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f383]) ).
thf(f390,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ X1 @ Y2 @ Y1 )
| ~ ( sK11 @ X1 @ Y0 @ Y1 )
| ~ ( sK11 @ X1 @ Y2 @ Y0 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ ( sK12 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y1 @ Y0 )
| ( sK11 @ X1 @ Y1 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK14 @ X1 @ Y2 @ Y1 )
| ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( sK14 @ X1 @ Y0 @ Y2 ) ) ) ) ) ) )
| ( ( confl @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f387]) ).
thf(f393,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ X1 @ Y2 @ Y1 )
| ~ ( sK11 @ X1 @ Y0 @ Y1 )
| ~ ( sK11 @ X1 @ Y2 @ Y0 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ ( sK12 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y1 @ Y0 )
| ( sK11 @ X1 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f390]) ).
thf(f396,plain,
! [X1: $i > $i > $o] :
( ( ( confl @ X1 )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ X1 @ Y2 @ Y1 )
| ~ ( sK11 @ X1 @ Y0 @ Y1 )
| ~ ( sK11 @ X1 @ Y2 @ Y0 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ ( sK12 @ X1 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y3 @ Y2 )
| ( Y1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f393]) ).
thf(f399,plain,
! [X1: $i > $i > $o] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK11 @ X1 @ Y2 @ Y1 )
| ~ ( sK11 @ X1 @ Y0 @ Y1 )
| ~ ( sK11 @ X1 @ Y2 @ Y0 ) ) ) ) )
| ( ( ( sK13 @ X1 )
!= ( sK12 @ X1 ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) )
| ( Y0 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK14 @ X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y0 @ Y1 ) ) ) )
| ( ( sK12 @ X1 )
= ( sK10 @ X1 ) ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f396]) ).
thf(f402,plain,
! [X1: $i > $i > $o] :
( ( ( ( sK12 @ X1 )
= ( sK10 @ X1 ) )
= $false )
| ( ( confl @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f399]) ).
thf(f406,plain,
! [X1: $i > $i > $o] :
( ( ( sK12 @ X1 )
!= ( sK10 @ X1 ) )
| ( ( confl @ X1 )
= $true ) ),
inference(equality_proxy_clausification,[],[f402]) ).
thf(f411,plain,
! [X1: $i > $i > $o] :
( ( confl @ X1 )
= $true ),
inference(forward_subsumption_resolution,[],[f406,f214]) ).
thf(f416,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK3 @ Y0 @ Y1 )
& ( trc @ sK3 @ Y0 @ Y2 ) )
=> ( join @ sK3 @ Y2 @ Y1 ) ) ) ) ) ),
inference(backward_demodulation,[],[f133,f411]) ).
thf(f418,plain,
( ( $true
= ( trc @ sK3 @ sK4 @ sK5 ) )
| ( $true = $false ) ),
inference(backward_demodulation,[],[f153,f411]) ).
thf(f419,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( trc @ sK3 @ sK4 @ X0 )
= $true ) ),
inference(backward_demodulation,[],[f282,f411]) ).
thf(f423,plain,
( $true
= ( trc @ sK3 @ sK4 @ sK5 ) ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f427,plain,
! [X0: $i] :
( ( trc @ sK3 @ sK4 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f419]) ).
thf(f434,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( trc @ sK3 @ Y0 @ Y1 )
& ( trc @ sK3 @ Y0 @ Y2 ) )
=> ( join @ sK3 @ Y2 @ Y1 ) ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f416]) ).
thf(f435,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( trc @ sK3 @ sK4 @ Y0 )
& ( trc @ sK3 @ sK4 @ Y1 ) )
=> ( join @ sK3 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f434]) ).
thf(f441,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( trc @ sK3 @ sK4 @ Y0 )
& ( trc @ sK3 @ sK4 @ Y1 ) )
=> ( join @ sK3 @ Y1 @ Y0 ) ) )
@ sK5 )
= $false ),
inference(sigma_proxy_clausification,[],[f435]) ).
thf(f442,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( trc @ sK3 @ sK4 @ sK5 )
& ( trc @ sK3 @ sK4 @ Y0 ) )
=> ( join @ sK3 @ Y0 @ sK5 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f441]) ).
thf(f447,plain,
( ( ^ [Y0: $i] :
( ( ( trc @ sK3 @ sK4 @ sK5 )
& ( trc @ sK3 @ sK4 @ Y0 ) )
=> ( join @ sK3 @ Y0 @ sK5 ) )
@ sK6 )
= $false ),
inference(sigma_proxy_clausification,[],[f442]) ).
thf(f448,plain,
( ( ( ( trc @ sK3 @ sK4 @ sK5 )
& ( trc @ sK3 @ sK4 @ sK6 ) )
=> ( join @ sK3 @ sK6 @ sK5 ) )
= $false ),
inference(beta-eta_normalization,[],[f447]) ).
thf(f451,plain,
( $false
= ( ( $true
& ( trc @ sK3 @ sK4 @ sK6 ) )
=> ( join @ sK3 @ sK6 @ sK5 ) ) ),
inference(forward_demodulation,[],[f448,f423]) ).
thf(f452,plain,
( $false
= ( ( trc @ sK3 @ sK4 @ sK6 )
=> ( join @ sK3 @ sK6 @ sK5 ) ) ),
inference(boolean_simplification,[],[f451]) ).
thf(f455,plain,
( $false
= ( $true
=> ( join @ sK3 @ sK6 @ sK5 ) ) ),
inference(forward_demodulation,[],[f452,f427]) ).
thf(f456,plain,
( ( join @ sK3 @ sK6 @ sK5 )
= $false ),
inference(boolean_simplification,[],[f455]) ).
thf(f506,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( asymm @ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f314]) ).
thf(f507,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y1 @ Y0 ) ) ) ) )
| ( ( asymm @ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f314]) ).
thf(f508,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( ( asymm @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f507]) ).
thf(f509,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X1 @ X2 @ Y0 )
| ~ ( X1 @ Y0 @ X2 ) ) ) )
| ( ( asymm @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f508]) ).
thf(f510,plain,
! [X1: $i > $i > $o] :
( ( ( asymm @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X1 @ Y0 @ Y1 )
| ~ ( X1 @ Y1 @ Y0 ) ) )
@ ( sK15 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f506]) ).
thf(f511,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X1 @ ( sK15 @ X1 ) @ Y0 )
| ~ ( X1 @ Y0 @ ( sK15 @ X1 ) ) ) ) )
| ( ( asymm @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f510]) ).
thf(f512,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( asymm @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( X1 @ X2 @ Y0 )
| ~ ( X1 @ Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f509]) ).
thf(f513,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ( ~ ( X1 @ X2 @ X3 )
| ~ ( X1 @ X3 @ X2 ) )
= $true )
| ( ( asymm @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f512]) ).
thf(f514,plain,
! [X1: $i > $i > $o] :
( ( ( asymm @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X1 @ ( sK15 @ X1 ) @ Y0 )
| ~ ( X1 @ Y0 @ ( sK15 @ X1 ) ) )
@ ( sK16 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f511]) ).
thf(f515,plain,
! [X1: $i > $i > $o] :
( ( ( asymm @ X1 )
= $true )
| ( $false
= ( ~ ( X1 @ ( sK15 @ X1 ) @ ( sK16 @ X1 ) )
| ~ ( X1 @ ( sK16 @ X1 ) @ ( sK15 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f514]) ).
thf(f516,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( $true
= ( ~ ( X1 @ X3 @ X2 ) ) )
| ( $true
= ( ~ ( X1 @ X2 @ X3 ) ) )
| ( ( asymm @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f513]) ).
thf(f517,plain,
! [X1: $i > $i > $o] :
( ( ( ~ ( X1 @ ( sK16 @ X1 ) @ ( sK15 @ X1 ) ) )
= $false )
| ( ( asymm @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f515]) ).
thf(f566,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( $true
= ( ~ ( X1 @ X2 @ X3 ) ) )
| ( ( X1 @ X3 @ X2 )
= $false )
| ( ( asymm @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f516]) ).
thf(f757,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK16 @ X1 ) @ ( sK15 @ X1 ) ) )
| ( ( asymm @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f517]) ).
thf(f784,plain,
! [X0: $i,X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK16 @ X1 ) @ X0 ) )
| ( ( asymm @ X1 )
= $true ) ),
inference(superposition,[],[f757,f214]) ).
thf(f892,plain,
! [X2: $i,X0: $i,X1: $i > $i > $o] :
( ( $true
= ( X1 @ X0 @ X2 ) )
| ( ( asymm @ X1 )
= $true ) ),
inference(superposition,[],[f784,f214]) ).
thf(f1109,plain,
( ( $true = $false )
| ( $true
= ( asymm @ ( join @ sK3 ) ) ) ),
inference(superposition,[],[f456,f892]) ).
thf(f1111,plain,
( $true
= ( asymm @ ( join @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f1109]) ).
thf(f2179,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
~ ( ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y6 @ Y5 )
| ~ ( Y0 @ Y6 @ Y5 ) ) ) )
| ( Y4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
| ~ ( Y4 @ Y5 @ Y6 )
| ~ ( Y4 @ Y7 @ Y5 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y4 @ Y5 @ Y6 )
| ~ ( Y0 @ Y5 @ Y6 ) ) ) )
| ( Y4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ~ ( Y4 @ Y5 @ Y6 )
| ( Y4 @ Y5 @ Y7 )
| ~ ( Y4 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
& ( Y1 != Y2 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y0 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y5 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y6 @ Y4 )
| ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y4 )
| ~ ( Y3 @ Y5 @ Y4 )
| ~ ( Y3 @ Y6 @ Y5 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( Y0 @ Y5 @ Y4 ) ) ) ) ) ) )
@ X1 )
= ( join @ X1 ) ),
inference(argument_congruence,[],[f55]) ).
thf(f2180,plain,
! [X1: $i > $i > $o] :
( ( ^ [Y0: $i,Y1: $i] :
~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
& ( Y0 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) ) ) ) ) )
= ( join @ X1 ) ),
inference(beta-eta_normalization,[],[f2179]) ).
thf(f2414,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( join @ X1 @ X2 )
= ( ^ [Y0: $i,Y1: $i] :
~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 @ Y4 )
| ~ ( X1 @ Y5 @ Y4 ) ) ) )
| ( Y3 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
| ~ ( Y3 @ Y4 @ Y5 )
| ~ ( Y3 @ Y6 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y4 @ Y5 )
| ~ ( X1 @ Y4 @ Y5 ) ) ) )
| ( Y3 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ~ ( Y3 @ Y4 @ Y5 )
| ( Y3 @ Y4 @ Y6 )
| ~ ( Y3 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
& ( Y0 != Y1 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( X1 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y4 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y5 @ Y3 )
| ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y3 )
| ~ ( Y2 @ Y4 @ Y3 )
| ~ ( Y2 @ Y5 @ Y4 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) ) ) ) )
@ X2 ) ),
inference(argument_congruence,[],[f2180]) ).
thf(f2415,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( join @ X1 @ X2 )
= ( ^ [Y0: $i] :
~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
& ( X2 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2414]) ).
thf(f2585,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( join @ X1 @ X2 @ X3 )
= ( ^ [Y0: $i] :
~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 @ Y3 )
| ~ ( X1 @ Y4 @ Y3 ) ) ) )
| ( Y2 @ X2 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y5 @ Y4 )
| ~ ( Y2 @ Y3 @ Y4 )
| ~ ( Y2 @ Y5 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y3 @ Y4 )
| ~ ( X1 @ Y3 @ Y4 ) ) ) )
| ( Y2 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y3 @ Y4 )
| ( Y2 @ Y3 @ Y5 )
| ~ ( Y2 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
& ( X2 != Y0 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ Y0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y4 @ Y2 )
| ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y2 )
| ~ ( Y1 @ Y3 @ Y2 )
| ~ ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) ) ) ) )
@ X3 ) ),
inference(argument_congruence,[],[f2415]) ).
thf(f2586,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( join @ X1 @ X2 @ X3 )
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X1 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X1 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ( X2 != X3 )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X3 @ X2 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X1 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X2 @ X3 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X1 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f2585]) ).
thf(f3093,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( ( join @ X0 @ X1 @ X1 )
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X0 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X0 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& ~ $true
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( refl @ (=) ) ) ),
inference(superposition,[],[f2586,f161]) ).
thf(f3172,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
| ~ ( X0 @ Y3 @ Y2 ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y4 @ Y3 )
| ~ ( Y1 @ Y2 @ Y3 )
| ~ ( Y1 @ Y4 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ~ ( X0 @ Y2 @ Y3 ) ) ) )
| ( Y1 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
& $false
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
= ( join @ X0 @ X1 @ X1 ) )
| ( $false
= ( refl @ (=) ) ) ),
inference(boolean_simplification,[],[f3093]) ).
thf(f3173,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( ( ~ ( $false
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y1 @ Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y3 @ Y1 )
| ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
= ( join @ X0 @ X1 @ X1 ) )
| ( $false
= ( refl @ (=) ) ) ),
inference(boolean_simplification,[],[f3172]) ).
thf(f3174,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( ( ~ ( $false
& ~ ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( Y0 @ X1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y1 )
| ~ ( Y0 @ Y2 @ Y1 )
| ~ ( Y0 @ Y3 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
| ~ ( X0 @ Y2 @ Y1 ) ) ) ) ) ) ) )
= ( join @ X0 @ X1 @ X1 ) )
| ( $false
= ( refl @ (=) ) ) ),
inference(boolean_simplification,[],[f3173]) ).
thf(f3175,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $false
= ( refl @ (=) ) )
| ( ( ~ $false )
= ( join @ X0 @ X1 @ X1 ) ) ),
inference(boolean_simplification,[],[f3174]) ).
thf(f3176,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( ( join @ X0 @ X1 @ X1 )
= $true )
| ( $false
= ( refl @ (=) ) ) ),
inference(boolean_simplification,[],[f3175]) ).
thf(f3282,plain,
! [X0: $i > $i > $o] :
( ( $true = $false )
| ( ( ~ $true ) = $true )
| ( $false
= ( refl @ (=) ) )
| ( ( asymm @ ( join @ X0 ) )
= $false ) ),
inference(superposition,[],[f566,f3176]) ).
thf(f3289,plain,
! [X0: $i > $i > $o] :
( ( $false
= ( refl @ (=) ) )
| ( ( asymm @ ( join @ X0 ) )
= $false )
| ( ( ~ $true ) = $true ) ),
inference(trivial_inequality_removal,[],[f3282]) ).
thf(f3290,plain,
! [X0: $i > $i > $o] :
( ( $false
= ( refl @ (=) ) )
| ( $true = $false )
| ( ( asymm @ ( join @ X0 ) )
= $false ) ),
inference(boolean_simplification,[],[f3289]) ).
thf(f3291,plain,
! [X0: $i > $i > $o] :
( ( ( asymm @ ( join @ X0 ) )
= $false )
| ( $false
= ( refl @ (=) ) ) ),
inference(trivial_inequality_removal,[],[f3290]) ).
thf(f3318,plain,
! [X0: $i > $i > $o] :
( ( $true = $false )
| ( ( asymm @ ( join @ X0 ) )
= $false ) ),
inference(forward_demodulation,[],[f3291,f202]) ).
thf(f3319,plain,
! [X0: $i > $i > $o] :
( ( asymm @ ( join @ X0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f3318]) ).
thf(f3342,plain,
$true = $false,
inference(backward_demodulation,[],[f1111,f3319]) ).
thf(f3343,plain,
$false,
inference(trivial_inequality_removal,[],[f3342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX184^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:16:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.36 % (1438769)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (1438777)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=4198535312: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)
% 0.21/0.36 % (1438774)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3180701700:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (1438775)lrs+10_16_si=on:nwc=1.5:random_seed=3280445423:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (1438778)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1841079269:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (1438776)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1613067200:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (1438780)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (1438780)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
% 0.21/0.36 % (1438776)Instruction limit reached!
% 0.21/0.36 % (1438776)------------------------------
% 0.21/0.36 % (1438776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1438776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1438776)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1438776)Termination reason: Instruction limit
% 0.21/0.36 % (1438776)Termination phase: shuffling
% 0.21/0.36 % (1438776)Time elapsed: 0.002 s
% 0.21/0.36 % (1438776)Peak memory usage: 10 MB
% 0.21/0.36 % (1438776)Instructions burned: 3 (million)
% 0.21/0.36 % (1438779)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2906178192:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (1438780)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=2458049839:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (1438775)Instruction limit reached!
% 0.21/0.36 % (1438775)------------------------------
% 0.21/0.36 % (1438775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1438775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1438775)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1438775)Termination reason: Instruction limit
% 0.21/0.36 % (1438775)Termination phase: Property scanning
% 0.21/0.36 % (1438775)Time elapsed: 0.008 s
% 0.21/0.36 % (1438775)Peak memory usage: 10 MB
% 0.21/0.36 % (1438775)Instructions burned: 18 (million)
% 0.21/0.36 % (1438778)Instruction limit reached!
% 0.21/0.36 % (1438778)------------------------------
% 0.21/0.36 % (1438778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1438778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1438778)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1438778)Termination reason: Instruction limit
% 0.21/0.36 % (1438778)Termination phase: Preprocessing 3
% 0.21/0.36 % (1438778)Time elapsed: 0.010 s
% 0.21/0.36 % (1438778)Peak memory usage: 10 MB
% 0.21/0.36 % (1438778)Instructions burned: 25 (million)
% 0.21/0.36 % (1438786)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2438555214:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (1438786)Instruction limit reached!
% 0.21/0.36 % (1438786)------------------------------
% 0.21/0.36 % (1438786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1438786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1438786)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1438786)Termination reason: Instruction limit
% 0.21/0.36 % (1438786)Termination phase: shuffling
% 0.21/0.36 % (1438786)Time elapsed: 0.003 s
% 0.21/0.36 % (1438786)Peak memory usage: 10 MB
% 0.21/0.36 % (1438786)Instructions burned: 6 (million)
% 0.21/0.36 % (1438790)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.96/0.41 % (1438789)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1488924506:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.96/0.41 % (1438790)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2555303016:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.96/0.41 % (1438789)Instruction limit reached!
% 0.96/0.41 % (1438789)------------------------------
% 0.96/0.41 % (1438789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.41 % (1438789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.41 % (1438789)CaDiCaL version: 2.1.3
% 0.96/0.41 % (1438789)Termination reason: Instruction limit
% 0.96/0.41 % (1438789)Termination phase: shuffling
% 0.96/0.41 % (1438789)Time elapsed: 0.003 s
% 0.96/0.41 % (1438789)Peak memory usage: 10 MB
% 0.96/0.41 % (1438789)Instructions burned: 6 (million)
% 0.96/0.41 % (1438790)Instruction limit reached!
% 0.96/0.41 % (1438790)------------------------------
% 0.96/0.41 % (1438790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.41 % (1438790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.41 % (1438790)CaDiCaL version: 2.1.3
% 0.96/0.41 % (1438790)Termination reason: Instruction limit
% 0.96/0.41 % (1438790)Termination phase: shuffling
% 0.96/0.41 % (1438790)Time elapsed: 0.003 s
% 0.96/0.41 % (1438790)Peak memory usage: 9 MB
% 0.96/0.41 % (1438790)Instructions burned: 8 (million)
% 0.96/0.41 % (1438779)Instruction limit reached!
% 0.96/0.41 % (1438779)------------------------------
% 0.96/0.41 % (1438779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.41 % (1438779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.41 % (1438779)CaDiCaL version: 2.1.3
% 0.96/0.41 % (1438779)Termination reason: Instruction limit
% 0.96/0.41 % (1438779)Termination phase: Saturation
% 0.96/0.41 % (1438779)Time elapsed: 0.032 s
% 0.96/0.41 % (1438779)Peak memory usage: 12 MB
% 0.96/0.41 % (1438779)Instructions burned: 76 (million)
% 0.96/0.41 % (1438774)Instruction limit reached!
% 0.96/0.41 % (1438774)------------------------------
% 0.96/0.41 % (1438774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.41 % (1438774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.41 % (1438774)CaDiCaL version: 2.1.3
% 0.96/0.41 % (1438774)Termination reason: Instruction limit
% 0.96/0.41 % (1438774)Termination phase: Saturation
% 0.96/0.41 % (1438774)Time elapsed: 0.041 s
% 0.96/0.41 % (1438774)Peak memory usage: 13 MB
% 0.96/0.41 % (1438774)Instructions burned: 96 (million)
% 0.96/0.41 % (1438792)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=286066033:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.96/0.41 % (1438795)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
% 0.96/0.41 % (1438795)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.96/0.41 % (1438795)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1801150823:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.96/0.41 % (1438792)Instruction limit reached!
% 0.96/0.41 % (1438792)------------------------------
% 0.96/0.41 % (1438792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.41 % (1438792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.41 % (1438792)CaDiCaL version: 2.1.3
% 0.96/0.41 % (1438792)Termination reason: Instruction limit
% 0.96/0.41 % (1438792)Termination phase: Property scanning
% 0.96/0.41 % (1438792)Time elapsed: 0.006 s
% 0.96/0.41 % (1438792)Peak memory usage: 10 MB
% 0.96/0.41 % (1438792)Instructions burned: 13 (million)
% 0.96/0.41 % (1438796)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1406575221:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.96/0.41 % (1438797)lrs+10_1_si=on:cs=on:random_seed=2499294425:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.96/0.41 % (1438798)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.96/0.44 % (1438797)Instruction limit reached!
% 0.96/0.44 % (1438797)------------------------------
% 0.96/0.44 % (1438797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.44 % (1438797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.44 % (1438797)CaDiCaL version: 2.1.3
% 0.96/0.44 % (1438797)Termination reason: Instruction limit
% 0.96/0.44 % (1438797)Termination phase: shuffling
% 0.96/0.44 % (1438797)Time elapsed: 0.004 s
% 0.96/0.44 % (1438797)Peak memory usage: 10 MB
% 0.96/0.44 % (1438797)Instructions burned: 8 (million)
% 0.96/0.44 % (1438798)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1410866789:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.96/0.44 % (1438795)Instruction limit reached!
% 0.96/0.44 % (1438795)------------------------------
% 0.96/0.44 % (1438795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.44 % (1438795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.44 % (1438795)CaDiCaL version: 2.1.3
% 0.96/0.44 % (1438795)Termination reason: Instruction limit
% 0.96/0.44 % (1438795)Termination phase: Property scanning
% 0.96/0.44 % (1438795)Time elapsed: 0.012 s
% 0.96/0.44 % (1438795)Peak memory usage: 10 MB
% 0.96/0.44 % (1438795)Instructions burned: 30 (million)
% 0.96/0.44 % (1438798)Instruction limit reached!
% 0.96/0.44 % (1438798)------------------------------
% 0.96/0.44 % (1438798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.44 % (1438798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.44 % (1438798)CaDiCaL version: 2.1.3
% 0.96/0.44 % (1438798)Termination reason: Instruction limit
% 0.96/0.44 % (1438798)Termination phase: shuffling
% 0.96/0.44 % (1438798)Time elapsed: 0.002 s
% 0.96/0.44 % (1438798)Peak memory usage: 9 MB
% 0.96/0.44 % (1438798)Instructions burned: 5 (million)
% 0.96/0.44 % (1438801)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3856549219:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.96/0.44 % (1438780)Instruction limit reached!
% 0.96/0.44 % (1438780)------------------------------
% 0.96/0.44 % (1438780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.44 % (1438780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.44 % (1438780)CaDiCaL version: 2.1.3
% 0.96/0.44 % (1438780)Termination reason: Instruction limit
% 0.96/0.44 % (1438780)Termination phase: Saturation
% 0.96/0.44 % (1438780)Time elapsed: 0.068 s
% 0.96/0.44 % (1438780)Peak memory usage: 14 MB
% 0.96/0.44 % (1438780)Instructions burned: 158 (million)
% 0.96/0.44 % (1438805)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4020347297:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.96/0.44 % (1438801)Refutation not found, incomplete strategy
% 0.96/0.44 % (1438801)------------------------------
% 0.96/0.44 % (1438801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.44 % (1438801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.44 % (1438801)CaDiCaL version: 2.1.3
% 0.96/0.44 % (1438801)Termination reason: Refutation not found, incomplete strategy
% 0.96/0.44 % (1438801)Time elapsed: 0.012 s
% 0.96/0.44 % (1438801)Peak memory usage: 12 MB
% 0.96/0.44 % (1438806)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1368242333:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.96/0.44 % (1438801)Instructions burned: 26 (million)
% 0.96/0.44 % (1438801)------------------------------
% 0.96/0.44 % (1438801)------------------------------
% 0.96/0.44 % (1438796)Instruction limit reached!
% 0.96/0.44 % (1438796)------------------------------
% 0.96/0.44 % (1438796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.44 % (1438796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.44 % (1438796)CaDiCaL version: 2.1.3
% 0.96/0.44 % (1438796)Termination reason: Instruction limit
% 0.96/0.44 % (1438796)Termination phase: Saturation
% 0.96/0.44 % (1438796)Time elapsed: 0.037 s
% 0.96/0.44 % (1438796)Peak memory usage: 13 MB
% 0.96/0.44 % (1438796)Instructions burned: 86 (million)
% 0.96/0.49 % (1438809)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3475819316:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.96/0.49 % (1438806)Instruction limit reached!
% 0.96/0.49 % (1438806)------------------------------
% 0.96/0.49 % (1438806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.49 % (1438806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.49 % (1438806)CaDiCaL version: 2.1.3
% 0.96/0.49 % (1438806)Termination reason: Instruction limit
% 0.96/0.49 % (1438806)Termination phase: SInE selection
% 0.96/0.49 % (1438806)Time elapsed: 0.011 s
% 0.96/0.49 % (1438806)Peak memory usage: 10 MB
% 0.96/0.49 % (1438806)Instructions burned: 27 (million)
% 0.96/0.49 % (1438812)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=405890730:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.96/0.49 % (1438807)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=445816072:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.96/0.49 % (1438813)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1488330174:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.96/0.49 % (1438812)Instruction limit reached!
% 0.96/0.49 % (1438812)------------------------------
% 0.96/0.49 % (1438812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.49 % (1438812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.49 % (1438812)CaDiCaL version: 2.1.3
% 0.96/0.49 % (1438812)Termination reason: Instruction limit
% 0.96/0.49 % (1438812)Termination phase: Property scanning
% 0.96/0.49 % (1438812)Time elapsed: 0.006 s
% 0.96/0.49 % (1438812)Peak memory usage: 10 MB
% 0.96/0.49 % (1438812)Instructions burned: 15 (million)
% 0.96/0.49 % (1438813)Instruction limit reached!
% 0.96/0.49 % (1438813)------------------------------
% 0.96/0.49 % (1438813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.49 % (1438813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.49 % (1438813)CaDiCaL version: 2.1.3
% 0.96/0.49 % (1438813)Termination reason: Instruction limit
% 0.96/0.49 % (1438813)Termination phase: shuffling
% 0.96/0.49 % (1438813)Time elapsed: 0.002 s
% 0.96/0.49 % (1438813)Peak memory usage: 10 MB
% 0.96/0.49 % (1438813)Instructions burned: 3 (million)
% 0.96/0.49 % (1438815)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=312926637:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.96/0.49 % (1438807)Instruction limit reached!
% 0.96/0.49 % (1438807)------------------------------
% 0.96/0.49 % (1438807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.49 % (1438807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.49 % (1438807)CaDiCaL version: 2.1.3
% 0.96/0.49 % (1438807)Termination reason: Instruction limit
% 0.96/0.49 % (1438807)Termination phase: Property scanning
% 0.96/0.49 % (1438807)Time elapsed: 0.010 s
% 0.96/0.49 % (1438807)Peak memory usage: 10 MB
% 0.96/0.49 % (1438807)Instructions burned: 14 (million)
% 0.96/0.49 % (1438815)Instruction limit reached!
% 0.96/0.49 % (1438815)------------------------------
% 0.96/0.49 % (1438815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.49 % (1438815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.49 % (1438815)CaDiCaL version: 2.1.3
% 0.96/0.49 % (1438815)Termination reason: Instruction limit
% 0.96/0.49 % (1438815)Termination phase: Property scanning
% 0.96/0.49 % (1438815)Time elapsed: 0.012 s
% 0.96/0.49 % (1438815)Peak memory usage: 10 MB
% 0.96/0.49 % (1438815)Instructions burned: 28 (million)
% 0.96/0.49 % (1438819)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3297467638:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.96/0.49 % (1438822)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 0.96/0.49 % (1438822)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.96/0.49 % (1438822)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1231153911:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.81/0.54 % (1438820)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4257984407:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.81/0.54 % (1438777)Instruction limit reached!
% 1.81/0.54 % (1438777)------------------------------
% 1.81/0.54 % (1438777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.54 % (1438777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.54 % (1438777)CaDiCaL version: 2.1.3
% 1.81/0.54 % (1438777)Termination reason: Instruction limit
% 1.81/0.54 % (1438777)Termination phase: Saturation
% 1.81/0.54 % (1438777)Time elapsed: 0.146 s
% 1.81/0.54 % (1438777)Peak memory usage: 18 MB
% 1.81/0.54 % (1438777)Instructions burned: 635 (million)
% 1.81/0.54 % (1438819)Instruction limit reached!
% 1.81/0.54 % (1438819)------------------------------
% 1.81/0.54 % (1438819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.54 % (1438819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.54 % (1438819)CaDiCaL version: 2.1.3
% 1.81/0.54 % (1438819)Termination reason: Instruction limit
% 1.81/0.54 % (1438819)Termination phase: Property scanning
% 1.81/0.54 % (1438819)Time elapsed: 0.011 s
% 1.81/0.54 % (1438819)Peak memory usage: 10 MB
% 1.81/0.54 % (1438819)Instructions burned: 26 (million)
% 1.81/0.54 % (1438823)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.81/0.54 % (1438822)Instruction limit reached!
% 1.81/0.54 % (1438822)------------------------------
% 1.81/0.54 % (1438822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.54 % (1438822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.54 % (1438822)CaDiCaL version: 2.1.3
% 1.81/0.54 % (1438822)Termination reason: Instruction limit
% 1.81/0.54 % (1438822)Termination phase: Property scanning
% 1.81/0.54 % (1438822)Time elapsed: 0.006 s
% 1.81/0.54 % (1438822)Peak memory usage: 9 MB
% 1.81/0.54 % (1438822)Instructions burned: 14 (million)
% 1.81/0.54 % (1438823)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3544414816:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.81/0.54 % (1438823)Instruction limit reached!
% 1.81/0.54 % (1438823)------------------------------
% 1.81/0.54 % (1438823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.54 % (1438823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.54 % (1438823)CaDiCaL version: 2.1.3
% 1.81/0.54 % (1438823)Termination reason: Instruction limit
% 1.81/0.54 % (1438823)Termination phase: shuffling
% 1.81/0.54 % (1438823)Time elapsed: 0.004 s
% 1.81/0.54 % (1438823)Peak memory usage: 10 MB
% 1.81/0.54 % (1438823)Instructions burned: 9 (million)
% 1.81/0.54 % (1438827)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1013101966:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.81/0.54 % (1438827)Instruction limit reached!
% 1.81/0.54 % (1438827)------------------------------
% 1.81/0.54 % (1438827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.54 % (1438827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.54 % (1438827)CaDiCaL version: 2.1.3
% 1.81/0.54 % (1438827)Termination reason: Instruction limit
% 1.81/0.54 % (1438827)Termination phase: Saturation
% 1.81/0.54 % (1438827)Time elapsed: 0.007 s
% 1.81/0.54 % (1438827)Peak memory usage: 11 MB
% 1.81/0.54 % (1438827)Instructions burned: 33 (million)
% 1.81/0.54 % (1438828)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2816755943:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.81/0.54 % (1438829)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=140853400:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.81/0.54 % (1438828)Instruction limit reached!
% 1.81/0.54 % (1438828)------------------------------
% 1.81/0.54 % (1438828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.58 % (1438828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.58 % (1438828)CaDiCaL version: 2.1.3
% 1.81/0.58 % (1438828)Termination reason: Instruction limit
% 1.81/0.58 % (1438828)Termination phase: shuffling
% 1.81/0.58 % (1438828)Time elapsed: 0.004 s
% 1.81/0.58 % (1438828)Peak memory usage: 10 MB
% 1.81/0.58 % (1438828)Instructions burned: 9 (million)
% 1.81/0.58 % (1438831)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1089315584:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.81/0.58 % (1438833)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1550071378:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.81/0.58 % (1438829)Instruction limit reached!
% 1.81/0.58 % (1438829)------------------------------
% 1.81/0.58 % (1438829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.58 % (1438829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.58 % (1438829)CaDiCaL version: 2.1.3
% 1.81/0.58 % (1438829)Termination reason: Instruction limit
% 1.81/0.58 % (1438829)Termination phase: Property scanning
% 1.81/0.58 % (1438829)Time elapsed: 0.010 s
% 1.81/0.58 % (1438829)Peak memory usage: 10 MB
% 1.81/0.58 % (1438829)Instructions burned: 25 (million)
% 1.81/0.58 % (1438831)Instruction limit reached!
% 1.81/0.58 % (1438831)------------------------------
% 1.81/0.58 % (1438831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.58 % (1438831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.58 % (1438831)CaDiCaL version: 2.1.3
% 1.81/0.58 % (1438831)Termination reason: Instruction limit
% 1.81/0.58 % (1438831)Termination phase: SInE selection
% 1.81/0.58 % (1438831)Time elapsed: 0.009 s
% 1.81/0.58 % (1438831)Peak memory usage: 10 MB
% 1.81/0.58 % (1438831)Instructions burned: 22 (million)
% 1.81/0.58 % (1438836)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=536184630:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.81/0.58 % (1438805)Instruction limit reached!
% 1.81/0.58 % (1438805)------------------------------
% 1.81/0.58 % (1438805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.58 % (1438805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.58 % (1438805)CaDiCaL version: 2.1.3
% 1.81/0.58 % (1438805)Termination reason: Instruction limit
% 1.81/0.58 % (1438805)Termination phase: Saturation
% 1.81/0.58 % (1438805)Time elapsed: 0.108 s
% 1.81/0.58 % (1438805)Peak memory usage: 15 MB
% 1.81/0.58 % (1438805)Instructions burned: 249 (million)
% 1.81/0.58 % (1438820)Instruction limit reached!
% 1.81/0.58 % (1438820)------------------------------
% 1.81/0.58 % (1438820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.58 % (1438820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.58 % (1438820)CaDiCaL version: 2.1.3
% 1.81/0.58 % (1438820)Termination reason: Instruction limit
% 1.81/0.58 % (1438820)Termination phase: Saturation
% 1.81/0.58 % (1438820)Time elapsed: 0.051 s
% 1.81/0.58 % (1438820)Peak memory usage: 13 MB
% 1.81/0.58 % (1438820)Instructions burned: 60 (million)
% 1.81/0.58 % (1438839)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=571086301:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.81/0.58 % (1438840)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2176835493:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.81/0.58 % (1438843)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.81/0.58 % (1438843)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3169070094:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.81/0.58 % (1438843)Instruction limit reached!
% 1.81/0.58 % (1438843)------------------------------
% 1.81/0.58 % (1438843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.81/0.58 % (1438843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/0.58 % (1438843)CaDiCaL version: 2.1.3
% 1.81/0.58 % (1438843)Termination reason: Instruction limit
% 1.81/0.58 % (1438843)Termination phase: shuffling
% 1.81/0.58 % (1438843)Time elapsed: 0.004 s
% 1.81/0.58 % (1438843)Peak memory usage: 9 MB
% 2.75/0.65 % (1438843)Instructions burned: 9 (million)
% 2.75/0.65 % (1438840)Instruction limit reached!
% 2.75/0.65 % (1438840)------------------------------
% 2.75/0.65 % (1438840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.65 % (1438840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.65 % (1438840)CaDiCaL version: 2.1.3
% 2.75/0.65 % (1438840)Termination reason: Instruction limit
% 2.75/0.65 % (1438840)Termination phase: Saturation
% 2.75/0.65 % (1438840)Time elapsed: 0.018 s
% 2.75/0.65 % (1438840)Peak memory usage: 12 MB
% 2.75/0.65 % (1438840)Instructions burned: 44 (million)
% 2.75/0.65 % (1438844)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=413460826:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.75/0.65 % (1438847)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3877193122:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.75/0.65 % (1438809)Instruction limit reached!
% 2.75/0.65 % (1438809)------------------------------
% 2.75/0.65 % (1438809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.65 % (1438809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.65 % (1438809)CaDiCaL version: 2.1.3
% 2.75/0.65 % (1438809)Termination reason: Instruction limit
% 2.75/0.65 % (1438809)Termination phase: Saturation
% 2.75/0.65 % (1438809)Time elapsed: 0.142 s
% 2.75/0.65 % (1438809)Peak memory usage: 16 MB
% 2.75/0.65 % (1438809)Instructions burned: 329 (million)
% 2.75/0.65 % (1438848)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.75/0.65 % (1438848)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=399252764:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.75/0.65 % (1438848)Instruction limit reached!
% 2.75/0.65 % (1438848)------------------------------
% 2.75/0.65 % (1438848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.65 % (1438848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.65 % (1438848)CaDiCaL version: 2.1.3
% 2.75/0.65 % (1438848)Termination reason: Instruction limit
% 2.75/0.65 % (1438848)Termination phase: shuffling
% 2.75/0.65 % (1438848)Time elapsed: 0.003 s
% 2.75/0.65 % (1438848)Peak memory usage: 9 MB
% 2.75/0.65 % (1438848)Instructions burned: 6 (million)
% 2.75/0.65 % (1438844)Refutation not found, incomplete strategy
% 2.75/0.65 % (1438844)------------------------------
% 2.75/0.65 % (1438844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.65 % (1438844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.65 % (1438844)CaDiCaL version: 2.1.3
% 2.75/0.65 % (1438844)Termination reason: Refutation not found, incomplete strategy
% 2.75/0.65 % (1438844)Time elapsed: 0.013 s
% 2.75/0.65 % (1438844)Peak memory usage: 12 MB
% 2.75/0.65 % (1438844)Instructions burned: 27 (million)
% 2.75/0.65 % (1438844)------------------------------
% 2.75/0.65 % (1438844)------------------------------
% 2.75/0.65 % (1438836)Instruction limit reached!
% 2.75/0.65 % (1438836)------------------------------
% 2.75/0.65 % (1438836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.75/0.65 % (1438836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/0.65 % (1438836)CaDiCaL version: 2.1.3
% 2.75/0.65 % (1438836)Termination reason: Instruction limit
% 2.75/0.65 % (1438836)Termination phase: Saturation
% 2.75/0.65 % (1438836)Time elapsed: 0.063 s
% 2.75/0.65 % (1438836)Peak memory usage: 14 MB
% 2.75/0.65 % (1438836)Instructions burned: 145 (million)
% 2.75/0.65 % (1438851)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3859920525:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.75/0.65 % (1438853)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=161484155:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.75/0.65 % (1438854)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2800160062:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.12/0.76 % (1438851)Instruction limit reached!
% 3.12/0.76 % (1438851)------------------------------
% 3.12/0.76 % (1438851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.76 % (1438851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.76 % (1438851)CaDiCaL version: 2.1.3
% 3.12/0.76 % (1438851)Termination reason: Instruction limit
% 3.12/0.76 % (1438851)Termination phase: Preprocessing 3
% 3.12/0.76 % (1438851)Time elapsed: 0.010 s
% 3.12/0.76 % (1438851)Peak memory usage: 10 MB
% 3.12/0.76 % (1438851)Instructions burned: 23 (million)
% 3.12/0.76 % (1438855)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3252549664:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 3.12/0.76 % (1438853)Instruction limit reached!
% 3.12/0.76 % (1438853)------------------------------
% 3.12/0.76 % (1438853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.76 % (1438853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.76 % (1438853)CaDiCaL version: 2.1.3
% 3.12/0.76 % (1438853)Termination reason: Instruction limit
% 3.12/0.76 % (1438853)Termination phase: Property scanning
% 3.12/0.76 % (1438853)Time elapsed: 0.008 s
% 3.12/0.76 % (1438853)Peak memory usage: 9 MB
% 3.12/0.76 % (1438853)Instructions burned: 20 (million)
% 3.12/0.76 % (1438839)Instruction limit reached!
% 3.12/0.76 % (1438839)------------------------------
% 3.12/0.76 % (1438839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.76 % (1438839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.76 % (1438839)CaDiCaL version: 2.1.3
% 3.12/0.76 % (1438839)Termination reason: Instruction limit
% 3.12/0.76 % (1438839)Termination phase: Saturation
% 3.12/0.76 % (1438839)Time elapsed: 0.084 s
% 3.12/0.76 % (1438839)Peak memory usage: 14 MB
% 3.12/0.76 % (1438839)Instructions burned: 194 (million)
% 3.12/0.76 % (1438860)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3183112380:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 3.12/0.76 % (1438861)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3320601695:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.12/0.76 % (1438862)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=718641618:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.12/0.76 % (1438860)Instruction limit reached!
% 3.12/0.76 % (1438860)------------------------------
% 3.12/0.76 % (1438860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.76 % (1438860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.76 % (1438860)CaDiCaL version: 2.1.3
% 3.12/0.76 % (1438860)Termination reason: Instruction limit
% 3.12/0.76 % (1438860)Termination phase: Property scanning
% 3.12/0.76 % (1438860)Time elapsed: 0.018 s
% 3.12/0.76 % (1438860)Peak memory usage: 11 MB
% 3.12/0.76 % (1438860)Instructions burned: 45 (million)
% 3.12/0.76 % (1438862)Instruction limit reached!
% 3.12/0.76 % (1438862)------------------------------
% 3.12/0.76 % (1438862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.76 % (1438862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.76 % (1438862)CaDiCaL version: 2.1.3
% 3.12/0.76 % (1438862)Termination reason: Instruction limit
% 3.12/0.76 % (1438862)Termination phase: Preprocessing 3
% 3.12/0.76 % (1438862)Time elapsed: 0.010 s
% 3.12/0.76 % (1438862)Peak memory usage: 10 MB
% 3.12/0.76 % (1438862)Instructions burned: 23 (million)
% 3.12/0.76 % (1438861)Refutation not found, incomplete strategy
% 3.12/0.76 % (1438861)------------------------------
% 3.12/0.76 % (1438861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.76 % (1438861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.76 % (1438861)CaDiCaL version: 2.1.3
% 3.12/0.76 % (1438861)Termination reason: Refutation not found, incomplete strategy
% 3.12/0.76 % (1438861)Time elapsed: 0.019 s
% 3.12/0.76 % (1438861)Peak memory usage: 12 MB
% 3.12/0.76 % (1438861)Instructions burned: 44 (million)
% 3.12/0.76 % (1438847)Instruction limit reached!
% 3.12/0.80 % (1438847)------------------------------
% 3.12/0.80 % (1438847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.80 % (1438847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.80 % (1438847)CaDiCaL version: 2.1.3
% 3.12/0.80 % (1438847)Termination reason: Instruction limit
% 3.12/0.80 % (1438847)Termination phase: Saturation
% 3.12/0.80 % (1438847)Time elapsed: 0.074 s
% 3.12/0.80 % (1438847)Peak memory usage: 14 MB
% 3.12/0.80 % (1438847)Instructions burned: 172 (million)
% 3.12/0.80 % (1438861)------------------------------
% 3.12/0.80 % (1438861)------------------------------
% 3.12/0.80 % (1438866)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.12/0.80 % (1438867)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=879100685:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.12/0.80 % (1438866)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1865570700:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.12/0.80 % (1438869)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3936260697:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.12/0.80 % (1438868)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=4021819962:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.12/0.80 % (1438867)Instruction limit reached!
% 3.12/0.80 % (1438867)------------------------------
% 3.12/0.80 % (1438867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.80 % (1438867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.80 % (1438867)CaDiCaL version: 2.1.3
% 3.12/0.80 % (1438867)Termination reason: Instruction limit
% 3.12/0.80 % (1438867)Termination phase: Property scanning
% 3.12/0.80 % (1438867)Time elapsed: 0.006 s
% 3.12/0.80 % (1438867)Peak memory usage: 10 MB
% 3.12/0.80 % (1438867)Instructions burned: 14 (million)
% 3.12/0.80 % (1438874)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=231136716:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.12/0.80 % (1438869)Instruction limit reached!
% 3.12/0.80 % (1438869)------------------------------
% 3.12/0.80 % (1438869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.80 % (1438869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.80 % (1438869)CaDiCaL version: 2.1.3
% 3.12/0.80 % (1438869)Termination reason: Instruction limit
% 3.12/0.80 % (1438869)Termination phase: Saturation
% 3.12/0.80 % (1438869)Time elapsed: 0.021 s
% 3.12/0.80 % (1438869)Peak memory usage: 12 MB
% 3.12/0.80 % (1438869)Instructions burned: 51 (million)
% 3.12/0.80 % (1438868)Instruction limit reached!
% 3.12/0.80 % (1438868)------------------------------
% 3.12/0.80 % (1438868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.80 % (1438868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.80 % (1438868)CaDiCaL version: 2.1.3
% 3.12/0.80 % (1438868)Termination reason: Instruction limit
% 3.12/0.80 % (1438868)Termination phase: Saturation
% 3.12/0.80 % (1438868)Time elapsed: 0.029 s
% 3.12/0.80 % (1438868)Peak memory usage: 13 MB
% 3.12/0.80 % (1438868)Instructions burned: 66 (million)
% 3.12/0.80 % (1438874)Instruction limit reached!
% 3.12/0.80 % (1438874)------------------------------
% 3.12/0.80 % (1438874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.12/0.80 % (1438874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/0.80 % (1438874)CaDiCaL version: 2.1.3
% 3.12/0.80 % (1438874)Termination reason: Instruction limit
% 3.12/0.80 % (1438874)Termination phase: Property scanning
% 3.12/0.80 % (1438874)Time elapsed: 0.013 s
% 3.12/0.80 % (1438874)Peak memory usage: 10 MB
% 3.12/0.80 % (1438874)Instructions burned: 32 (million)
% 3.12/0.80 % (1438876)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=981218616:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 3.12/0.80 % (1438877)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1376568835:cond=on:i=34:hud=10:nm=10:rtra=on_2996 on theBenchmark for (2996ds/34Mi)
% 4.13/0.90 % (1438878)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=563854795:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2996 on theBenchmark for (2996ds/67Mi)
% 4.13/0.90 % (1438877)Instruction limit reached!
% 4.13/0.90 % (1438877)------------------------------
% 4.13/0.90 % (1438877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.90 % (1438877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.90 % (1438877)CaDiCaL version: 2.1.3
% 4.13/0.90 % (1438877)Termination reason: Instruction limit
% 4.13/0.90 % (1438877)Termination phase: Saturation
% 4.13/0.90 % (1438877)Time elapsed: 0.015 s
% 4.13/0.90 % (1438877)Peak memory usage: 11 MB
% 4.13/0.90 % (1438877)Instructions burned: 35 (million)
% 4.13/0.90 % (1438882)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 4.13/0.90 % (1438866)Instruction limit reached!
% 4.13/0.90 % (1438866)------------------------------
% 4.13/0.90 % (1438866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.90 % (1438866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.90 % (1438882)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3869806009:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 4.13/0.90 % (1438866)CaDiCaL version: 2.1.3
% 4.13/0.90 % (1438866)Termination reason: Instruction limit
% 4.13/0.90 % (1438866)Termination phase: Saturation
% 4.13/0.90 % (1438866)Time elapsed: 0.089 s
% 4.13/0.90 % (1438866)Peak memory usage: 14 MB
% 4.13/0.90 % (1438866)Instructions burned: 202 (million)
% 4.13/0.90 % (1438878)Instruction limit reached!
% 4.13/0.90 % (1438878)------------------------------
% 4.13/0.90 % (1438878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.90 % (1438878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.90 % (1438878)CaDiCaL version: 2.1.3
% 4.13/0.90 % (1438878)Termination reason: Instruction limit
% 4.13/0.90 % (1438878)Termination phase: Saturation
% 4.13/0.90 % (1438878)Time elapsed: 0.039 s
% 4.13/0.90 % (1438878)Peak memory usage: 13 MB
% 4.13/0.90 % (1438878)Instructions burned: 67 (million)
% 4.13/0.90 % (1438876)Instruction limit reached!
% 4.13/0.90 % (1438876)------------------------------
% 4.13/0.90 % (1438876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.90 % (1438876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.90 % (1438876)CaDiCaL version: 2.1.3
% 4.13/0.90 % (1438876)Termination reason: Instruction limit
% 4.13/0.90 % (1438876)Termination phase: Saturation
% 4.13/0.90 % (1438876)Time elapsed: 0.060 s
% 4.13/0.90 % (1438876)Peak memory usage: 13 MB
% 4.13/0.90 % (1438876)Instructions burned: 139 (million)
% 4.13/0.90 % (1438884)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3218133136:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 4.13/0.90 % (1438885)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1424572970:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 4.13/0.90 % (1438886)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3119037806:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 4.13/0.90 % (1438886)Refutation not found, incomplete strategy
% 4.13/0.90 % (1438886)------------------------------
% 4.13/0.90 % (1438886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.90 % (1438886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.90 % (1438886)CaDiCaL version: 2.1.3
% 4.13/0.90 % (1438886)Termination reason: Refutation not found, incomplete strategy
% 4.13/0.90 % (1438886)Time elapsed: 0.012 s
% 4.13/0.90 % (1438886)Peak memory usage: 12 MB
% 4.13/0.90 % (1438886)Instructions burned: 27 (million)
% 4.13/0.90 % (1438886)------------------------------
% 4.13/0.90 % (1438886)------------------------------
% 4.13/0.90 % (1438890)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4218826249:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 4.13/0.90 % (1438882)Instruction limit reached!
% 4.13/0.90 % (1438882)------------------------------
% 4.13/0.90 % (1438882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.90 % (1438882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.99 % (1438882)CaDiCaL version: 2.1.3
% 4.13/0.99 % (1438882)Termination reason: Instruction limit
% 4.13/0.99 % (1438882)Termination phase: Saturation
% 4.13/0.99 % (1438882)Time elapsed: 0.071 s
% 4.13/0.99 % (1438882)Peak memory usage: 12 MB
% 4.13/0.99 % (1438882)Instructions burned: 180 (million)
% 4.13/0.99 % (1438833)Instruction limit reached!
% 4.13/0.99 % (1438833)------------------------------
% 4.13/0.99 % (1438833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.99 % (1438833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.99 % (1438833)CaDiCaL version: 2.1.3
% 4.13/0.99 % (1438833)Termination reason: Instruction limit
% 4.13/0.99 % (1438833)Termination phase: Saturation
% 4.13/0.99 % (1438833)Time elapsed: 0.316 s
% 4.13/0.99 % (1438833)Peak memory usage: 17 MB
% 4.13/0.99 % (1438833)Instructions burned: 1241 (million)
% 4.13/0.99 % (1438885)Instruction limit reached!
% 4.13/0.99 % (1438885)------------------------------
% 4.13/0.99 % (1438885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.99 % (1438885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.99 % (1438885)CaDiCaL version: 2.1.3
% 4.13/0.99 % (1438885)Termination reason: Instruction limit
% 4.13/0.99 % (1438885)Termination phase: Saturation
% 4.13/0.99 % (1438885)Time elapsed: 0.042 s
% 4.13/0.99 % (1438885)Peak memory usage: 13 MB
% 4.13/0.99 % (1438885)Instructions burned: 96 (million)
% 4.13/0.99 % (1438893)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=802878538:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 4.13/0.99 % (1438893)Refutation not found, incomplete strategy
% 4.13/0.99 % (1438893)------------------------------
% 4.13/0.99 % (1438893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.99 % (1438893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.99 % (1438893)CaDiCaL version: 2.1.3
% 4.13/0.99 % (1438893)Termination reason: Refutation not found, incomplete strategy
% 4.13/0.99 % (1438893)Time elapsed: 0.007 s
% 4.13/0.99 % (1438893)Peak memory usage: 12 MB
% 4.13/0.99 % (1438893)Instructions burned: 31 (million)
% 4.13/0.99 % (1438892)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3399596533:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 4.13/0.99 % (1438893)------------------------------
% 4.13/0.99 % (1438893)------------------------------
% 4.13/0.99 % (1438894)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3742934718:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 4.13/0.99 % (1438898)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2762561122:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 4.13/0.99 % (1438854)Instruction limit reached!
% 4.13/0.99 % (1438854)------------------------------
% 4.13/0.99 % (1438854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.99 % (1438854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.99 % (1438854)CaDiCaL version: 2.1.3
% 4.13/0.99 % (1438854)Termination reason: Instruction limit
% 4.13/0.99 % (1438854)Termination phase: Saturation
% 4.13/0.99 % (1438854)Time elapsed: 0.258 s
% 4.13/0.99 % (1438854)Peak memory usage: 16 MB
% 4.13/0.99 % (1438854)Instructions burned: 317 (million)
% 4.13/0.99 % (1438894)Instruction limit reached!
% 4.13/0.99 % (1438894)------------------------------
% 4.13/0.99 % (1438894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.99 % (1438894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.99 % (1438894)CaDiCaL version: 2.1.3
% 4.13/0.99 % (1438894)Termination reason: Instruction limit
% 4.13/0.99 % (1438894)Termination phase: Saturation
% 4.13/0.99 % (1438894)Time elapsed: 0.018 s
% 4.13/0.99 % (1438894)Peak memory usage: 12 MB
% 4.13/0.99 % (1438894)Instructions burned: 44 (million)
% 4.13/0.99 % (1438898)Refutation not found, incomplete strategy
% 4.13/0.99 % (1438898)------------------------------
% 4.13/0.99 % (1438898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.13/0.99 % (1438898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/0.99 % (1438898)CaDiCaL version: 2.1.3
% 4.13/0.99 % (1438898)Termination reason: Refutation not found, incomplete strategy
% 4.13/0.99 % (1438898)Time elapsed: 0.010 s
% 4.13/0.99 % (1438898)Peak memory usage: 12 MB
% 5.52/1.07 % (1438898)Instructions burned: 46 (million)
% 5.52/1.07 % (1438898)------------------------------
% 5.52/1.07 % (1438898)------------------------------
% 5.52/1.07 % (1438902)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=4103661443:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2994 on theBenchmark for (2994ds/65Mi)
% 5.52/1.07 % (1438884)Instruction limit reached!
% 5.52/1.07 % (1438884)------------------------------
% 5.52/1.07 % (1438884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.07 % (1438884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.07 % (1438884)CaDiCaL version: 2.1.3
% 5.52/1.07 % (1438884)Termination reason: Instruction limit
% 5.52/1.07 % (1438884)Termination phase: Saturation
% 5.52/1.07 % (1438884)Time elapsed: 0.108 s
% 5.52/1.07 % (1438884)Peak memory usage: 15 MB
% 5.52/1.07 % (1438884)Instructions burned: 247 (million)
% 5.52/1.07 % (1438901)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3348715644:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 5.52/1.07 % (1438900)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=4068219861:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 5.52/1.07 % (1438902)Instruction limit reached!
% 5.52/1.07 % (1438902)------------------------------
% 5.52/1.07 % (1438902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.07 % (1438902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.07 % (1438902)CaDiCaL version: 2.1.3
% 5.52/1.07 % (1438902)Termination reason: Instruction limit
% 5.52/1.07 % (1438902)Termination phase: Saturation
% 5.52/1.07 % (1438902)Time elapsed: 0.015 s
% 5.52/1.07 % (1438902)Peak memory usage: 13 MB
% 5.52/1.07 % (1438902)Instructions burned: 65 (million)
% 5.52/1.07 % (1438906)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1202117304:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2994 on theBenchmark for (2994ds/105Mi)
% 5.52/1.07 % (1438907)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3395097508:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2994 on theBenchmark for (2994ds/5755Mi)
% 5.52/1.07 % (1438901)Instruction limit reached!
% 5.52/1.07 % (1438901)------------------------------
% 5.52/1.07 % (1438901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.07 % (1438901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.07 % (1438901)CaDiCaL version: 2.1.3
% 5.52/1.07 % (1438901)Termination reason: Instruction limit
% 5.52/1.07 % (1438901)Termination phase: Saturation
% 5.52/1.07 % (1438901)Time elapsed: 0.041 s
% 5.52/1.07 % (1438901)Peak memory usage: 13 MB
% 5.52/1.07 % (1438901)Instructions burned: 96 (million)
% 5.52/1.07 % (1438910)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3433092299:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/375Mi)
% 5.52/1.07 % (1438906)Instruction limit reached!
% 5.52/1.07 % (1438906)------------------------------
% 5.52/1.07 % (1438906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.07 % (1438906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.07 % (1438906)CaDiCaL version: 2.1.3
% 5.52/1.07 % (1438906)Termination reason: Instruction limit
% 5.52/1.07 % (1438906)Termination phase: Saturation
% 5.52/1.07 % (1438906)Time elapsed: 0.043 s
% 5.52/1.07 % (1438906)Peak memory usage: 12 MB
% 5.52/1.07 % (1438906)Instructions burned: 107 (million)
% 5.52/1.07 % (1438912)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3559475070:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2993 on theBenchmark for (2993ds/495Mi)
% 5.52/1.07 % (1438855)Instruction limit reached!
% 5.52/1.07 % (1438855)------------------------------
% 5.52/1.07 % (1438855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.07 % (1438855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.07 % (1438855)CaDiCaL version: 2.1.3
% 5.52/1.14 % (1438855)Termination reason: Instruction limit
% 5.52/1.14 % (1438855)Termination phase: Saturation
% 5.52/1.14 % (1438855)Time elapsed: 0.363 s
% 5.52/1.14 % (1438855)Peak memory usage: 21 MB
% 5.52/1.14 % (1438855)Instructions burned: 855 (million)
% 5.52/1.14 % (1438907)Refutation not found, incomplete strategy
% 5.52/1.14 % (1438907)------------------------------
% 5.52/1.14 % (1438907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.14 % (1438907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.14 % (1438907)CaDiCaL version: 2.1.3
% 5.52/1.14 % (1438907)Termination reason: Refutation not found, incomplete strategy
% 5.52/1.14 % (1438907)Time elapsed: 0.072 s
% 5.52/1.14 % (1438907)Peak memory usage: 14 MB
% 5.52/1.14 % (1438907)Instructions burned: 313 (million)
% 5.52/1.14 % (1438907)------------------------------
% 5.52/1.14 % (1438907)------------------------------
% 5.52/1.14 % (1438915)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=763578481:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2993 on theBenchmark for (2993ds/91Mi)
% 5.52/1.14 % (1438914)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3113311996:cond=on:i=34:hud=10:nm=10:rtra=on_2993 on theBenchmark for (2993ds/34Mi)
% 5.52/1.14 % (1438914)Instruction limit reached!
% 5.52/1.14 % (1438914)------------------------------
% 5.52/1.14 % (1438914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.14 % (1438914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.14 % (1438914)CaDiCaL version: 2.1.3
% 5.52/1.14 % (1438914)Termination reason: Instruction limit
% 5.52/1.14 % (1438914)Termination phase: Saturation
% 5.52/1.14 % (1438914)Time elapsed: 0.015 s
% 5.52/1.14 % (1438914)Peak memory usage: 11 MB
% 5.52/1.14 % (1438914)Instructions burned: 35 (million)
% 5.52/1.14 % (1438915)Instruction limit reached!
% 5.52/1.14 % (1438915)------------------------------
% 5.52/1.14 % (1438915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.14 % (1438915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.14 % (1438915)CaDiCaL version: 2.1.3
% 5.52/1.14 % (1438915)Termination reason: Instruction limit
% 5.52/1.14 % (1438915)Termination phase: Saturation
% 5.52/1.14 % (1438915)Time elapsed: 0.022 s
% 5.52/1.14 % (1438915)Peak memory usage: 13 MB
% 5.52/1.14 % (1438915)Instructions burned: 91 (million)
% 5.52/1.14 % (1438919)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1929513225:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2993 on theBenchmark for (2993ds/22Mi)
% 5.52/1.14 % (1438918)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=1841596986:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2993 on theBenchmark for (2993ds/66Mi)
% 5.52/1.14 % (1438919)Instruction limit reached!
% 5.52/1.14 % (1438919)------------------------------
% 5.52/1.14 % (1438919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.14 % (1438919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.14 % (1438919)CaDiCaL version: 2.1.3
% 5.52/1.14 % (1438919)Termination reason: Instruction limit
% 5.52/1.14 % (1438919)Termination phase: Property scanning
% 5.52/1.14 % (1438919)Time elapsed: 0.006 s
% 5.52/1.14 % (1438919)Peak memory usage: 10 MB
% 5.52/1.14 % (1438919)Instructions burned: 28 (million)
% 5.52/1.14 % (1438922)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=822500793:i=338:bd=all:ins=4:rtra=on_2992 on theBenchmark for (2992ds/338Mi)
% 5.52/1.14 % (1438918)Refutation not found, incomplete strategy
% 5.52/1.14 % (1438918)------------------------------
% 5.52/1.14 % (1438918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.52/1.14 % (1438918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.14 % (1438918)CaDiCaL version: 2.1.3
% 5.52/1.14 % (1438918)Termination reason: Refutation not found, incomplete strategy
% 5.52/1.14 % (1438918)Time elapsed: 0.013 s
% 5.52/1.14 % (1438918)Peak memory usage: 12 MB
% 5.52/1.14 % (1438918)Instructions burned: 27 (million)
% 5.52/1.14 % (1438918)------------------------------
% 5.52/1.14 % (1438918)------------------------------
% 5.52/1.14 % (1438924)lrs+10_1_sil=128000:si=on:urr=on:random_seed=4101482669:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/28Mi)
% 6.20/1.21 % (1438892)Instruction limit reached!
% 6.20/1.21 % (1438892)------------------------------
% 6.20/1.21 % (1438892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.21 % (1438892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.21 % (1438892)CaDiCaL version: 2.1.3
% 6.20/1.21 % (1438892)Termination reason: Instruction limit
% 6.20/1.21 % (1438892)Termination phase: Saturation
% 6.20/1.21 % (1438892)Time elapsed: 0.222 s
% 6.20/1.21 % (1438892)Peak memory usage: 18 MB
% 6.20/1.21 % (1438892)Instructions burned: 517 (million)
% 6.20/1.21 % (1438924)Instruction limit reached!
% 6.20/1.21 % (1438924)------------------------------
% 6.20/1.21 % (1438924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.21 % (1438924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.21 % (1438924)CaDiCaL version: 2.1.3
% 6.20/1.21 % (1438924)Termination reason: Instruction limit
% 6.20/1.21 % (1438924)Termination phase: Preprocessing 3
% 6.20/1.21 % (1438924)Time elapsed: 0.012 s
% 6.20/1.21 % (1438924)Peak memory usage: 10 MB
% 6.20/1.21 % (1438924)Instructions burned: 28 (million)
% 6.20/1.21 % (1438926)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 6.20/1.21 % (1438926)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=1379288717:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2992 on theBenchmark for (2992ds/137Mi)
% 6.20/1.21 % (1438927)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=4093946387:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2992 on theBenchmark for (2992ds/340Mi)
% 6.20/1.21 % (1438900)Instruction limit reached!
% 6.20/1.21 % (1438900)------------------------------
% 6.20/1.21 % (1438900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.21 % (1438900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.21 % (1438900)CaDiCaL version: 2.1.3
% 6.20/1.21 % (1438900)Termination reason: Instruction limit
% 6.20/1.21 % (1438900)Termination phase: Saturation
% 6.20/1.21 % (1438900)Time elapsed: 0.212 s
% 6.20/1.21 % (1438900)Peak memory usage: 17 MB
% 6.20/1.21 % (1438900)Instructions burned: 450 (million)
% 6.20/1.21 % (1438910)Instruction limit reached!
% 6.20/1.21 % (1438910)------------------------------
% 6.20/1.21 % (1438910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.21 % (1438910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.21 % (1438910)CaDiCaL version: 2.1.3
% 6.20/1.21 % (1438910)Termination reason: Instruction limit
% 6.20/1.21 % (1438910)Termination phase: Saturation
% 6.20/1.21 % (1438910)Time elapsed: 0.161 s
% 6.20/1.21 % (1438910)Peak memory usage: 16 MB
% 6.20/1.21 % (1438910)Instructions burned: 377 (million)
% 6.20/1.21 % (1438922)Instruction limit reached!
% 6.20/1.21 % (1438922)------------------------------
% 6.20/1.21 % (1438922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.20/1.21 % (1438922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.20/1.21 % (1438922)CaDiCaL version: 2.1.3
% 6.20/1.21 % (1438922)Termination reason: Instruction limit
% 6.20/1.21 % (1438922)Termination phase: Saturation
% 6.20/1.21 % (1438922)Time elapsed: 0.077 s
% 6.20/1.21 % (1438922)Peak memory usage: 15 MB
% 6.20/1.21 % (1438922)Instructions burned: 339 (million)
% 6.20/1.21 % (1438931)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 6.20/1.21 % (1438932)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2636863198:i=116:ep=RSTC:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/116Mi)
% 6.20/1.21 % (1438931)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=1573190526:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/373Mi)
% 6.20/1.21 % (1438930)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=2002332784:i=227:sd=1:bd=all:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/227Mi)
% 6.20/1.21 % (1438930)Refutation not found, incomplete strategy
% 6.20/1.21 % (1438930)------------------------------
% 6.20/1.21 % (1438930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.31 % (1438930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.31 % (1438930)CaDiCaL version: 2.1.3
% 6.76/1.31 % (1438930)Termination reason: Refutation not found, incomplete strategy
% 6.76/1.31 % (1438930)Time elapsed: 0.013 s
% 6.76/1.31 % (1438930)Peak memory usage: 12 MB
% 6.76/1.31 % (1438930)Instructions burned: 28 (million)
% 6.76/1.31 % (1438930)------------------------------
% 6.76/1.31 % (1438930)------------------------------
% 6.76/1.31 % (1438926)Instruction limit reached!
% 6.76/1.31 % (1438926)------------------------------
% 6.76/1.31 % (1438926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.31 % (1438926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.31 % (1438926)CaDiCaL version: 2.1.3
% 6.76/1.31 % (1438926)Termination reason: Instruction limit
% 6.76/1.31 % (1438926)Termination phase: Saturation
% 6.76/1.31 % (1438926)Time elapsed: 0.059 s
% 6.76/1.31 % (1438926)Peak memory usage: 13 MB
% 6.76/1.31 % (1438926)Instructions burned: 139 (million)
% 6.76/1.31 % (1438932)Instruction limit reached!
% 6.76/1.31 % (1438932)------------------------------
% 6.76/1.31 % (1438932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.31 % (1438932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.31 % (1438932)CaDiCaL version: 2.1.3
% 6.76/1.31 % (1438932)Termination reason: Instruction limit
% 6.76/1.31 % (1438932)Termination phase: Saturation
% 6.76/1.31 % (1438932)Time elapsed: 0.027 s
% 6.76/1.31 % (1438932)Peak memory usage: 13 MB
% 6.76/1.31 % (1438932)Instructions burned: 119 (million)
% 6.76/1.31 % (1438936)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3041843900:i=575:rtra=on_2991 on theBenchmark for (2991ds/575Mi)
% 6.76/1.31 % (1438938)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=4117397722:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/9840Mi)
% 6.76/1.31 % (1438937)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3829566578:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2991 on theBenchmark for (2991ds/270Mi)
% 6.76/1.31 % (1438912)Instruction limit reached!
% 6.76/1.31 % (1438912)------------------------------
% 6.76/1.31 % (1438912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.31 % (1438912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.31 % (1438912)CaDiCaL version: 2.1.3
% 6.76/1.31 % (1438912)Termination reason: Instruction limit
% 6.76/1.31 % (1438912)Termination phase: Saturation
% 6.76/1.31 % (1438912)Time elapsed: 0.212 s
% 6.76/1.31 % (1438912)Peak memory usage: 17 MB
% 6.76/1.31 % (1438912)Instructions burned: 497 (million)
% 6.76/1.31 % (1438890)Instruction limit reached!
% 6.76/1.31 % (1438890)------------------------------
% 6.76/1.31 % (1438890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.31 % (1438890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.31 % (1438890)CaDiCaL version: 2.1.3
% 6.76/1.31 % (1438890)Termination reason: Instruction limit
% 6.76/1.31 % (1438890)Termination phase: Saturation
% 6.76/1.31 % (1438890)Time elapsed: 0.371 s
% 6.76/1.31 % (1438890)Peak memory usage: 20 MB
% 6.76/1.31 % (1438890)Instructions burned: 874 (million)
% 6.76/1.31 % (1438942)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2795610403:i=421:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/421Mi)
% 6.76/1.31 % (1438943)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 6.76/1.31 % (1438942)Refutation not found, incomplete strategy
% 6.76/1.31 % (1438942)------------------------------
% 6.76/1.31 % (1438942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.31 % (1438942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.31 % (1438942)CaDiCaL version: 2.1.3
% 6.76/1.31 % (1438942)Termination reason: Refutation not found, incomplete strategy
% 6.76/1.31 % (1438942)Time elapsed: 0.013 s
% 6.76/1.31 % (1438942)Peak memory usage: 12 MB
% 6.76/1.31 % (1438942)Instructions burned: 27 (million)
% 7.31/1.42 % (1438942)------------------------------
% 7.31/1.42 % (1438942)------------------------------
% 7.31/1.42 % (1438943)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2120915323:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/270Mi)
% 7.31/1.42 % (1438945)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1200956583:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/31Mi)
% 7.31/1.42 % (1438927)Instruction limit reached!
% 7.31/1.42 % (1438927)------------------------------
% 7.31/1.42 % (1438927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.31/1.42 % (1438927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/1.42 % (1438927)CaDiCaL version: 2.1.3
% 7.31/1.42 % (1438927)Termination reason: Instruction limit
% 7.31/1.42 % (1438927)Termination phase: Saturation
% 7.31/1.42 % (1438927)Time elapsed: 0.142 s
% 7.31/1.42 % (1438927)Peak memory usage: 14 MB
% 7.31/1.42 % (1438927)Instructions burned: 340 (million)
% 7.31/1.42 % (1438943)Refutation not found, incomplete strategy
% 7.31/1.42 % (1438943)------------------------------
% 7.31/1.42 % (1438943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.31/1.42 % (1438943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/1.42 % (1438943)CaDiCaL version: 2.1.3
% 7.31/1.42 % (1438943)Termination reason: Refutation not found, incomplete strategy
% 7.31/1.42 % (1438943)Time elapsed: 0.024 s
% 7.31/1.42 % (1438943)Peak memory usage: 12 MB
% 7.31/1.42 % (1438943)Instructions burned: 55 (million)
% 7.31/1.42 % (1438943)------------------------------
% 7.31/1.42 % (1438943)------------------------------
% 7.31/1.42 % (1438945)Instruction limit reached!
% 7.31/1.42 % (1438945)------------------------------
% 7.31/1.42 % (1438945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.31/1.42 % (1438945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/1.42 % (1438945)CaDiCaL version: 2.1.3
% 7.31/1.42 % (1438945)Termination reason: Instruction limit
% 7.31/1.42 % (1438945)Termination phase: Property scanning
% 7.31/1.42 % (1438945)Time elapsed: 0.013 s
% 7.31/1.42 % (1438945)Peak memory usage: 10 MB
% 7.31/1.42 % (1438945)Instructions burned: 31 (million)
% 7.31/1.42 % (1438948)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 7.31/1.42 % (1438948)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
% 7.31/1.42 % (1438948)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=207257106:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2990 on theBenchmark for (2990ds/1440Mi)
% 7.31/1.42 % (1438949)dis+10_2_sil=128000:si=on:random_seed=3632679220:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2990 on theBenchmark for (2990ds/339Mi)
% 7.31/1.42 % (1438950)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1646746689:i=111:add=on:fgj=on:rtra=on:fdi=1024_2990 on theBenchmark for (2990ds/111Mi)
% 7.31/1.42 % (1438949)Refutation not found, incomplete strategy
% 7.31/1.42 % (1438949)------------------------------
% 7.31/1.42 % (1438949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.31/1.42 % (1438949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/1.42 % (1438949)CaDiCaL version: 2.1.3
% 7.31/1.42 % (1438949)Termination reason: Refutation not found, incomplete strategy
% 7.31/1.42 % (1438949)Time elapsed: 0.014 s
% 7.31/1.42 % (1438949)Peak memory usage: 12 MB
% 7.31/1.42 % (1438949)Instructions burned: 30 (million)
% 7.31/1.42 % (1438949)------------------------------
% 7.31/1.42 % (1438949)------------------------------
% 7.31/1.42 % (1438931)Instruction limit reached!
% 7.31/1.42 % (1438931)------------------------------
% 7.31/1.42 % (1438931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.31/1.42 % (1438931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/1.42 % (1438931)CaDiCaL version: 2.1.3
% 7.31/1.42 % (1438931)Termination reason: Instruction limit
% 7.31/1.42 % (1438931)Termination phase: Saturation
% 7.31/1.42 % (1438931)Time elapsed: 0.151 s
% 7.31/1.42 % (1438931)Peak memory usage: 14 MB
% 7.75/1.54 % (1438931)Instructions burned: 375 (million)
% 7.75/1.54 % (1438937)Instruction limit reached!
% 7.75/1.54 % (1438937)------------------------------
% 7.75/1.54 % (1438937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.75/1.54 % (1438937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.54 % (1438937)CaDiCaL version: 2.1.3
% 7.75/1.54 % (1438937)Termination reason: Instruction limit
% 7.75/1.54 % (1438937)Termination phase: Saturation
% 7.75/1.54 % (1438937)Time elapsed: 0.113 s
% 7.75/1.54 % (1438937)Peak memory usage: 13 MB
% 7.75/1.54 % (1438937)Instructions burned: 274 (million)
% 7.75/1.54 % (1438954)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1956889346:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2990 on theBenchmark for (2990ds/122Mi)
% 7.75/1.54 % (1438955)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=2798030862:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/136Mi)
% 7.75/1.54 % (1438956)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2608257484:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2990 on theBenchmark for (2990ds/232Mi)
% 7.75/1.54 % (1438950)Instruction limit reached!
% 7.75/1.54 % (1438950)------------------------------
% 7.75/1.54 % (1438950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.75/1.54 % (1438950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.54 % (1438950)CaDiCaL version: 2.1.3
% 7.75/1.54 % (1438950)Termination reason: Instruction limit
% 7.75/1.54 % (1438950)Termination phase: Saturation
% 7.75/1.54 % (1438950)Time elapsed: 0.048 s
% 7.75/1.54 % (1438950)Peak memory usage: 13 MB
% 7.75/1.54 % (1438950)Instructions burned: 111 (million)
% 7.75/1.54 % (1438960)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=2038518826:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2989 on theBenchmark for (2989ds/1254Mi)
% 7.75/1.54 % (1438954)Instruction limit reached!
% 7.75/1.54 % (1438954)------------------------------
% 7.75/1.54 % (1438954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.75/1.54 % (1438954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.54 % (1438954)CaDiCaL version: 2.1.3
% 7.75/1.54 % (1438954)Termination reason: Instruction limit
% 7.75/1.54 % (1438954)Termination phase: Saturation
% 7.75/1.54 % (1438954)Time elapsed: 0.052 s
% 7.75/1.54 % (1438954)Peak memory usage: 13 MB
% 7.75/1.54 % (1438954)Instructions burned: 123 (million)
% 7.75/1.54 % (1438955)Instruction limit reached!
% 7.75/1.54 % (1438955)------------------------------
% 7.75/1.54 % (1438955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.75/1.54 % (1438955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.54 % (1438955)CaDiCaL version: 2.1.3
% 7.75/1.54 % (1438955)Termination reason: Instruction limit
% 7.75/1.54 % (1438955)Termination phase: Saturation
% 7.75/1.54 % (1438955)Time elapsed: 0.059 s
% 7.75/1.54 % (1438955)Peak memory usage: 13 MB
% 7.75/1.54 % (1438955)Instructions burned: 138 (million)
% 7.75/1.54 % (1438962)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 7.75/1.54 % (1438962)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=2662713941:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2989 on theBenchmark for (2989ds/281Mi)
% 7.75/1.54 % (1438963)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2191733552:i=619:add=on:rtra=on_2989 on theBenchmark for (2989ds/619Mi)
% 7.75/1.54 % (1438960)Refutation not found, incomplete strategy
% 7.75/1.54 % (1438960)------------------------------
% 7.75/1.54 % (1438960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.75/1.54 % (1438960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.75/1.54 % (1438960)CaDiCaL version: 2.1.3
% 7.75/1.54 % (1438960)Termination reason: Refutation not found, incomplete strategy
% 7.75/1.54 % (1438960)Time elapsed: 0.047 s
% 7.75/1.54 % (1438960)Peak memory usage: 13 MB
% 8.72/1.81 % (1438960)Instructions burned: 104 (million)
% 8.72/1.81 % (1438960)------------------------------
% 8.72/1.81 % (1438960)------------------------------
% 8.72/1.81 % (1438963)Refutation not found, incomplete strategy
% 8.72/1.81 % (1438963)------------------------------
% 8.72/1.81 % (1438963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.81 % (1438963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.81 % (1438963)CaDiCaL version: 2.1.3
% 8.72/1.81 % (1438963)Termination reason: Refutation not found, incomplete strategy
% 8.72/1.81 % (1438963)Time elapsed: 0.024 s
% 8.72/1.81 % (1438963)Peak memory usage: 13 MB
% 8.72/1.81 % (1438963)Instructions burned: 55 (million)
% 8.72/1.81 % (1438963)------------------------------
% 8.72/1.81 % (1438963)------------------------------
% 8.72/1.81 % (1438966)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3372631265:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/865Mi)
% 8.72/1.81 % (1438956)Instruction limit reached!
% 8.72/1.81 % (1438956)------------------------------
% 8.72/1.81 % (1438956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.81 % (1438956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.81 % (1438956)CaDiCaL version: 2.1.3
% 8.72/1.81 % (1438956)Termination reason: Instruction limit
% 8.72/1.81 % (1438956)Termination phase: Saturation
% 8.72/1.81 % (1438956)Time elapsed: 0.100 s
% 8.72/1.81 % (1438956)Peak memory usage: 14 MB
% 8.72/1.81 % (1438956)Instructions burned: 234 (million)
% 8.72/1.81 % (1438936)Instruction limit reached!
% 8.72/1.81 % (1438936)------------------------------
% 8.72/1.81 % (1438936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.81 % (1438936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.81 % (1438936)CaDiCaL version: 2.1.3
% 8.72/1.81 % (1438936)Termination reason: Instruction limit
% 8.72/1.81 % (1438936)Termination phase: Saturation
% 8.72/1.81 % (1438936)Time elapsed: 0.251 s
% 8.72/1.81 % (1438936)Peak memory usage: 18 MB
% 8.72/1.81 % (1438936)Instructions burned: 575 (million)
% 8.72/1.81 % (1438968)lrs+10_1_sil=128000:si=on:urr=on:random_seed=898703565:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2989 on theBenchmark for (2989ds/212Mi)
% 8.72/1.81 % (1438969)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=41527073:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/130Mi)
% 8.72/1.81 % (1438970)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3677935038:st=1.5:i=346:rtra=on:ss=axioms_2988 on theBenchmark for (2988ds/346Mi)
% 8.72/1.81 % (1438970)Refutation not found, incomplete strategy
% 8.72/1.81 % (1438970)------------------------------
% 8.72/1.81 % (1438970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.81 % (1438970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.81 % (1438970)CaDiCaL version: 2.1.3
% 8.72/1.81 % (1438970)Termination reason: Refutation not found, incomplete strategy
% 8.72/1.81 % (1438970)Time elapsed: 0.014 s
% 8.72/1.81 % (1438970)Peak memory usage: 12 MB
% 8.72/1.81 % (1438970)Instructions burned: 31 (million)
% 8.72/1.81 % (1438970)------------------------------
% 8.72/1.81 % (1438970)------------------------------
% 8.72/1.81 % (1438974)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=3085989828:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2988 on theBenchmark for (2988ds/152Mi)
% 8.72/1.81 % (1438969)Instruction limit reached!
% 8.72/1.81 % (1438969)------------------------------
% 8.72/1.81 % (1438969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.81 % (1438969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.81 % (1438969)CaDiCaL version: 2.1.3
% 8.72/1.81 % (1438969)Termination reason: Instruction limit
% 8.72/1.81 % (1438969)Termination phase: Saturation
% 8.72/1.81 % (1438969)Time elapsed: 0.057 s
% 8.72/1.81 % (1438969)Peak memory usage: 14 MB
% 8.72/1.81 % (1438969)Instructions burned: 131 (million)
% 8.72/1.81 % (1438974)Refutation not found, incomplete strategy
% 8.72/1.81 % (1438974)------------------------------
% 8.72/1.81 % (1438974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.72/1.81 % (1438974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/1.81 % (1438974)CaDiCaL version: 2.1.3
% 8.72/1.81 % (1438974)Termination reason: Refutation not found, incomplete strategy
% 10.04/1.97 % (1438974)Time elapsed: 0.024 s
% 10.04/1.97 % (1438974)Peak memory usage: 13 MB
% 10.04/1.97 % (1438974)Instructions burned: 56 (million)
% 10.04/1.97 % (1438974)------------------------------
% 10.04/1.97 % (1438974)------------------------------
% 10.04/1.97 % (1438962)Instruction limit reached!
% 10.04/1.97 % (1438962)------------------------------
% 10.04/1.97 % (1438962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.04/1.97 % (1438962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.04/1.97 % (1438962)CaDiCaL version: 2.1.3
% 10.04/1.97 % (1438962)Termination reason: Instruction limit
% 10.04/1.97 % (1438962)Termination phase: Saturation
% 10.04/1.97 % (1438962)Time elapsed: 0.129 s
% 10.04/1.97 % (1438962)Peak memory usage: 13 MB
% 10.04/1.97 % (1438962)Instructions burned: 281 (million)
% 10.04/1.97 % (1438976)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1425925301:i=75:ep=R:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/75Mi)
% 10.04/1.97 % (1438977)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=1417277201:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2988 on theBenchmark for (2988ds/387Mi)
% 10.04/1.97 % (1438968)Instruction limit reached!
% 10.04/1.97 % (1438968)------------------------------
% 10.04/1.97 % (1438968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.04/1.97 % (1438968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.04/1.97 % (1438968)CaDiCaL version: 2.1.3
% 10.04/1.97 % (1438968)Termination reason: Instruction limit
% 10.04/1.97 % (1438968)Termination phase: Saturation
% 10.04/1.97 % (1438968)Time elapsed: 0.093 s
% 10.04/1.97 % (1438968)Peak memory usage: 15 MB
% 10.04/1.97 % (1438968)Instructions burned: 213 (million)
% 10.04/1.97 % (1438978)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1385042234:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2988 on theBenchmark for (2988ds/148Mi)
% 10.04/1.97 % (1438976)Instruction limit reached!
% 10.04/1.97 % (1438976)------------------------------
% 10.04/1.97 % (1438976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.04/1.97 % (1438976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.04/1.97 % (1438976)CaDiCaL version: 2.1.3
% 10.04/1.97 % (1438976)Termination reason: Instruction limit
% 10.04/1.97 % (1438976)Termination phase: Saturation
% 10.04/1.97 % (1438976)Time elapsed: 0.033 s
% 10.04/1.97 % (1438976)Peak memory usage: 12 MB
% 10.04/1.97 % (1438976)Instructions burned: 77 (million)
% 10.04/1.97 % (1438981)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3327570764:i=161:piset=and:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/161Mi)
% 10.04/1.97 % (1438984)lrs+10_1_sil=128000:si=on:random_seed=3379111691:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/888Mi)
% 10.04/1.97 % (1438978)Instruction limit reached!
% 10.04/1.97 % (1438978)------------------------------
% 10.04/1.97 % (1438978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.04/1.97 % (1438978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.04/1.97 % (1438978)CaDiCaL version: 2.1.3
% 10.04/1.97 % (1438978)Termination reason: Instruction limit
% 10.04/1.97 % (1438978)Termination phase: Saturation
% 10.04/1.97 % (1438978)Time elapsed: 0.058 s
% 10.04/1.97 % (1438978)Peak memory usage: 11 MB
% 10.04/1.97 % (1438978)Instructions burned: 148 (million)
% 10.04/1.97 % (1438986)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=3031862978:i=136:add=on:ins=4:rtra=on:sup=off_2987 on theBenchmark for (2987ds/136Mi)
% 10.04/1.97 % (1438981)Instruction limit reached!
% 10.04/1.97 % (1438981)------------------------------
% 10.04/1.97 % (1438981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.04/1.97 % (1438981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.04/1.97 % (1438981)CaDiCaL version: 2.1.3
% 10.04/1.97 % (1438981)Termination reason: Instruction limit
% 10.04/1.97 % (1438981)Termination phase: Saturation
% 10.04/1.97 % (1438981)Time elapsed: 0.070 s
% 10.04/1.97 % (1438981)Peak memory usage: 14 MB
% 10.04/1.97 % (1438981)Instructions burned: 162 (million)
% 10.04/1.97 % (1438986)Refutation not found, incomplete strategy
% 10.04/1.97 % (1438986)------------------------------
% 10.04/1.97 % (1438986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.74/2.12 % (1438986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.74/2.12 % (1438986)CaDiCaL version: 2.1.3
% 12.74/2.12 % (1438986)Termination reason: Refutation not found, incomplete strategy
% 12.74/2.12 % (1438986)Time elapsed: 0.020 s
% 12.74/2.12 % (1438986)Peak memory usage: 13 MB
% 12.74/2.12 % (1438986)Instructions burned: 47 (million)
% 12.74/2.12 % (1438986)------------------------------
% 12.74/2.12 % (1438986)------------------------------
% 12.74/2.12 % (1438988)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1880101729:i=88:s2at=3:nm=2:rtra=on:rawr=on_2987 on theBenchmark for (2987ds/88Mi)
% 12.74/2.12 % (1438989)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1891696233:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2986 on theBenchmark for (2986ds/93Mi)
% 12.74/2.12 % (1438988)Instruction limit reached!
% 12.74/2.12 % (1438988)------------------------------
% 12.74/2.12 % (1438988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.74/2.12 % (1438988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.74/2.12 % (1438988)CaDiCaL version: 2.1.3
% 12.74/2.12 % (1438988)Termination reason: Instruction limit
% 12.74/2.12 % (1438988)Termination phase: Saturation
% 12.74/2.12 % (1438988)Time elapsed: 0.039 s
% 12.74/2.12 % (1438988)Peak memory usage: 13 MB
% 12.74/2.12 % (1438988)Instructions burned: 89 (million)
% 12.74/2.12 % (1438989)Instruction limit reached!
% 12.74/2.12 % (1438989)------------------------------
% 12.74/2.12 % (1438989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.74/2.12 % (1438989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.74/2.12 % (1438989)CaDiCaL version: 2.1.3
% 12.74/2.12 % (1438989)Termination reason: Instruction limit
% 12.74/2.12 % (1438989)Termination phase: Saturation
% 12.74/2.12 % (1438989)Time elapsed: 0.038 s
% 12.74/2.12 % (1438989)Peak memory usage: 12 MB
% 12.74/2.12 % (1438989)Instructions burned: 95 (million)
% 12.74/2.12 % (1438992)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2403772726:i=2186:rtra=on:ixr=off_2986 on theBenchmark for (2986ds/2186Mi)
% 12.74/2.12 % (1438977)Instruction limit reached!
% 12.74/2.12 % (1438977)------------------------------
% 12.74/2.12 % (1438977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.74/2.12 % (1438977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.74/2.12 % (1438977)CaDiCaL version: 2.1.3
% 12.74/2.12 % (1438977)Termination reason: Instruction limit
% 12.74/2.12 % (1438977)Termination phase: Saturation
% 12.74/2.12 % (1438977)Time elapsed: 0.173 s
% 12.74/2.12 % (1438977)Peak memory usage: 14 MB
% 12.74/2.12 % (1438977)Instructions burned: 389 (million)
% 12.74/2.12 % (1438993)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4248022854:s2a=on:i=240:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/240Mi)
% 12.74/2.12 % (1438995)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=462422244:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2986 on theBenchmark for (2986ds/805Mi)
% 12.74/2.12 % (1438966)Instruction limit reached!
% 12.74/2.12 % (1438966)------------------------------
% 12.74/2.12 % (1438966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.74/2.12 % (1438966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.74/2.12 % (1438966)CaDiCaL version: 2.1.3
% 12.74/2.12 % (1438966)Termination reason: Instruction limit
% 12.74/2.12 % (1438966)Termination phase: Saturation
% 12.74/2.12 % (1438966)Time elapsed: 0.421 s
% 12.74/2.12 % (1438966)Peak memory usage: 18 MB
% 12.74/2.12 % (1438966)Instructions burned: 866 (million)
% 12.74/2.12 % (1438998)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 12.74/2.12 % (1438998)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=4089839366:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2984 on theBenchmark for (2984ds/391Mi)
% 12.74/2.12 % (1438948)Instruction limit reached!
% 12.74/2.12 % (1438948)------------------------------
% 12.74/2.12 % (1438948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.24 % (1438948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.24 % (1438948)CaDiCaL version: 2.1.3
% 13.67/2.24 % (1438948)Termination reason: Instruction limit
% 13.67/2.24 % (1438948)Termination phase: Saturation
% 13.67/2.24 % (1438948)Time elapsed: 0.623 s
% 13.67/2.24 % (1438948)Peak memory usage: 27 MB
% 13.67/2.24 % (1438948)Instructions burned: 1442 (million)
% 13.67/2.24 % (1438993)Instruction limit reached!
% 13.67/2.24 % (1438993)------------------------------
% 13.67/2.24 % (1438993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.24 % (1438993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.24 % (1438993)CaDiCaL version: 2.1.3
% 13.67/2.24 % (1438993)Termination reason: Instruction limit
% 13.67/2.24 % (1438993)Termination phase: Saturation
% 13.67/2.24 % (1438993)Time elapsed: 0.192 s
% 13.67/2.24 % (1438993)Peak memory usage: 15 MB
% 13.67/2.24 % (1438993)Instructions burned: 241 (million)
% 13.67/2.24 % (1439000)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=2448057630:i=355:av=off:fsr=off:rtra=on:ixr=off_2984 on theBenchmark for (2984ds/355Mi)
% 13.67/2.24 % (1439001)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=2788750361:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/314Mi)
% 13.67/2.24 % (1439001)Refutation not found, incomplete strategy
% 13.67/2.24 % (1439001)------------------------------
% 13.67/2.24 % (1439001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.24 % (1439001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.24 % (1439001)CaDiCaL version: 2.1.3
% 13.67/2.24 % (1439001)Termination reason: Refutation not found, incomplete strategy
% 13.67/2.24 % (1439001)Time elapsed: 0.013 s
% 13.67/2.24 % (1439001)Peak memory usage: 13 MB
% 13.67/2.24 % (1439001)Instructions burned: 29 (million)
% 13.67/2.24 % (1439001)------------------------------
% 13.67/2.24 % (1439001)------------------------------
% 13.67/2.24 % (1438984)Instruction limit reached!
% 13.67/2.24 % (1438984)------------------------------
% 13.67/2.24 % (1438984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.24 % (1438984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.24 % (1438984)CaDiCaL version: 2.1.3
% 13.67/2.24 % (1438984)Termination reason: Instruction limit
% 13.67/2.24 % (1438984)Termination phase: Saturation
% 13.67/2.24 % (1438984)Time elapsed: 0.377 s
% 13.67/2.24 % (1438984)Peak memory usage: 21 MB
% 13.67/2.24 % (1438984)Instructions burned: 888 (million)
% 13.67/2.24 % (1439004)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=2970617526:s2a=on:i=251:fsr=off:rtra=on_2983 on theBenchmark for (2983ds/251Mi)
% 13.67/2.24 % (1439005)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=2815410677:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2983 on theBenchmark for (2983ds/2470Mi)
% 13.67/2.24 % (1438998)Instruction limit reached!
% 13.67/2.24 % (1438998)------------------------------
% 13.67/2.24 % (1438998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.24 % (1438998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.24 % (1438998)CaDiCaL version: 2.1.3
% 13.67/2.24 % (1438998)Termination reason: Instruction limit
% 13.67/2.24 % (1438998)Termination phase: Saturation
% 13.67/2.24 % (1438998)Time elapsed: 0.178 s
% 13.67/2.24 % (1438998)Peak memory usage: 13 MB
% 13.67/2.24 % (1438998)Instructions burned: 391 (million)
% 13.67/2.24 % (1439004)Instruction limit reached!
% 13.67/2.24 % (1439004)------------------------------
% 13.67/2.24 % (1439004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.67/2.24 % (1439004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.67/2.24 % (1439004)CaDiCaL version: 2.1.3
% 13.67/2.24 % (1439004)Termination reason: Instruction limit
% 13.67/2.24 % (1439004)Termination phase: Saturation
% 13.67/2.24 % (1439004)Time elapsed: 0.096 s
% 13.67/2.24 % (1439004)Peak memory usage: 13 MB
% 13.67/2.24 % (1439004)Instructions burned: 251 (million)
% 13.67/2.24 % (1439008)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=127414603:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2982 on theBenchmark for (2982ds/673Mi)
% 14.80/2.44 % (1439000)Instruction limit reached!
% 14.80/2.44 % (1439000)------------------------------
% 14.80/2.44 % (1439000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.80/2.44 % (1439000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.80/2.44 % (1439000)CaDiCaL version: 2.1.3
% 14.80/2.44 % (1439000)Termination reason: Instruction limit
% 14.80/2.44 % (1439000)Termination phase: Saturation
% 14.80/2.44 % (1439000)Time elapsed: 0.153 s
% 14.80/2.44 % (1439000)Peak memory usage: 16 MB
% 14.80/2.44 % (1439000)Instructions burned: 355 (million)
% 14.80/2.44 % (1439009)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2520694143:i=116:ep=RSTC:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/116Mi)
% 14.80/2.44 % (1439011)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=997006641:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2982 on theBenchmark for (2982ds/270Mi)
% 14.80/2.44 % (1438995)Instruction limit reached!
% 14.80/2.44 % (1438995)------------------------------
% 14.80/2.44 % (1438995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.80/2.44 % (1438995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.80/2.44 % (1438995)CaDiCaL version: 2.1.3
% 14.80/2.44 % (1438995)Termination reason: Instruction limit
% 14.80/2.44 % (1438995)Termination phase: Saturation
% 14.80/2.44 % (1438995)Time elapsed: 0.396 s
% 14.80/2.44 % (1438995)Peak memory usage: 20 MB
% 14.80/2.44 % (1438995)Instructions burned: 805 (million)
% 14.80/2.44 % (1439009)Instruction limit reached!
% 14.80/2.44 % (1439009)------------------------------
% 14.80/2.44 % (1439009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.80/2.44 % (1439009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.80/2.44 % (1439009)CaDiCaL version: 2.1.3
% 14.80/2.44 % (1439009)Termination reason: Instruction limit
% 14.80/2.44 % (1439009)Termination phase: Saturation
% 14.80/2.44 % (1439009)Time elapsed: 0.051 s
% 14.80/2.44 % (1439009)Peak memory usage: 13 MB
% 14.80/2.44 % (1439009)Instructions burned: 118 (million)
% 14.80/2.44 % (1439015)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 14.80/2.44 % (1439015)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=2179468868:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2982 on theBenchmark for (2982ds/39Mi)
% 14.80/2.44 % (1439014)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=3037954723:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2982 on theBenchmark for (2982ds/30Mi)
% 14.80/2.44 % (1439014)Instruction limit reached!
% 14.80/2.44 % (1439014)------------------------------
% 14.80/2.44 % (1439014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.80/2.44 % (1439014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.80/2.44 % (1439014)CaDiCaL version: 2.1.3
% 14.80/2.44 % (1439014)Termination reason: Instruction limit
% 14.80/2.44 % (1439014)Termination phase: Preprocessing 3
% 14.80/2.44 % (1439014)Time elapsed: 0.013 s
% 14.80/2.44 % (1439014)Peak memory usage: 10 MB
% 14.80/2.44 % (1439014)Instructions burned: 30 (million)
% 14.80/2.44 % (1439015)Instruction limit reached!
% 14.80/2.44 % (1439015)------------------------------
% 14.80/2.44 % (1439015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.80/2.44 % (1439015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.80/2.44 % (1439015)CaDiCaL version: 2.1.3
% 14.80/2.44 % (1439015)Termination reason: Instruction limit
% 14.80/2.44 % (1439015)Termination phase: Saturation
% 14.80/2.44 % (1439015)Time elapsed: 0.017 s
% 14.80/2.44 % (1439015)Peak memory usage: 11 MB
% 14.80/2.44 % (1439015)Instructions burned: 40 (million)
% 14.80/2.44 % (1439018)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2399841266:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2981 on theBenchmark for (2981ds/365Mi)
% 14.80/2.44 % (1439019)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1225785925:i=158:av=off:rtra=on_2981 on theBenchmark for (2981ds/158Mi)
% 14.80/2.44 % (1439011)Instruction limit reached!
% 14.80/2.44 % (1439011)------------------------------
% 14.80/2.44 % (1439011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.22/2.65 % (1439011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.22/2.65 % (1439011)CaDiCaL version: 2.1.3
% 16.22/2.65 % (1439011)Termination reason: Instruction limit
% 16.22/2.65 % (1439011)Termination phase: Saturation
% 16.22/2.65 % (1439011)Time elapsed: 0.113 s
% 16.22/2.65 % (1439011)Peak memory usage: 13 MB
% 16.22/2.65 % (1439011)Instructions burned: 271 (million)
% 16.22/2.65 % (1439022)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 16.22/2.65 % (1439022)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3122457340:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/252Mi)
% 16.22/2.65 % (1439022)Refutation not found, incomplete strategy
% 16.22/2.65 % (1439022)------------------------------
% 16.22/2.65 % (1439022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.22/2.65 % (1439022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.22/2.65 % (1439022)CaDiCaL version: 2.1.3
% 16.22/2.65 % (1439022)Termination reason: Refutation not found, incomplete strategy
% 16.22/2.65 % (1439022)Time elapsed: 0.024 s
% 16.22/2.65 % (1439022)Peak memory usage: 13 MB
% 16.22/2.65 % (1439022)Instructions burned: 55 (million)
% 16.22/2.65 % (1439022)------------------------------
% 16.22/2.65 % (1439022)------------------------------
% 16.22/2.65 % (1439019)Instruction limit reached!
% 16.22/2.65 % (1439019)------------------------------
% 16.22/2.65 % (1439019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.22/2.65 % (1439019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.22/2.65 % (1439019)CaDiCaL version: 2.1.3
% 16.22/2.65 % (1439019)Termination reason: Instruction limit
% 16.22/2.65 % (1439019)Termination phase: Saturation
% 16.22/2.65 % (1439019)Time elapsed: 0.070 s
% 16.22/2.65 % (1439019)Peak memory usage: 13 MB
% 16.22/2.65 % (1439019)Instructions burned: 158 (million)
% 16.22/2.65 % (1439024)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2565891394:i=213:rtra=on:ss=axioms_2980 on theBenchmark for (2980ds/213Mi)
% 16.22/2.65 % (1439025)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=2038180825:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2980 on theBenchmark for (2980ds/160Mi)
% 16.22/2.65 % (1439024)Refutation not found, incomplete strategy
% 16.22/2.65 % (1439024)------------------------------
% 16.22/2.65 % (1439024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.22/2.65 % (1439024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.22/2.65 % (1439024)CaDiCaL version: 2.1.3
% 16.22/2.65 % (1439024)Termination reason: Refutation not found, incomplete strategy
% 16.22/2.65 % (1439024)Time elapsed: 0.011 s
% 16.22/2.65 % (1439024)Peak memory usage: 12 MB
% 16.22/2.65 % (1439024)Instructions burned: 25 (million)
% 16.22/2.65 % (1439024)------------------------------
% 16.22/2.65 % (1439024)------------------------------
% 16.22/2.65 % (1439028)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=3203222525:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/763Mi)
% 16.22/2.65 % (1439025)Refutation not found, incomplete strategy
% 16.22/2.65 % (1439025)------------------------------
% 16.22/2.65 % (1439025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.22/2.65 % (1439025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.22/2.65 % (1439025)CaDiCaL version: 2.1.3
% 16.22/2.65 % (1439025)Termination reason: Refutation not found, incomplete strategy
% 16.22/2.65 % (1439025)Time elapsed: 0.027 s
% 16.22/2.65 % (1439025)Peak memory usage: 13 MB
% 16.22/2.65 % (1439025)Instructions burned: 65 (million)
% 16.22/2.65 % (1439025)------------------------------
% 16.22/2.65 % (1439025)------------------------------
% 16.22/2.65 % (1439030)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 16.22/2.65 % (1439030)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1580797007:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2980 on theBenchmark for (2980ds/237Mi)
% 17.04/2.72 % (1439028)Refutation not found, incomplete strategy
% 17.04/2.72 % (1439028)------------------------------
% 17.04/2.72 % (1439028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.04/2.72 % (1439028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/2.72 % (1439028)CaDiCaL version: 2.1.3
% 17.04/2.72 % (1439028)Termination reason: Refutation not found, incomplete strategy
% 17.04/2.72 % (1439028)Time elapsed: 0.023 s
% 17.04/2.72 % (1439028)Peak memory usage: 13 MB
% 17.04/2.72 % (1439028)Instructions burned: 53 (million)
% 17.04/2.72 % (1439028)------------------------------
% 17.04/2.72 % (1439028)------------------------------
% 17.04/2.72 % (1439032)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=228915629:s2a=on:i=386:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/386Mi)
% 17.04/2.72 % (1439008)Instruction limit reached!
% 17.04/2.72 % (1439008)------------------------------
% 17.04/2.72 % (1439008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.04/2.72 % (1439008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/2.72 % (1439008)CaDiCaL version: 2.1.3
% 17.04/2.72 % (1439008)Termination reason: Instruction limit
% 17.04/2.72 % (1439008)Termination phase: Saturation
% 17.04/2.72 % (1439008)Time elapsed: 0.292 s
% 17.04/2.72 % (1439008)Peak memory usage: 18 MB
% 17.04/2.72 % (1439008)Instructions burned: 675 (million)
% 17.04/2.72 % (1439034)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=2738042620:i=300:piset=and:nm=32:rtra=on_2979 on theBenchmark for (2979ds/300Mi)
% 17.04/2.72 % (1439018)Instruction limit reached!
% 17.04/2.72 % (1439018)------------------------------
% 17.04/2.72 % (1439018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.04/2.72 % (1439018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/2.72 % (1439018)CaDiCaL version: 2.1.3
% 17.04/2.72 % (1439018)Termination reason: Instruction limit
% 17.04/2.72 % (1439018)Termination phase: Saturation
% 17.04/2.72 % (1439018)Time elapsed: 0.190 s
% 17.04/2.72 % (1439018)Peak memory usage: 17 MB
% 17.04/2.72 % (1439018)Instructions burned: 366 (million)
% 17.04/2.72 % (1439036)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=3360639135:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2979 on theBenchmark for (2979ds/567Mi)
% 17.04/2.72 % (1439030)Instruction limit reached!
% 17.04/2.72 % (1439030)------------------------------
% 17.04/2.72 % (1439030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.04/2.72 % (1439030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/2.72 % (1439030)CaDiCaL version: 2.1.3
% 17.04/2.72 % (1439030)Termination reason: Instruction limit
% 17.04/2.72 % (1439030)Termination phase: Saturation
% 17.04/2.72 % (1439030)Time elapsed: 0.103 s
% 17.04/2.72 % (1439030)Peak memory usage: 15 MB
% 17.04/2.72 % (1439030)Instructions burned: 238 (million)
% 17.04/2.72 % (1439038)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=4081546415:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2979 on theBenchmark for (2979ds/379Mi)
% 17.04/2.72 % (1439034)Instruction limit reached!
% 17.04/2.72 % (1439034)------------------------------
% 17.04/2.72 % (1439034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.04/2.72 % (1439034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/2.72 % (1439034)CaDiCaL version: 2.1.3
% 17.04/2.72 % (1439034)Termination reason: Instruction limit
% 17.04/2.72 % (1439034)Termination phase: Saturation
% 17.04/2.72 % (1439034)Time elapsed: 0.130 s
% 17.04/2.72 % (1439034)Peak memory usage: 16 MB
% 17.04/2.72 % (1439034)Instructions burned: 302 (million)
% 17.04/2.72 % (1439032)Instruction limit reached!
% 17.04/2.72 % (1439032)------------------------------
% 17.04/2.72 % (1439032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.04/2.72 % (1439032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.04/2.72 % (1439032)CaDiCaL version: 2.1.3
% 17.04/2.72 % (1439032)Termination reason: Instruction limit
% 17.04/2.72 % (1439032)Termination phase: Saturation
% 17.04/2.72 % (1439032)Time elapsed: 0.168 s
% 17.04/2.72 % (1439032)Peak memory usage: 14 MB
% 17.04/2.72 % (1439032)Instructions burned: 387 (million)
% 17.04/2.72 % (1439040)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=3496674228:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2978 on theBenchmark for (2978ds/429Mi)
% 17.75/2.83 % (1439041)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=3705985891:i=478:bd=all:rtra=on_2978 on theBenchmark for (2978ds/478Mi)
% 17.75/2.83 % (1439038)Instruction limit reached!
% 17.75/2.83 % (1439038)------------------------------
% 17.75/2.83 % (1439038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.75/2.83 % (1439038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.75/2.83 % (1439038)CaDiCaL version: 2.1.3
% 17.75/2.83 % (1439038)Termination reason: Instruction limit
% 17.75/2.83 % (1439038)Termination phase: Saturation
% 17.75/2.83 % (1439038)Time elapsed: 0.164 s
% 17.75/2.83 % (1439038)Peak memory usage: 17 MB
% 17.75/2.83 % (1439038)Instructions burned: 379 (million)
% 17.75/2.83 % (1439044)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3751915876:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2977 on theBenchmark for (2977ds/445Mi)
% 17.75/2.83 % (1439036)Instruction limit reached!
% 17.75/2.83 % (1439036)------------------------------
% 17.75/2.83 % (1439036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.75/2.83 % (1439036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.75/2.83 % (1439036)CaDiCaL version: 2.1.3
% 17.75/2.83 % (1439036)Termination reason: Instruction limit
% 17.75/2.83 % (1439036)Termination phase: Saturation
% 17.75/2.83 % (1439036)Time elapsed: 0.248 s
% 17.75/2.83 % (1439036)Peak memory usage: 15 MB
% 17.75/2.83 % (1439036)Instructions burned: 568 (million)
% 17.75/2.83 % (1439046)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=1872028152:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2976 on theBenchmark for (2976ds/71Mi)
% 17.75/2.83 % (1439046)Instruction limit reached!
% 17.75/2.83 % (1439046)------------------------------
% 17.75/2.83 % (1439046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.75/2.83 % (1439046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.75/2.83 % (1439046)CaDiCaL version: 2.1.3
% 17.75/2.83 % (1439046)Termination reason: Instruction limit
% 17.75/2.83 % (1439046)Termination phase: Saturation
% 17.75/2.83 % (1439046)Time elapsed: 0.032 s
% 17.75/2.83 % (1439046)Peak memory usage: 13 MB
% 17.75/2.83 % (1439046)Instructions burned: 72 (million)
% 17.75/2.83 % (1439040)Instruction limit reached!
% 17.75/2.83 % (1439040)------------------------------
% 17.75/2.83 % (1439040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.75/2.83 % (1439040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.75/2.83 % (1439040)CaDiCaL version: 2.1.3
% 17.75/2.83 % (1439040)Termination reason: Instruction limit
% 17.75/2.83 % (1439040)Termination phase: Saturation
% 17.75/2.83 % (1439040)Time elapsed: 0.183 s
% 17.75/2.83 % (1439040)Peak memory usage: 17 MB
% 17.75/2.83 % (1439040)Instructions burned: 429 (million)
% 17.75/2.83 % (1439048)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1310263923:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2976 on theBenchmark for (2976ds/302Mi)
% 17.75/2.83 % (1439048)Refutation not found, incomplete strategy
% 17.75/2.83 % (1439048)------------------------------
% 17.75/2.83 % (1439048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.75/2.83 % (1439048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.75/2.83 % (1439048)CaDiCaL version: 2.1.3
% 17.75/2.83 % (1439048)Termination reason: Refutation not found, incomplete strategy
% 17.75/2.83 % (1439048)Time elapsed: 0.013 s
% 17.75/2.83 % (1439048)Peak memory usage: 13 MB
% 17.75/2.83 % (1439048)Instructions burned: 27 (million)
% 17.75/2.83 % (1439049)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=2642220432:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2976 on theBenchmark for (2976ds/4980Mi)
% 17.75/2.83 % (1439048)------------------------------
% 17.75/2.83 % (1439048)------------------------------
% 17.75/2.83 % (1439041)Instruction limit reached!
% 17.75/2.83 % (1439041)------------------------------
% 17.75/2.83 % (1439041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.75/2.83 % (1439041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.75/2.83 % (1439041)CaDiCaL version: 2.1.3
% 17.75/2.83 % (1439041)Termination reason: Instruction limit
% 17.75/2.83 % (1439041)Termination phase: Saturation
% 17.75/2.83 % (1439041)Time elapsed: 0.202 s
% 17.75/2.83 % (1439041)Peak memory usage: 17 MB
% 18.29/3.06 % (1439041)Instructions burned: 479 (million)
% 18.29/3.06 % (1439049)Refutation not found, incomplete strategy
% 18.29/3.06 % (1439049)------------------------------
% 18.29/3.06 % (1439049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.29/3.06 % (1439049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.29/3.06 % (1439049)CaDiCaL version: 2.1.3
% 18.29/3.06 % (1439049)Termination reason: Refutation not found, incomplete strategy
% 18.29/3.06 % (1439049)Time elapsed: 0.012 s
% 18.29/3.06 % (1439049)Peak memory usage: 12 MB
% 18.29/3.06 % (1439049)Instructions burned: 27 (million)
% 18.29/3.06 % (1439049)------------------------------
% 18.29/3.06 % (1439049)------------------------------
% 18.29/3.06 % (1439052)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
% 18.29/3.06 % (1439052)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 18.29/3.06 % (1438992)Instruction limit reached!
% 18.29/3.06 % (1438992)------------------------------
% 18.29/3.06 % (1438992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.29/3.06 % (1438992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.29/3.06 % (1438992)CaDiCaL version: 2.1.3
% 18.29/3.06 % (1438992)Termination reason: Instruction limit
% 18.29/3.06 % (1438992)Termination phase: Saturation
% 18.29/3.06 % (1438992)Time elapsed: 1.046 s
% 18.29/3.06 % (1438992)Peak memory usage: 19 MB
% 18.29/3.06 % (1438992)Instructions burned: 2187 (million)
% 18.29/3.06 % (1439052)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1918868869:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2975 on theBenchmark for (2975ds/100Mi)
% 18.29/3.06 % (1439053)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=4204299330:i=76:piset=equals:rtra=on:ntd=on_2975 on theBenchmark for (2975ds/76Mi)
% 18.29/3.06 % (1439054)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=3761077122:i=289:rtra=on_2975 on theBenchmark for (2975ds/289Mi)
% 18.29/3.06 % (1439055)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=3443214967:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2975 on theBenchmark for (2975ds/493Mi)
% 18.29/3.06 % (1439053)Instruction limit reached!
% 18.29/3.06 % (1439053)------------------------------
% 18.29/3.06 % (1439053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.29/3.06 % (1439053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.29/3.06 % (1439053)CaDiCaL version: 2.1.3
% 18.29/3.06 % (1439053)Termination reason: Instruction limit
% 18.29/3.06 % (1439053)Termination phase: Saturation
% 18.29/3.06 % (1439053)Time elapsed: 0.033 s
% 18.29/3.06 % (1439053)Peak memory usage: 13 MB
% 18.29/3.06 % (1439053)Instructions burned: 77 (million)
% 18.29/3.06 % (1439054)Refutation not found, incomplete strategy
% 18.29/3.06 % (1439054)------------------------------
% 18.29/3.06 % (1439054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.29/3.06 % (1439054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.29/3.06 % (1439054)CaDiCaL version: 2.1.3
% 18.29/3.06 % (1439054)Termination reason: Refutation not found, incomplete strategy
% 18.29/3.06 % (1439054)Time elapsed: 0.028 s
% 18.29/3.06 % (1439054)Peak memory usage: 13 MB
% 18.29/3.06 % (1439054)Instructions burned: 66 (million)
% 18.29/3.06 % (1439054)------------------------------
% 18.29/3.06 % (1439054)------------------------------
% 18.29/3.06 % (1439052)Instruction limit reached!
% 18.29/3.06 % (1439052)------------------------------
% 18.29/3.06 % (1439052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.29/3.06 % (1439052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.29/3.06 % (1439052)CaDiCaL version: 2.1.3
% 18.29/3.06 % (1439052)Termination reason: Instruction limit
% 18.29/3.06 % (1439052)Termination phase: Saturation
% 18.29/3.06 % (1439052)Time elapsed: 0.043 s
% 18.29/3.06 % (1439052)Peak memory usage: 13 MB
% 18.29/3.06 % (1439052)Instructions burned: 101 (million)
% 18.29/3.06 % (1439061)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 20.79/3.31 % (1439060)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2949806087:cond=on:i=34:hud=10:nm=10:rtra=on_2975 on theBenchmark for (2975ds/34Mi)
% 20.79/3.31 % (1439061)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=2540837421:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2975 on theBenchmark for (2975ds/372Mi)
% 20.79/3.31 % (1439062)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=1274154659:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2975 on theBenchmark for (2975ds/670Mi)
% 20.79/3.31 % (1439060)Instruction limit reached!
% 20.79/3.31 % (1439060)------------------------------
% 20.79/3.31 % (1439060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.79/3.31 % (1439060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.79/3.31 % (1439060)CaDiCaL version: 2.1.3
% 20.79/3.31 % (1439060)Termination reason: Instruction limit
% 20.79/3.31 % (1439060)Termination phase: Saturation
% 20.79/3.31 % (1439060)Time elapsed: 0.015 s
% 20.79/3.31 % (1439060)Peak memory usage: 11 MB
% 20.79/3.31 % (1439060)Instructions burned: 36 (million)
% 20.79/3.31 % (1439044)Instruction limit reached!
% 20.79/3.31 % (1439044)------------------------------
% 20.79/3.31 % (1439044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.79/3.31 % (1439044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.79/3.31 % (1439044)CaDiCaL version: 2.1.3
% 20.79/3.31 % (1439044)Termination reason: Instruction limit
% 20.79/3.31 % (1439044)Termination phase: Saturation
% 20.79/3.31 % (1439044)Time elapsed: 0.193 s
% 20.79/3.31 % (1439044)Peak memory usage: 17 MB
% 20.79/3.31 % (1439044)Instructions burned: 446 (million)
% 20.79/3.31 % (1439061)Refutation not found, incomplete strategy
% 20.79/3.31 % (1439061)------------------------------
% 20.79/3.31 % (1439061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.79/3.31 % (1439061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.79/3.31 % (1439061)CaDiCaL version: 2.1.3
% 20.79/3.31 % (1439061)Termination reason: Refutation not found, incomplete strategy
% 20.79/3.31 % (1439061)Time elapsed: 0.024 s
% 20.79/3.31 % (1439061)Peak memory usage: 13 MB
% 20.79/3.31 % (1439061)Instructions burned: 54 (million)
% 20.79/3.31 % (1439061)------------------------------
% 20.79/3.31 % (1439061)------------------------------
% 20.79/3.31 % (1439066)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1478662865:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2975 on theBenchmark for (2975ds/647Mi)
% 20.79/3.31 % (1439067)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=1630727907:i=857:add=off:kws=frequency:rtra=on:ntd=on_2974 on theBenchmark for (2974ds/857Mi)
% 20.79/3.31 % (1439068)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=1837357502:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2974 on theBenchmark for (2974ds/693Mi)
% 20.79/3.31 % (1439067)Refutation not found, incomplete strategy
% 20.79/3.31 % (1439067)------------------------------
% 20.79/3.31 % (1439067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.79/3.31 % (1439067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.79/3.31 % (1439067)CaDiCaL version: 2.1.3
% 20.79/3.31 % (1439067)Termination reason: Refutation not found, incomplete strategy
% 20.79/3.31 % (1439067)Time elapsed: 0.023 s
% 20.79/3.31 % (1439067)Peak memory usage: 12 MB
% 20.79/3.31 % (1439067)Instructions burned: 55 (million)
% 20.79/3.31 % (1439067)------------------------------
% 20.79/3.31 % (1439067)------------------------------
% 20.79/3.31 % (1439072)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=2379548360:i=285:hud=10:bd=all:rtra=on:ss=axioms_2974 on theBenchmark for (2974ds/285Mi)
% 20.79/3.31 % (1439072)Refutation not found, incomplete strategy
% 20.79/3.31 % (1439072)------------------------------
% 20.79/3.31 % (1439072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.79/3.31 % (1439072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.95/3.52 % (1439072)CaDiCaL version: 2.1.3
% 21.95/3.52 % (1439072)Termination reason: Refutation not found, incomplete strategy
% 21.95/3.52 % (1439072)Time elapsed: 0.026 s
% 21.95/3.52 % (1439072)Peak memory usage: 13 MB
% 21.95/3.52 % (1439072)Instructions burned: 53 (million)
% 21.95/3.52 % (1439072)------------------------------
% 21.95/3.52 % (1439072)------------------------------
% 21.95/3.52 % (1439074)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 21.95/3.52 % (1439074)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=3430195029:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2974 on theBenchmark for (2974ds/52Mi)
% 21.95/3.52 % (1439074)Instruction limit reached!
% 21.95/3.52 % (1439074)------------------------------
% 21.95/3.52 % (1439074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.95/3.52 % (1439074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.95/3.52 % (1439074)CaDiCaL version: 2.1.3
% 21.95/3.52 % (1439074)Termination reason: Instruction limit
% 21.95/3.52 % (1439074)Termination phase: Saturation
% 21.95/3.52 % (1439074)Time elapsed: 0.023 s
% 21.95/3.52 % (1439074)Peak memory usage: 12 MB
% 21.95/3.52 % (1439074)Instructions burned: 55 (million)
% 21.95/3.52 % (1439076)dis+10_1_si=on:random_seed=2784119043:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2973 on theBenchmark for (2973ds/407Mi)
% 21.95/3.52 % (1439055)Instruction limit reached!
% 21.95/3.52 % (1439055)------------------------------
% 21.95/3.52 % (1439055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.95/3.52 % (1439055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.95/3.52 % (1439055)CaDiCaL version: 2.1.3
% 21.95/3.52 % (1439055)Termination reason: Instruction limit
% 21.95/3.52 % (1439055)Termination phase: Saturation
% 21.95/3.52 % (1439055)Time elapsed: 0.217 s
% 21.95/3.52 % (1439055)Peak memory usage: 14 MB
% 21.95/3.52 % (1439055)Instructions burned: 493 (million)
% 21.95/3.52 % (1439078)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1037450148:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2973 on theBenchmark for (2973ds/2240Mi)
% 21.95/3.52 % (1439062)Instruction limit reached!
% 21.95/3.52 % (1439062)------------------------------
% 21.95/3.52 % (1439062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.95/3.52 % (1439062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.95/3.52 % (1439062)CaDiCaL version: 2.1.3
% 21.95/3.52 % (1439062)Termination reason: Instruction limit
% 21.95/3.52 % (1439062)Termination phase: Saturation
% 21.95/3.52 % (1439062)Time elapsed: 0.281 s
% 21.95/3.52 % (1439062)Peak memory usage: 19 MB
% 21.95/3.52 % (1439062)Instructions burned: 670 (million)
% 21.95/3.52 % (1439080)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=2325550812:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2972 on theBenchmark for (2972ds/336Mi)
% 21.95/3.52 % (1439066)Instruction limit reached!
% 21.95/3.52 % (1439066)------------------------------
% 21.95/3.52 % (1439066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.95/3.52 % (1439066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.95/3.52 % (1439066)CaDiCaL version: 2.1.3
% 21.95/3.52 % (1439066)Termination reason: Instruction limit
% 21.95/3.52 % (1439066)Termination phase: Saturation
% 21.95/3.52 % (1439066)Time elapsed: 0.274 s
% 21.95/3.52 % (1439066)Peak memory usage: 19 MB
% 21.95/3.52 % (1439066)Instructions burned: 647 (million)
% 21.95/3.52 % (1439005)Instruction limit reached!
% 21.95/3.52 % (1439005)------------------------------
% 21.95/3.52 % (1439005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.95/3.52 % (1439005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.95/3.52 % (1439005)CaDiCaL version: 2.1.3
% 21.95/3.52 % (1439005)Termination reason: Instruction limit
% 21.95/3.52 % (1439005)Termination phase: Saturation
% 21.95/3.52 % (1439005)Time elapsed: 1.159 s
% 21.95/3.52 % (1439005)Peak memory usage: 22 MB
% 21.95/3.52 % (1439005)Instructions burned: 2471 (million)
% 21.95/3.52 % (1439082)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=1514891946:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2972 on theBenchmark for (2972ds/1142Mi)
% 21.95/3.52 % (1439083)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=4187390851:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2971 on theBenchmark for (2971ds/376Mi)
% 22.88/3.64 % (1439076)Instruction limit reached!
% 22.88/3.64 % (1439076)------------------------------
% 22.88/3.64 % (1439076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.88/3.64 % (1439076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.88/3.64 % (1439076)CaDiCaL version: 2.1.3
% 22.88/3.64 % (1439076)Termination reason: Instruction limit
% 22.88/3.64 % (1439076)Termination phase: Saturation
% 22.88/3.64 % (1439076)Time elapsed: 0.176 s
% 22.88/3.64 % (1439076)Peak memory usage: 17 MB
% 22.88/3.64 % (1439076)Instructions burned: 410 (million)
% 22.88/3.64 % (1439068)Instruction limit reached!
% 22.88/3.64 % (1439068)------------------------------
% 22.88/3.64 % (1439068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.88/3.64 % (1439086)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=26369864:i=766:bd=all:rtra=on_2971 on theBenchmark for (2971ds/766Mi)
% 22.88/3.64 % (1439068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.88/3.64 % (1439068)CaDiCaL version: 2.1.3
% 22.88/3.64 % (1439068)Termination reason: Instruction limit
% 22.88/3.64 % (1439068)Termination phase: Saturation
% 22.88/3.64 % (1439068)Time elapsed: 0.324 s
% 22.88/3.64 % (1439068)Peak memory usage: 14 MB
% 22.88/3.64 % (1439068)Instructions burned: 695 (million)
% 22.88/3.64 % (1439088)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 22.88/3.64 % (1439088)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=92842001:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2971 on theBenchmark for (2971ds/959Mi)
% 22.88/3.64 % (1439080)Instruction limit reached!
% 22.88/3.64 % (1439080)------------------------------
% 22.88/3.64 % (1439080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.88/3.64 % (1439080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.88/3.64 % (1439080)CaDiCaL version: 2.1.3
% 22.88/3.64 % (1439080)Termination reason: Instruction limit
% 22.88/3.64 % (1439080)Termination phase: Saturation
% 22.88/3.64 % (1439080)Time elapsed: 0.146 s
% 22.88/3.64 % (1439080)Peak memory usage: 16 MB
% 22.88/3.64 % (1439080)Instructions burned: 336 (million)
% 22.88/3.64 % (1439090)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=3637960570:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2970 on theBenchmark for (2970ds/6359Mi)
% 22.88/3.64 % (1439083)Instruction limit reached!
% 22.88/3.64 % (1439083)------------------------------
% 22.88/3.64 % (1439083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.88/3.64 % (1439083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.88/3.64 % (1439083)CaDiCaL version: 2.1.3
% 22.88/3.64 % (1439083)Termination reason: Instruction limit
% 22.88/3.64 % (1439083)Termination phase: Saturation
% 22.88/3.64 % (1439083)Time elapsed: 0.164 s
% 22.88/3.64 % (1439083)Peak memory usage: 16 MB
% 22.88/3.64 % (1439083)Instructions burned: 378 (million)
% 22.88/3.64 % (1439092)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=897562556:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2970 on theBenchmark for (2970ds/35Mi)
% 22.88/3.64 % (1439092)Instruction limit reached!
% 22.88/3.64 % (1439092)------------------------------
% 22.88/3.64 % (1439092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.88/3.64 % (1439092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.88/3.64 % (1439092)CaDiCaL version: 2.1.3
% 22.88/3.64 % (1439092)Termination reason: Instruction limit
% 22.88/3.64 % (1439092)Termination phase: Property scanning
% 22.88/3.64 % (1439092)Time elapsed: 0.015 s
% 22.88/3.64 % (1439092)Peak memory usage: 10 MB
% 22.88/3.64 % (1439092)Instructions burned: 37 (million)
% 22.88/3.64 % (1439094)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=2311325185:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2969 on theBenchmark for (2969ds/53Mi)
% 22.88/3.64 % (1439094)Instruction limit reached!
% 22.88/3.64 % (1439094)------------------------------
% 22.88/3.64 % (1439094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.67/3.71 % (1439094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.67/3.71 % (1439094)CaDiCaL version: 2.1.3
% 23.67/3.71 % (1439094)Termination reason: Instruction limit
% 23.67/3.71 % (1439094)Termination phase: Saturation
% 23.67/3.71 % (1439094)Time elapsed: 0.025 s
% 23.67/3.71 % (1439094)Peak memory usage: 13 MB
% 23.67/3.71 % (1439094)Instructions burned: 54 (million)
% 23.67/3.71 % (1439096)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=2693058687:s2a=on:i=876:s2at=6:nm=2:rtra=on_2969 on theBenchmark for (2969ds/876Mi)
% 23.67/3.71 % (1438938)Instruction limit reached!
% 23.67/3.71 % (1438938)------------------------------
% 23.67/3.71 % (1438938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.67/3.71 % (1438938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.67/3.71 % (1438938)CaDiCaL version: 2.1.3
% 23.67/3.71 % (1438938)Termination reason: Instruction limit
% 23.67/3.71 % (1438938)Termination phase: Saturation
% 23.67/3.71 % (1438938)Time elapsed: 2.317 s
% 23.67/3.71 % (1438938)Peak memory usage: 48 MB
% 23.67/3.71 % (1438938)Instructions burned: 9843 (million)
% 23.67/3.71 % (1439082)Refutation not found, incomplete strategy
% 23.67/3.71 % (1439082)------------------------------
% 23.67/3.71 % (1439082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.67/3.71 % (1439082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.67/3.71 % (1439082)CaDiCaL version: 2.1.3
% 23.67/3.71 % (1439082)Termination reason: Refutation not found, incomplete strategy
% 23.67/3.71 % (1439082)Time elapsed: 0.363 s
% 23.67/3.71 % (1439082)Peak memory usage: 16 MB
% 23.67/3.71 % (1439082)Instructions burned: 816 (million)
% 23.67/3.71 % (1439082)------------------------------
% 23.67/3.71 % (1439082)------------------------------
% 23.67/3.71 % (1439086)Instruction limit reached!
% 23.67/3.71 % (1439086)------------------------------
% 23.67/3.71 % (1439086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.67/3.71 % (1439086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.67/3.71 % (1439086)CaDiCaL version: 2.1.3
% 23.67/3.71 % (1439086)Termination reason: Instruction limit
% 23.67/3.71 % (1439086)Termination phase: Saturation
% 23.67/3.71 % (1439086)Time elapsed: 0.328 s
% 23.67/3.71 % (1439086)Peak memory usage: 20 MB
% 23.67/3.71 % (1439086)Instructions burned: 766 (million)
% 23.67/3.71 % (1439098)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=31354743:i=57:ep=R:rtra=on:ntd=on_2968 on theBenchmark for (2968ds/57Mi)
% 23.67/3.71 % (1439099)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 23.67/3.71 % (1439099)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3990253996:i=306:bd=all:rtra=on_2968 on theBenchmark for (2968ds/306Mi)
% 23.67/3.71 % (1439098)Instruction limit reached!
% 23.67/3.71 % (1439098)------------------------------
% 23.67/3.71 % (1439098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.67/3.71 % (1439098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.67/3.71 % (1439098)CaDiCaL version: 2.1.3
% 23.67/3.71 % (1439098)Termination reason: Instruction limit
% 23.67/3.71 % (1439098)Termination phase: Saturation
% 23.67/3.71 % (1439098)Time elapsed: 0.013 s
% 23.67/3.71 % (1439098)Peak memory usage: 11 MB
% 23.67/3.71 % (1439098)Instructions burned: 62 (million)
% 23.67/3.71 % (1439100)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=2787306447:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2968 on theBenchmark for (2968ds/262Mi)
% 23.67/3.71 % (1439103)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 23.67/3.71 % (1439103)ott+1002_16_sil=128000:si=on:random_seed=2312943584:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2968 on theBenchmark for (2968ds/409Mi)
% 23.67/3.71 % (1439088)Instruction limit reached!
% 23.67/3.71 % (1439088)------------------------------
% 23.67/3.71 % (1439088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.67/3.71 % (1439088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.67/3.71 % (1439088)CaDiCaL version: 2.1.3
% 23.67/3.71 % (1439088)Termination reason: Instruction limit
% 23.67/3.71 % (1439088)Termination phase: Saturation
% 24.23/3.84 % (1439088)Time elapsed: 0.404 s
% 24.23/3.84 % (1439088)Peak memory usage: 22 MB
% 24.23/3.84 % (1439088)Instructions burned: 960 (million)
% 24.23/3.84 % (1439106)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=2682992608:s2a=on:i=381:rtra=on_2967 on theBenchmark for (2967ds/381Mi)
% 24.23/3.84 % (1439103)Instruction limit reached!
% 24.23/3.84 % (1439103)------------------------------
% 24.23/3.84 % (1439103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.23/3.84 % (1439103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.23/3.84 % (1439103)CaDiCaL version: 2.1.3
% 24.23/3.84 % (1439103)Termination reason: Instruction limit
% 24.23/3.84 % (1439103)Termination phase: Saturation
% 24.23/3.84 % (1439103)Time elapsed: 0.094 s
% 24.23/3.84 % (1439103)Peak memory usage: 17 MB
% 24.23/3.84 % (1439103)Instructions burned: 412 (million)
% 24.23/3.84 % (1439100)Instruction limit reached!
% 24.23/3.84 % (1439100)------------------------------
% 24.23/3.84 % (1439100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.23/3.84 % (1439100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.23/3.84 % (1439100)CaDiCaL version: 2.1.3
% 24.23/3.84 % (1439100)Termination reason: Instruction limit
% 24.23/3.84 % (1439100)Termination phase: Saturation
% 24.23/3.84 % (1439100)Time elapsed: 0.114 s
% 24.23/3.84 % (1439100)Peak memory usage: 15 MB
% 24.23/3.84 % (1439100)Instructions burned: 263 (million)
% 24.23/3.84 % (1439108)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3586506901:cond=on:i=324:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/324Mi)
% 24.23/3.84 % (1439099)Instruction limit reached!
% 24.23/3.84 % (1439099)------------------------------
% 24.23/3.84 % (1439099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.23/3.84 % (1439099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.23/3.84 % (1439099)CaDiCaL version: 2.1.3
% 24.23/3.84 % (1439099)Termination reason: Instruction limit
% 24.23/3.84 % (1439099)Termination phase: Saturation
% 24.23/3.84 % (1439099)Time elapsed: 0.133 s
% 24.23/3.84 % (1439099)Peak memory usage: 16 MB
% 24.23/3.84 % (1439099)Instructions burned: 308 (million)
% 24.23/3.84 % (1439110)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=1256782943:i=240:kws=inv_precedence:rtra=on_2966 on theBenchmark for (2966ds/240Mi)
% 24.23/3.84 % (1439111)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 24.23/3.84 % (1439111)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1792719034:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/124Mi)
% 24.23/3.84 % (1439110)Refutation not found, incomplete strategy
% 24.23/3.84 % (1439110)------------------------------
% 24.23/3.84 % (1439110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.23/3.84 % (1439110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.23/3.84 % (1439110)CaDiCaL version: 2.1.3
% 24.23/3.84 % (1439110)Termination reason: Refutation not found, incomplete strategy
% 24.23/3.84 % (1439110)Time elapsed: 0.023 s
% 24.23/3.84 % (1439110)Peak memory usage: 13 MB
% 24.23/3.84 % (1439110)Instructions burned: 51 (million)
% 24.23/3.84 % (1439110)------------------------------
% 24.23/3.84 % (1439110)------------------------------
% 24.23/3.84 % (1439114)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=713819518:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2966 on theBenchmark for (2966ds/223Mi)
% 24.23/3.84 % (1439108)Instruction limit reached!
% 24.23/3.84 % (1439108)------------------------------
% 24.23/3.84 % (1439108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.23/3.84 % (1439108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.23/3.84 % (1439108)CaDiCaL version: 2.1.3
% 24.23/3.84 % (1439108)Termination reason: Instruction limit
% 24.23/3.84 % (1439108)Termination phase: Saturation
% 24.23/3.84 % (1439108)Time elapsed: 0.080 s
% 24.23/3.84 % (1439108)Peak memory usage: 13 MB
% 24.23/3.84 % (1439108)Instructions burned: 325 (million)
% 24.23/3.84 % (1439111)Instruction limit reached!
% 24.23/3.84 % (1439111)------------------------------
% 24.23/3.84 % (1439111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.23/3.84 % (1439111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.23/3.84 % (1439111)CaDiCaL version: 2.1.3
% 26.96/4.11 % (1439111)Termination reason: Instruction limit
% 26.96/4.11 % (1439111)Termination phase: Saturation
% 26.96/4.11 % (1439111)Time elapsed: 0.053 s
% 26.96/4.11 % (1439111)Peak memory usage: 13 MB
% 26.96/4.11 % (1439111)Instructions burned: 124 (million)
% 26.96/4.11 % (1439116)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1311987235:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2966 on theBenchmark for (2966ds/282Mi)
% 26.96/4.11 % (1439114)Refutation not found, incomplete strategy
% 26.96/4.11 % (1439114)------------------------------
% 26.96/4.11 % (1439114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.96/4.11 % (1439114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.96/4.11 % (1439114)CaDiCaL version: 2.1.3
% 26.96/4.11 % (1439114)Termination reason: Refutation not found, incomplete strategy
% 26.96/4.11 % (1439114)Time elapsed: 0.030 s
% 26.96/4.11 % (1439114)Peak memory usage: 13 MB
% 26.96/4.11 % (1439114)Instructions burned: 70 (million)
% 26.96/4.11 % (1439114)------------------------------
% 26.96/4.11 % (1439114)------------------------------
% 26.96/4.11 % (1439117)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=2666303398:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2965 on theBenchmark for (2965ds/464Mi)
% 26.96/4.11 % (1439119)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3823964218:i=88:s2at=3:nm=2:rtra=on:rawr=on_2965 on theBenchmark for (2965ds/88Mi)
% 26.96/4.11 % (1439117)Refutation not found, incomplete strategy
% 26.96/4.11 % (1439117)------------------------------
% 26.96/4.11 % (1439117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.96/4.11 % (1439117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.96/4.11 % (1439117)CaDiCaL version: 2.1.3
% 26.96/4.11 % (1439117)Termination reason: Refutation not found, incomplete strategy
% 26.96/4.11 % (1439117)Time elapsed: 0.015 s
% 26.96/4.11 % (1439117)Peak memory usage: 12 MB
% 26.96/4.11 % (1439117)Instructions burned: 33 (million)
% 26.96/4.11 % (1439117)------------------------------
% 26.96/4.11 % (1439117)------------------------------
% 26.96/4.11 % (1439096)Instruction limit reached!
% 26.96/4.11 % (1439096)------------------------------
% 26.96/4.11 % (1439096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.96/4.11 % (1439096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.96/4.11 % (1439096)CaDiCaL version: 2.1.3
% 26.96/4.11 % (1439096)Termination reason: Instruction limit
% 26.96/4.11 % (1439096)Termination phase: Saturation
% 26.96/4.11 % (1439096)Time elapsed: 0.361 s
% 26.96/4.11 % (1439096)Peak memory usage: 17 MB
% 26.96/4.11 % (1439096)Instructions burned: 877 (million)
% 26.96/4.11 % (1439122)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2231836168:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2965 on theBenchmark for (2965ds/280Mi)
% 26.96/4.11 % (1439106)Instruction limit reached!
% 26.96/4.11 % (1439106)------------------------------
% 26.96/4.11 % (1439106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.96/4.11 % (1439106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.96/4.11 % (1439106)CaDiCaL version: 2.1.3
% 26.96/4.11 % (1439106)Termination reason: Instruction limit
% 26.96/4.11 % (1439106)Termination phase: Saturation
% 26.96/4.11 % (1439106)Time elapsed: 0.165 s
% 26.96/4.11 % (1439106)Peak memory usage: 16 MB
% 26.96/4.11 % (1439123)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 26.96/4.11 % (1439106)Instructions burned: 382 (million)
% 26.96/4.11 % (1439123)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3477023650:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2965 on theBenchmark for (2965ds/4386Mi)
% 26.96/4.11 % (1439119)Instruction limit reached!
% 26.96/4.11 % (1439119)------------------------------
% 26.96/4.11 % (1439119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.96/4.11 % (1439119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.96/4.11 % (1439119)CaDiCaL version: 2.1.3
% 26.96/4.11 % (1439119)Termination reason: Instruction limit
% 26.96/4.11 % (1439119)Termination phase: Saturation
% 26.96/4.11 % (1439119)Time elapsed: 0.039 s
% 26.96/4.11 % (1439119)Peak memory usage: 13 MB
% 26.96/4.11 % (1439119)Instructions burned: 89 (million)
% 28.29/4.31 % (1439125)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 28.29/4.31 % (1439125)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 28.29/4.31 % (1439125)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=2010985689:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2965 on theBenchmark for (2965ds/483Mi)
% 28.29/4.31 % (1439127)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2402258604:i=73:rtra=on_2965 on theBenchmark for (2965ds/73Mi)
% 28.29/4.31 % (1439116)Instruction limit reached!
% 28.29/4.31 % (1439116)------------------------------
% 28.29/4.31 % (1439116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.29/4.31 % (1439116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.29/4.31 % (1439116)CaDiCaL version: 2.1.3
% 28.29/4.31 % (1439116)Termination reason: Instruction limit
% 28.29/4.31 % (1439116)Termination phase: Saturation
% 28.29/4.31 % (1439116)Time elapsed: 0.096 s
% 28.29/4.31 % (1439116)Peak memory usage: 15 MB
% 28.29/4.31 % (1439116)Instructions burned: 284 (million)
% 28.29/4.31 % (1439127)Instruction limit reached!
% 28.29/4.31 % (1439127)------------------------------
% 28.29/4.31 % (1439127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.29/4.31 % (1439127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.29/4.31 % (1439127)CaDiCaL version: 2.1.3
% 28.29/4.31 % (1439127)Termination reason: Instruction limit
% 28.29/4.31 % (1439127)Termination phase: Saturation
% 28.29/4.31 % (1439127)Time elapsed: 0.032 s
% 28.29/4.31 % (1439127)Peak memory usage: 13 MB
% 28.29/4.31 % (1439127)Instructions burned: 74 (million)
% 28.29/4.31 % (1439130)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1340762504:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2964 on theBenchmark for (2964ds/176Mi)
% 28.29/4.31 % (1439131)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 28.29/4.31 % (1439131)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=1975477857:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2964 on theBenchmark for (2964ds/39Mi)
% 28.29/4.31 % (1439131)Instruction limit reached!
% 28.29/4.31 % (1439131)------------------------------
% 28.29/4.31 % (1439131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.29/4.31 % (1439131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.29/4.31 % (1439131)CaDiCaL version: 2.1.3
% 28.29/4.31 % (1439131)Termination reason: Instruction limit
% 28.29/4.31 % (1439131)Termination phase: Saturation
% 28.29/4.31 % (1439131)Time elapsed: 0.016 s
% 28.29/4.31 % (1439131)Peak memory usage: 11 MB
% 28.29/4.31 % (1439131)Instructions burned: 39 (million)
% 28.29/4.31 % (1439122)Instruction limit reached!
% 28.29/4.31 % (1439122)------------------------------
% 28.29/4.31 % (1439122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.29/4.31 % (1439122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.29/4.31 % (1439122)CaDiCaL version: 2.1.3
% 28.29/4.31 % (1439122)Termination reason: Instruction limit
% 28.29/4.31 % (1439122)Termination phase: Saturation
% 28.29/4.31 % (1439122)Time elapsed: 0.115 s
% 28.29/4.31 % (1439122)Peak memory usage: 13 MB
% 28.29/4.31 % (1439122)Instructions burned: 282 (million)
% 28.29/4.31 % (1439134)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3352510013:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2964 on theBenchmark for (2964ds/708Mi)
% 28.29/4.31 % (1439135)WARNING Broken Constraint: if sine_to_age_tolerance(3) 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
% 28.29/4.31 % (1439135)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=1794714405:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2964 on theBenchmark for (2964ds/252Mi)
% 28.29/4.31 % (1439130)Instruction limit reached!
% 28.29/4.31 % (1439130)------------------------------
% 28.29/4.31 % (1439130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.69/4.48 % (1439130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.69/4.48 % (1439130)CaDiCaL version: 2.1.3
% 28.69/4.48 % (1439130)Termination reason: Instruction limit
% 28.69/4.48 % (1439130)Termination phase: Saturation
% 28.69/4.48 % (1439130)Time elapsed: 0.072 s
% 28.69/4.48 % (1439130)Peak memory usage: 13 MB
% 28.69/4.48 % (1439130)Instructions burned: 176 (million)
% 28.69/4.48 % (1439135)Refutation not found, incomplete strategy
% 28.69/4.48 % (1439135)------------------------------
% 28.69/4.48 % (1439135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.69/4.48 % (1439135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.69/4.48 % (1439135)CaDiCaL version: 2.1.3
% 28.69/4.48 % (1439135)Termination reason: Refutation not found, incomplete strategy
% 28.69/4.48 % (1439135)Time elapsed: 0.024 s
% 28.69/4.48 % (1439135)Peak memory usage: 13 MB
% 28.69/4.48 % (1439135)Instructions burned: 55 (million)
% 28.69/4.48 % (1439135)------------------------------
% 28.69/4.48 % (1439135)------------------------------
% 28.69/4.48 % (1439138)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=3554801378:i=823:fsr=off:rtra=on_2964 on theBenchmark for (2964ds/823Mi)
% 28.69/4.48 % (1439140)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 28.69/4.48 % (1439140)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=974974507:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2963 on theBenchmark for (2963ds/16202Mi)
% 28.69/4.48 % (1439078)Instruction limit reached!
% 28.69/4.48 % (1439078)------------------------------
% 28.69/4.48 % (1439078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.69/4.48 % (1439078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.69/4.48 % (1439078)CaDiCaL version: 2.1.3
% 28.69/4.48 % (1439078)Termination reason: Instruction limit
% 28.69/4.48 % (1439078)Termination phase: Saturation
% 28.69/4.48 % (1439078)Time elapsed: 1.024 s
% 28.69/4.48 % (1439078)Peak memory usage: 21 MB
% 28.69/4.48 % (1439078)Instructions burned: 2241 (million)
% 28.69/4.48 % (1439142)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=1286279826:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2962 on theBenchmark for (2962ds/300Mi)
% 28.69/4.48 % (1439125)Instruction limit reached!
% 28.69/4.48 % (1439125)------------------------------
% 28.69/4.48 % (1439125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.69/4.48 % (1439125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.69/4.48 % (1439125)CaDiCaL version: 2.1.3
% 28.69/4.48 % (1439125)Termination reason: Instruction limit
% 28.69/4.48 % (1439125)Termination phase: Saturation
% 28.69/4.48 % (1439125)Time elapsed: 0.290 s
% 28.69/4.48 % (1439125)Peak memory usage: 16 MB
% 28.69/4.48 % (1439125)Instructions burned: 484 (million)
% 28.69/4.48 % (1439144)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 28.69/4.48 % (1439144)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 28.69/4.48 % (1439144)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=3383807135:i=177:add=on:bd=preordered:rtra=on:rawr=on_2962 on theBenchmark for (2962ds/177Mi)
% 28.69/4.48 % (1439142)Instruction limit reached!
% 28.69/4.48 % (1439142)------------------------------
% 28.69/4.48 % (1439142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.69/4.48 % (1439142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.69/4.48 % (1439142)CaDiCaL version: 2.1.3
% 28.69/4.48 % (1439142)Termination reason: Instruction limit
% 28.69/4.48 % (1439142)Termination phase: Saturation
% 28.69/4.48 % (1439142)Time elapsed: 0.131 s
% 28.69/4.48 % (1439142)Peak memory usage: 14 MB
% 28.69/4.48 % (1439142)Instructions burned: 302 (million)
% 28.69/4.48 % (1439144)Instruction limit reached!
% 28.69/4.48 % (1439144)------------------------------
% 28.69/4.48 % (1439144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.69/4.48 % (1439144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.69/4.48 % (1439144)CaDiCaL version: 2.1.3
% 28.69/4.48 % (1439144)Termination reason: Instruction limit
% 28.69/4.48 % (1439144)Termination phase: Saturation
% 28.69/4.48 % (1439144)Time elapsed: 0.078 s
% 31.74/5.02 % (1439144)Peak memory usage: 15 MB
% 31.74/5.02 % (1439144)Instructions burned: 179 (million)
% 31.74/5.02 % (1439146)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=4148894165:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2961 on theBenchmark for (2961ds/715Mi)
% 31.74/5.02 % (1439134)Instruction limit reached!
% 31.74/5.02 % (1439134)------------------------------
% 31.74/5.02 % (1439134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.74/5.02 % (1439134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.74/5.02 % (1439134)CaDiCaL version: 2.1.3
% 31.74/5.02 % (1439134)Termination reason: Instruction limit
% 31.74/5.02 % (1439134)Termination phase: Saturation
% 31.74/5.02 % (1439134)Time elapsed: 0.311 s
% 31.74/5.02 % (1439134)Peak memory usage: 20 MB
% 31.74/5.02 % (1439134)Instructions burned: 708 (million)
% 31.74/5.02 % (1439148)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 31.74/5.02 % (1439148)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 31.74/5.02 % (1439146)Refutation not found, incomplete strategy
% 31.74/5.02 % (1439146)------------------------------
% 31.74/5.02 % (1439146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.74/5.02 % (1439146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.74/5.02 % (1439146)CaDiCaL version: 2.1.3
% 31.74/5.02 % (1439146)Termination reason: Refutation not found, incomplete strategy
% 31.74/5.02 % (1439146)Time elapsed: 0.015 s
% 31.74/5.02 % (1439146)Peak memory usage: 12 MB
% 31.74/5.02 % (1439146)Instructions burned: 34 (million)
% 31.74/5.02 % (1439146)------------------------------
% 31.74/5.02 % (1439146)------------------------------
% 31.74/5.02 % (1439148)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=1655862985:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2961 on theBenchmark for (2961ds/230Mi)
% 31.74/5.02 % (1439150)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 31.74/5.02 % (1439148)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 31.74/5.02 % (1439149)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=525325983:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2961 on theBenchmark for (2961ds/606Mi)
% 31.74/5.02 % (1439150)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=1086913734:lrd=on:i=841:nm=0:rtra=on_2961 on theBenchmark for (2961ds/841Mi)
% 31.74/5.02 % (1439148)Instruction limit reached!
% 31.74/5.02 % (1439148)------------------------------
% 31.74/5.02 % (1439148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.74/5.02 % (1439148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.74/5.02 % (1439148)CaDiCaL version: 2.1.3
% 31.74/5.02 % (1439148)Termination reason: Instruction limit
% 31.74/5.02 % (1439148)Termination phase: Saturation
% 31.74/5.02 % (1439148)Time elapsed: 0.118 s
% 31.74/5.02 % (1439148)Peak memory usage: 15 MB
% 31.74/5.02 % (1439148)Instructions burned: 231 (million)
% 31.74/5.02 % (1439138)Instruction limit reached!
% 31.74/5.02 % (1439138)------------------------------
% 31.74/5.02 % (1439138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.74/5.02 % (1439138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.74/5.02 % (1439138)CaDiCaL version: 2.1.3
% 31.74/5.02 % (1439138)Termination reason: Instruction limit
% 31.74/5.02 % (1439138)Termination phase: Saturation
% 31.74/5.02 % (1439138)Time elapsed: 0.396 s
% 31.74/5.02 % (1439138)Peak memory usage: 15 MB
% 31.74/5.02 % (1439138)Instructions burned: 824 (million)
% 31.74/5.02 % (1439154)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2754641856:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2959 on theBenchmark for (2959ds/445Mi)
% 31.74/5.02 % (1439155)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=1217417095:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2959 on theBenchmark for (2959ds/71Mi)
% 31.74/5.02 % (1439155)Instruction limit reached!
% 31.74/5.02 % (1439155)------------------------------
% 31.74/5.02 % (1439155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.80/5.24 % (1439155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.80/5.24 % (1439155)CaDiCaL version: 2.1.3
% 34.80/5.24 % (1439155)Termination reason: Instruction limit
% 34.80/5.24 % (1439155)Termination phase: Saturation
% 34.80/5.24 % (1439155)Time elapsed: 0.032 s
% 34.80/5.24 % (1439155)Peak memory usage: 13 MB
% 34.80/5.24 % (1439155)Instructions burned: 71 (million)
% 34.80/5.24 % (1439158)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
% 34.80/5.24 % (1439158)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 34.80/5.24 % (1439158)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1863776455:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2959 on theBenchmark for (2959ds/100Mi)
% 34.80/5.24 % (1439158)Instruction limit reached!
% 34.80/5.24 % (1439158)------------------------------
% 34.80/5.24 % (1439158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.80/5.24 % (1439158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.80/5.24 % (1439158)CaDiCaL version: 2.1.3
% 34.80/5.24 % (1439158)Termination reason: Instruction limit
% 34.80/5.24 % (1439158)Termination phase: Saturation
% 34.80/5.24 % (1439158)Time elapsed: 0.043 s
% 34.80/5.24 % (1439158)Peak memory usage: 13 MB
% 34.80/5.24 % (1439158)Instructions burned: 101 (million)
% 34.80/5.24 % (1439160)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 34.80/5.24 % (1439160)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=3915030844:i=1352:add=on:aac=none:rtra=on_2958 on theBenchmark for (2958ds/1352Mi)
% 34.80/5.24 % (1439149)Instruction limit reached!
% 34.80/5.24 % (1439149)------------------------------
% 34.80/5.24 % (1439149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.80/5.24 % (1439149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.80/5.24 % (1439149)CaDiCaL version: 2.1.3
% 34.80/5.24 % (1439149)Termination reason: Instruction limit
% 34.80/5.24 % (1439149)Termination phase: Saturation
% 34.80/5.24 % (1439149)Time elapsed: 0.261 s
% 34.80/5.24 % (1439149)Peak memory usage: 19 MB
% 34.80/5.24 % (1439149)Instructions burned: 608 (million)
% 34.80/5.24 % (1439160)Refutation not found, incomplete strategy
% 34.80/5.24 % (1439160)------------------------------
% 34.80/5.24 % (1439160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.80/5.24 % (1439160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.80/5.24 % (1439160)CaDiCaL version: 2.1.3
% 34.80/5.24 % (1439160)Termination reason: Refutation not found, incomplete strategy
% 34.80/5.24 % (1439160)Time elapsed: 0.029 s
% 34.80/5.24 % (1439160)Peak memory usage: 13 MB
% 34.80/5.24 % (1439160)Instructions burned: 61 (million)
% 34.80/5.24 % (1439160)------------------------------
% 34.80/5.24 % (1439160)------------------------------
% 34.80/5.24 % (1439162)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=1546664458:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2958 on theBenchmark for (2958ds/646Mi)
% 34.80/5.24 % (1439163)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=518404442:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2958 on theBenchmark for (2958ds/1924Mi)
% 34.80/5.24 % (1439154)Instruction limit reached!
% 34.80/5.24 % (1439154)------------------------------
% 34.80/5.24 % (1439154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.80/5.24 % (1439154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.80/5.24 % (1439154)CaDiCaL version: 2.1.3
% 34.80/5.24 % (1439154)Termination reason: Instruction limit
% 34.80/5.24 % (1439154)Termination phase: Saturation
% 34.80/5.24 % (1439154)Time elapsed: 0.193 s
% 34.80/5.24 % (1439154)Peak memory usage: 17 MB
% 34.80/5.24 % (1439154)Instructions burned: 445 (million)
% 34.80/5.24 % (1439166)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=2868110635:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2957 on theBenchmark for (2957ds/984Mi)
% 35.81/5.49 % (1439150)Instruction limit reached!
% 35.81/5.49 % (1439150)------------------------------
% 35.81/5.49 % (1439150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.81/5.49 % (1439150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.81/5.49 % (1439150)CaDiCaL version: 2.1.3
% 35.81/5.49 % (1439150)Termination reason: Instruction limit
% 35.81/5.49 % (1439150)Termination phase: Saturation
% 35.81/5.49 % (1439150)Time elapsed: 0.347 s
% 35.81/5.49 % (1439150)Peak memory usage: 20 MB
% 35.81/5.49 % (1439150)Instructions burned: 842 (million)
% 35.81/5.49 % (1439168)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=1816995979:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2957 on theBenchmark for (2957ds/592Mi)
% 35.81/5.49 % (1439162)Instruction limit reached!
% 35.81/5.49 % (1439162)------------------------------
% 35.81/5.49 % (1439162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.81/5.49 % (1439162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.81/5.49 % (1439162)CaDiCaL version: 2.1.3
% 35.81/5.49 % (1439162)Termination reason: Instruction limit
% 35.81/5.49 % (1439162)Termination phase: Saturation
% 35.81/5.49 % (1439162)Time elapsed: 0.289 s
% 35.81/5.49 % (1439162)Peak memory usage: 18 MB
% 35.81/5.49 % (1439162)Instructions burned: 648 (million)
% 35.81/5.49 % (1439170)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=1665662818:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2955 on theBenchmark for (2955ds/872Mi)
% 35.81/5.49 % (1439168)Instruction limit reached!
% 35.81/5.49 % (1439168)------------------------------
% 35.81/5.49 % (1439168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.81/5.49 % (1439168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.81/5.49 % (1439168)CaDiCaL version: 2.1.3
% 35.81/5.49 % (1439168)Termination reason: Instruction limit
% 35.81/5.49 % (1439168)Termination phase: Saturation
% 35.81/5.49 % (1439168)Time elapsed: 0.254 s
% 35.81/5.49 % (1439168)Peak memory usage: 18 MB
% 35.81/5.49 % (1439168)Instructions burned: 594 (million)
% 35.81/5.49 % (1439172)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 35.81/5.49 % (1439172)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3486894364:i=999:add=on:rtra=on_2954 on theBenchmark for (2954ds/999Mi)
% 35.81/5.49 % (1439166)Instruction limit reached!
% 35.81/5.49 % (1439166)------------------------------
% 35.81/5.49 % (1439166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.81/5.49 % (1439166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.81/5.49 % (1439166)CaDiCaL version: 2.1.3
% 35.81/5.49 % (1439166)Termination reason: Instruction limit
% 35.81/5.49 % (1439166)Termination phase: Saturation
% 35.81/5.49 % (1439166)Time elapsed: 0.413 s
% 35.81/5.49 % (1439166)Peak memory usage: 21 MB
% 35.81/5.49 % (1439166)Instructions burned: 985 (million)
% 35.81/5.49 % (1439174)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 35.81/5.49 % (1439174)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=488072941:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2953 on theBenchmark for (2953ds/244Mi)
% 35.81/5.49 % (1439174)Refutation not found, incomplete strategy
% 35.81/5.49 % (1439174)------------------------------
% 35.81/5.49 % (1439174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.81/5.49 % (1439174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.81/5.49 % (1439174)CaDiCaL version: 2.1.3
% 35.81/5.49 % (1439174)Termination reason: Refutation not found, incomplete strategy
% 35.81/5.49 % (1439174)Time elapsed: 0.024 s
% 35.81/5.49 % (1439174)Peak memory usage: 13 MB
% 35.81/5.49 % (1439174)Instructions burned: 54 (million)
% 35.81/5.49 % (1439174)------------------------------
% 35.81/5.49 % (1439174)------------------------------
% 35.81/5.49 % (1439176)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=675413362:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2952 on theBenchmark for (2952ds/113Mi)
% 35.81/5.49 % (1439176)Instruction limit reached!
% 35.81/5.49 % (1439176)------------------------------
% 35.81/5.49 % (1439176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.37/5.99 % (1439176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.37/5.99 % (1439176)CaDiCaL version: 2.1.3
% 37.37/5.99 % (1439176)Termination reason: Instruction limit
% 37.37/5.99 % (1439176)Termination phase: Saturation
% 37.37/5.99 % (1439176)Time elapsed: 0.049 s
% 37.37/5.99 % (1439176)Peak memory usage: 13 MB
% 37.37/5.99 % (1439176)Instructions burned: 115 (million)
% 37.37/5.99 % (1439178)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3508558453:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2952 on theBenchmark for (2952ds/7795Mi)
% 37.37/5.99 % (1439178)Refutation not found, incomplete strategy
% 37.37/5.99 % (1439178)------------------------------
% 37.37/5.99 % (1439178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.37/5.99 % (1439178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.37/5.99 % (1439178)CaDiCaL version: 2.1.3
% 37.37/5.99 % (1439178)Termination reason: Refutation not found, incomplete strategy
% 37.37/5.99 % (1439178)Time elapsed: 0.012 s
% 37.37/5.99 % (1439178)Peak memory usage: 12 MB
% 37.37/5.99 % (1439178)Instructions burned: 26 (million)
% 37.37/5.99 % (1439178)------------------------------
% 37.37/5.99 % (1439178)------------------------------
% 37.37/5.99 % (1439180)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2750942797:st=2:i=5026:sd=1:rtra=on:ss=axioms_2951 on theBenchmark for (2951ds/5026Mi)
% 37.37/5.99 % (1439163)Instruction limit reached!
% 37.37/5.99 % (1439163)------------------------------
% 37.37/5.99 % (1439163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.37/5.99 % (1439163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.37/5.99 % (1439163)CaDiCaL version: 2.1.3
% 37.37/5.99 % (1439163)Termination reason: Instruction limit
% 37.37/5.99 % (1439163)Termination phase: Saturation
% 37.37/5.99 % (1439163)Time elapsed: 0.655 s
% 37.37/5.99 % (1439163)Peak memory usage: 30 MB
% 37.37/5.99 % (1439163)Instructions burned: 1925 (million)
% 37.37/5.99 % (1439182)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 37.37/5.99 % (1439182)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=9262830:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2951 on theBenchmark for (2951ds/763Mi)
% 37.37/5.99 % (1439182)Refutation not found, incomplete strategy
% 37.37/5.99 % (1439182)------------------------------
% 37.37/5.99 % (1439182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.37/5.99 % (1439182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.37/5.99 % (1439182)CaDiCaL version: 2.1.3
% 37.37/5.99 % (1439182)Termination reason: Refutation not found, incomplete strategy
% 37.37/5.99 % (1439182)Time elapsed: 0.007 s
% 37.37/5.99 % (1439182)Peak memory usage: 12 MB
% 37.37/5.99 % (1439182)Instructions burned: 29 (million)
% 37.37/5.99 % (1439182)------------------------------
% 37.37/5.99 % (1439182)------------------------------
% 37.37/5.99 % (1439184)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=613957686:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2951 on theBenchmark for (2951ds/1144Mi)
% 37.37/5.99 % (1439170)Instruction limit reached!
% 37.37/5.99 % (1439170)------------------------------
% 37.37/5.99 % (1439170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.37/5.99 % (1439170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.37/5.99 % (1439170)CaDiCaL version: 2.1.3
% 37.37/5.99 % (1439170)Termination reason: Instruction limit
% 37.37/5.99 % (1439170)Termination phase: Saturation
% 37.37/5.99 % (1439170)Time elapsed: 0.449 s
% 37.37/5.99 % (1439170)Peak memory usage: 20 MB
% 37.37/5.99 % (1439170)Instructions burned: 873 (million)
% 37.37/5.99 % (1439186)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 37.37/5.99 % (1439186)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=3051444491:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2950 on theBenchmark for (2950ds/52Mi)
% 37.37/5.99 % (1439186)Instruction limit reached!
% 37.37/5.99 % (1439186)------------------------------
% 37.37/5.99 % (1439186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.02/6.41 % (1439186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.02/6.41 % (1439186)CaDiCaL version: 2.1.3
% 43.02/6.41 % (1439186)Termination reason: Instruction limit
% 43.02/6.41 % (1439186)Termination phase: Saturation
% 43.02/6.41 % (1439186)Time elapsed: 0.024 s
% 43.02/6.41 % (1439186)Peak memory usage: 12 MB
% 43.02/6.41 % (1439186)Instructions burned: 54 (million)
% 43.02/6.41 % (1439188)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=4088520217:i=1724:fsr=off:rtra=on:fe=abstraction_2950 on theBenchmark for (2950ds/1724Mi)
% 43.02/6.41 % (1439172)Instruction limit reached!
% 43.02/6.41 % (1439172)------------------------------
% 43.02/6.41 % (1439172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.02/6.41 % (1439172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.02/6.41 % (1439172)CaDiCaL version: 2.1.3
% 43.02/6.41 % (1439172)Termination reason: Instruction limit
% 43.02/6.41 % (1439172)Termination phase: Saturation
% 43.02/6.41 % (1439172)Time elapsed: 0.482 s
% 43.02/6.41 % (1439172)Peak memory usage: 18 MB
% 43.02/6.41 % (1439172)Instructions burned: 1000 (million)
% 43.02/6.41 % (1439190)dis-1004_128_to=kbo:sil=128000:tgt=full:si=on:fdtod=off:sp=const_frequency:spb=goal:uwa=off:slsqc=3:slsq=on:random_seed=2786095874:i=439:add=on:slsql=off:rtra=on:ntd=on_2949 on theBenchmark for (2949ds/439Mi)
% 43.02/6.41 % (1439184)Instruction limit reached!
% 43.02/6.41 % (1439184)------------------------------
% 43.02/6.41 % (1439184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.02/6.41 % (1439184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.02/6.41 % (1439184)CaDiCaL version: 2.1.3
% 43.02/6.41 % (1439184)Termination reason: Instruction limit
% 43.02/6.41 % (1439184)Termination phase: Saturation
% 43.02/6.41 % (1439184)Time elapsed: 0.259 s
% 43.02/6.41 % (1439184)Peak memory usage: 25 MB
% 43.02/6.41 % (1439184)Instructions burned: 1147 (million)
% 43.02/6.41 % (1439192)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1191256040:i=6395:sd=1:rtra=on:ss=axioms_2948 on theBenchmark for (2948ds/6395Mi)
% 43.02/6.41 % (1439192)Refutation not found, incomplete strategy
% 43.02/6.41 % (1439192)------------------------------
% 43.02/6.41 % (1439192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.02/6.41 % (1439192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.02/6.41 % (1439192)CaDiCaL version: 2.1.3
% 43.02/6.41 % (1439192)Termination reason: Refutation not found, incomplete strategy
% 43.02/6.41 % (1439192)Time elapsed: 0.007 s
% 43.02/6.41 % (1439192)Peak memory usage: 12 MB
% 43.02/6.41 % (1439192)Instructions burned: 27 (million)
% 43.02/6.41 % (1439192)------------------------------
% 43.02/6.41 % (1439192)------------------------------
% 43.02/6.41 % (1439194)WARNING Broken Constraint: if ho_split_queue_lambda_weight(5) has been set then ho_split_queue(off) is equal to on
% 43.02/6.41 % (1439194)ott+2_16:1_sil=128000:si=on:hsqlw=5:sos=on:urr=on:bce=on:uwa=off:random_seed=3666485763:i=6762:add=off:bd=all:rtra=on:ss=axioms:ntd=on_2948 on theBenchmark for (2948ds/6762Mi)
% 43.02/6.41 % (1439194)Refutation not found, incomplete strategy
% 43.02/6.41 % (1439194)------------------------------
% 43.02/6.41 % (1439194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.02/6.41 % (1439194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.02/6.41 % (1439194)CaDiCaL version: 2.1.3
% 43.02/6.41 % (1439194)Termination reason: Refutation not found, incomplete strategy
% 43.02/6.41 % (1439194)Time elapsed: 0.006 s
% 43.02/6.41 % (1439194)Peak memory usage: 12 MB
% 43.02/6.41 % (1439194)Instructions burned: 27 (million)
% 43.02/6.41 % (1439194)------------------------------
% 43.02/6.41 % (1439194)------------------------------
% 43.02/6.41 % (1439196)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 43.02/6.41 % (1439196)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=3113642379:s2a=on:i=376:add=on:rtra=on:fe=axiom:fdi=1024_2948 on theBenchmark for (2948ds/376Mi)
% 43.02/6.41 % (1439190)Instruction limit reached!
% 43.02/6.41 % (1439190)------------------------------
% 43.02/6.41 % (1439190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.02/6.41 % (1439190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.02/6.41 % (1439190)CaDiCaL version: 2.1.3
% 44.66/6.83 % (1439190)Termination reason: Instruction limit
% 44.66/6.83 % (1439190)Termination phase: Saturation
% 44.66/6.83 % (1439190)Time elapsed: 0.193 s
% 44.66/6.83 % (1439190)Peak memory usage: 16 MB
% 44.66/6.83 % (1439190)Instructions burned: 441 (million)
% 44.66/6.83 % (1439198)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=2911463293:i=965:bd=all:ins=4:rtra=on_2947 on theBenchmark for (2947ds/965Mi)
% 44.66/6.83 % (1439196)Instruction limit reached!
% 44.66/6.83 % (1439196)------------------------------
% 44.66/6.83 % (1439196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.66/6.83 % (1439196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.66/6.83 % (1439196)CaDiCaL version: 2.1.3
% 44.66/6.83 % (1439196)Termination reason: Instruction limit
% 44.66/6.83 % (1439196)Termination phase: Saturation
% 44.66/6.83 % (1439196)Time elapsed: 0.096 s
% 44.66/6.83 % (1439196)Peak memory usage: 14 MB
% 44.66/6.83 % (1439196)Instructions burned: 377 (million)
% 44.66/6.83 % (1439200)lrs+10_1_sil=128000:si=on:urr=on:random_seed=148348215:i=5013:sd=1:rtra=on:ss=axioms:sgt=64_2947 on theBenchmark for (2947ds/5013Mi)
% 44.66/6.83 % (1439123)Instruction limit reached!
% 44.66/6.83 % (1439123)------------------------------
% 44.66/6.83 % (1439123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.66/6.83 % (1439123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.66/6.83 % (1439123)CaDiCaL version: 2.1.3
% 44.66/6.83 % (1439123)Termination reason: Instruction limit
% 44.66/6.83 % (1439123)Termination phase: Saturation
% 44.66/6.83 % (1439123)Time elapsed: 1.843 s
% 44.66/6.83 % (1439123)Peak memory usage: 17 MB
% 44.66/6.83 % (1439123)Instructions burned: 4388 (million)
% 44.66/6.83 % (1439202)dis+2_1_tgt=full:si=on:uwa=one_side_interpreted:random_seed=2143143320:i=1583:kws=inv_frequency:bd=preordered:nm=0:rtra=on_2946 on theBenchmark for (2946ds/1583Mi)
% 44.66/6.83 % (1439198)Instruction limit reached!
% 44.66/6.83 % (1439198)------------------------------
% 44.66/6.83 % (1439198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.66/6.83 % (1439198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.66/6.83 % (1439198)CaDiCaL version: 2.1.3
% 44.66/6.83 % (1439198)Termination reason: Instruction limit
% 44.66/6.83 % (1439198)Termination phase: Saturation
% 44.66/6.83 % (1439198)Time elapsed: 0.448 s
% 44.66/6.83 % (1439198)Peak memory usage: 16 MB
% 44.66/6.83 % (1439198)Instructions burned: 965 (million)
% 44.66/6.83 % (1439090)Instruction limit reached!
% 44.66/6.83 % (1439090)------------------------------
% 44.66/6.83 % (1439090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 44.66/6.83 % (1439090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 44.66/6.83 % (1439090)CaDiCaL version: 2.1.3
% 44.66/6.83 % (1439090)Termination reason: Instruction limit
% 44.66/6.83 % (1439090)Termination phase: Saturation
% 44.66/6.83 % (1439090)Time elapsed: 2.770 s
% 44.66/6.83 % (1439090)Peak memory usage: 66 MB
% 44.66/6.83 % (1439090)Instructions burned: 6359 (million)
% 44.66/6.83 % (1439204)WARNING Broken Constraint: if sine_level_split_queue_ratios(1,32) has been set then sine_level_split_queue(off) is equal to on
% 44.66/6.83 % (1439204)WARNING Broken Constraint: if ho_split_queue_cutoffs(2) has been set then ho_split_queue(off) is equal to on
% 44.66/6.83 % (1439204)WARNING Broken Constraint: if sine_to_age_generality_threshold(16) 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
% 44.66/6.83 % (1439204)WARNING Broken Constraint: if ho_split_queue_ratios(4,1) has been set then ho_split_queue(off) is equal to on
% 44.66/6.83 % (1439204)ott+1002_1_slsqr=1,32:sil=128000:fde=none:e2e=on:hsqc=2:si=on:sp=const_min:sos=on:uwa=interpreted_only:s2agt=16:chr=on:random_seed=1943085275:hsqr=4,1:avsq=on:cond=on:i=1774:add=on:avsqr=1,16:kws=arity_squared:nm=120:rtra=on:fe=abstraction:ss=axioms_2942 on theBenchmark for (2942ds/1774Mi)
% 44.66/6.83 % (1439205)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=845414743:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2942 on theBenchmark for (2942ds/515Mi)
% 44.66/6.83 % (1439204)Refutation not found, incomplete strategy
% 44.66/6.83 % (1439204)------------------------------
% 44.66/6.83 % (1439204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.07/7.29 % (1439204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.07/7.29 % (1439204)CaDiCaL version: 2.1.3
% 49.07/7.29 % (1439204)Termination reason: Refutation not found, incomplete strategy
% 49.07/7.29 % (1439204)Time elapsed: 0.012 s
% 49.07/7.29 % (1439204)Peak memory usage: 12 MB
% 49.07/7.29 % (1439204)Instructions burned: 26 (million)
% 49.07/7.29 % (1439204)------------------------------
% 49.07/7.29 % (1439204)------------------------------
% 49.07/7.29 % (1439208)WARNING Broken Constraint: if sine_to_age_generality_threshold(60) 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
% 49.07/7.29 % (1439208)lrs-30_5:1_sil=128000:drc=off:sas=cadical:si=on:lma=off:cbe=off:uwa=one_side_interpreted:s2agt=60:lwlo=on:random_seed=225230904:avsq=on:i=1297:add=on:avsqr=1,8:rtra=on:fsd=on_2942 on theBenchmark for (2942ds/1297Mi)
% 49.07/7.29 % (1439188)Instruction limit reached!
% 49.07/7.29 % (1439188)------------------------------
% 49.07/7.29 % (1439188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.07/7.29 % (1439188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.07/7.29 % (1439188)CaDiCaL version: 2.1.3
% 49.07/7.29 % (1439188)Termination reason: Instruction limit
% 49.07/7.29 % (1439188)Termination phase: Saturation
% 49.07/7.29 % (1439188)Time elapsed: 0.873 s
% 49.07/7.29 % (1439188)Peak memory usage: 22 MB
% 49.07/7.29 % (1439188)Instructions burned: 1725 (million)
% 49.07/7.29 % (1439210)dis+1002_1_to=lpo:drc=ordering:fde=none:bsd=on:si=on:ser=on:sp=const_min:cbe=off:uwa=off:flr=on:random_seed=2130889057:s2a=on:i=611:rtra=on:gsp=on_2941 on theBenchmark for (2941ds/611Mi)
% 49.07/7.29 % (1439210)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 49.07/7.29 % (1439205)Instruction limit reached!
% 49.07/7.29 % (1439205)------------------------------
% 49.07/7.29 % (1439205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.07/7.29 % (1439205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.07/7.29 % (1439205)CaDiCaL version: 2.1.3
% 49.07/7.29 % (1439205)Termination reason: Instruction limit
% 49.07/7.29 % (1439205)Termination phase: Saturation
% 49.07/7.29 % (1439205)Time elapsed: 0.216 s
% 49.07/7.29 % (1439205)Peak memory usage: 18 MB
% 49.07/7.29 % (1439205)Instructions burned: 517 (million)
% 49.07/7.29 % (1439212)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 49.07/7.29 % (1439212)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3953060219:i=72:bd=all:rtra=on_2940 on theBenchmark for (2940ds/72Mi)
% 49.07/7.29 % (1439202)Instruction limit reached!
% 49.07/7.29 % (1439202)------------------------------
% 49.07/7.29 % (1439202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.07/7.29 % (1439202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.07/7.29 % (1439202)CaDiCaL version: 2.1.3
% 49.07/7.29 % (1439202)Termination reason: Instruction limit
% 49.07/7.29 % (1439202)Termination phase: Saturation
% 49.07/7.29 % (1439202)Time elapsed: 0.668 s
% 49.07/7.29 % (1439202)Peak memory usage: 26 MB
% 49.07/7.29 % (1439202)Instructions burned: 1585 (million)
% 49.07/7.29 % (1439212)Instruction limit reached!
% 49.07/7.29 % (1439212)------------------------------
% 49.07/7.29 % (1439212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 49.07/7.29 % (1439212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 49.07/7.29 % (1439212)CaDiCaL version: 2.1.3
% 49.07/7.29 % (1439212)Termination reason: Instruction limit
% 49.07/7.29 % (1439212)Termination phase: Saturation
% 49.07/7.29 % (1439212)Time elapsed: 0.031 s
% 49.07/7.29 % (1439212)Peak memory usage: 12 MB
% 49.07/7.29 % (1439212)Instructions burned: 74 (million)
% 49.07/7.29 % (1439214)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3699289008:hsq=on:hsqr=16,1:s2a=on:i=6580:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2939 on theBenchmark for (2939ds/6580Mi)
% 49.07/7.29 % (1439215)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=1663080105:i=6209:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2939 on theBenchmark for (2939ds/6209Mi)
% 49.07/7.29 % (1439210)Instruction limit reached!
% 49.07/7.29 % (1439210)------------------------------
% 49.07/7.29 % (1439210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.19/8.14 % (1439210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.19/8.14 % (1439210)CaDiCaL version: 2.1.3
% 55.19/8.14 % (1439210)Termination reason: Instruction limit
% 55.19/8.14 % (1439210)Termination phase: Saturation
% 55.19/8.14 % (1439210)Time elapsed: 0.256 s
% 55.19/8.14 % (1439210)Peak memory usage: 17 MB
% 55.19/8.14 % (1439210)Instructions burned: 613 (million)
% 55.19/8.14 % (1439218)lrs+1002_14_sil=128000:e2e=on:si=on:urr=on:nwc=1.2:random_seed=1346432263:cond=fast:i=1003:bd=all:fsr=off:rtra=on:sup=off_2938 on theBenchmark for (2938ds/1003Mi)
% 55.19/8.14 % (1439208)Instruction limit reached!
% 55.19/8.14 % (1439208)------------------------------
% 55.19/8.14 % (1439208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.19/8.14 % (1439208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.19/8.14 % (1439208)CaDiCaL version: 2.1.3
% 55.19/8.14 % (1439208)Termination reason: Instruction limit
% 55.19/8.14 % (1439208)Termination phase: Saturation
% 55.19/8.14 % (1439208)Time elapsed: 0.551 s
% 55.19/8.14 % (1439208)Peak memory usage: 24 MB
% 55.19/8.14 % (1439208)Instructions burned: 1298 (million)
% 55.19/8.14 % (1439220)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 55.19/8.14 % (1439220)ott+1002_16_sil=128000:si=on:random_seed=996800138:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2936 on theBenchmark for (2936ds/409Mi)
% 55.19/8.14 % (1439200)Instruction limit reached!
% 55.19/8.14 % (1439200)------------------------------
% 55.19/8.14 % (1439200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.19/8.14 % (1439200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.19/8.14 % (1439200)CaDiCaL version: 2.1.3
% 55.19/8.14 % (1439200)Termination reason: Instruction limit
% 55.19/8.14 % (1439200)Termination phase: Saturation
% 55.19/8.14 % (1439200)Time elapsed: 1.154 s
% 55.19/8.14 % (1439200)Peak memory usage: 57 MB
% 55.19/8.14 % (1439200)Instructions burned: 5013 (million)
% 55.19/8.14 % (1439222)ott+10_1024_sil=128000:tgt=ground:cnfonf=lazy_pi_sigma_gen:si=on:sp=const_frequency:sos=on:lma=off:bsr=on:uwa=one_side_interpreted:nwc=20:random_seed=2563094597:cond=on:i=403:kws=precedence:erml=3:bs=unit_only:bd=all:rtra=on:ss=axioms:er=known:ntd=on_2935 on theBenchmark for (2935ds/403Mi)
% 55.19/8.14 % (1439222)Refutation not found, incomplete strategy
% 55.19/8.14 % (1439222)------------------------------
% 55.19/8.14 % (1439222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.19/8.14 % (1439222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.19/8.14 % (1439222)CaDiCaL version: 2.1.3
% 55.19/8.14 % (1439222)Termination reason: Refutation not found, incomplete strategy
% 55.19/8.14 % (1439222)Time elapsed: 0.014 s
% 55.19/8.14 % (1439222)Peak memory usage: 12 MB
% 55.19/8.14 % (1439222)Instructions burned: 30 (million)
% 55.19/8.14 % (1439222)------------------------------
% 55.19/8.14 % (1439222)------------------------------
% 55.19/8.14 % (1439224)lrs+10_1_sil=128000:fde=none:cnfonf=lazy_pi_sigma_gen:si=on:random_seed=568546515:st=2:i=6843:sd=2:bd=all:rtra=on:sup=off:ss=axioms_2934 on theBenchmark for (2934ds/6843Mi)
% 55.19/8.14 % (1439220)Instruction limit reached!
% 55.19/8.14 % (1439220)------------------------------
% 55.19/8.14 % (1439220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.19/8.14 % (1439220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.19/8.14 % (1439220)CaDiCaL version: 2.1.3
% 55.19/8.14 % (1439220)Termination reason: Instruction limit
% 55.19/8.14 % (1439220)Termination phase: Saturation
% 55.19/8.14 % (1439220)Time elapsed: 0.217 s
% 55.19/8.14 % (1439220)Peak memory usage: 17 MB
% 55.19/8.14 % (1439220)Instructions burned: 411 (million)
% 55.19/8.14 % (1439226)lrs+10_2:1_si=on:random_seed=22877508:s2a=on:i=506:rtra=on:fe=abstraction_2934 on theBenchmark for (2934ds/506Mi)
% 55.19/8.14 % (1439218)Instruction limit reached!
% 55.19/8.14 % (1439218)------------------------------
% 55.19/8.14 % (1439218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.19/8.14 % (1439218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.19/8.14 % (1439218)CaDiCaL version: 2.1.3
% 55.19/8.14 % (1439218)Termination reason: Instruction limit
% 55.19/8.14 % (1439218)Termination phase: Saturation
% 55.19/8.14 % (1439218)Time elapsed: 0.407 s
% 55.19/8.14 % (1439218)Peak memory usage: 18 MB
% 59.34/8.82 % (1439218)Instructions burned: 1004 (million)
% 59.34/8.82 % (1439228)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2065289062:uwa_fpi=on:i=888:doe=on:bd=preordered:rtra=on:fsd=on_2934 on theBenchmark for (2934ds/888Mi)
% 59.34/8.82 % (1439226)Instruction limit reached!
% 59.34/8.82 % (1439226)------------------------------
% 59.34/8.82 % (1439226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.34/8.82 % (1439226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.34/8.82 % (1439226)CaDiCaL version: 2.1.3
% 59.34/8.82 % (1439226)Termination reason: Instruction limit
% 59.34/8.82 % (1439226)Termination phase: Saturation
% 59.34/8.82 % (1439226)Time elapsed: 0.253 s
% 59.34/8.82 % (1439226)Peak memory usage: 17 MB
% 59.34/8.82 % (1439226)Instructions burned: 507 (million)
% 59.34/8.82 % (1439230)WARNING Broken Constraint: if positive_literal_split_queue_ratios(32,1) has been set then positive_literal_split_queue(off) is equal to on
% 59.34/8.82 % (1439230)ott+1002_3:2_to=kbo:sil=128000:cnfonf=lazy_gen:si=on:sp=reverse_frequency:lma=off:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=1.5:random_seed=796504409:cond=fast:i=416:fgj=on:bd=preordered:rtra=on_2931 on theBenchmark for (2931ds/416Mi)
% 59.34/8.82 % (1439228)Instruction limit reached!
% 59.34/8.82 % (1439228)------------------------------
% 59.34/8.82 % (1439228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.34/8.82 % (1439228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.34/8.82 % (1439228)CaDiCaL version: 2.1.3
% 59.34/8.82 % (1439228)Termination reason: Instruction limit
% 59.34/8.82 % (1439228)Termination phase: Saturation
% 59.34/8.82 % (1439228)Time elapsed: 0.392 s
% 59.34/8.82 % (1439228)Peak memory usage: 14 MB
% 59.34/8.82 % (1439228)Instructions burned: 889 (million)
% 59.34/8.82 % (1439180)Instruction limit reached!
% 59.34/8.82 % (1439180)------------------------------
% 59.34/8.82 % (1439180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.34/8.82 % (1439180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.34/8.82 % (1439180)CaDiCaL version: 2.1.3
% 59.34/8.82 % (1439180)Termination reason: Instruction limit
% 59.34/8.82 % (1439180)Termination phase: Saturation
% 59.34/8.82 % (1439180)Time elapsed: 2.184 s
% 59.34/8.82 % (1439180)Peak memory usage: 58 MB
% 59.34/8.82 % (1439180)Instructions burned: 5027 (million)
% 59.34/8.82 % (1439232)dis+10_3:2_sfv=off:to=kbo:plsq=on:fde=unused:e2e=on:si=on:sp=reverse_frequency:acc=on:uwa=off:fd=preordered:slsqc=1:pe=on:slsq=on:random_seed=3343403109:hsq=on:hsqr=16,1:avsq=on:s2a=on:i=13534:hsql=off:nm=16:nicw=on:ins=20:rtra=on:ss=axioms:ntd=on_2929 on theBenchmark for (2929ds/13534Mi)
% 59.34/8.82 % (1439230)Instruction limit reached!
% 59.34/8.82 % (1439230)------------------------------
% 59.34/8.82 % (1439230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.34/8.82 % (1439230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.34/8.82 % (1439230)CaDiCaL version: 2.1.3
% 59.34/8.82 % (1439230)Termination reason: Instruction limit
% 59.34/8.82 % (1439230)Termination phase: Saturation
% 59.34/8.82 % (1439230)Time elapsed: 0.174 s
% 59.34/8.82 % (1439230)Peak memory usage: 16 MB
% 59.34/8.82 % (1439230)Instructions burned: 418 (million)
% 59.34/8.82 % (1439233)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(10) has been set then forward_subsumption_demodulation(off) is equal to on
% 59.34/8.82 % (1439233)dis+1002_3_tgt=ground:cnfonf=lazy_simp:si=on:sp=unary_first:cbe=off:uwa=ground:updr=off:random_seed=3277803967:i=206:fgj=on:hud=10:nm=30:rtra=on:fsdmm=10_2929 on theBenchmark for (2929ds/206Mi)
% 59.34/8.82 % (1439232)Refutation not found, incomplete strategy
% 59.34/8.82 % (1439232)------------------------------
% 59.34/8.82 % (1439232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.34/8.82 % (1439232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.34/8.82 % (1439232)CaDiCaL version: 2.1.3
% 59.34/8.82 % (1439232)Termination reason: Refutation not found, incomplete strategy
% 59.34/8.82 % (1439232)Time elapsed: 0.012 s
% 59.34/8.82 % (1439232)Peak memory usage: 12 MB
% 59.34/8.82 % (1439232)Instructions burned: 28 (million)
% 59.34/8.82 % (1439232)------------------------------
% 59.34/8.82 % (1439232)------------------------------
% 59.34/8.82 % (1439235)dis+1010_1_sfv=off:slsqr=2,1:to=kbo:plsq=on:cnfonf=lazy_simp:si=on:cbe=off:uwa=hol:nwc=2:s2agt=16:slsq=on:random_seed=1242565882:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2295:avsqr=1,16:aac=none:hud=3:rtra=on_2929 on theBenchmark for (2929ds/2295Mi)
% 63.71/9.49 % (1439237)ott+1010_1_to=lpo:sil=128000:fde=none:si=on:sp=unary_first:uwa=off:nwc=1:random_seed=278508149:i=637:piset=not:ep=RST:bd=all:av=off:rtra=on_2929 on theBenchmark for (2929ds/637Mi)
% 63.71/9.49 % (1439233)Instruction limit reached!
% 63.71/9.49 % (1439233)------------------------------
% 63.71/9.49 % (1439233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439233)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439233)Termination reason: Instruction limit
% 63.71/9.49 % (1439233)Termination phase: Saturation
% 63.71/9.49 % (1439233)Time elapsed: 0.081 s
% 63.71/9.49 % (1439233)Peak memory usage: 12 MB
% 63.71/9.49 % (1439233)Instructions burned: 207 (million)
% 63.71/9.49 % (1439240)dis+1002_15:31_sil=128000:cnfonf=lazy_not_gen:si=on:cbe=off:uwa=off:random_seed=257935347:hsq=on:i=667:rtra=on:ixr=off_2928 on theBenchmark for (2928ds/667Mi)
% 63.71/9.49 % (1439237)Instruction limit reached!
% 63.71/9.49 % (1439237)------------------------------
% 63.71/9.49 % (1439237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439237)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439237)Termination reason: Instruction limit
% 63.71/9.49 % (1439237)Termination phase: Saturation
% 63.71/9.49 % (1439237)Time elapsed: 0.268 s
% 63.71/9.49 % (1439237)Peak memory usage: 17 MB
% 63.71/9.49 % (1439237)Instructions burned: 638 (million)
% 63.71/9.49 % (1439242)lrs-1004_16_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:lma=off:uwa=off:random_seed=1590903496:i=1801:bd=preordered:nm=32:rtra=on:fdi=1024_2926 on theBenchmark for (2926ds/1801Mi)
% 63.71/9.49 % (1439240)Instruction limit reached!
% 63.71/9.49 % (1439240)------------------------------
% 63.71/9.49 % (1439240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439240)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439240)Termination reason: Instruction limit
% 63.71/9.49 % (1439240)Termination phase: Saturation
% 63.71/9.49 % (1439240)Time elapsed: 0.310 s
% 63.71/9.49 % (1439240)Peak memory usage: 14 MB
% 63.71/9.49 % (1439240)Instructions burned: 669 (million)
% 63.71/9.49 % (1439244)lrs+1002_1024_anc=all_dependent:sil=128000:drc=off:cnfonf=lazy_not_be_gen:si=on:cbe=off:cs=on:random_seed=4129535747:i=555:aac=none:rtra=on:fe=abstraction:ntd=on_2925 on theBenchmark for (2925ds/555Mi)
% 63.71/9.49 % (1439244)Instruction limit reached!
% 63.71/9.49 % (1439244)------------------------------
% 63.71/9.49 % (1439244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439244)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439244)Termination reason: Instruction limit
% 63.71/9.49 % (1439244)Termination phase: Saturation
% 63.71/9.49 % (1439244)Time elapsed: 0.224 s
% 63.71/9.49 % (1439244)Peak memory usage: 12 MB
% 63.71/9.49 % (1439244)Instructions burned: 555 (million)
% 63.71/9.49 % (1439246)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3355041188:i=88:s2at=3:nm=2:rtra=on:rawr=on_2923 on theBenchmark for (2923ds/88Mi)
% 63.71/9.49 % (1439246)Instruction limit reached!
% 63.71/9.49 % (1439246)------------------------------
% 63.71/9.49 % (1439246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439246)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439246)Termination reason: Instruction limit
% 63.71/9.49 % (1439246)Termination phase: Saturation
% 63.71/9.49 % (1439246)Time elapsed: 0.039 s
% 63.71/9.49 % (1439246)Peak memory usage: 13 MB
% 63.71/9.49 % (1439246)Instructions burned: 89 (million)
% 63.71/9.49 % (1439248)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=3177505005:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2922 on theBenchmark for (2922ds/280Mi)
% 63.71/9.49 % (1439248)Instruction limit reached!
% 63.71/9.49 % (1439248)------------------------------
% 63.71/9.49 % (1439248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439248)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439248)Termination reason: Instruction limit
% 63.71/9.49 % (1439248)Termination phase: Saturation
% 63.71/9.49 % (1439248)Time elapsed: 0.121 s
% 63.71/9.49 % (1439248)Peak memory usage: 13 MB
% 63.71/9.49 % (1439248)Instructions burned: 280 (million)
% 63.71/9.49 % (1439250)dis+10_5:4_e2e=on:si=on:urr=on:uwa=interpreted_only:nwc=3:random_seed=957694855:s2a=on:i=3166:bd=preordered:rtra=on_2921 on theBenchmark for (2921ds/3166Mi)
% 63.71/9.49 % (1439235)Instruction limit reached!
% 63.71/9.49 % (1439235)------------------------------
% 63.71/9.49 % (1439235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439235)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439235)Termination reason: Instruction limit
% 63.71/9.49 % (1439235)Termination phase: Saturation
% 63.71/9.49 % (1439235)Time elapsed: 0.978 s
% 63.71/9.49 % (1439235)Peak memory usage: 24 MB
% 63.71/9.49 % (1439235)Instructions burned: 2298 (million)
% 63.71/9.49 % (1439252)WARNING Broken Constraint: if avatar_split_queue_ratios(1,2) has been set then avatar_split_queue(off) is equal to on
% 63.71/9.49 % (1439252)lrs+1010_128_to=kbo:plsq=on:plsqc=4:cnfonf=lazy_pi_sigma_gen:bsd=on:si=on:sp=occurrence:sos=on:plsql=on:random_seed=1303359683:i=4201:add=off:avsqr=1,2:bsdmm=10:fsr=off:rtra=on:fe=axiom_2919 on theBenchmark for (2919ds/4201Mi)
% 63.71/9.49 % (1439252)Refutation not found, incomplete strategy
% 63.71/9.49 % (1439252)------------------------------
% 63.71/9.49 % (1439252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439252)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439252)Termination reason: Refutation not found, incomplete strategy
% 63.71/9.49 % (1439252)Time elapsed: 0.026 s
% 63.71/9.49 % (1439252)Peak memory usage: 13 MB
% 63.71/9.49 % (1439252)Instructions burned: 126 (million)
% 63.71/9.49 % (1439252)------------------------------
% 63.71/9.49 % (1439252)------------------------------
% 63.71/9.49 % (1439254)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3439264785:i=2352:rtra=on:ixr=off_2919 on theBenchmark for (2919ds/2352Mi)
% 63.71/9.49 % (1439242)Instruction limit reached!
% 63.71/9.49 % (1439242)------------------------------
% 63.71/9.49 % (1439242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439242)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439242)Termination reason: Instruction limit
% 63.71/9.49 % (1439242)Termination phase: Saturation
% 63.71/9.49 % (1439242)Time elapsed: 0.998 s
% 63.71/9.49 % (1439242)Peak memory usage: 21 MB
% 63.71/9.49 % (1439242)Instructions burned: 1803 (million)
% 63.71/9.49 % (1439256)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 63.71/9.49 % (1439256)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=572310819:st=2:s2a=on:i=452:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2916 on theBenchmark for (2916ds/452Mi)
% 63.71/9.49 % (1439256)Instruction limit reached!
% 63.71/9.49 % (1439256)------------------------------
% 63.71/9.49 % (1439256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439256)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439256)Termination reason: Instruction limit
% 63.71/9.49 % (1439256)Termination phase: Saturation
% 63.71/9.49 % (1439256)Time elapsed: 0.188 s
% 63.71/9.49 % (1439256)Peak memory usage: 13 MB
% 63.71/9.49 % (1439256)Instructions burned: 454 (million)
% 63.71/9.49 % (1439258)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 63.71/9.49 % (1439258)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 63.71/9.49 % (1439258)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=4278390833:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2914 on theBenchmark for (2914ds/483Mi)
% 63.71/9.49 % (1439254)Instruction limit reached!
% 63.71/9.49 % (1439254)------------------------------
% 63.71/9.49 % (1439254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439254)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439254)Termination reason: Instruction limit
% 63.71/9.49 % (1439254)Termination phase: Saturation
% 63.71/9.49 % (1439254)Time elapsed: 0.657 s
% 63.71/9.49 % (1439254)Peak memory usage: 20 MB
% 63.71/9.49 % (1439254)Instructions burned: 2356 (million)
% 63.71/9.49 % (1439260)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3865314650:cts=off:i=168:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2912 on theBenchmark for (2912ds/168Mi)
% 63.71/9.49 % (1439260)Instruction limit reached!
% 63.71/9.49 % (1439260)------------------------------
% 63.71/9.49 % (1439260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439260)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439260)Termination reason: Instruction limit
% 63.71/9.49 % (1439260)Termination phase: Saturation
% 63.71/9.49 % (1439260)Time elapsed: 0.035 s
% 63.71/9.49 % (1439260)Peak memory usage: 12 MB
% 63.71/9.49 % (1439260)Instructions burned: 171 (million)
% 63.71/9.49 % (1439262)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=929930431:hsq=on:hsqr=16,1:s2a=on:i=17240:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2912 on theBenchmark for (2912ds/17240Mi)
% 63.71/9.49 % (1439214)Instruction limit reached!
% 63.71/9.49 % (1439214)------------------------------
% 63.71/9.49 % (1439214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439214)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439214)Termination reason: Instruction limit
% 63.71/9.49 % (1439214)Termination phase: Saturation
% 63.71/9.49 % (1439214)Time elapsed: 2.791 s
% 63.71/9.49 % (1439214)Peak memory usage: 69 MB
% 63.71/9.49 % (1439214)Instructions burned: 6583 (million)
% 63.71/9.49 % (1439264)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:sp=unary_first:uwa=off:sac=on:random_seed=2568594031:i=2022:fsr=off:rtra=on:ixr=off_2911 on theBenchmark for (2911ds/2022Mi)
% 63.71/9.49 % (1439258)Instruction limit reached!
% 63.71/9.49 % (1439258)------------------------------
% 63.71/9.49 % (1439258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439258)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439258)Termination reason: Instruction limit
% 63.71/9.49 % (1439258)Termination phase: Saturation
% 63.71/9.49 % (1439258)Time elapsed: 0.290 s
% 63.71/9.49 % (1439258)Peak memory usage: 16 MB
% 63.71/9.49 % (1439258)Instructions burned: 484 (million)
% 63.71/9.49 % (1439266)lrs+1010_3:1_sil=128000:tgt=full:plsq=on:drc=ordering:cnfonf=lazy_not_be_gen:si=on:etr=on:sp=reverse_arity:plsqr=32,1:urr=on:uwa=off:foolp=on:nwc=0.5:random_seed=3107350537:i=2274:kws=precedence:bd=preordered:av=off:rtra=on_2911 on theBenchmark for (2911ds/2274Mi)
% 63.71/9.49 % (1439215)Instruction limit reached!
% 63.71/9.49 % (1439215)------------------------------
% 63.71/9.49 % (1439215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439215)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439215)Termination reason: Instruction limit
% 63.71/9.49 % (1439215)Termination phase: Saturation
% 63.71/9.49 % (1439215)Time elapsed: 3.050 s
% 63.71/9.49 % (1439215)Peak memory usage: 70 MB
% 63.71/9.49 % (1439215)Instructions burned: 6211 (million)
% 63.71/9.49 % (1439268)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=733467722:i=555:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2909 on theBenchmark for (2909ds/555Mi)
% 63.71/9.49 % (1439266) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1438769-1439266"...
% 63.71/9.49 % (1439266)...printing done.
% 63.71/9.49 % (1439266)Refutation found. Thanks to Tanya!
% 63.71/9.49 % SZS status Theorem for theBenchmark
% 63.71/9.49 % SZS output start Proof for theBenchmark
% See solution above
% 63.71/9.49 % (1439266)------------------------------
% 63.71/9.49 % (1439266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 63.71/9.49 % (1439266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 63.71/9.49 % (1439266)CaDiCaL version: 2.1.3
% 63.71/9.49 % (1439266)Termination reason: Refutation
% 63.71/9.49 % (1439266)Time elapsed: 0.348 s
% 63.71/9.49 % (1439266)Peak memory usage: 15 MB
% 63.71/9.49 % (1439266)Instructions burned: 788 (million)
% 63.71/9.49 % (1438769)Success in time 9.249 s
% 63.71/9.49 % Vampire exiting
%------------------------------------------------------------------------------