%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV157^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:37:55 AM UTC 2026
% Result : Theorem 2.78s 0.57s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 22
% Syntax : Number of formulae : 322 ( 44 unt; 0 typ; 21 def)
% Number of atoms : 3381 ( 262 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 11513 ( 369 ~; 618 |; 616 &;7359 @)
% ( 21 <=>; 929 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 892 ( 892 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 75 usr; 55 con; 0-4 aty)
% (1601 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1899 ( 0 sgn 241 !; 0 ?;1899 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK0: a ).
thf(func_def_19,type,
sK1: a > a > $o ).
thf(func_def_20,type,
sK2: a > a > $o ).
thf(func_def_21,type,
sK3: a ).
thf(func_def_22,type,
sK4: a > a > $o ).
thf(func_def_24,type,
sK6: a ).
thf(func_def_25,type,
sK7: a ).
thf(func_def_26,type,
sK8: a > a > $o ).
thf(func_def_27,type,
sK9: a ).
thf(func_def_28,type,
sK10: a ).
thf(func_def_29,type,
sK11: a ).
thf(func_def_30,type,
sK12: a > a > $o ).
thf(func_def_31,type,
sK13: a ).
thf(func_def_32,type,
sK14: a ).
thf(func_def_33,type,
sK15: a ).
thf(func_def_34,type,
sK16: a ).
thf(func_def_35,type,
sK17: a > a > $o ).
thf(func_def_36,type,
sK18: a ).
thf(func_def_37,type,
sK19: a ).
thf(func_def_38,type,
sK20: a ).
thf(func_def_39,type,
sK21: a ).
thf(func_def_40,type,
sK22: a ).
thf(func_def_41,type,
sK23: a > a > $o ).
thf(func_def_42,type,
sK24: a ).
thf(func_def_43,type,
sK25: a ).
thf(func_def_44,type,
sK26: a ).
thf(func_def_45,type,
sK27: a ).
thf(func_def_46,type,
sK28: a ).
thf(func_def_47,type,
sK29: a ).
thf(func_def_48,type,
sK30: a ).
thf(func_def_49,type,
sK31: a ).
thf(func_def_50,type,
sK32: a ).
thf(func_def_51,type,
sK33: a ).
thf(func_def_52,type,
sK34: a ).
thf(func_def_53,type,
sK35: a ).
thf(func_def_54,type,
sK36: a ).
thf(func_def_55,type,
sK37: a ).
thf(func_def_56,type,
sK38: a ).
thf(f1,conjecture,
! [X2: a,X1: a > a > $o,X0: a > a > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ~ ( ( ! [X7: a,X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X9: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM250G_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a,X1: a > a > $o,X0: a > a > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) )
| ~ ( ( ! [X7: a,X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X10: a,X8: a] :
( ( ( X4 @ X9 @ X10 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X10 ) ) )
=> ( X4 @ X6 @ X7 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X10: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X9 @ X10 ) )
=> ( X4 @ X8 @ X10 ) )
& ! [X9: a,X8: a] :
( ( ( X1 @ X8 @ X9 )
| ( X0 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X7 ) ) )
& ! [X5: a,X6: a] :
( ( ! [X4: a > a > $o] :
( ( ! [X9: a,X8: a] :
( ( X1 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) )
& ! [X9: a,X7: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) ) )
=> ( X4 @ X5 @ X6 ) )
| ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( X0 @ X8 @ X9 )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X7: a,X9: a,X8: a] :
( ( ( X4 @ X9 @ X7 )
& ( X4 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X7 ) )
& ! [X9: a,X8: a] :
( ( ( X0 @ X8 @ X9 )
| ( X1 @ X8 @ X9 ) )
=> ( X4 @ X8 @ X9 ) ) )
=> ( X4 @ X5 @ X6 ) ) ) )
=> ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ! [X5: a,X7: a,X6: a] :
( ( ( X4 @ X6 @ X7 )
& ( X4 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X7 ) ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a,X1: a > a > $o,X2: a > a > $o,X3: a] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X2 @ X6 @ X5 )
| ( X1 @ X6 @ X5 ) )
=> ( X4 @ X6 @ X5 ) )
& ! [X7: a,X8: a,X9: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X7 @ X8 ) )
=> ( X4 @ X7 @ X9 ) ) )
=> ( X4 @ X0 @ X3 ) )
| ~ ( ( ! [X10: a,X11: a,X12: a] :
( ( ! [X13: a > a > $o] :
( ( ! [X14: a,X15: a,X16: a] :
( ( ( X13 @ X16 @ X14 )
& ( X13 @ X14 @ X15 ) )
=> ( X13 @ X16 @ X15 ) )
& ! [X17: a,X18: a] :
( ( ( X2 @ X18 @ X17 )
| ( X1 @ X18 @ X17 ) )
=> ( X13 @ X18 @ X17 ) ) )
=> ( X13 @ X11 @ X12 ) )
& ! [X19: a > a > $o] :
( ( ! [X20: a,X21: a] :
( ( ( X2 @ X20 @ X21 )
| ( X1 @ X20 @ X21 ) )
=> ( X19 @ X20 @ X21 ) )
& ! [X22: a,X23: a,X24: a] :
( ( ( X19 @ X22 @ X23 )
& ( X19 @ X24 @ X22 ) )
=> ( X19 @ X24 @ X23 ) ) )
=> ( X19 @ X12 @ X10 ) ) )
=> ! [X25: a > a > $o] :
( ( ! [X26: a,X27: a,X28: a] :
( ( ( X25 @ X26 @ X27 )
& ( X25 @ X27 @ X28 ) )
=> ( X25 @ X26 @ X28 ) )
& ! [X29: a,X30: a] :
( ( ( X1 @ X30 @ X29 )
| ( X2 @ X30 @ X29 ) )
=> ( X25 @ X30 @ X29 ) ) )
=> ( X25 @ X11 @ X10 ) ) )
& ! [X31: a,X32: a] :
( ( ! [X33: a > a > $o] :
( ( ! [X34: a,X35: a] :
( ( X1 @ X35 @ X34 )
=> ( X33 @ X35 @ X34 ) )
& ! [X36: a,X37: a,X38: a] :
( ( ( X33 @ X36 @ X37 )
& ( X33 @ X38 @ X36 ) )
=> ( X33 @ X38 @ X37 ) ) )
=> ( X33 @ X31 @ X32 ) )
| ! [X39: a > a > $o] :
( ( ! [X40: a,X41: a,X42: a] :
( ( ( X39 @ X41 @ X42 )
& ( X39 @ X40 @ X41 ) )
=> ( X39 @ X40 @ X42 ) )
& ! [X43: a,X44: a] :
( ( X2 @ X44 @ X43 )
=> ( X39 @ X44 @ X43 ) ) )
=> ( X39 @ X31 @ X32 ) ) )
=> ! [X45: a > a > $o] :
( ( ! [X46: a,X47: a,X48: a] :
( ( ( X45 @ X47 @ X46 )
& ( X45 @ X48 @ X47 ) )
=> ( X45 @ X48 @ X46 ) )
& ! [X49: a,X50: a] :
( ( ( X2 @ X50 @ X49 )
| ( X1 @ X50 @ X49 ) )
=> ( X45 @ X50 @ X49 ) ) )
=> ( X45 @ X31 @ X32 ) ) ) )
=> ! [X51: a > a > $o] :
( ( ! [X52: a,X53: a] :
( ( ( X2 @ X52 @ X53 )
| ( X1 @ X52 @ X53 ) )
=> ( X51 @ X52 @ X53 ) )
& ! [X54: a,X55: a,X56: a] :
( ( ( X51 @ X56 @ X55 )
& ( X51 @ X54 @ X56 ) )
=> ( X51 @ X54 @ X55 ) ) )
=> ( X51 @ X0 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( !! @ a
@ ^ [Y3: a] :
( ~ ( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y1 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y8 @ Y7 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y2 @ Y7 @ Y8 )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y2 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y8 )
& ( Y6 @ Y8 @ Y9 ) )
=> ( Y6 @ Y7 @ Y9 ) ) ) ) ) )
=> ( Y6 @ Y5 @ Y4 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y8 @ Y10 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y9 @ Y8 )
| ( Y1 @ Y9 @ Y8 ) )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y4 @ Y6 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y2 @ Y8 @ Y9 )
| ( Y1 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 @ Y9 )
& ( Y7 @ Y8 @ Y10 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y4 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y1 @ Y8 @ Y9 )
| ( Y2 @ Y8 @ Y9 ) )
=> ( Y7 @ Y8 @ Y9 ) ) ) )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( ( Y7 @ Y9 @ Y8 )
& ( Y7 @ Y10 @ Y9 ) )
=> ( Y7 @ Y10 @ Y8 ) ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y6 @ Y5 )
| ( Y1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y2 @ Y5 @ Y6 )
| ( Y1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y0 ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f8]) ).
thf(f11,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ sK0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ sK0 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f13,plain,
( $false
= ( ^ [Y0: a > a > $o] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( !! @ a
@ ^ [Y2: a] :
( ~ ( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y0 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y7 @ Y6 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y1 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y7 )
& ( Y5 @ Y7 @ Y8 ) )
=> ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
=> ( Y5 @ Y4 @ Y3 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y7 @ Y9 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y8 @ Y7 )
| ( Y0 @ Y8 @ Y7 ) )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y3 @ Y5 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y1 @ Y7 @ Y8 )
| ( Y0 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 @ Y8 )
& ( Y6 @ Y7 @ Y9 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y0 @ Y7 @ Y8 )
| ( Y1 @ Y7 @ Y8 ) )
=> ( Y6 @ Y7 @ Y8 ) ) ) )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( ( Y6 @ Y8 @ Y7 )
& ( Y6 @ Y9 @ Y8 ) )
=> ( Y6 @ Y9 @ Y7 ) ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y4 )
& ( Y3 @ Y4 @ Y5 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y5 @ Y4 )
| ( Y0 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 @ sK0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y1 @ Y4 @ Y5 )
| ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ sK0 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( sK1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ sK0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( ^ [Y0: a > a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ~ ( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( sK1 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y6 @ Y5 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y0 @ Y5 @ Y6 )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
| ( sK1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y6 @ Y7 ) )
=> ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y6 @ Y8 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y7 @ Y6 )
| ( sK1 @ Y7 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y2 @ Y4 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y0 @ Y6 @ Y7 )
| ( sK1 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 @ Y7 )
& ( Y5 @ Y6 @ Y8 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( sK1 @ Y6 @ Y7 )
| ( Y0 @ Y6 @ Y7 ) )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( ( Y5 @ Y7 @ Y6 )
& ( Y5 @ Y8 @ Y7 ) )
=> ( Y5 @ Y8 @ Y6 ) ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y3 )
& ( Y2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y4 @ Y3 )
| ( sK1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 @ sK0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y0 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ sK0 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( !! @ a
@ ^ [Y0: a] :
( ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK1 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ~ ( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK1 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y5 @ Y4 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( sK2 @ Y4 @ Y5 )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y5 @ Y6 ) )
=> ( Y3 @ Y4 @ Y6 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y5 @ Y7 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y6 @ Y5 )
| ( sK1 @ Y6 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 @ Y3 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK2 @ Y5 @ Y6 )
| ( sK1 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 @ Y6 )
& ( Y4 @ Y5 @ Y7 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( sK1 @ Y5 @ Y6 )
| ( sK2 @ Y5 @ Y6 ) )
=> ( Y4 @ Y5 @ Y6 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( ( Y4 @ Y6 @ Y5 )
& ( Y4 @ Y7 @ Y6 ) )
=> ( Y4 @ Y7 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 @ sK0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK0 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f20,plain,
( ( ~ ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK3 @ sK0 ) )
= $false ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( ( sK4 @ sK3 @ sK0 )
= $false ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y2 @ Y0 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f22]) ).
thf(f29,plain,
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f20]) ).
thf(f32,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f33,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f34,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f36,definition,
( spl5_1
<=> ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f38,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl5_2
<=> ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f42,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f34,f40,f36]) ).
thf(f44,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f45,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK1 @ X1 @ Y0 ) )
=> ( sK4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl5_2 ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f48,definition,
( spl5_3
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f50,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f52,definition,
( spl5_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f54,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,plain,
( spl5_3
| spl5_4
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f46,f40,f52,f48]) ).
thf(f56,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK1 @ X1 @ Y0 ) )
=> ( sK4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f57,plain,
! [X2: a,X1: a] :
( $true
= ( ( ( sK2 @ X1 @ X2 )
| ( sK1 @ X1 @ X2 ) )
=> ( sK4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK1 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y3 @ Y4 )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y4 @ Y5 ) )
=> ( Y2 @ Y3 @ Y5 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK6 )
= $false )
| ~ spl5_3 ),
inference(sigma_proxy_clausification,[],[f50]) ).
thf(f59,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) ) ) )
= $false )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f63,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK1 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y2 @ Y4 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK6 ) ) ) )
@ sK7 )
= $false )
| ~ spl5_3 ),
inference(sigma_proxy_clausification,[],[f59]) ).
thf(f64,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
= $false )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f66,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ~ spl5_3 ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) )
| ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) ) )
| ~ spl5_3 ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f74,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) )
@ sK8 )
= $false )
| ~ spl5_3 ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f75,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y1 )
& ( sK8 @ Y1 @ Y2 ) )
=> ( sK8 @ Y0 @ Y2 ) ) ) ) ) )
=> ( sK8 @ sK7 @ sK6 ) )
= $false )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f86,plain,
( ( $false
= ( sK8 @ sK7 @ sK6 ) )
| ~ spl5_3 ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f87,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y1 )
& ( sK8 @ Y1 @ Y2 ) )
=> ( sK8 @ Y0 @ Y2 ) ) ) ) ) ) )
| ~ spl5_3 ),
inference(imp_proxy_clausification,[],[f75]) ).
thf(f92,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ~ spl5_3 ),
inference(or_proxy_clausification,[],[f67]) ).
thf(f94,definition,
( spl5_5
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f96,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f98,definition,
( spl5_6
<=> ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f100,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f98]) ).
thf(f114,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y1 )
& ( sK4 @ Y1 @ Y0 ) )
=> ( sK4 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f115,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK4 @ Y0 @ X1 ) )
=> ( sK4 @ Y1 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f118,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ Y0 )
& ( sK4 @ Y0 @ X1 ) )
=> ( sK4 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f119,plain,
! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ X2 )
& ( sK4 @ X2 @ X1 ) )
=> ( sK4 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f123,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y4 @ Y6 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
| ( sK1 @ Y5 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 @ Y2 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y4 @ Y5 )
| ( sK1 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 @ Y5 )
& ( Y3 @ Y4 @ Y6 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK1 @ Y4 @ Y5 )
| ( sK2 @ Y4 @ Y5 ) )
=> ( Y3 @ Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y3 @ Y5 @ Y4 )
& ( Y3 @ Y6 @ Y5 ) )
=> ( Y3 @ Y6 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ sK9 )
= $false )
| ~ spl5_4 ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f124,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK9 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f134,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y3 @ Y5 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
| ( sK1 @ Y4 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ sK9 @ Y1 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y3 @ Y4 )
| ( sK1 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 @ Y4 )
& ( Y2 @ Y3 @ Y5 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y0 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK1 @ Y3 @ Y4 )
| ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y2 @ Y4 @ Y3 )
& ( Y2 @ Y5 @ Y4 ) )
=> ( Y2 @ Y5 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
@ sK10 )
= $false )
| ~ spl5_4 ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f135,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK9 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK1 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) ) )
= $false )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f143,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
| ( sK1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ sK9 @ Y0 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y2 @ Y3 )
| ( sK1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y2 @ Y4 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) )
=> ( Y1 @ sK10 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK1 @ Y2 @ Y3 )
| ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y4 @ Y3 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK10 @ Y0 ) ) ) )
@ sK11 )
= $false )
| ~ spl5_4 ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f144,plain,
( ( ( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) ) )
=> ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) ) )
= $false )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f154,plain,
( ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) ) )
= $false )
| ~ spl5_4 ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f155,plain,
( ( $true
= ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK11 ) ) )
& ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) ) ) )
| ~ spl5_4 ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f156,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK1 @ Y1 @ Y2 )
| ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK11 ) )
@ sK12 )
= $false )
| ~ spl5_4 ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f157,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y1 @ Y0 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y2 @ Y0 ) ) ) ) ) )
=> ( sK12 @ sK10 @ sK11 ) )
= $false )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( ( sK12 @ sK10 @ sK11 )
= $false )
| ~ spl5_4 ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y1 @ Y0 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl5_4 ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f164,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) ) ) )
| ~ spl5_4 ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f165,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK11 ) ) ) )
| ~ spl5_4 ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f166,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y1 @ Y0 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ~ spl5_4 ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f167,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
| ~ spl5_4 ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f168,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y1 @ Y2 )
| ( sK1 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK10 @ sK9 ) )
@ X1 ) )
| ~ spl5_4 ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f169,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y0 @ Y2 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK10 @ sK9 ) ) )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK1 @ Y0 @ Y1 )
| ( sK2 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ~ spl5_4 ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f171,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK1 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK12 @ X1 @ Y0 ) ) )
= $true )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f173,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK1 @ X1 @ Y0 )
| ( sK2 @ X1 @ Y0 ) )
=> ( sK12 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl5_4 ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK1 @ X1 @ X2 )
| ( sK2 @ X1 @ X2 ) )
=> ( sK12 @ X1 @ X2 ) )
= $true )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK9 @ sK11 ) )
@ X1 ) )
| ~ spl5_4 ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f176,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK9 @ sK11 ) ) )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f190,plain,
( ! [X1: a] :
( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y1 @ Y0 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true )
| ~ spl5_4 ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f191,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y0 @ X1 )
& ( sK12 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ X1 ) ) ) ) )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f198,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y0 @ X1 )
& ( sK12 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ X1 ) ) )
@ X2 ) )
| ~ spl5_4 ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f199,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK12 @ X2 @ X1 )
& ( sK12 @ Y0 @ X2 ) )
=> ( sK12 @ Y0 @ X1 ) ) ) )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f214,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK12 @ X2 @ X1 )
& ( sK12 @ Y0 @ X2 ) )
=> ( sK12 @ Y0 @ X1 ) )
@ X3 ) )
| ~ spl5_4 ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f215,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ( ( sK12 @ X2 @ X1 )
& ( sK12 @ X3 @ X2 ) )
=> ( sK12 @ X3 @ X1 ) ) )
| ~ spl5_4 ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f231,plain,
( ! [X0: a] :
( $true
= ( ( ( sK12 @ X0 @ sK11 )
& ( sK12 @ sK10 @ X0 ) )
=> $false ) )
| ~ spl5_4 ),
inference(superposition,[],[f215,f158]) ).
thf(f234,plain,
( ! [X0: a] :
( $true
= ( ~ ( ( sK12 @ X0 @ sK11 )
& ( sK12 @ sK10 @ X0 ) ) ) )
| ~ spl5_4 ),
inference(boolean_simplification,[],[f231]) ).
thf(f239,plain,
( ! [X0: a] :
( ( ( sK12 @ X0 @ sK11 )
& ( sK12 @ sK10 @ X0 ) )
= $false )
| ~ spl5_4 ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f246,plain,
( ! [X0: a] :
( ( ( sK12 @ X0 @ sK11 )
= $false )
| ( ( sK12 @ sK10 @ X0 )
= $false ) )
| ~ spl5_4 ),
inference(and_proxy_clausification,[],[f239]) ).
thf(f324,plain,
( ( ( sK12 @ sK9 @ sK11 )
= $false )
| ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
=> $false ) )
| ~ spl5_4 ),
inference(superposition,[],[f169,f246]) ).
thf(f341,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ( ( sK12 @ sK9 @ sK11 )
= $false )
| ~ spl5_4 ),
inference(boolean_simplification,[],[f324]) ).
thf(f358,definition,
( spl5_8
<=> ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f359,plain,
( ( $true
!= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) ) )
| spl5_8 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f360,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f363,definition,
( spl5_9
<=> ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f365,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) ) ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f363]) ).
thf(f367,definition,
( spl5_10
<=> ( ( sK12 @ sK9 @ sK11 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f369,plain,
( ( ( sK12 @ sK9 @ sK11 )
= $false )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f370,plain,
( spl5_9
| spl5_10
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f341,f52,f367,f363]) ).
thf(f392,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl5_9 ),
inference(not_proxy_clausification,[],[f365]) ).
thf(f412,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl5_9 ),
inference(and_proxy_clausification,[],[f392]) ).
thf(f414,definition,
( spl5_11
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
thf(f416,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f414]) ).
thf(f418,definition,
( spl5_12
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f420,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f418]) ).
thf(f431,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl5_4
| ~ spl5_10 ),
inference(superposition,[],[f176,f369]) ).
thf(f441,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl5_4
| ~ spl5_10 ),
inference(boolean_simplification,[],[f431]) ).
thf(f461,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl5_8 ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f479,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl5_8 ),
inference(and_proxy_clausification,[],[f461]) ).
thf(f481,definition,
( spl5_13
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition]) ).
thf(f483,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f481]) ).
thf(f485,definition,
( spl5_14
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition]) ).
thf(f487,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f485]) ).
thf(f489,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) ) )
| spl5_8 ),
inference(not_proxy_clausification,[],[f359]) ).
thf(f490,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
| ( sK1 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) )
@ X1 ) )
| ~ spl5_1 ),
inference(pi_proxy_clausification,[],[f38]) ).
thf(f491,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
=> ( X1 @ sK3 @ sK0 ) ) )
| ~ spl5_1 ),
inference(beta-eta_normalization,[],[f490]) ).
thf(f492,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) ) ) )
| spl5_8 ),
inference(and_proxy_clausification,[],[f489]) ).
thf(f495,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) )
=> $false )
= $true )
| ~ spl5_1 ),
inference(superposition,[],[f491,f23]) ).
thf(f502,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl5_1 ),
inference(boolean_simplification,[],[f495]) ).
thf(f505,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ X1 ) )
| spl5_8 ),
inference(pi_proxy_clausification,[],[f492]) ).
thf(f506,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK1 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) ) )
= $true )
| spl5_8 ),
inference(beta-eta_normalization,[],[f505]) ).
thf(f509,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ X1 )
| ( sK1 @ Y0 @ X1 ) )
=> ( sK12 @ Y0 @ X1 ) )
@ X2 ) )
| spl5_8 ),
inference(pi_proxy_clausification,[],[f506]) ).
thf(f574,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl5_1 ),
inference(not_proxy_clausification,[],[f502]) ).
thf(f577,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl5_1 ),
inference(and_proxy_clausification,[],[f574]) ).
thf(f579,definition,
( spl5_15
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_15])],[avatar_definition]) ).
thf(f581,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f579]) ).
thf(f583,definition,
( spl5_16
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_16])],[avatar_definition]) ).
thf(f585,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f583]) ).
thf(f586,plain,
( spl5_15
| spl5_16
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f577,f36,f583,f579]) ).
thf(f589,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) )
@ sK13 )
= $false )
| ~ spl5_15 ),
inference(sigma_proxy_clausification,[],[f581]) ).
thf(f590,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK13 )
| ( sK1 @ Y0 @ sK13 ) )
=> ( sK4 @ Y0 @ sK13 ) ) )
= $false )
| ~ spl5_15 ),
inference(beta-eta_normalization,[],[f589]) ).
thf(f600,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK13 )
| ( sK1 @ Y0 @ sK13 ) )
=> ( sK4 @ Y0 @ sK13 ) )
@ sK14 )
= $false )
| ~ spl5_15 ),
inference(sigma_proxy_clausification,[],[f590]) ).
thf(f601,plain,
( ( ( ( ( sK2 @ sK14 @ sK13 )
| ( sK1 @ sK14 @ sK13 ) )
=> ( sK4 @ sK14 @ sK13 ) )
= $false )
| ~ spl5_15 ),
inference(beta-eta_normalization,[],[f600]) ).
thf(f602,plain,
( ( $true = $false )
| ~ spl5_15 ),
inference(forward_demodulation,[],[f601,f57]) ).
thf(f603,plain,
( $false
| ~ spl5_15 ),
inference(trivial_inequality_removal,[],[f602]) ).
thf(f604,plain,
~ spl5_15,
inference(avatar_contradiction_clause,[],[f603]) ).
thf(f625,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK4 @ Y2 @ Y0 )
& ( sK4 @ Y0 @ Y1 ) )
=> ( sK4 @ Y2 @ Y1 ) ) ) )
@ sK15 )
= $false )
| ~ spl5_16 ),
inference(sigma_proxy_clausification,[],[f585]) ).
thf(f626,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ sK15 )
& ( sK4 @ sK15 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl5_16 ),
inference(beta-eta_normalization,[],[f625]) ).
thf(f627,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK4 @ Y1 @ sK15 )
& ( sK4 @ sK15 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) )
@ sK16 ) )
| ~ spl5_16 ),
inference(sigma_proxy_clausification,[],[f626]) ).
thf(f628,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK4 @ Y0 @ sK15 )
& ( sK4 @ sK15 @ sK16 ) )
=> ( sK4 @ Y0 @ sK16 ) ) )
= $false )
| ~ spl5_16 ),
inference(beta-eta_normalization,[],[f627]) ).
thf(f629,plain,
( ( $true = $false )
| ~ spl5_16 ),
inference(forward_demodulation,[],[f628,f119]) ).
thf(f630,plain,
( $false
| ~ spl5_16 ),
inference(trivial_inequality_removal,[],[f629]) ).
thf(f631,plain,
~ spl5_16,
inference(avatar_contradiction_clause,[],[f630]) ).
thf(f667,plain,
( ! [X1: a > a > $o] :
( $true
= ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK1 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) )
@ X1 ) )
| ~ spl5_5 ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f668,plain,
( ! [X1: a > a > $o] :
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y2 @ Y1 )
& ( X1 @ Y1 @ Y0 ) )
=> ( X1 @ Y2 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK7 @ sK6 ) )
= $true )
| ~ spl5_5 ),
inference(beta-eta_normalization,[],[f667]) ).
thf(f672,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y2 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ Y2 @ Y0 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl5_3
| ~ spl5_5 ),
inference(superposition,[],[f668,f86]) ).
thf(f673,plain,
( ( ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y2 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ Y2 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl5_3
| ~ spl5_5 ),
inference(boolean_simplification,[],[f672]) ).
thf(f717,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y1 )
& ( sK8 @ Y1 @ Y2 ) )
=> ( sK8 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ~ spl5_3 ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f718,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
| ~ spl5_3 ),
inference(and_proxy_clausification,[],[f87]) ).
thf(f736,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ~ spl5_3 ),
inference(pi_proxy_clausification,[],[f718]) ).
thf(f737,plain,
( ! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK1 @ X1 @ Y0 ) )
=> ( sK8 @ X1 @ Y0 ) ) )
= $true )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f736]) ).
thf(f738,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ X1 @ Y0 )
| ( sK1 @ X1 @ Y0 ) )
=> ( sK8 @ X1 @ Y0 ) )
@ X2 ) )
| ~ spl5_3 ),
inference(pi_proxy_clausification,[],[f737]) ).
thf(f739,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK2 @ X1 @ X2 )
| ( sK1 @ X1 @ X2 ) )
=> ( sK8 @ X1 @ X2 ) )
= $true )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f738]) ).
thf(f763,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y1 )
& ( sK8 @ Y1 @ Y2 ) )
=> ( sK8 @ Y0 @ Y2 ) ) ) )
@ X1 ) )
| ~ spl5_3 ),
inference(pi_proxy_clausification,[],[f717]) ).
thf(f764,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK8 @ X1 @ Y0 )
& ( sK8 @ Y0 @ Y1 ) )
=> ( sK8 @ X1 @ Y1 ) ) ) ) )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f763]) ).
thf(f766,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK8 @ X1 @ Y0 )
& ( sK8 @ Y0 @ Y1 ) )
=> ( sK8 @ X1 @ Y1 ) ) )
@ X2 ) )
| ~ spl5_3 ),
inference(pi_proxy_clausification,[],[f764]) ).
thf(f767,plain,
( ! [X2: a,X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK8 @ X1 @ X2 )
& ( sK8 @ X2 @ Y0 ) )
=> ( sK8 @ X1 @ Y0 ) ) ) )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f766]) ).
thf(f780,plain,
( ! [X2: a,X3: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK8 @ X1 @ X2 )
& ( sK8 @ X2 @ Y0 ) )
=> ( sK8 @ X1 @ Y0 ) )
@ X3 ) )
| ~ spl5_3 ),
inference(pi_proxy_clausification,[],[f767]) ).
thf(f781,plain,
( ! [X2: a,X3: a,X1: a] :
( ( ( ( sK8 @ X1 @ X2 )
& ( sK8 @ X2 @ X3 ) )
=> ( sK8 @ X1 @ X3 ) )
= $true )
| ~ spl5_3 ),
inference(beta-eta_normalization,[],[f780]) ).
thf(f840,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y2 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ Y2 @ Y0 ) ) ) ) ) ) )
| ~ spl5_3
| ~ spl5_5 ),
inference(not_proxy_clausification,[],[f673]) ).
thf(f848,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y2 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl5_3
| ~ spl5_5 ),
inference(and_proxy_clausification,[],[f840]) ).
thf(f850,definition,
( spl5_17
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y2 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ Y2 @ Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
thf(f852,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y2 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ Y2 @ Y0 ) ) ) ) )
= $false )
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f850]) ).
thf(f854,definition,
( spl5_18
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition]) ).
thf(f856,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f854]) ).
thf(f857,plain,
( spl5_17
| spl5_18
| ~ spl5_3
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f848,f94,f48,f854,f850]) ).
thf(f867,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK1 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) )
@ sK18 )
= $false )
| ~ spl5_18 ),
inference(sigma_proxy_clausification,[],[f856]) ).
thf(f868,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ sK18 @ Y0 )
=> ( sK8 @ sK18 @ Y0 ) ) )
= $false )
| ~ spl5_18 ),
inference(beta-eta_normalization,[],[f867]) ).
thf(f869,plain,
( ( ( ^ [Y0: a] :
( ( sK1 @ sK18 @ Y0 )
=> ( sK8 @ sK18 @ Y0 ) )
@ sK19 )
= $false )
| ~ spl5_18 ),
inference(sigma_proxy_clausification,[],[f868]) ).
thf(f870,plain,
( ( ( ( sK1 @ sK18 @ sK19 )
=> ( sK8 @ sK18 @ sK19 ) )
= $false )
| ~ spl5_18 ),
inference(beta-eta_normalization,[],[f869]) ).
thf(f871,plain,
( ( $false
= ( sK8 @ sK18 @ sK19 ) )
| ~ spl5_18 ),
inference(imp_proxy_clausification,[],[f870]) ).
thf(f872,plain,
( ( $true
= ( sK1 @ sK18 @ sK19 ) )
| ~ spl5_18 ),
inference(imp_proxy_clausification,[],[f870]) ).
thf(f877,plain,
( ( $true
= ( ( ( sK2 @ sK18 @ sK19 )
| ( sK1 @ sK18 @ sK19 ) )
=> $false ) )
| ~ spl5_3
| ~ spl5_18 ),
inference(superposition,[],[f739,f871]) ).
thf(f880,plain,
( ( ( ~ ( ( sK2 @ sK18 @ sK19 )
| ( sK1 @ sK18 @ sK19 ) ) )
= $true )
| ~ spl5_3
| ~ spl5_18 ),
inference(boolean_simplification,[],[f877]) ).
thf(f885,plain,
( ( ( ~ ( ( sK2 @ sK18 @ sK19 )
| $true ) )
= $true )
| ~ spl5_3
| ~ spl5_18 ),
inference(forward_demodulation,[],[f880,f872]) ).
thf(f886,plain,
( ( $true = ( ~ $true ) )
| ~ spl5_3
| ~ spl5_18 ),
inference(boolean_simplification,[],[f885]) ).
thf(f887,plain,
( ( $true = $false )
| ~ spl5_3
| ~ spl5_18 ),
inference(boolean_simplification,[],[f886]) ).
thf(f888,plain,
( $false
| ~ spl5_3
| ~ spl5_18 ),
inference(trivial_inequality_removal,[],[f887]) ).
thf(f889,plain,
( ~ spl5_3
| ~ spl5_18 ),
inference(avatar_contradiction_clause,[],[f888]) ).
thf(f907,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y2 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ Y2 @ Y0 ) ) ) )
@ sK20 )
= $false )
| ~ spl5_17 ),
inference(sigma_proxy_clausification,[],[f852]) ).
thf(f908,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK8 @ Y1 @ Y0 )
& ( sK8 @ Y0 @ sK20 ) )
=> ( sK8 @ Y1 @ sK20 ) ) ) )
= $false )
| ~ spl5_17 ),
inference(beta-eta_normalization,[],[f907]) ).
thf(f909,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK8 @ Y1 @ Y0 )
& ( sK8 @ Y0 @ sK20 ) )
=> ( sK8 @ Y1 @ sK20 ) ) )
@ sK21 )
= $false )
| ~ spl5_17 ),
inference(sigma_proxy_clausification,[],[f908]) ).
thf(f910,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK8 @ Y0 @ sK21 )
& ( sK8 @ sK21 @ sK20 ) )
=> ( sK8 @ Y0 @ sK20 ) ) )
= $false )
| ~ spl5_17 ),
inference(beta-eta_normalization,[],[f909]) ).
thf(f911,plain,
( ( ( ^ [Y0: a] :
( ( ( sK8 @ Y0 @ sK21 )
& ( sK8 @ sK21 @ sK20 ) )
=> ( sK8 @ Y0 @ sK20 ) )
@ sK22 )
= $false )
| ~ spl5_17 ),
inference(sigma_proxy_clausification,[],[f910]) ).
thf(f912,plain,
( ( $false
= ( ( ( sK8 @ sK22 @ sK21 )
& ( sK8 @ sK21 @ sK20 ) )
=> ( sK8 @ sK22 @ sK20 ) ) )
| ~ spl5_17 ),
inference(beta-eta_normalization,[],[f911]) ).
thf(f913,plain,
( ( $true = $false )
| ~ spl5_3
| ~ spl5_17 ),
inference(forward_demodulation,[],[f912,f781]) ).
thf(f914,plain,
( $false
| ~ spl5_3
| ~ spl5_17 ),
inference(trivial_inequality_removal,[],[f913]) ).
thf(f915,plain,
( ~ spl5_3
| ~ spl5_17 ),
inference(avatar_contradiction_clause,[],[f914]) ).
thf(f916,plain,
( spl5_5
| spl5_6
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f92,f48,f98,f94]) ).
thf(f928,plain,
( ! [X1: a > a > $o] :
( ( ^ [Y0: a > a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK7 @ sK6 ) )
@ X1 )
= $true )
| ~ spl5_6 ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f929,plain,
( ! [X1: a > a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( X1 @ Y0 @ Y2 )
& ( X1 @ Y2 @ Y1 ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK7 @ sK6 ) ) )
| ~ spl5_6 ),
inference(beta-eta_normalization,[],[f928]) ).
thf(f935,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y2 )
& ( sK8 @ Y2 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl5_3
| ~ spl5_6 ),
inference(superposition,[],[f929,f86]) ).
thf(f940,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y2 )
& ( sK8 @ Y2 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl5_3
| ~ spl5_6 ),
inference(boolean_simplification,[],[f935]) ).
thf(f976,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y2 )
& ( sK8 @ Y2 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl5_3
| ~ spl5_6 ),
inference(not_proxy_clausification,[],[f940]) ).
thf(f984,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y2 )
& ( sK8 @ Y2 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl5_3
| ~ spl5_6 ),
inference(and_proxy_clausification,[],[f976]) ).
thf(f986,definition,
( spl5_19
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y2 )
& ( sK8 @ Y2 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition]) ).
thf(f988,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y2 )
& ( sK8 @ Y2 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f986]) ).
thf(f990,definition,
( spl5_20
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition]) ).
thf(f992,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
= $false )
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f990]) ).
thf(f993,plain,
( spl5_19
| spl5_20
| ~ spl5_3
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f984,f98,f48,f990,f986]) ).
thf(f1003,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK8 @ Y0 @ Y1 ) ) )
@ sK24 ) )
| ~ spl5_20 ),
inference(sigma_proxy_clausification,[],[f992]) ).
thf(f1004,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK24 @ Y0 )
=> ( sK8 @ sK24 @ Y0 ) ) )
= $false )
| ~ spl5_20 ),
inference(beta-eta_normalization,[],[f1003]) ).
thf(f1005,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ sK24 @ Y0 )
=> ( sK8 @ sK24 @ Y0 ) )
@ sK25 )
= $false )
| ~ spl5_20 ),
inference(sigma_proxy_clausification,[],[f1004]) ).
thf(f1006,plain,
( ( ( ( sK2 @ sK24 @ sK25 )
=> ( sK8 @ sK24 @ sK25 ) )
= $false )
| ~ spl5_20 ),
inference(beta-eta_normalization,[],[f1005]) ).
thf(f1007,plain,
( ( ( sK8 @ sK24 @ sK25 )
= $false )
| ~ spl5_20 ),
inference(imp_proxy_clausification,[],[f1006]) ).
thf(f1008,plain,
( ( ( sK2 @ sK24 @ sK25 )
= $true )
| ~ spl5_20 ),
inference(imp_proxy_clausification,[],[f1006]) ).
thf(f1014,plain,
( ( $true
= ( ( ( sK2 @ sK24 @ sK25 )
| ( sK1 @ sK24 @ sK25 ) )
=> $false ) )
| ~ spl5_3
| ~ spl5_20 ),
inference(superposition,[],[f739,f1007]) ).
thf(f1020,plain,
( ( ( ~ ( ( sK2 @ sK24 @ sK25 )
| ( sK1 @ sK24 @ sK25 ) ) )
= $true )
| ~ spl5_3
| ~ spl5_20 ),
inference(boolean_simplification,[],[f1014]) ).
thf(f1025,plain,
( ( $true
= ( ~ ( $true
| ( sK1 @ sK24 @ sK25 ) ) ) )
| ~ spl5_3
| ~ spl5_20 ),
inference(forward_demodulation,[],[f1020,f1008]) ).
thf(f1026,plain,
( ( $true = ( ~ $true ) )
| ~ spl5_3
| ~ spl5_20 ),
inference(boolean_simplification,[],[f1025]) ).
thf(f1027,plain,
( ( $true = $false )
| ~ spl5_3
| ~ spl5_20 ),
inference(boolean_simplification,[],[f1026]) ).
thf(f1028,plain,
( $false
| ~ spl5_3
| ~ spl5_20 ),
inference(trivial_inequality_removal,[],[f1027]) ).
thf(f1029,plain,
( ~ spl5_3
| ~ spl5_20 ),
inference(avatar_contradiction_clause,[],[f1028]) ).
thf(f1045,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK8 @ Y0 @ Y2 )
& ( sK8 @ Y2 @ Y1 ) )
=> ( sK8 @ Y0 @ Y1 ) ) ) )
@ sK26 )
= $false )
| ~ spl5_19 ),
inference(sigma_proxy_clausification,[],[f988]) ).
thf(f1046,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK8 @ sK26 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ sK26 @ Y0 ) ) ) )
= $false )
| ~ spl5_19 ),
inference(beta-eta_normalization,[],[f1045]) ).
thf(f1047,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK8 @ sK26 @ Y1 )
& ( sK8 @ Y1 @ Y0 ) )
=> ( sK8 @ sK26 @ Y0 ) ) )
@ sK27 )
= $false )
| ~ spl5_19 ),
inference(sigma_proxy_clausification,[],[f1046]) ).
thf(f1048,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK8 @ sK26 @ Y0 )
& ( sK8 @ Y0 @ sK27 ) )
=> ( sK8 @ sK26 @ sK27 ) ) )
= $false )
| ~ spl5_19 ),
inference(beta-eta_normalization,[],[f1047]) ).
thf(f1049,plain,
( ( ( ^ [Y0: a] :
( ( ( sK8 @ sK26 @ Y0 )
& ( sK8 @ Y0 @ sK27 ) )
=> ( sK8 @ sK26 @ sK27 ) )
@ sK28 )
= $false )
| ~ spl5_19 ),
inference(sigma_proxy_clausification,[],[f1048]) ).
thf(f1050,plain,
( ( ( ( ( sK8 @ sK26 @ sK28 )
& ( sK8 @ sK28 @ sK27 ) )
=> ( sK8 @ sK26 @ sK27 ) )
= $false )
| ~ spl5_19 ),
inference(beta-eta_normalization,[],[f1049]) ).
thf(f1051,plain,
( ( $true = $false )
| ~ spl5_3
| ~ spl5_19 ),
inference(forward_demodulation,[],[f1050,f781]) ).
thf(f1052,plain,
( $false
| ~ spl5_3
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f1051]) ).
thf(f1053,plain,
( ~ spl5_3
| ~ spl5_19 ),
inference(avatar_contradiction_clause,[],[f1052]) ).
thf(f1186,plain,
( spl5_14
| spl5_13
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f479,f358,f481,f485]) ).
thf(f1488,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y0 @ Y2 )
& ( sK12 @ Y2 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
@ sK29 )
= $false )
| ~ spl5_14 ),
inference(sigma_proxy_clausification,[],[f487]) ).
thf(f1489,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ sK29 @ Y1 )
& ( sK12 @ Y1 @ Y0 ) )
=> ( sK12 @ sK29 @ Y0 ) ) ) )
= $false )
| ~ spl5_14 ),
inference(beta-eta_normalization,[],[f1488]) ).
thf(f1490,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ sK29 @ Y1 )
& ( sK12 @ Y1 @ Y0 ) )
=> ( sK12 @ sK29 @ Y0 ) ) )
@ sK30 ) )
| ~ spl5_14 ),
inference(sigma_proxy_clausification,[],[f1489]) ).
thf(f1491,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK12 @ sK29 @ Y0 )
& ( sK12 @ Y0 @ sK30 ) )
=> ( sK12 @ sK29 @ sK30 ) ) )
= $false )
| ~ spl5_14 ),
inference(beta-eta_normalization,[],[f1490]) ).
thf(f1492,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK12 @ sK29 @ Y0 )
& ( sK12 @ Y0 @ sK30 ) )
=> ( sK12 @ sK29 @ sK30 ) )
@ sK31 ) )
| ~ spl5_14 ),
inference(sigma_proxy_clausification,[],[f1491]) ).
thf(f1493,plain,
( ( $false
= ( ( ( sK12 @ sK29 @ sK31 )
& ( sK12 @ sK31 @ sK30 ) )
=> ( sK12 @ sK29 @ sK30 ) ) )
| ~ spl5_14 ),
inference(beta-eta_normalization,[],[f1492]) ).
thf(f1495,plain,
( ( $true
= ( ( sK12 @ sK29 @ sK31 )
& ( sK12 @ sK31 @ sK30 ) ) )
| ~ spl5_14 ),
inference(imp_proxy_clausification,[],[f1493]) ).
thf(f1511,plain,
( ( $true
= ( sK12 @ sK31 @ sK30 ) )
| ~ spl5_14 ),
inference(and_proxy_clausification,[],[f1495]) ).
thf(f1517,plain,
( ( ( ( ( sK12 @ sK29 @ sK31 )
& $true )
=> ( sK12 @ sK29 @ sK30 ) )
= $false )
| ~ spl5_14 ),
inference(superposition,[],[f1493,f1511]) ).
thf(f1518,plain,
( ! [X0: a] :
( $true
= ( ( $true
& ( sK12 @ X0 @ sK31 ) )
=> ( sK12 @ X0 @ sK30 ) ) )
| ~ spl5_4
| ~ spl5_14 ),
inference(superposition,[],[f215,f1511]) ).
thf(f1526,plain,
( ! [X0: a] :
( $true
= ( ( sK12 @ X0 @ sK31 )
=> ( sK12 @ X0 @ sK30 ) ) )
| ~ spl5_4
| ~ spl5_14 ),
inference(boolean_simplification,[],[f1518]) ).
thf(f1527,plain,
( ( ( ( sK12 @ sK29 @ sK31 )
=> ( sK12 @ sK29 @ sK30 ) )
= $false )
| ~ spl5_14 ),
inference(boolean_simplification,[],[f1517]) ).
thf(f1528,plain,
( ( $true = $false )
| ~ spl5_4
| ~ spl5_14 ),
inference(forward_demodulation,[],[f1527,f1526]) ).
thf(f1529,plain,
( $false
| ~ spl5_4
| ~ spl5_14 ),
inference(trivial_inequality_removal,[],[f1528]) ).
thf(f1530,plain,
( ~ spl5_4
| ~ spl5_14 ),
inference(avatar_contradiction_clause,[],[f1529]) ).
thf(f1531,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
| ( sK1 @ Y1 @ Y0 ) )
=> ( sK12 @ Y1 @ Y0 ) ) )
@ sK32 )
= $false )
| ~ spl5_13 ),
inference(sigma_proxy_clausification,[],[f483]) ).
thf(f1532,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK32 )
| ( sK1 @ Y0 @ sK32 ) )
=> ( sK12 @ Y0 @ sK32 ) ) )
= $false )
| ~ spl5_13 ),
inference(beta-eta_normalization,[],[f1531]) ).
thf(f1533,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK32 )
| ( sK1 @ Y0 @ sK32 ) )
=> ( sK12 @ Y0 @ sK32 ) )
@ sK33 )
= $false )
| ~ spl5_13 ),
inference(sigma_proxy_clausification,[],[f1532]) ).
thf(f1534,plain,
( ( ( ( ( sK2 @ sK33 @ sK32 )
| ( sK1 @ sK33 @ sK32 ) )
=> ( sK12 @ sK33 @ sK32 ) )
= $false )
| ~ spl5_13 ),
inference(beta-eta_normalization,[],[f1533]) ).
thf(f1535,plain,
( ( ( sK12 @ sK33 @ sK32 )
= $false )
| ~ spl5_13 ),
inference(imp_proxy_clausification,[],[f1534]) ).
thf(f1536,plain,
( ( $true
= ( ( sK2 @ sK33 @ sK32 )
| ( sK1 @ sK33 @ sK32 ) ) )
| ~ spl5_13 ),
inference(imp_proxy_clausification,[],[f1534]) ).
thf(f1553,plain,
( ( $true
= ( sK2 @ sK33 @ sK32 ) )
| ( $true
= ( sK1 @ sK33 @ sK32 ) )
| ~ spl5_13 ),
inference(or_proxy_clausification,[],[f1536]) ).
thf(f1561,definition,
( spl5_25
<=> ( $true
= ( sK2 @ sK33 @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition]) ).
thf(f1563,plain,
( ( $true
= ( sK2 @ sK33 @ sK32 ) )
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f1561]) ).
thf(f1565,definition,
( spl5_26
<=> ( $true
= ( sK1 @ sK33 @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_26])],[avatar_definition]) ).
thf(f1567,plain,
( ( $true
= ( sK1 @ sK33 @ sK32 ) )
| ~ spl5_26 ),
inference(avatar_component_clause,[],[f1565]) ).
thf(f1568,plain,
( spl5_25
| spl5_26
| ~ spl5_13 ),
inference(avatar_split_clause,[],[f1553,f481,f1565,f1561]) ).
thf(f1573,plain,
( ( $true
= ( ( ( sK1 @ sK33 @ sK32 )
| $true )
=> ( sK12 @ sK33 @ sK32 ) ) )
| ~ spl5_4
| ~ spl5_25 ),
inference(superposition,[],[f174,f1563]) ).
thf(f1579,plain,
( ( $true
= ( $true
=> ( sK12 @ sK33 @ sK32 ) ) )
| ~ spl5_4
| ~ spl5_25 ),
inference(boolean_simplification,[],[f1573]) ).
thf(f1580,plain,
( ( $true
= ( sK12 @ sK33 @ sK32 ) )
| ~ spl5_4
| ~ spl5_25 ),
inference(boolean_simplification,[],[f1579]) ).
thf(f1587,plain,
( ( $true = $false )
| ~ spl5_4
| ~ spl5_13
| ~ spl5_25 ),
inference(forward_demodulation,[],[f1580,f1535]) ).
thf(f1588,plain,
( $false
| ~ spl5_4
| ~ spl5_13
| ~ spl5_25 ),
inference(trivial_inequality_removal,[],[f1587]) ).
thf(f1589,plain,
( ~ spl5_4
| ~ spl5_13
| ~ spl5_25 ),
inference(avatar_contradiction_clause,[],[f1588]) ).
thf(f1619,plain,
( ( $true
= ( ( $true
| ( sK2 @ sK33 @ sK32 ) )
=> ( sK12 @ sK33 @ sK32 ) ) )
| ~ spl5_4
| ~ spl5_26 ),
inference(superposition,[],[f174,f1567]) ).
thf(f1624,plain,
( ( $true
= ( $true
=> ( sK12 @ sK33 @ sK32 ) ) )
| ~ spl5_4
| ~ spl5_26 ),
inference(boolean_simplification,[],[f1619]) ).
thf(f1625,plain,
( ( $true
= ( sK12 @ sK33 @ sK32 ) )
| ~ spl5_4
| ~ spl5_26 ),
inference(boolean_simplification,[],[f1624]) ).
thf(f1635,plain,
( ( $true = $false )
| ~ spl5_4
| ~ spl5_13
| ~ spl5_26 ),
inference(forward_demodulation,[],[f1625,f1535]) ).
thf(f1636,plain,
( $false
| ~ spl5_4
| ~ spl5_13
| ~ spl5_26 ),
inference(trivial_inequality_removal,[],[f1635]) ).
thf(f1637,plain,
( ~ spl5_4
| ~ spl5_13
| ~ spl5_26 ),
inference(avatar_contradiction_clause,[],[f1636]) ).
thf(f1642,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK2 @ X2 @ X1 )
| ( sK1 @ X2 @ X1 ) )
=> ( sK12 @ X2 @ X1 ) )
= $true )
| spl5_8 ),
inference(beta-eta_normalization,[],[f509]) ).
thf(f1722,plain,
( spl5_11
| spl5_12
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f412,f363,f418,f414]) ).
thf(f1759,plain,
( ( $true = ( ~ $true ) )
| ~ spl5_4
| spl5_8
| ~ spl5_10 ),
inference(forward_demodulation,[],[f441,f489]) ).
thf(f1760,plain,
( ( $true = $false )
| ~ spl5_4
| spl5_8
| ~ spl5_10 ),
inference(boolean_simplification,[],[f1759]) ).
thf(f1761,plain,
( $false
| ~ spl5_4
| spl5_8
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f1760]) ).
thf(f1762,plain,
( ~ spl5_4
| spl5_8
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f1761]) ).
thf(f1805,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y0 @ Y1 )
| ( sK1 @ Y0 @ Y1 ) )
=> ( sK12 @ Y0 @ Y1 ) ) )
@ sK34 ) )
| ~ spl5_12 ),
inference(sigma_proxy_clausification,[],[f420]) ).
thf(f1806,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ sK34 @ Y0 )
| ( sK1 @ sK34 @ Y0 ) )
=> ( sK12 @ sK34 @ Y0 ) ) )
= $false )
| ~ spl5_12 ),
inference(beta-eta_normalization,[],[f1805]) ).
thf(f1816,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ sK34 @ Y0 )
| ( sK1 @ sK34 @ Y0 ) )
=> ( sK12 @ sK34 @ Y0 ) )
@ sK35 )
= $false )
| ~ spl5_12 ),
inference(sigma_proxy_clausification,[],[f1806]) ).
thf(f1817,plain,
( ( ( ( ( sK2 @ sK34 @ sK35 )
| ( sK1 @ sK34 @ sK35 ) )
=> ( sK12 @ sK34 @ sK35 ) )
= $false )
| ~ spl5_12 ),
inference(beta-eta_normalization,[],[f1816]) ).
thf(f1818,plain,
( ( $true = $false )
| spl5_8
| ~ spl5_12 ),
inference(forward_demodulation,[],[f1817,f1642]) ).
thf(f1819,plain,
( $false
| spl5_8
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f1818]) ).
thf(f1820,plain,
( spl5_8
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f1819]) ).
thf(f1928,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK12 @ Y2 @ Y1 )
& ( sK12 @ Y0 @ Y2 ) )
=> ( sK12 @ Y0 @ Y1 ) ) ) )
@ sK36 )
= $false )
| ~ spl5_11 ),
inference(sigma_proxy_clausification,[],[f416]) ).
thf(f1929,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 @ Y0 )
& ( sK12 @ sK36 @ Y1 ) )
=> ( sK12 @ sK36 @ Y0 ) ) ) )
= $false )
| ~ spl5_11 ),
inference(beta-eta_normalization,[],[f1928]) ).
thf(f1940,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK12 @ Y1 @ Y0 )
& ( sK12 @ sK36 @ Y1 ) )
=> ( sK12 @ sK36 @ Y0 ) ) )
@ sK37 ) )
| ~ spl5_11 ),
inference(sigma_proxy_clausification,[],[f1929]) ).
thf(f1941,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK12 @ Y0 @ sK37 )
& ( sK12 @ sK36 @ Y0 ) )
=> ( sK12 @ sK36 @ sK37 ) ) )
= $false )
| ~ spl5_11 ),
inference(beta-eta_normalization,[],[f1940]) ).
thf(f1953,plain,
( ( ( ^ [Y0: a] :
( ( ( sK12 @ Y0 @ sK37 )
& ( sK12 @ sK36 @ Y0 ) )
=> ( sK12 @ sK36 @ sK37 ) )
@ sK38 )
= $false )
| ~ spl5_11 ),
inference(sigma_proxy_clausification,[],[f1941]) ).
thf(f1954,plain,
( ( ( ( ( sK12 @ sK38 @ sK37 )
& ( sK12 @ sK36 @ sK38 ) )
=> ( sK12 @ sK36 @ sK37 ) )
= $false )
| ~ spl5_11 ),
inference(beta-eta_normalization,[],[f1953]) ).
thf(f1955,plain,
( ( $true = $false )
| ~ spl5_4
| ~ spl5_11 ),
inference(forward_demodulation,[],[f1954,f215]) ).
thf(f1956,plain,
( $false
| ~ spl5_4
| ~ spl5_11 ),
inference(trivial_inequality_removal,[],[f1955]) ).
thf(f1957,plain,
( ~ spl5_4
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f1956]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( ~ spl5_2
| spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
( ~ spl5_4
| spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f370]) ).
cnf(s9,plain,
( ~ spl5_1
| spl5_15
| spl5_16 ),
inference(sat_conversion,[],[f586]) ).
cnf(s10,plain,
~ spl5_15,
inference(sat_conversion,[],[f604]) ).
cnf(s11,plain,
~ spl5_16,
inference(sat_conversion,[],[f631]) ).
cnf(s12,plain,
( ~ spl5_3
| ~ spl5_5
| spl5_17
| spl5_18 ),
inference(sat_conversion,[],[f857]) ).
cnf(s13,plain,
( ~ spl5_3
| ~ spl5_18 ),
inference(sat_conversion,[],[f889]) ).
cnf(s14,plain,
( ~ spl5_3
| ~ spl5_17 ),
inference(sat_conversion,[],[f915]) ).
cnf(s15,plain,
( ~ spl5_3
| spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f916]) ).
cnf(s16,plain,
( ~ spl5_3
| ~ spl5_6
| spl5_19
| spl5_20 ),
inference(sat_conversion,[],[f993]) ).
cnf(s17,plain,
( ~ spl5_3
| ~ spl5_20 ),
inference(sat_conversion,[],[f1029]) ).
cnf(s18,plain,
( ~ spl5_3
| ~ spl5_19 ),
inference(sat_conversion,[],[f1053]) ).
cnf(s19,plain,
( ~ spl5_8
| spl5_13
| spl5_14 ),
inference(sat_conversion,[],[f1186]) ).
cnf(s22,plain,
( ~ spl5_4
| ~ spl5_14 ),
inference(sat_conversion,[],[f1530]) ).
cnf(s23,plain,
( ~ spl5_13
| spl5_25
| spl5_26 ),
inference(sat_conversion,[],[f1568]) ).
cnf(s24,plain,
( ~ spl5_4
| ~ spl5_13
| ~ spl5_25 ),
inference(sat_conversion,[],[f1589]) ).
cnf(s25,plain,
( ~ spl5_4
| ~ spl5_13
| ~ spl5_26 ),
inference(sat_conversion,[],[f1637]) ).
cnf(s26,plain,
( ~ spl5_9
| spl5_11
| spl5_12 ),
inference(sat_conversion,[],[f1722]) ).
cnf(s29,plain,
( ~ spl5_4
| spl5_8
| ~ spl5_10 ),
inference(sat_conversion,[],[f1762]) ).
cnf(s30,plain,
( spl5_8
| ~ spl5_12 ),
inference(sat_conversion,[],[f1820]) ).
cnf(s31,plain,
( ~ spl5_4
| ~ spl5_11 ),
inference(sat_conversion,[],[f1957]) ).
cnf(s32,plain,
~ spl5_1,
inference(rat,[],[s9,s11,s10]) ).
cnf(s33,plain,
spl5_2,
inference(rat,[],[s1,s32]) ).
cnf(s34,plain,
( ~ spl5_13
| ~ spl5_4 ),
inference(rat,[],[s23,s24,s25]) ).
cnf(s35,plain,
~ spl5_4,
inference(rat,[],[s5,s26,s29,s30,s19,s34,s22,s31]) ).
cnf(s36,plain,
spl5_3,
inference(rat,[],[s2,s33,s35]) ).
cnf(s37,plain,
~ spl5_19,
inference(rat,[],[s18,s36]) ).
cnf(s38,plain,
~ spl5_20,
inference(rat,[],[s17,s36]) ).
cnf(s39,plain,
~ spl5_6,
inference(rat,[],[s16,s38,s37,s36]) ).
cnf(s40,plain,
spl5_5,
inference(rat,[],[s15,s39,s36]) ).
cnf(s41,plain,
~ spl5_17,
inference(rat,[],[s14,s36]) ).
cnf(s42,plain,
~ spl5_18,
inference(rat,[],[s13,s36]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s12,s42,s40,s41,s36]) ).
thf(f1958,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV157^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.00/0.12 % WCLimit : 300
% 0.00/0.12 % DateTime : Tue Sep 29 15:16:34 UTC 2026
% 0.00/0.12 % CPUTime :
% 0.00/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.14 Running higher-order theorem proving
% 0.12/0.15 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
% 0.74/0.26 % (232253)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.26 % (232262)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=969356271:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.26 % (232266)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.26 % (232266)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
% 0.74/0.26 % (232265)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3641585042:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.26 % (232262)Instruction limit reached!
% 0.74/0.26 % (232262)------------------------------
% 0.74/0.26 % (232262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.26 % (232262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.26 % (232262)CaDiCaL version: 2.1.3
% 0.74/0.26 % (232262)Termination reason: Instruction limit
% 0.74/0.26 % (232262)Termination phase: Preprocessing 3
% 0.74/0.26 % (232262)Time elapsed: 0.002 s
% 0.74/0.26 % (232262)Peak memory usage: 10 MB
% 0.74/0.26 % (232262)Instructions burned: 4 (million)
% 0.74/0.26 % (232259)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3069549410:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.26 % (232264)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2007867254:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.26 % (232263)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=355791710: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)
% 0.74/0.26 % (232266)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=1675898575:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.26 % (232260)lrs+10_16_si=on:nwc=1.5:random_seed=2806673932:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.26 % (232260)Instruction limit reached!
% 0.74/0.26 % (232260)------------------------------
% 0.74/0.26 % (232260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.26 % (232260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.26 % (232260)CaDiCaL version: 2.1.3
% 0.74/0.26 % (232260)Termination reason: Instruction limit
% 0.74/0.26 % (232260)Termination phase: Saturation
% 0.74/0.26 % (232260)Time elapsed: 0.008 s
% 0.74/0.26 % (232260)Peak memory usage: 11 MB
% 0.74/0.26 % (232260)Instructions burned: 19 (million)
% 0.74/0.26 % (232275)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3998832696:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.26 % (232264)Instruction limit reached!
% 0.74/0.26 % (232264)------------------------------
% 0.74/0.26 % (232264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.26 % (232264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.26 % (232264)CaDiCaL version: 2.1.3
% 0.74/0.26 % (232264)Termination reason: Instruction limit
% 0.74/0.26 % (232264)Termination phase: Saturation
% 0.74/0.26 % (232264)Time elapsed: 0.011 s
% 0.74/0.26 % (232264)Peak memory usage: 12 MB
% 0.74/0.26 % (232264)Instructions burned: 25 (million)
% 0.74/0.26 % (232275)Instruction limit reached!
% 0.74/0.26 % (232275)------------------------------
% 0.74/0.26 % (232275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.26 % (232275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.26 % (232275)CaDiCaL version: 2.1.3
% 0.74/0.26 % (232275)Termination reason: Instruction limit
% 0.74/0.26 % (232275)Termination phase: Preprocessing 3
% 0.74/0.26 % (232275)Time elapsed: 0.001 s
% 0.74/0.26 % (232275)Peak memory usage: 10 MB
% 0.74/0.26 % (232275)Instructions burned: 5 (million)
% 0.74/0.26 % (232286)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.26 % (232286)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=519617510:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.29 % (232286)Instruction limit reached!
% 0.74/0.29 % (232286)------------------------------
% 0.74/0.29 % (232286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.29 % (232286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.29 % (232286)CaDiCaL version: 2.1.3
% 0.74/0.29 % (232286)Termination reason: Instruction limit
% 0.74/0.29 % (232286)Termination phase: Saturation
% 0.74/0.29 % (232286)Time elapsed: 0.002 s
% 0.74/0.29 % (232286)Peak memory usage: 11 MB
% 0.74/0.29 % (232286)Instructions burned: 8 (million)
% 0.74/0.29 % (232283)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3125435977:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.29 % (232283)Instruction limit reached!
% 0.74/0.29 % (232283)------------------------------
% 0.74/0.29 % (232283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.29 % (232283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.29 % (232283)CaDiCaL version: 2.1.3
% 0.74/0.29 % (232283)Termination reason: Instruction limit
% 0.74/0.29 % (232283)Termination phase: Property scanning
% 0.74/0.29 % (232283)Time elapsed: 0.003 s
% 0.74/0.29 % (232283)Peak memory usage: 10 MB
% 0.74/0.29 % (232283)Instructions burned: 7 (million)
% 0.74/0.29 % (232287)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=312181651:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.29 % (232265)Instruction limit reached!
% 0.74/0.29 % (232265)------------------------------
% 0.74/0.29 % (232265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.29 % (232265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.29 % (232265)CaDiCaL version: 2.1.3
% 0.74/0.29 % (232265)Termination reason: Instruction limit
% 0.74/0.29 % (232265)Termination phase: Saturation
% 0.74/0.29 % (232265)Time elapsed: 0.034 s
% 0.74/0.29 % (232265)Peak memory usage: 13 MB
% 0.74/0.29 % (232265)Instructions burned: 75 (million)
% 0.74/0.29 % (232291)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
% 0.74/0.29 % (232291)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.29 % (232287)Instruction limit reached!
% 0.74/0.29 % (232287)------------------------------
% 0.74/0.29 % (232287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.29 % (232287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.29 % (232287)CaDiCaL version: 2.1.3
% 0.74/0.29 % (232287)Termination reason: Instruction limit
% 0.74/0.29 % (232287)Termination phase: Saturation
% 0.74/0.29 % (232287)Time elapsed: 0.006 s
% 0.74/0.29 % (232287)Peak memory usage: 12 MB
% 0.74/0.29 % (232287)Instructions burned: 13 (million)
% 0.74/0.29 % (232259)Instruction limit reached!
% 0.74/0.29 % (232259)------------------------------
% 0.74/0.29 % (232259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.29 % (232259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.29 % (232259)CaDiCaL version: 2.1.3
% 0.74/0.29 % (232259)Termination reason: Instruction limit
% 0.74/0.29 % (232259)Termination phase: Saturation
% 0.74/0.29 % (232259)Time elapsed: 0.037 s
% 0.74/0.29 % (232259)Peak memory usage: 13 MB
% 0.74/0.29 % (232259)Instructions burned: 87 (million)
% 0.74/0.29 % (232291)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3272793718:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.29 % (232291)Instruction limit reached!
% 0.74/0.29 % (232291)------------------------------
% 0.74/0.29 % (232291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.29 % (232291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.29 % (232291)CaDiCaL version: 2.1.3
% 0.74/0.29 % (232291)Termination reason: Instruction limit
% 0.74/0.29 % (232291)Termination phase: Saturation
% 0.74/0.29 % (232291)Time elapsed: 0.007 s
% 0.74/0.29 % (232291)Peak memory usage: 12 MB
% 0.74/0.33 % (232291)Instructions burned: 30 (million)
% 0.74/0.33 % (232294)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=1527813988:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.33 % (232296)lrs+10_1_si=on:cs=on:random_seed=1446329624:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.33 % (232299)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.33 % (232296)Instruction limit reached!
% 0.74/0.33 % (232296)------------------------------
% 0.74/0.33 % (232296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.33 % (232296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.33 % (232296)CaDiCaL version: 2.1.3
% 0.74/0.33 % (232296)Termination reason: Instruction limit
% 0.74/0.33 % (232296)Termination phase: Saturation
% 0.74/0.33 % (232296)Time elapsed: 0.004 s
% 0.74/0.33 % (232296)Peak memory usage: 11 MB
% 0.74/0.33 % (232296)Instructions burned: 10 (million)
% 0.74/0.33 % (232300)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2461786836:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.33 % (232302)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1421225577:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.74/0.33 % (232299)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=3694991297:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.33 % (232299)Instruction limit reached!
% 0.74/0.33 % (232299)------------------------------
% 0.74/0.33 % (232299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.33 % (232299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.33 % (232299)CaDiCaL version: 2.1.3
% 0.74/0.33 % (232299)Termination reason: Instruction limit
% 0.74/0.33 % (232299)Termination phase: Property scanning
% 0.74/0.33 % (232299)Time elapsed: 0.005 s
% 0.74/0.33 % (232299)Peak memory usage: 9 MB
% 0.74/0.33 % (232299)Instructions burned: 3 (million)
% 0.74/0.33 % (232300)Instruction limit reached!
% 0.74/0.33 % (232300)------------------------------
% 0.74/0.33 % (232300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.33 % (232300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.33 % (232300)CaDiCaL version: 2.1.3
% 0.74/0.33 % (232300)Termination reason: Instruction limit
% 0.74/0.33 % (232300)Termination phase: Saturation
% 0.74/0.33 % (232300)Time elapsed: 0.017 s
% 0.74/0.33 % (232300)Peak memory usage: 12 MB
% 0.74/0.33 % (232300)Instructions burned: 39 (million)
% 0.74/0.33 % (232307)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4039197394:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.74/0.33 % (232266)Instruction limit reached!
% 0.74/0.33 % (232266)------------------------------
% 0.74/0.33 % (232266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.33 % (232266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.33 % (232266)CaDiCaL version: 2.1.3
% 0.74/0.33 % (232266)Termination reason: Instruction limit
% 0.74/0.33 % (232266)Termination phase: Saturation
% 0.74/0.33 % (232266)Time elapsed: 0.073 s
% 0.74/0.33 % (232266)Peak memory usage: 13 MB
% 0.74/0.33 % (232266)Instructions burned: 157 (million)
% 0.74/0.33 % (232312)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=388736199:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.74/0.33 % (232307)Instruction limit reached!
% 0.74/0.33 % (232307)------------------------------
% 0.74/0.33 % (232307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.33 % (232307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.33 % (232307)CaDiCaL version: 2.1.3
% 0.74/0.33 % (232307)Termination reason: Instruction limit
% 0.74/0.33 % (232307)Termination phase: Saturation
% 0.74/0.33 % (232307)Time elapsed: 0.013 s
% 0.74/0.33 % (232307)Peak memory usage: 12 MB
% 0.74/0.33 % (232307)Instructions burned: 26 (million)
% 0.74/0.33 % (232294)Instruction limit reached!
% 0.74/0.33 % (232294)------------------------------
% 1.54/0.40 % (232294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.40 % (232294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.40 % (232294)CaDiCaL version: 2.1.3
% 1.54/0.40 % (232294)Termination reason: Instruction limit
% 1.54/0.40 % (232294)Termination phase: Saturation
% 1.54/0.40 % (232294)Time elapsed: 0.038 s
% 1.54/0.40 % (232294)Peak memory usage: 13 MB
% 1.54/0.40 % (232294)Instructions burned: 86 (million)
% 1.54/0.40 % (232312)Instruction limit reached!
% 1.54/0.40 % (232312)------------------------------
% 1.54/0.40 % (232312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.40 % (232312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.40 % (232312)CaDiCaL version: 2.1.3
% 1.54/0.40 % (232312)Termination reason: Instruction limit
% 1.54/0.40 % (232312)Termination phase: Saturation
% 1.54/0.40 % (232312)Time elapsed: 0.004 s
% 1.54/0.40 % (232312)Peak memory usage: 12 MB
% 1.54/0.40 % (232312)Instructions burned: 15 (million)
% 1.54/0.40 % (232317)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1044582142:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 1.54/0.40 % (232316)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=808285566:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 1.54/0.40 % (232317)Instruction limit reached!
% 1.54/0.40 % (232317)------------------------------
% 1.54/0.40 % (232317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.40 % (232317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.40 % (232317)CaDiCaL version: 2.1.3
% 1.54/0.40 % (232317)Termination reason: Instruction limit
% 1.54/0.40 % (232317)Termination phase: Saturation
% 1.54/0.40 % (232317)Time elapsed: 0.007 s
% 1.54/0.40 % (232317)Peak memory usage: 12 MB
% 1.54/0.40 % (232317)Instructions burned: 15 (million)
% 1.54/0.40 % (232322)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=699415950: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)
% 1.54/0.40 % (232322)Instruction limit reached!
% 1.54/0.40 % (232322)------------------------------
% 1.54/0.40 % (232322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.40 % (232322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.40 % (232322)CaDiCaL version: 2.1.3
% 1.54/0.40 % (232322)Termination reason: Instruction limit
% 1.54/0.40 % (232322)Termination phase: Property scanning
% 1.54/0.40 % (232322)Time elapsed: 0.001 s
% 1.54/0.40 % (232322)Peak memory usage: 10 MB
% 1.54/0.40 % (232322)Instructions burned: 5 (million)
% 1.54/0.40 % (232323)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2896445417:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.54/0.40 % (232324)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2221987577:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.54/0.40 % (232332)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
% 1.54/0.40 % (232332)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.54/0.40 % (232332)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=1234271121:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.54/0.40 % (232324)Instruction limit reached!
% 1.54/0.40 % (232324)------------------------------
% 1.54/0.40 % (232324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.40 % (232324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.40 % (232324)CaDiCaL version: 2.1.3
% 1.54/0.40 % (232324)Termination reason: Instruction limit
% 1.54/0.40 % (232324)Termination phase: Saturation
% 1.54/0.40 % (232324)Time elapsed: 0.010 s
% 1.54/0.40 % (232324)Peak memory usage: 11 MB
% 1.54/0.40 % (232324)Instructions burned: 23 (million)
% 1.54/0.40 % (232323)Instruction limit reached!
% 1.54/0.40 % (232323)------------------------------
% 1.54/0.40 % (232323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.44 % (232323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.44 % (232323)CaDiCaL version: 2.1.3
% 1.54/0.44 % (232323)Termination reason: Instruction limit
% 1.54/0.44 % (232323)Termination phase: Saturation
% 1.54/0.44 % (232323)Time elapsed: 0.011 s
% 1.54/0.44 % (232323)Peak memory usage: 12 MB
% 1.54/0.44 % (232323)Instructions burned: 27 (million)
% 1.54/0.44 % (232330)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2210613425:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.54/0.44 % (232332)Instruction limit reached!
% 1.54/0.44 % (232332)------------------------------
% 1.54/0.44 % (232332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.44 % (232332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.44 % (232332)CaDiCaL version: 2.1.3
% 1.54/0.44 % (232332)Termination reason: Instruction limit
% 1.54/0.44 % (232332)Termination phase: Saturation
% 1.54/0.44 % (232332)Time elapsed: 0.005 s
% 1.54/0.44 % (232332)Peak memory usage: 12 MB
% 1.54/0.44 % (232332)Instructions burned: 17 (million)
% 1.54/0.44 % (232343)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=747652623:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.54/0.44 % (232343)Instruction limit reached!
% 1.54/0.44 % (232343)------------------------------
% 1.54/0.44 % (232343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.44 % (232343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.44 % (232343)CaDiCaL version: 2.1.3
% 1.54/0.44 % (232343)Termination reason: Instruction limit
% 1.54/0.44 % (232343)Termination phase: Property scanning
% 1.54/0.44 % (232343)Time elapsed: 0.002 s
% 1.54/0.44 % (232343)Peak memory usage: 10 MB
% 1.54/0.44 % (232343)Instructions burned: 9 (million)
% 1.54/0.44 % (232340)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.54/0.44 % (232340)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=8719694:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.54/0.44 % (232342)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=3890605071:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.54/0.44 % (232340)Instruction limit reached!
% 1.54/0.44 % (232340)------------------------------
% 1.54/0.44 % (232340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.44 % (232340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.44 % (232340)CaDiCaL version: 2.1.3
% 1.54/0.44 % (232340)Termination reason: Instruction limit
% 1.54/0.44 % (232340)Termination phase: Saturation
% 1.54/0.44 % (232340)Time elapsed: 0.004 s
% 1.54/0.44 % (232340)Peak memory usage: 11 MB
% 1.54/0.44 % (232340)Instructions burned: 9 (million)
% 1.54/0.44 % (232347)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3063940444:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.54/0.44 % (232330)Instruction limit reached!
% 1.54/0.44 % (232330)------------------------------
% 1.54/0.44 % (232330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.44 % (232330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.44 % (232330)CaDiCaL version: 2.1.3
% 1.54/0.44 % (232330)Termination reason: Instruction limit
% 1.54/0.44 % (232330)Termination phase: Saturation
% 1.54/0.44 % (232330)Time elapsed: 0.028 s
% 1.54/0.44 % (232330)Peak memory usage: 12 MB
% 1.54/0.44 % (232330)Instructions burned: 61 (million)
% 1.54/0.44 % (232342)Instruction limit reached!
% 1.54/0.44 % (232342)------------------------------
% 1.54/0.44 % (232342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.54/0.44 % (232342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.54/0.44 % (232342)CaDiCaL version: 2.1.3
% 1.54/0.44 % (232342)Termination reason: Instruction limit
% 1.54/0.44 % (232342)Termination phase: Saturation
% 1.54/0.44 % (232342)Time elapsed: 0.014 s
% 1.54/0.44 % (232342)Peak memory usage: 12 MB
% 1.54/0.44 % (232342)Instructions burned: 33 (million)
% 1.54/0.44 % (232347)Instruction limit reached!
% 1.54/0.44 % (232347)------------------------------
% 2.14/0.51 % (232347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.51 % (232347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.51 % (232347)CaDiCaL version: 2.1.3
% 2.14/0.51 % (232347)Termination reason: Instruction limit
% 2.14/0.51 % (232347)Termination phase: Saturation
% 2.14/0.51 % (232347)Time elapsed: 0.008 s
% 2.14/0.51 % (232347)Peak memory usage: 11 MB
% 2.14/0.51 % (232347)Instructions burned: 27 (million)
% 2.14/0.51 % (232302)Instruction limit reached!
% 2.14/0.51 % (232302)------------------------------
% 2.14/0.51 % (232302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.51 % (232302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.51 % (232302)CaDiCaL version: 2.1.3
% 2.14/0.51 % (232302)Termination reason: Instruction limit
% 2.14/0.51 % (232302)Termination phase: Saturation
% 2.14/0.51 % (232302)Time elapsed: 0.098 s
% 2.14/0.51 % (232302)Peak memory usage: 13 MB
% 2.14/0.51 % (232302)Instructions burned: 253 (million)
% 2.14/0.51 % (232350)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1747109334:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.14/0.51 % (232353)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2776839455:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.14/0.51 % (232356)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3155613890:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.14/0.51 % (232357)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2226255908:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.14/0.51 % (232358)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1291351687:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.14/0.51 % (232350)Instruction limit reached!
% 2.14/0.51 % (232350)------------------------------
% 2.14/0.51 % (232350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.51 % (232350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.51 % (232350)CaDiCaL version: 2.1.3
% 2.14/0.51 % (232350)Termination reason: Instruction limit
% 2.14/0.51 % (232350)Termination phase: Saturation
% 2.14/0.51 % (232350)Time elapsed: 0.014 s
% 2.14/0.51 % (232350)Peak memory usage: 12 MB
% 2.14/0.51 % (232350)Instructions burned: 20 (million)
% 2.14/0.51 % (232358)Instruction limit reached!
% 2.14/0.51 % (232358)------------------------------
% 2.14/0.51 % (232358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.51 % (232358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.51 % (232358)CaDiCaL version: 2.1.3
% 2.14/0.51 % (232358)Termination reason: Instruction limit
% 2.14/0.51 % (232358)Termination phase: Saturation
% 2.14/0.51 % (232358)Time elapsed: 0.019 s
% 2.14/0.51 % (232358)Peak memory usage: 12 MB
% 2.14/0.51 % (232358)Instructions burned: 42 (million)
% 2.14/0.51 % (232369)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.14/0.51 % (232369)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1086235080:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 2.14/0.51 % (232369)Instruction limit reached!
% 2.14/0.51 % (232369)------------------------------
% 2.14/0.51 % (232369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.51 % (232369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.51 % (232369)CaDiCaL version: 2.1.3
% 2.14/0.51 % (232369)Termination reason: Instruction limit
% 2.14/0.51 % (232369)Termination phase: Saturation
% 2.14/0.51 % (232369)Time elapsed: 0.004 s
% 2.14/0.51 % (232369)Peak memory usage: 12 MB
% 2.14/0.51 % (232369)Instructions burned: 8 (million)
% 2.14/0.51 % (232370)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1141784097:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.14/0.51 % (232263)Instruction limit reached!
% 2.14/0.51 % (232263)------------------------------
% 2.14/0.51 % (232263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.14/0.51 % (232263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232263)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232263)Termination reason: Instruction limit
% 2.78/0.57 % (232263)Termination phase: Saturation
% 2.78/0.57 % (232263)Time elapsed: 0.226 s
% 2.78/0.57 % (232263)Peak memory usage: 14 MB
% 2.78/0.57 % (232263)Instructions burned: 634 (million)
% 2.78/0.57 % (232374)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=3209287744: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)
% 2.78/0.57 % (232316)Instruction limit reached!
% 2.78/0.57 % (232316)------------------------------
% 2.78/0.57 % (232316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232316)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232316)Termination reason: Instruction limit
% 2.78/0.57 % (232316)Termination phase: Saturation
% 2.78/0.57 % (232316)Time elapsed: 0.138 s
% 2.78/0.57 % (232316)Peak memory usage: 13 MB
% 2.78/0.57 % (232316)Instructions burned: 328 (million)
% 2.78/0.57 % (232356)Instruction limit reached!
% 2.78/0.57 % (232356)------------------------------
% 2.78/0.57 % (232356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232356)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232356)Termination reason: Instruction limit
% 2.78/0.57 % (232356)Termination phase: Saturation
% 2.78/0.57 % (232356)Time elapsed: 0.065 s
% 2.78/0.57 % (232356)Peak memory usage: 13 MB
% 2.78/0.57 % (232356)Instructions burned: 145 (million)
% 2.78/0.57 % (232377)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.78/0.57 % (232380)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=4110038171:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.78/0.57 % (232377)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2547819192:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.78/0.57 % (232357)Instruction limit reached!
% 2.78/0.57 % (232357)------------------------------
% 2.78/0.57 % (232357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232357)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232357)Termination reason: Instruction limit
% 2.78/0.57 % (232357)Termination phase: Saturation
% 2.78/0.57 % (232357)Time elapsed: 0.075 s
% 2.78/0.57 % (232357)Peak memory usage: 12 MB
% 2.78/0.57 % (232357)Instructions burned: 193 (million)
% 2.78/0.57 % (232377)Instruction limit reached!
% 2.78/0.57 % (232377)------------------------------
% 2.78/0.57 % (232377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232377)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232377)Termination reason: Instruction limit
% 2.78/0.57 % (232377)Termination phase: Saturation
% 2.78/0.57 % (232377)Time elapsed: 0.003 s
% 2.78/0.57 % (232377)Peak memory usage: 11 MB
% 2.78/0.57 % (232377)Instructions burned: 7 (million)
% 2.78/0.57 % (232380)Instruction limit reached!
% 2.78/0.57 % (232380)------------------------------
% 2.78/0.57 % (232380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232380)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232380)Termination reason: Instruction limit
% 2.78/0.57 % (232380)Termination phase: Saturation
% 2.78/0.57 % (232380)Time elapsed: 0.006 s
% 2.78/0.57 % (232380)Peak memory usage: 12 MB
% 2.78/0.57 % (232380)Instructions burned: 24 (million)
% 2.78/0.57 % (232382)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2367571671:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.78/0.57 % (232382)Instruction limit reached!
% 2.78/0.57 % (232382)------------------------------
% 2.78/0.57 % (232382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232382)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232382)Termination reason: Instruction limit
% 2.78/0.57 % (232382)Termination phase: Saturation
% 2.78/0.57 % (232382)Time elapsed: 0.009 s
% 2.78/0.57 % (232382)Peak memory usage: 13 MB
% 2.78/0.57 % (232382)Instructions burned: 20 (million)
% 2.78/0.57 % (232385)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=3001429655:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.78/0.57 % (232388)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=1505433588: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)
% 2.78/0.57 % (232390)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=1665082949: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)
% 2.78/0.57 % (232393)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2550403683:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.78/0.57 % (232390)Instruction limit reached!
% 2.78/0.57 % (232390)------------------------------
% 2.78/0.57 % (232390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232390)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232390)Termination reason: Instruction limit
% 2.78/0.57 % (232390)Termination phase: Saturation
% 2.78/0.57 % (232390)Time elapsed: 0.020 s
% 2.78/0.57 % (232390)Peak memory usage: 12 MB
% 2.78/0.57 % (232390)Instructions burned: 45 (million)
% 2.78/0.57 % (232370)Instruction limit reached!
% 2.78/0.57 % (232370)------------------------------
% 2.78/0.57 % (232370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232370)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232370)Termination reason: Instruction limit
% 2.78/0.57 % (232370)Termination phase: Saturation
% 2.78/0.57 % (232370)Time elapsed: 0.083 s
% 2.78/0.57 % (232370)Peak memory usage: 13 MB
% 2.78/0.57 % (232370)Instructions burned: 182 (million)
% 2.78/0.57 % (232402)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1581233387: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)
% 2.78/0.57 % (232403)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.78/0.57 % (232374)Instruction limit reached!
% 2.78/0.57 % (232374)------------------------------
% 2.78/0.57 % (232374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232374)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232374)Termination reason: Instruction limit
% 2.78/0.57 % (232374)Termination phase: Saturation
% 2.78/0.57 % (232374)Time elapsed: 0.080 s
% 2.78/0.57 % (232374)Peak memory usage: 13 MB
% 2.78/0.57 % (232374)Instructions burned: 171 (million)
% 2.78/0.57 % (232403)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=4290679708:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.78/0.57 % (232402)Instruction limit reached!
% 2.78/0.57 % (232402)------------------------------
% 2.78/0.57 % (232402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232402)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232402)Termination reason: Instruction limit
% 2.78/0.57 % (232402)Termination phase: Saturation
% 2.78/0.57 % (232402)Time elapsed: 0.011 s
% 2.78/0.57 % (232402)Peak memory usage: 12 MB
% 2.78/0.57 % (232402)Instructions burned: 23 (million)
% 2.78/0.57 % (232410)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2744157193:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.78/0.57 % (232411)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=835012042:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 2.78/0.57 % (232410)Instruction limit reached!
% 2.78/0.57 % (232410)------------------------------
% 2.78/0.57 % (232410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232410)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232410)Termination reason: Instruction limit
% 2.78/0.57 % (232410)Termination phase: Saturation
% 2.78/0.57 % (232410)Time elapsed: 0.006 s
% 2.78/0.57 % (232410)Peak memory usage: 12 MB
% 2.78/0.57 % (232410)Instructions burned: 13 (million)
% 2.78/0.57 % (232415)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=13601592:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 2.78/0.57 % (232411)Instruction limit reached!
% 2.78/0.57 % (232411)------------------------------
% 2.78/0.57 % (232411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232411)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232411)Termination reason: Instruction limit
% 2.78/0.57 % (232411)Termination phase: Saturation
% 2.78/0.57 % (232411)Time elapsed: 0.034 s
% 2.78/0.57 % (232411)Peak memory usage: 13 MB
% 2.78/0.57 % (232411)Instructions burned: 67 (million)
% 2.78/0.57 % (232385) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-232253-232385"...
% 2.78/0.57 % (232415)Instruction limit reached!
% 2.78/0.57 % (232415)------------------------------
% 2.78/0.57 % (232415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232415)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232415)Termination reason: Instruction limit
% 2.78/0.57 % (232415)Termination phase: Saturation
% 2.78/0.57 % (232415)Time elapsed: 0.023 s
% 2.78/0.57 % (232415)Peak memory usage: 12 MB
% 2.78/0.57 % (232415)Instructions burned: 51 (million)
% 2.78/0.57 % (232422)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2281671519:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 2.78/0.57 % (232385)...printing done.
% 2.78/0.57 % (232385)Refutation found. Thanks to Tanya!
% 2.78/0.57 % SZS status Theorem for theBenchmark
% 2.78/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/0.57 % (232385)------------------------------
% 2.78/0.57 % (232385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.78/0.57 % (232385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/0.57 % (232385)CaDiCaL version: 2.1.3
% 2.78/0.57 % (232385)Termination reason: Refutation
% 2.78/0.57 % (232385)Time elapsed: 0.124 s
% 2.78/0.57 % (232385)Peak memory usage: 16 MB
% 2.78/0.57 % (232385)Instructions burned: 339 (million)
% 2.78/0.57 % (232253)Success in time 0.411 s
% 2.78/0.57 % Vampire exiting
%------------------------------------------------------------------------------