%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU468^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:29:44 AM UTC 2026
% Result : Theorem 0.24s 0.40s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 20
% Syntax : Number of formulae : 219 ( 41 unt; 0 typ; 15 def)
% Number of atoms : 2121 ( 380 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 3675 ( 399 ~; 622 |; 95 &;2074 @)
% ( 14 <=>; 179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 420 ( 420 >; 0 *; 0 +; 0 <<)
% Number of symbols : 112 ( 108 usr; 20 con; 0-5 aty)
% ( 292 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 495 ( 0 sgn 110 !; 0 ?; 495 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
vAND: $o > $o > $o ).
thf(func_def_33,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sF0: $o ).
thf(func_def_45,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
sK1: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_50,type,
sK2: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_51,type,
sK3: $i > ( $i > $i > $o ) > $i > $i > $i > $o ).
thf(func_def_52,type,
sK4: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_53,type,
sK5: ( $i > $i > $o ) > $i ).
thf(func_def_54,type,
sK6: ( $i > $i > $o ) > $i ).
thf(func_def_55,type,
sK7: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_56,type,
sK8: ( $i > $i > $o ) > $i ).
thf(func_def_57,type,
sK9: ( $i > $i > $o ) > $i ).
thf(func_def_58,type,
sK10: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_59,type,
sK11: ( $i > $i > $o ) > $i ).
thf(func_def_60,type,
sK12: ( $i > $i > $o ) > $i ).
thf(func_def_61,type,
sK13: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_62,type,
sK14: ( $i > $i > $o ) > $i ).
thf(func_def_63,type,
sK15: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_64,type,
sK16: ( $i > $i > $o ) > $i ).
thf(func_def_65,type,
sK17: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_66,type,
sK18: ( $i > $i > $o ) > $i ).
thf(func_def_67,type,
sK19: ( $i > $i > $o ) > $i ).
thf(func_def_68,type,
sK20: ( $i > $i > $o ) > $i ).
thf(func_def_69,type,
sK21: $i > ( $i > $i > $o ) > $i > $i > $i > $o ).
thf(func_def_70,type,
sK22: ( $i > $i > $o ) > $i ).
thf(func_def_71,type,
sK23: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_72,type,
sK24: ( $i > $i > $o ) > $i ).
thf(func_def_73,type,
sK25: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_74,type,
sK26: ( $i > $i > $o ) > $i ).
thf(func_def_75,type,
sK27: ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK28: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK29: ( $i > $i > $o ) > $i ).
thf(func_def_78,type,
sK30: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_79,type,
sK31: ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK32: ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK33: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_82,type,
sK34: ( $i > $i > $o ) > $i ).
thf(func_def_83,type,
sK35: ( $i > $i > $o ) > ( $i > $i > $o ) > $i ).
thf(func_def_84,type,
sK36: ( $i > $i > $o ) > $i ).
thf(func_def_85,type,
sK37: $i > $i > $o ).
thf(func_def_86,type,
sK38: $i > $i > $o ).
thf(func_def_89,type,
sK41: ( $i > $i > $o ) > $i ).
thf(func_def_90,type,
sK42: ( $i > $i > $o ) > $i ).
thf(func_def_91,type,
sK43: ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
sK44: ( $i > $i > $o ) > $i ).
thf(func_def_93,type,
sK45: ( $i > $i > $o ) > $i ).
thf(func_def_94,type,
sK46: ( $i > $i > $o ) > $i ).
thf(func_def_95,type,
sK47: $i > $i > $o ).
thf(f1,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f5,axiom,
( mono
= ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X1: $i > $i > $o] :
( ( subrel @ X1 @ X2 )
=> ( subrel @ ( X0 @ X1 ) @ ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',monotonic) ).
thf(f13,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= trans ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f14,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( trans @ X3 )
& ( subrel @ X0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
= tc ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive_closure) ).
thf(f30,conjecture,
mono @ tc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_op_is_monotonic) ).
thf(f31,negated_conjecture,
~ ( mono @ tc ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f32,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X1 @ X2 ) ) )
= trans ),
inference(rectify,[],[f13]) ).
thf(f33,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( mono
= ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ( subrel @ X2 @ X1 )
=> ( subrel @ ( X0 @ X2 ) @ ( X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f37,plain,
( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( subrel @ Y1 @ Y2 )
=> ( subrel @ ( Y0 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f52,plain,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( trans @ X3 )
& ( subrel @ X0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
= tc ),
inference(rectify,[],[f14]) ).
thf(f53,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( subrel @ Y0 @ Y3 )
& ( trans @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f62,plain,
~ ( mono @ tc ),
inference(rectify,[],[f31]) ).
thf(f63,plain,
( ( mono @ tc )
!= $true ),
inference(fool_elimination,[],[f62]) ).
thf(f86,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
inference(rectify,[],[f1]) ).
thf(f87,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( ( mono @ tc )
!= $true ),
inference(flattening,[],[f63]) ).
thf(f95,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f110,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f112,plain,
( ( mono @ tc )
!= $true ),
inference(cnf_transformation,[],[f88]) ).
thf(f113,plain,
( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( subrel @ Y1 @ Y2 )
=> ( subrel @ ( Y0 @ Y1 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f116,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( subrel @ Y0 @ Y3 )
& ( trans @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f122,plain,
( mono
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f113,f95,f95]) ).
thf(f123,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f116,f95,f110]) ).
thf(f136,plain,
( ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f112,f122,f123]) ).
thf(f137,definition,
( sF0
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f138,plain,
sF0 != $true,
inference(definition_folding,[],[f136,f137]) ).
thf(f139,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: ( $i > $i > $o ) > $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ Y1
@ Y2 )
=> ( ^ [Y3: $i > $i > $o,Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
@ ( Y0 @ Y1 )
@ ( Y0 @ Y2 ) ) ) ) )
@ ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f137]) ).
thf(f324,plain,
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f325,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y0 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) )
& ( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y5 @ Y6 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK37 ) ) ),
inference(sigma_proxy_clausification,[],[f324]) ).
thf(f326,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK37 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK37 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f325]) ).
thf(f327,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK37 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK37 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y4 @ Y5 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) )
@ sK38 ) ) ),
inference(sigma_proxy_clausification,[],[f326]) ).
thf(f328,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( sK38 @ Y1 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK37 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK38 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f327]) ).
thf(f329,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK37 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK38 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f330,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( sK38 @ Y1 @ Y0 ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f331,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( sK38 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK37 @ Y0 @ X1 )
=> ( sK38 @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( sK37 @ Y0 @ X1 )
=> ( sK38 @ Y0 @ X1 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK37 @ X2 @ X1 )
=> ( sK38 @ X2 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK37 @ X2 @ X1 ) )
| ( ( sK38 @ X2 @ X1 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f336,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK37 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK38 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y3 @ Y4 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK39 ) ) ),
inference(sigma_proxy_clausification,[],[f329]) ).
thf(f337,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK37 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK39 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK38 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK39 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f338,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK37 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK39 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK38 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK39 ) ) ) )
@ sK40 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f337]) ).
thf(f339,plain,
( ( $false
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK37 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK40 @ sK39 ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK38 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK40 @ sK39 ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f338]) ).
thf(f340,plain,
( ( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK38 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK40 @ sK39 ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f339]) ).
thf(f341,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK37 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK40 @ sK39 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f339]) ).
thf(f342,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK37 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK40 @ sK39 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK40 @ sK39 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f342]) ).
thf(f344,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( sF0 = $true )
| ( ( X1 @ sK40 @ sK39 )
= $true ) ),
inference(imp_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
| ( sF0 = $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) )
@ ( sK41 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y0 @ Y1 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) )
@ ( sK41 @ X1 ) ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK37 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) )
@ ( sK42 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK37 @ Y0 @ ( sK42 @ X1 ) )
=> ( X1 @ Y0 @ ( sK42 @ X1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ Y0 )
& ( X1 @ Y1 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f349,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK37 @ Y0 @ ( sK42 @ X1 ) )
=> ( X1 @ Y0 @ ( sK42 @ X1 ) ) )
@ ( sK43 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ Y0 )
& ( X1 @ Y1 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK37 @ Y0 @ ( sK42 @ X1 ) )
=> ( X1 @ Y0 @ ( sK42 @ X1 ) ) )
@ ( sK43 @ X1 ) ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ Y0 )
& ( X1 @ Y1 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y1 @ Y0 ) ) )
@ ( sK44 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X1: $i > $i > $o] :
( ( ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
=> ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
= $false )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ Y0 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK44 @ X1 ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f350]) ).
thf(f352,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( sF0 = $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ Y0 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK44 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ Y0 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK44 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f351]) ).
thf(f354,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ Y0 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK44 @ X1 ) ) )
@ ( sK45 @ X1 ) )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X1: $i > $i > $o] :
( ( ( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ ( sK45 @ X1 ) @ ( sK41 @ X1 ) ) )
=> ( X1 @ ( sK45 @ X1 ) @ ( sK44 @ X1 ) ) )
= $false )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f354]) ).
thf(f356,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( sF0 = $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( $false
= ( X1 @ ( sK45 @ X1 ) @ ( sK44 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ ( sK45 @ X1 ) @ ( sK41 @ X1 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f355]) ).
thf(f358,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( X1 @ ( sK45 @ X1 ) @ ( sK41 @ X1 ) )
= $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f357]) ).
thf(f360,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ Y0 @ ( sK41 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK44 @ X1 ) ) )
@ ( sK46 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f352]) ).
thf(f361,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( $false
= ( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ ( sK46 @ X1 ) @ ( sK41 @ X1 ) ) )
=> ( X1 @ ( sK46 @ X1 ) @ ( sK44 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f360]) ).
thf(f362,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( sF0 = $true )
| ( $false
= ( X1 @ ( sK46 @ X1 ) @ ( sK44 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( sF0 = $true )
| ( ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
& ( X1 @ ( sK46 @ X1 ) @ ( sK41 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f361]) ).
thf(f364,plain,
! [X1: $i > $i > $o] :
( ( sF0 = $true )
| ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( X1 @ ( sK46 @ X1 ) @ ( sK41 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( sF0 = $true )
| ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f363]) ).
thf(f366,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK38 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK40 @ sK39 ) )
@ sK47 ) ) ),
inference(sigma_proxy_clausification,[],[f340]) ).
thf(f367,plain,
( ( sF0 = $true )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK38 @ Y1 @ Y0 )
=> ( sK47 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK47 @ Y0 @ Y1 )
& ( sK47 @ Y2 @ Y0 ) )
=> ( sK47 @ Y2 @ Y1 ) ) ) ) ) )
=> ( sK47 @ sK40 @ sK39 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f366]) ).
thf(f368,plain,
( ( sF0 = $true )
| ( $false
= ( sK47 @ sK40 @ sK39 ) ) ),
inference(imp_proxy_clausification,[],[f367]) ).
thf(f369,plain,
( ( sF0 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK38 @ Y1 @ Y0 )
=> ( sK47 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK47 @ Y0 @ Y1 )
& ( sK47 @ Y2 @ Y0 ) )
=> ( sK47 @ Y2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f367]) ).
thf(f370,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK47 @ Y0 @ Y1 )
& ( sK47 @ Y2 @ Y0 ) )
=> ( sK47 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f369]) ).
thf(f371,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK38 @ Y1 @ Y0 )
=> ( sK47 @ Y1 @ Y0 ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f369]) ).
thf(f372,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK38 @ Y1 @ Y0 )
=> ( sK47 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK38 @ Y0 @ X1 )
=> ( sK47 @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK38 @ Y0 @ X1 )
=> ( sK47 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK38 @ X2 @ X1 )
=> ( sK47 @ X2 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X1: $i] :
( ( ( sK47 @ X2 @ X1 )
= $true )
| ( sF0 = $true )
| ( $false
= ( sK38 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f375]) ).
thf(f377,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK47 @ Y0 @ Y1 )
& ( sK47 @ Y2 @ Y0 ) )
=> ( sK47 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f370]) ).
thf(f378,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK47 @ X1 @ Y0 )
& ( sK47 @ Y1 @ X1 ) )
=> ( sK47 @ Y1 @ Y0 ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f377]) ).
thf(f379,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK47 @ X1 @ Y0 )
& ( sK47 @ Y1 @ X1 ) )
=> ( sK47 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK47 @ X1 @ X2 )
& ( sK47 @ Y0 @ X1 ) )
=> ( sK47 @ Y0 @ X2 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f381,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK47 @ X1 @ X2 )
& ( sK47 @ Y0 @ X1 ) )
=> ( sK47 @ Y0 @ X2 ) )
@ X3 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( ( sK47 @ X1 @ X2 )
& ( sK47 @ X3 @ X1 ) )
=> ( sK47 @ X3 @ X2 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f383,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK47 @ X3 @ X2 )
= $true )
| ( $false
= ( ( sK47 @ X1 @ X2 )
& ( sK47 @ X3 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f382]) ).
thf(f384,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK47 @ X1 @ X2 ) )
| ( ( sK47 @ X3 @ X1 )
= $false )
| ( ( sK47 @ X3 @ X2 )
= $true )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f383]) ).
thf(f534,definition,
( spl48_38
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( sK37 @ X2 @ X1 ) )
| ( ( sK38 @ X2 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl48_38])],[avatar_definition]) ).
thf(f535,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( sK37 @ X2 @ X1 ) )
| ( ( sK38 @ X2 @ X1 )
= $true ) )
| ~ spl48_38 ),
inference(avatar_component_clause,[],[f534]) ).
thf(f537,definition,
( spl48_39
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl48_39])],[avatar_definition]) ).
thf(f540,plain,
( spl48_38
| spl48_39 ),
inference(avatar_split_clause,[],[f335,f537,f534]) ).
thf(f542,definition,
( spl48_40
<=> ! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
= $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl48_40])],[avatar_definition]) ).
thf(f543,plain,
( ! [X1: $i > $i > $o] :
( ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
= $true )
| ( ( X1 @ sK40 @ sK39 )
= $true ) )
| ~ spl48_40 ),
inference(avatar_component_clause,[],[f542]) ).
thf(f544,plain,
( spl48_39
| spl48_40 ),
inference(avatar_split_clause,[],[f359,f542,f537]) ).
thf(f546,definition,
( spl48_41
<=> ! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( X1 @ ( sK45 @ X1 ) @ ( sK41 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl48_41])],[avatar_definition]) ).
thf(f547,plain,
( ! [X1: $i > $i > $o] :
( ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( X1 @ ( sK45 @ X1 ) @ ( sK41 @ X1 ) )
= $true )
| ( ( X1 @ sK40 @ sK39 )
= $true ) )
| ~ spl48_41 ),
inference(avatar_component_clause,[],[f546]) ).
thf(f548,plain,
( spl48_39
| spl48_41 ),
inference(avatar_split_clause,[],[f358,f546,f537]) ).
thf(f550,definition,
( spl48_42
<=> ! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( X1 @ ( sK45 @ X1 ) @ ( sK44 @ X1 ) ) )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl48_42])],[avatar_definition]) ).
thf(f551,plain,
( ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK45 @ X1 ) @ ( sK44 @ X1 ) ) )
| ( ( sK37 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) )
= $true )
| ( ( X1 @ sK40 @ sK39 )
= $true ) )
| ~ spl48_42 ),
inference(avatar_component_clause,[],[f550]) ).
thf(f552,plain,
( spl48_42
| spl48_39 ),
inference(avatar_split_clause,[],[f356,f537,f550]) ).
thf(f554,definition,
( spl48_43
<=> ! [X1: $i > $i > $o] :
( ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
= $true )
| ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl48_43])],[avatar_definition]) ).
thf(f555,plain,
( ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( X1 @ ( sK41 @ X1 ) @ ( sK44 @ X1 ) )
= $true ) )
| ~ spl48_43 ),
inference(avatar_component_clause,[],[f554]) ).
thf(f556,plain,
( spl48_39
| spl48_43 ),
inference(avatar_split_clause,[],[f365,f554,f537]) ).
thf(f558,definition,
( spl48_44
<=> ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( ( X1 @ ( sK46 @ X1 ) @ ( sK41 @ X1 ) )
= $true )
| ( ( X1 @ sK40 @ sK39 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl48_44])],[avatar_definition]) ).
thf(f559,plain,
( ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( ( X1 @ ( sK46 @ X1 ) @ ( sK41 @ X1 ) )
= $true ) )
| ~ spl48_44 ),
inference(avatar_component_clause,[],[f558]) ).
thf(f560,plain,
( spl48_39
| spl48_44 ),
inference(avatar_split_clause,[],[f364,f558,f537]) ).
thf(f562,definition,
( spl48_45
<=> ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) )
| ( $false
= ( X1 @ ( sK46 @ X1 ) @ ( sK44 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl48_45])],[avatar_definition]) ).
thf(f563,plain,
( ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK46 @ X1 ) @ ( sK44 @ X1 ) ) )
| ( ( X1 @ sK40 @ sK39 )
= $true )
| ( $false
= ( X1 @ ( sK43 @ X1 ) @ ( sK42 @ X1 ) ) ) )
| ~ spl48_45 ),
inference(avatar_component_clause,[],[f562]) ).
thf(f564,plain,
( spl48_45
| spl48_39 ),
inference(avatar_split_clause,[],[f362,f537,f562]) ).
thf(f566,definition,
( spl48_46
<=> ! [X2: $i,X1: $i] :
( ( ( sK47 @ X2 @ X1 )
= $true )
| ( $false
= ( sK38 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl48_46])],[avatar_definition]) ).
thf(f567,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( sK38 @ X2 @ X1 ) )
| ( ( sK47 @ X2 @ X1 )
= $true ) )
| ~ spl48_46 ),
inference(avatar_component_clause,[],[f566]) ).
thf(f568,plain,
( spl48_39
| spl48_46 ),
inference(avatar_split_clause,[],[f376,f566,f537]) ).
thf(f570,definition,
( spl48_47
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( sK47 @ X1 @ X2 ) )
| ( ( sK47 @ X3 @ X2 )
= $true )
| ( ( sK47 @ X3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl48_47])],[avatar_definition]) ).
thf(f571,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK47 @ X1 @ X2 ) )
| ( ( sK47 @ X3 @ X1 )
= $false )
| ( ( sK47 @ X3 @ X2 )
= $true ) )
| ~ spl48_47 ),
inference(avatar_component_clause,[],[f570]) ).
thf(f572,plain,
( spl48_39
| spl48_47 ),
inference(avatar_split_clause,[],[f384,f570,f537]) ).
thf(f574,definition,
( spl48_48
<=> ( $false
= ( sK47 @ sK40 @ sK39 ) ) ),
introduced(definition,[new_symbols(definition,[spl48_48])],[avatar_definition]) ).
thf(f576,plain,
( ( $false
= ( sK47 @ sK40 @ sK39 ) )
| ~ spl48_48 ),
inference(avatar_component_clause,[],[f574]) ).
thf(f577,plain,
( spl48_39
| spl48_48 ),
inference(avatar_split_clause,[],[f368,f574,f537]) ).
thf(f578,plain,
~ spl48_39,
inference(avatar_split_clause,[],[f138,f537]) ).
thf(f607,plain,
( ! [X0: $i > $i > $o] :
( ( ( X0 @ sK40 @ sK39 )
= $true )
| ( ( X0 @ ( sK41 @ X0 ) @ ( sK44 @ X0 ) )
= $true )
| ( $false = $true )
| ( ( sK38 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true ) )
| ~ spl48_38
| ~ spl48_40 ),
inference(constrained_superposition,[],[f535,f543]) ).
thf(f608,plain,
( ! [X0: $i > $i > $o] :
( ( ( sK38 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true )
| ( ( X0 @ sK40 @ sK39 )
= $true )
| ( ( X0 @ ( sK41 @ X0 ) @ ( sK44 @ X0 ) )
= $true ) )
| ~ spl48_38
| ~ spl48_40 ),
inference(trivial_inequality_removal,[],[f607]) ).
thf(f611,plain,
( ! [X0: $i > $i > $o] :
( ( ( X0 @ ( sK45 @ X0 ) @ ( sK41 @ X0 ) )
= $true )
| ( ( sK38 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true )
| ( ( X0 @ sK40 @ sK39 )
= $true )
| ( $false = $true ) )
| ~ spl48_38
| ~ spl48_41 ),
inference(constrained_superposition,[],[f535,f547]) ).
thf(f612,plain,
( ! [X0: $i > $i > $o] :
( ( ( sK38 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true )
| ( ( X0 @ sK40 @ sK39 )
= $true )
| ( ( X0 @ ( sK45 @ X0 ) @ ( sK41 @ X0 ) )
= $true ) )
| ~ spl48_38
| ~ spl48_41 ),
inference(trivial_inequality_removal,[],[f611]) ).
thf(f708,plain,
( ! [X0: $i > $i > $o] :
( ( ( sK47 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true )
| ( ( X0 @ sK40 @ sK39 )
= $true )
| ( ( X0 @ ( sK41 @ X0 ) @ ( sK44 @ X0 ) )
= $true )
| ( $false = $true ) )
| ~ spl48_38
| ~ spl48_40
| ~ spl48_46 ),
inference(constrained_superposition,[],[f608,f567]) ).
thf(f720,plain,
( ! [X0: $i > $i > $o] :
( ( ( sK47 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true )
| ( ( X0 @ ( sK41 @ X0 ) @ ( sK44 @ X0 ) )
= $true )
| ( ( X0 @ sK40 @ sK39 )
= $true ) )
| ~ spl48_38
| ~ spl48_40
| ~ spl48_46 ),
inference(trivial_inequality_removal,[],[f708]) ).
thf(f764,plain,
( ! [X0: $i > $i > $o] :
( ( ( X0 @ sK40 @ sK39 )
= $true )
| ( ( X0 @ ( sK45 @ X0 ) @ ( sK41 @ X0 ) )
= $true )
| ( $false = $true )
| ( ( sK47 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true ) )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_46 ),
inference(constrained_superposition,[],[f612,f567]) ).
thf(f770,plain,
( ! [X0: $i > $i > $o] :
( ( ( sK47 @ ( sK43 @ X0 ) @ ( sK42 @ X0 ) )
= $true )
| ( ( X0 @ sK40 @ sK39 )
= $true )
| ( ( X0 @ ( sK45 @ X0 ) @ ( sK41 @ X0 ) )
= $true ) )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_46 ),
inference(trivial_inequality_removal,[],[f764]) ).
thf(f825,plain,
( ( $false = $true )
| ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_40
| ~ spl48_43
| ~ spl48_46 ),
inference(constrained_superposition,[],[f555,f720]) ).
thf(f826,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( $false = $true )
| ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_40
| ~ spl48_43
| ~ spl48_46 ),
inference(duplicate_literal_removal,[],[f825]) ).
thf(f827,plain,
( ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ~ spl48_38
| ~ spl48_40
| ~ spl48_43
| ~ spl48_46 ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f836,plain,
( ( $false = $true )
| ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_40
| ~ spl48_43
| ~ spl48_46
| ~ spl48_48 ),
inference(forward_demodulation,[],[f827,f576]) ).
thf(f837,plain,
( ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_40
| ~ spl48_43
| ~ spl48_46
| ~ spl48_48 ),
inference(trivial_inequality_removal,[],[f836]) ).
thf(f845,definition,
( spl48_57
<=> ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl48_57])],[avatar_definition]) ).
thf(f846,plain,
( ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
!= $true )
| spl48_57 ),
inference(avatar_component_clause,[],[f845]) ).
thf(f847,plain,
( ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_57 ),
inference(avatar_component_clause,[],[f845]) ).
thf(f849,definition,
( spl48_58
<=> ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl48_58])],[avatar_definition]) ).
thf(f851,plain,
( ( ( sK47 @ ( sK41 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_58 ),
inference(avatar_component_clause,[],[f849]) ).
thf(f854,plain,
( spl48_58
| ~ spl48_38
| ~ spl48_40
| ~ spl48_43
| ~ spl48_46
| ~ spl48_48 ),
inference(avatar_split_clause,[],[f837,f574,f566,f554,f542,f534,f849]) ).
thf(f859,plain,
( ! [X0: $i] :
( ( $false
= ( sK47 @ X0 @ ( sK41 @ sK47 ) ) )
| ( ( sK47 @ X0 @ ( sK44 @ sK47 ) )
= $true )
| ( $false = $true ) )
| ~ spl48_47
| ~ spl48_58 ),
inference(constrained_superposition,[],[f851,f571]) ).
thf(f861,plain,
( ! [X0: $i] :
( ( $false
= ( sK47 @ X0 @ ( sK41 @ sK47 ) ) )
| ( ( sK47 @ X0 @ ( sK44 @ sK47 ) )
= $true ) )
| ~ spl48_47
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f859]) ).
thf(f867,plain,
( ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ( $false = $true )
| ~ spl48_47
| ~ spl48_57
| ~ spl48_58 ),
inference(constrained_superposition,[],[f847,f861]) ).
thf(f868,plain,
( ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_47
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f867]) ).
thf(f872,plain,
( ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $false )
| ( $false = $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ~ spl48_45
| ~ spl48_47
| ~ spl48_57
| ~ spl48_58 ),
inference(constrained_superposition,[],[f868,f563]) ).
thf(f875,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $false )
| ~ spl48_45
| ~ spl48_47
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f872]) ).
thf(f879,plain,
( ( $false = $true )
| ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $false )
| ~ spl48_45
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(forward_demodulation,[],[f875,f576]) ).
thf(f880,plain,
( ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $false )
| ~ spl48_45
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f879]) ).
thf(f895,plain,
( ( $false = $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_44
| ~ spl48_46 ),
inference(constrained_superposition,[],[f770,f559]) ).
thf(f897,plain,
( ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( $false = $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(constrained_superposition,[],[f880,f770]) ).
thf(f901,plain,
( ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( $false = $true )
| ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_44
| ~ spl48_46 ),
inference(duplicate_literal_removal,[],[f895]) ).
thf(f902,plain,
( ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_44
| ~ spl48_46 ),
inference(trivial_inequality_removal,[],[f901]) ).
thf(f905,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f897]) ).
thf(f913,plain,
( ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( $false = $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(forward_demodulation,[],[f905,f576]) ).
thf(f914,plain,
( ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f913]) ).
thf(f919,plain,
( ( $false = $true )
| ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(constrained_superposition,[],[f861,f914]) ).
thf(f923,plain,
( ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f919]) ).
thf(f928,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( $false = $true )
| ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(constrained_superposition,[],[f551,f923]) ).
thf(f930,plain,
( ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ( ( sK47 @ sK40 @ sK39 )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f928]) ).
thf(f933,plain,
( ( $false = $true )
| ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(forward_demodulation,[],[f930,f576]) ).
thf(f934,plain,
( ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f933]) ).
thf(f938,plain,
( ( $false = $true )
| ( ( sK38 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(constrained_superposition,[],[f535,f934]) ).
thf(f939,plain,
( ( ( sK38 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f938]) ).
thf(f941,plain,
( ( $false = $true )
| ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(constrained_superposition,[],[f939,f567]) ).
thf(f944,plain,
( ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f941]) ).
thf(f948,plain,
( ( $false = $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(forward_demodulation,[],[f944,f880]) ).
thf(f949,plain,
( $false
| ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(trivial_inequality_removal,[],[f948]) ).
thf(f950,plain,
( ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(avatar_contradiction_clause,[],[f949]) ).
thf(f953,plain,
( ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( $false = $true )
| ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_44
| ~ spl48_46
| ~ spl48_48 ),
inference(forward_demodulation,[],[f902,f576]) ).
thf(f954,plain,
( ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_41
| ~ spl48_44
| ~ spl48_46
| ~ spl48_48 ),
inference(trivial_inequality_removal,[],[f953]) ).
thf(f956,definition,
( spl48_59
<=> ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl48_59])],[avatar_definition]) ).
thf(f958,plain,
( ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_59 ),
inference(avatar_component_clause,[],[f956]) ).
thf(f960,plain,
( spl48_57
| spl48_59
| ~ spl48_38
| ~ spl48_41
| ~ spl48_44
| ~ spl48_46
| ~ spl48_48 ),
inference(avatar_split_clause,[],[f954,f574,f566,f558,f546,f534,f956,f845]) ).
thf(f965,plain,
( ( $false = $true )
| ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_47
| ~ spl48_58
| ~ spl48_59 ),
inference(constrained_superposition,[],[f958,f861]) ).
thf(f969,plain,
( ( ( sK47 @ ( sK45 @ sK47 ) @ ( sK44 @ sK47 ) )
= $true )
| ~ spl48_47
| ~ spl48_58
| ~ spl48_59 ),
inference(trivial_inequality_removal,[],[f965]) ).
thf(f979,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ( $false = $true )
| ~ spl48_42
| ~ spl48_47
| ~ spl48_58
| ~ spl48_59 ),
inference(constrained_superposition,[],[f551,f969]) ).
thf(f980,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_42
| ~ spl48_47
| ~ spl48_58
| ~ spl48_59 ),
inference(trivial_inequality_removal,[],[f979]) ).
thf(f984,plain,
( ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ( $false = $true )
| ~ spl48_42
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(forward_demodulation,[],[f980,f576]) ).
thf(f985,plain,
( ( ( sK37 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_42
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(trivial_inequality_removal,[],[f984]) ).
thf(f988,plain,
( ( $false = $true )
| ( ( sK38 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(constrained_superposition,[],[f985,f535]) ).
thf(f990,plain,
( ( ( sK38 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(trivial_inequality_removal,[],[f988]) ).
thf(f992,plain,
( ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ( $false = $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(constrained_superposition,[],[f990,f567]) ).
thf(f994,plain,
( ( ( sK47 @ ( sK43 @ sK47 ) @ ( sK42 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(trivial_inequality_removal,[],[f992]) ).
thf(f1012,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ( $false = $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_44
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(constrained_superposition,[],[f559,f994]) ).
thf(f1019,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ( ( sK47 @ ( sK46 @ sK47 ) @ ( sK41 @ sK47 ) )
= $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_44
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_58
| ~ spl48_59 ),
inference(trivial_inequality_removal,[],[f1012]) ).
thf(f1021,plain,
( ( ( sK47 @ sK40 @ sK39 )
= $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_44
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| spl48_57
| ~ spl48_58
| ~ spl48_59 ),
inference(forward_subsumption_resolution,[],[f1019,f846]) ).
thf(f1025,plain,
( ( $false = $true )
| ~ spl48_38
| ~ spl48_42
| ~ spl48_44
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| spl48_57
| ~ spl48_58
| ~ spl48_59 ),
inference(forward_demodulation,[],[f1021,f576]) ).
thf(f1026,plain,
( $false
| ~ spl48_38
| ~ spl48_42
| ~ spl48_44
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| spl48_57
| ~ spl48_58
| ~ spl48_59 ),
inference(trivial_inequality_removal,[],[f1025]) ).
thf(f1027,plain,
( ~ spl48_38
| ~ spl48_42
| ~ spl48_44
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| spl48_57
| ~ spl48_58
| ~ spl48_59 ),
inference(avatar_contradiction_clause,[],[f1026]) ).
cnf(s37,plain,
( spl48_38
| spl48_39 ),
inference(sat_conversion,[],[f540]) ).
cnf(s38,plain,
( spl48_39
| spl48_40 ),
inference(sat_conversion,[],[f544]) ).
cnf(s39,plain,
( spl48_39
| spl48_41 ),
inference(sat_conversion,[],[f548]) ).
cnf(s40,plain,
( spl48_39
| spl48_42 ),
inference(sat_conversion,[],[f552]) ).
cnf(s41,plain,
( spl48_39
| spl48_43 ),
inference(sat_conversion,[],[f556]) ).
cnf(s42,plain,
( spl48_39
| spl48_44 ),
inference(sat_conversion,[],[f560]) ).
cnf(s43,plain,
( spl48_39
| spl48_45 ),
inference(sat_conversion,[],[f564]) ).
cnf(s44,plain,
( spl48_39
| spl48_46 ),
inference(sat_conversion,[],[f568]) ).
cnf(s45,plain,
( spl48_39
| spl48_47 ),
inference(sat_conversion,[],[f572]) ).
cnf(s46,plain,
( spl48_39
| spl48_48 ),
inference(sat_conversion,[],[f577]) ).
cnf(s47,plain,
~ spl48_39,
inference(sat_conversion,[],[f578]) ).
cnf(s66,plain,
( ~ spl48_38
| ~ spl48_40
| ~ spl48_43
| ~ spl48_46
| ~ spl48_48
| spl48_58 ),
inference(sat_conversion,[],[f854]) ).
cnf(s69,plain,
( ~ spl48_38
| ~ spl48_41
| ~ spl48_42
| ~ spl48_45
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| ~ spl48_57
| ~ spl48_58 ),
inference(sat_conversion,[],[f950]) ).
cnf(s71,plain,
( ~ spl48_38
| ~ spl48_41
| ~ spl48_44
| ~ spl48_46
| ~ spl48_48
| spl48_57
| spl48_59 ),
inference(sat_conversion,[],[f960]) ).
cnf(s73,plain,
( ~ spl48_38
| ~ spl48_42
| ~ spl48_44
| ~ spl48_46
| ~ spl48_47
| ~ spl48_48
| spl48_57
| ~ spl48_58
| ~ spl48_59 ),
inference(sat_conversion,[],[f1027]) ).
cnf(s74,plain,
spl48_48,
inference(rat,[],[s46,s47]) ).
cnf(s75,plain,
spl48_47,
inference(rat,[],[s45,s47]) ).
cnf(s76,plain,
spl48_46,
inference(rat,[],[s44,s47]) ).
cnf(s78,plain,
spl48_45,
inference(rat,[],[s43,s47]) ).
cnf(s79,plain,
spl48_44,
inference(rat,[],[s42,s47]) ).
cnf(s80,plain,
spl48_43,
inference(rat,[],[s41,s47]) ).
cnf(s81,plain,
spl48_42,
inference(rat,[],[s40,s47]) ).
cnf(s82,plain,
spl48_41,
inference(rat,[],[s39,s47]) ).
cnf(s83,plain,
spl48_40,
inference(rat,[],[s38,s47]) ).
cnf(s84,plain,
spl48_38,
inference(rat,[],[s37,s47]) ).
cnf(s85,plain,
spl48_58,
inference(rat,[],[s66,s83,s74,s76,s80,s84]) ).
cnf(s88,plain,
~ spl48_57,
inference(rat,[],[s69,s84,s82,s74,s75,s76,s78,s81,s85]) ).
cnf(s90,plain,
~ spl48_59,
inference(rat,[],[s73,s85,s84,s81,s74,s75,s76,s79,s88]) ).
cnf(s91,plain,
$false,
inference(rat,[],[s71,s84,s82,s74,s76,s79,s90,s88]) ).
thf(f1028,plain,
$false,
inference(avatar_sat_refutation,[],[s91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU468^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:44:52 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.09/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.40 % (1304126)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.40 % (1304133)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1500577904:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.40 % (1304131)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2726019316:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.40 % (1304133)Instruction limit reached!
% 0.24/0.40 % (1304133)------------------------------
% 0.24/0.40 % (1304133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (1304133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (1304133)CaDiCaL version: 2.1.3
% 0.24/0.40 % (1304133)Termination reason: Instruction limit
% 0.24/0.40 % (1304133)Termination phase: Function definition elimination
% 0.24/0.40 % (1304133)Time elapsed: 0.004 s
% 0.24/0.40 % (1304133)Peak memory usage: 10 MB
% 0.24/0.40 % (1304133)Instructions burned: 8 (million)
% 0.24/0.40 % (1304137)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.40 % (1304137)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
% 0.24/0.40 % (1304132)lrs+10_16_si=on:nwc=1.5:random_seed=79439749:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.40 % (1304135)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1601211669:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.40 % (1304134)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=14490114: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)
% 0.24/0.40 % (1304136)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4199230905:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.40 % (1304137)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=362056795:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.40 % (1304132)Instruction limit reached!
% 0.24/0.40 % (1304132)------------------------------
% 0.24/0.40 % (1304132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (1304132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (1304132)CaDiCaL version: 2.1.3
% 0.24/0.40 % (1304132)Termination reason: Instruction limit
% 0.24/0.40 % (1304132)Termination phase: Saturation
% 0.24/0.40 % (1304132)Time elapsed: 0.016 s
% 0.24/0.40 % (1304132)Peak memory usage: 12 MB
% 0.24/0.40 % (1304132)Instructions burned: 18 (million)
% 0.24/0.40 % (1304135)Instruction limit reached!
% 0.24/0.40 % (1304135)------------------------------
% 0.24/0.40 % (1304135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (1304135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (1304135)CaDiCaL version: 2.1.3
% 0.24/0.40 % (1304135)Termination reason: Instruction limit
% 0.24/0.40 % (1304135)Termination phase: Saturation
% 0.24/0.40 % (1304135)Time elapsed: 0.024 s
% 0.24/0.40 % (1304135)Peak memory usage: 12 MB
% 0.24/0.40 % (1304135)Instructions burned: 25 (million)
% 0.24/0.40 % (1304140)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3560639507:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.40 % (1304146)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1795696736:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.24/0.40 % (1304146)Instruction limit reached!
% 0.24/0.40 % (1304146)------------------------------
% 0.24/0.40 % (1304146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (1304146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (1304146)CaDiCaL version: 2.1.3
% 0.24/0.40 % (1304146)Termination reason: Instruction limit
% 0.24/0.40 % (1304146)Termination phase: Function definition elimination
% 0.24/0.40 % (1304146)Time elapsed: 0.003 s
% 0.24/0.40 % (1304146)Peak memory usage: 10 MB
% 0.24/0.40 % (1304146)Instructions burned: 7 (million)
% 0.24/0.40 % (1304140)Instruction limit reached!
% 0.24/0.40 % (1304140)------------------------------
% 0.24/0.40 % (1304140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (1304140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (1304140)CaDiCaL version: 2.1.3
% 0.24/0.40 % (1304140)Termination reason: Instruction limit
% 0.24/0.40 % (1304140)Termination phase: Property scanning
% 0.24/0.40 % (1304140)Time elapsed: 0.006 s
% 0.24/0.40 % (1304140)Peak memory usage: 10 MB
% 0.24/0.40 % (1304140)Instructions burned: 4 (million)
% 0.24/0.40 % (1304137) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1304126-1304137"...
% 0.24/0.40 % (1304136)Instruction limit reached!
% 0.24/0.40 % (1304136)------------------------------
% 0.24/0.40 % (1304136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (1304136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (1304136)CaDiCaL version: 2.1.3
% 0.24/0.40 % (1304136)Termination reason: Instruction limit
% 0.24/0.40 % (1304136)Termination phase: Saturation
% 0.24/0.40 % (1304136)Time elapsed: 0.065 s
% 0.24/0.40 % (1304136)Peak memory usage: 13 MB
% 0.24/0.40 % (1304136)Instructions burned: 75 (million)
% 0.24/0.40 % (1304150)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=268568215:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.24/0.40 % (1304151)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
% 0.24/0.40 % (1304151)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.24/0.40 % (1304137)...printing done.
% 0.24/0.40 % (1304137)Refutation found. Thanks to Tanya!
% 0.24/0.40 % SZS status Theorem for theBenchmark
% 0.24/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.40 % (1304137)------------------------------
% 0.24/0.40 % (1304137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.40 % (1304137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.40 % (1304137)CaDiCaL version: 2.1.3
% 0.24/0.40 % (1304137)Termination reason: Refutation
% 0.24/0.40 % (1304137)Time elapsed: 0.069 s
% 0.24/0.40 % (1304137)Peak memory usage: 13 MB
% 0.24/0.40 % (1304137)Instructions burned: 76 (million)
% 0.24/0.40 % (1304126)Success in time 0.121 s
% 0.24/0.40 % Vampire exiting
%------------------------------------------------------------------------------