%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU473^1 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:29:45 AM UTC 2026
% Result : Theorem 1.19s 0.59s
% Output : Refutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 10
% Syntax : Number of formulae : 141 ( 93 unt; 0 typ; 2 def)
% Number of atoms : 1591 ( 191 equ; 0 cnn)
% Maximal formula atoms : 2 ( 11 avg)
% Number of connectives : 4737 ( 57 ~; 156 |; 230 &;3144 @)
% ( 2 <=>; 412 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 612 ( 612 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 11 con; 0-4 aty)
% ( 736 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 889 ( 0 sgn 38 !; 0 ?; 889 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
sK0: $i > $i > $o ).
thf(func_def_49,type,
sK1: $i > $i > $o ).
thf(func_def_52,type,
sK4: $i > $i > $o ).
thf(func_def_53,type,
sK5: $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,
( ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X1: $i > $i > $o] :
( ( subrel @ X1 @ X2 )
=> ( subrel @ ( X0 @ X1 ) @ ( X0 @ X2 ) ) ) )
= mono ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',monotonic) ).
thf(f8,axiom,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).
thf(f12,axiom,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',symmetric_closure) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
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(f16,axiom,
( trsc
= ( ^ [X0: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive_reflexive_symmetric_closure) ).
thf(f30,conjecture,
mono @ trsc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure_op_is_monotonic) ).
thf(f31,negated_conjecture,
~ ( mono @ trsc ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f38,plain,
( ( ^ [X0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X2: $i > $i > $o] :
( ( subrel @ X2 @ X1 )
=> ( subrel @ ( X0 @ X2 ) @ ( X0 @ X1 ) ) ) )
= mono ),
inference(rectify,[],[f5]) ).
thf(f39,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,[],[f38]) ).
thf(f40,plain,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
| ( X1 = X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f41,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f52,plain,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f53,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f56,plain,
~ ( mono @ trsc ),
inference(rectify,[],[f31]) ).
thf(f57,plain,
( $true
= ( ~ ( mono @ trsc ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
( sc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
| ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f59,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f67,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
inference(rectify,[],[f1]) ).
thf(f68,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,[],[f67]) ).
thf(f81,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(f82,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,[],[f81]) ).
thf(f83,plain,
( trsc
= ( ^ [Y0: $i > $i > $o] : ( sc @ ( rc @ ( tc @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f89,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,[],[f39]) ).
thf(f96,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,[],[f82]) ).
thf(f99,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f100,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,[],[f68]) ).
thf(f102,plain,
( sc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f104,plain,
( trsc
= ( ^ [Y0: $i > $i > $o] : ( sc @ ( rc @ ( tc @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f110,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f111,plain,
( $true
= ( ~ ( mono @ trsc ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f121,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,[],[f89,f100,f100]) ).
thf(f122,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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f96,f100,f110]) ).
thf(f124,plain,
( trsc
= ( ^ [Y0: $i > $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y3 @ Y2 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 @ Y2 @ Y3 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( ^ [Y5: $i > $i > $o,Y6: $i > $i > $o] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
@ Y1
@ Y4 )
& ( ^ [Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
@ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f104,f102,f99,f122]) ).
thf(f135,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 > $i > $o,Y2: $i,Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
| ( Y1 @ Y3 @ Y2 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 @ Y2 @ Y3 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y4: $i > $i > $o] :
( ( ( ^ [Y5: $i > $i > $o,Y6: $i > $i > $o] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( Y5 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) )
@ Y1
@ Y4 )
& ( ^ [Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( !! @ $i
@ ^ [Y8: $i] :
( ( ( Y5 @ Y7 @ Y8 )
& ( Y5 @ Y8 @ Y6 ) )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
@ Y4 ) )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f111,f121,f124]) ).
thf(f136,plain,
( $true
= ( ~ ( !! @ ( $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] :
( ( ( Y3 = Y2 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y2 = Y3 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( ( 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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y2 = Y3 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,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] :
( ( ( Y3 = Y2 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y2 = Y3 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( ( 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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y2 = Y3 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( $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] :
( ( ( Y3 = Y2 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y2 = Y3 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) )
=> ( ( 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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y3 @ Y2 ) ) )
| ( Y2 = Y3 )
| ( !! @ ( $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 @ Y6 @ Y7 )
& ( Y4 @ Y7 @ Y5 ) )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f137]) ).
thf(f140,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( ( 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 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $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 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f142,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( sK0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) )
& ( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( ( Y3 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) )
=> ( ( 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 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
| ( Y1 = Y2 )
| ( !! @ ( $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 @ Y5 @ Y6 )
& ( Y3 @ Y6 @ Y4 ) )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK1 @ Y1 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( ( Y1 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( ( Y1 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK1 @ Y1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f143]) ).
thf(f146,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK1 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK1 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK1 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
=> ( sK1 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
=> ( ( Y1 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
| ( Y0 = Y1 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( sK1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) )
& ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( Y2 @ Y4 @ Y5 )
& ( Y2 @ Y5 @ Y3 ) )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f152,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( Y0 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
| ( sK2 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) )
=> ( ( Y0 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK1 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
| ( sK2 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK1 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( Y0 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
| ( sK2 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) )
=> ( ( Y0 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK1 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 @ sK2 ) ) )
| ( sK2 = Y0 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( sK1 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y3 @ Y4 )
& ( Y1 @ Y4 @ Y2 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( ( ( sK3 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( ( sK3 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
( ( ( sK3 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f157,plain,
( ( ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( $false
= ( ( sK3 = sK2 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f159,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( $false
= ( sK2 = sK3 ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f175,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f176,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y1 @ Y2 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK4 @ sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
( $false
= ( sK4 @ sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y1 @ Y2 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f183,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y1 @ Y2 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f178]) ).
thf(f184,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f178]) ).
thf(f185,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 @ X1 )
=> ( sK4 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 @ X1 )
=> ( sK4 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X2 @ X1 )
=> ( sK4 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f235,plain,
( $false
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f236,plain,
( $false
= ( sK3 = sK2 ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f240,plain,
( $false
= ( ( $false
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( $false
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(constrained_superposition,[],[f154,f236]) ).
thf(f241,plain,
( $false
= ( ( $false
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(boolean_simplification,[],[f240]) ).
thf(f242,plain,
( $false
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( sK2 = sK3 )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(boolean_simplification,[],[f241]) ).
thf(f245,plain,
( $false
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| $false
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| $false
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(forward_demodulation,[],[f242,f160]) ).
thf(f246,plain,
( $false
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| $false
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(boolean_simplification,[],[f245]) ).
thf(f247,plain,
( $false
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(boolean_simplification,[],[f246]) ).
thf(f250,plain,
( ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( $false
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) )
= $false ),
inference(forward_demodulation,[],[f247,f235]) ).
thf(f251,plain,
( $false
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(boolean_simplification,[],[f250]) ).
thf(f252,plain,
( $false
= ( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
=> $false ) ),
inference(forward_demodulation,[],[f251,f159]) ).
thf(f253,plain,
( $false
= ( ~ ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ) ),
inference(boolean_simplification,[],[f252]) ).
thf(f254,plain,
( $false
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f255,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y2 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) )
=> ( sK5 @ sK3 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f254]) ).
thf(f267,plain,
( $false
= ( sK5 @ sK3 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f268,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y2 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f273,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y2 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f274,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f275,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 @ X1 )
=> ( sK5 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 @ X1 )
=> ( sK5 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK1 @ X2 @ X1 )
=> ( sK5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f337,plain,
( $true
= ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) )
| ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f338,plain,
( ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) )
| ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f337]) ).
thf(f340,definition,
( spl6_1
<=> ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f342,plain,
( ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) ) ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f340]) ).
thf(f344,definition,
( spl6_2
<=> ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f346,plain,
( ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f344]) ).
thf(f347,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f338,f344,f340]) ).
thf(f348,plain,
( ! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 )
= $true )
| ~ spl6_2 ),
inference(pi_proxy_clausification,[],[f346]) ).
thf(f349,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) ) )
| ~ spl6_2 ),
inference(beta-eta_normalization,[],[f348]) ).
thf(f354,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y1 @ Y2 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f349,f177]) ).
thf(f359,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK4 @ Y1 @ Y2 )
& ( sK4 @ Y2 @ Y0 ) )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ~ spl6_2 ),
inference(boolean_simplification,[],[f354]) ).
thf(f362,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
& $true ) ) )
| ~ spl6_2 ),
inference(forward_demodulation,[],[f359,f183]) ).
thf(f363,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl6_2 ),
inference(boolean_simplification,[],[f362]) ).
thf(f366,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl6_2 ),
inference(not_proxy_clausification,[],[f363]) ).
thf(f367,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK4 @ Y1 @ Y0 ) ) )
@ sK7 ) )
| ~ spl6_2 ),
inference(sigma_proxy_clausification,[],[f366]) ).
thf(f368,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK7 )
=> ( sK4 @ Y0 @ sK7 ) ) ) )
| ~ spl6_2 ),
inference(beta-eta_normalization,[],[f367]) ).
thf(f369,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK7 )
=> ( sK4 @ Y0 @ sK7 ) )
@ sK8 ) )
| ~ spl6_2 ),
inference(sigma_proxy_clausification,[],[f368]) ).
thf(f370,plain,
( ( $false
= ( ( sK0 @ sK8 @ sK7 )
=> ( sK4 @ sK8 @ sK7 ) ) )
| ~ spl6_2 ),
inference(beta-eta_normalization,[],[f369]) ).
thf(f371,plain,
( ( $false
= ( sK4 @ sK8 @ sK7 ) )
| ~ spl6_2 ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f372,plain,
( ( ( sK0 @ sK8 @ sK7 )
= $true )
| ~ spl6_2 ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f388,plain,
( ( ( $true
=> ( sK1 @ sK8 @ sK7 ) )
= $true )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f149,f372]) ).
thf(f389,plain,
( ( $true
= ( sK1 @ sK8 @ sK7 ) )
| ~ spl6_2 ),
inference(boolean_simplification,[],[f388]) ).
thf(f392,plain,
( ( ( $true
=> ( sK4 @ sK8 @ sK7 ) )
= $true )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f188,f389]) ).
thf(f394,plain,
( ( ( sK4 @ sK8 @ sK7 )
= $true )
| ~ spl6_2 ),
inference(boolean_simplification,[],[f392]) ).
thf(f397,plain,
( ( $false = $true )
| ~ spl6_2 ),
inference(forward_demodulation,[],[f394,f371]) ).
thf(f398,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f399,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f398]) ).
thf(f400,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK2 ) )
@ X1 ) )
| ~ spl6_1 ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f401,plain,
( ! [X1: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( X1 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y1 @ Y2 )
& ( X1 @ Y2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) )
=> ( X1 @ sK3 @ sK2 ) )
= $true )
| ~ spl6_1 ),
inference(beta-eta_normalization,[],[f400]) ).
thf(f406,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y2 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) )
=> $false )
= $true )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f401,f267]) ).
thf(f411,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK5 @ Y1 @ Y2 )
& ( sK5 @ Y2 @ Y0 ) )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true )
| ~ spl6_1 ),
inference(boolean_simplification,[],[f406]) ).
thf(f416,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) )
& $true ) )
= $true )
| ~ spl6_1 ),
inference(forward_demodulation,[],[f411,f273]) ).
thf(f417,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl6_1 ),
inference(boolean_simplification,[],[f416]) ).
thf(f418,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) ) ) )
| ~ spl6_1 ),
inference(not_proxy_clausification,[],[f417]) ).
thf(f419,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK5 @ Y1 @ Y0 ) ) )
@ sK9 ) )
| ~ spl6_1 ),
inference(sigma_proxy_clausification,[],[f418]) ).
thf(f420,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK9 )
=> ( sK5 @ Y0 @ sK9 ) ) )
= $false )
| ~ spl6_1 ),
inference(beta-eta_normalization,[],[f419]) ).
thf(f421,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK9 )
=> ( sK5 @ Y0 @ sK9 ) )
@ sK10 ) )
| ~ spl6_1 ),
inference(sigma_proxy_clausification,[],[f420]) ).
thf(f422,plain,
( ( $false
= ( ( sK0 @ sK10 @ sK9 )
=> ( sK5 @ sK10 @ sK9 ) ) )
| ~ spl6_1 ),
inference(beta-eta_normalization,[],[f421]) ).
thf(f423,plain,
( ( $false
= ( sK5 @ sK10 @ sK9 ) )
| ~ spl6_1 ),
inference(imp_proxy_clausification,[],[f422]) ).
thf(f424,plain,
( ( ( sK0 @ sK10 @ sK9 )
= $true )
| ~ spl6_1 ),
inference(imp_proxy_clausification,[],[f422]) ).
thf(f452,plain,
( ( $true
= ( $true
=> ( sK1 @ sK10 @ sK9 ) ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f149,f424]) ).
thf(f454,plain,
( ( $true
= ( sK1 @ sK10 @ sK9 ) )
| ~ spl6_1 ),
inference(boolean_simplification,[],[f452]) ).
thf(f455,plain,
( ( $true
= ( $true
=> ( sK5 @ sK10 @ sK9 ) ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f278,f454]) ).
thf(f460,plain,
( ( $true
= ( sK5 @ sK10 @ sK9 ) )
| ~ spl6_1 ),
inference(boolean_simplification,[],[f455]) ).
thf(f461,plain,
( ( $false = $true )
| ~ spl6_1 ),
inference(forward_demodulation,[],[f460,f423]) ).
thf(f462,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f463,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f462]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f347]) ).
cnf(s2,plain,
~ spl6_2,
inference(sat_conversion,[],[f399]) ).
cnf(s3,plain,
~ spl6_1,
inference(sat_conversion,[],[f463]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f464,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU473^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n014.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 13:42:30 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.32 Running higher-order theorem proving
% 0.29/0.35 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
% 1.19/0.55 % (2677150)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.19/0.55 % (2677156)lrs+10_16_si=on:nwc=1.5:random_seed=1896274649:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.19/0.55 % (2677156)Instruction limit reached!
% 1.19/0.55 % (2677156)------------------------------
% 1.19/0.55 % (2677156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.55 % (2677156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.55 % (2677156)CaDiCaL version: 2.1.3
% 1.19/0.55 % (2677156)Termination reason: Instruction limit
% 1.19/0.55 % (2677156)Termination phase: Saturation
% 1.19/0.55 % (2677156)Time elapsed: 0.008 s
% 1.19/0.55 % (2677156)Peak memory usage: 11 MB
% 1.19/0.55 % (2677156)Instructions burned: 19 (million)
% 1.19/0.55 % (2677161)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.19/0.55 % (2677161)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
% 1.19/0.55 % (2677157)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2073398425:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.19/0.55 % (2677155)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2305939883:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.19/0.55 % (2677158)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=1011197732: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)
% 1.19/0.55 % (2677160)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1998197244:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.19/0.55 % (2677159)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2895930369:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.19/0.55 % (2677161)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=1833051393:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.19/0.55 % (2677157)Instruction limit reached!
% 1.19/0.55 % (2677157)------------------------------
% 1.19/0.55 % (2677157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.55 % (2677157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.55 % (2677157)CaDiCaL version: 2.1.3
% 1.19/0.55 % (2677157)Termination reason: Instruction limit
% 1.19/0.55 % (2677157)Termination phase: Property scanning
% 1.19/0.55 % (2677157)Time elapsed: 0.003 s
% 1.19/0.55 % (2677157)Peak memory usage: 9 MB
% 1.19/0.55 % (2677157)Instructions burned: 3 (million)
% 1.19/0.55 % (2677159)Instruction limit reached!
% 1.19/0.55 % (2677159)------------------------------
% 1.19/0.55 % (2677159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.55 % (2677159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.55 % (2677159)CaDiCaL version: 2.1.3
% 1.19/0.55 % (2677159)Termination reason: Instruction limit
% 1.19/0.55 % (2677159)Termination phase: Saturation
% 1.19/0.55 % (2677159)Time elapsed: 0.023 s
% 1.19/0.55 % (2677159)Peak memory usage: 11 MB
% 1.19/0.55 % (2677159)Instructions burned: 24 (million)
% 1.19/0.55 % (2677163)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1830727746:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.19/0.55 % (2677163)Instruction limit reached!
% 1.19/0.55 % (2677163)------------------------------
% 1.19/0.55 % (2677163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.55 % (2677163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.55 % (2677163)CaDiCaL version: 2.1.3
% 1.19/0.55 % (2677163)Termination reason: Instruction limit
% 1.19/0.55 % (2677163)Termination phase: shuffling
% 1.19/0.55 % (2677163)Time elapsed: 0.002 s
% 1.19/0.55 % (2677163)Peak memory usage: 9 MB
% 1.19/0.55 % (2677163)Instructions burned: 2 (million)
% 1.19/0.55 % (2677170)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=687031325:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.19/0.59 % (2677170)Instruction limit reached!
% 1.19/0.59 % (2677170)------------------------------
% 1.19/0.59 % (2677170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677170)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677170)Termination reason: Instruction limit
% 1.19/0.59 % (2677170)Termination phase: Property scanning
% 1.19/0.59 % (2677170)Time elapsed: 0.005 s
% 1.19/0.59 % (2677170)Peak memory usage: 10 MB
% 1.19/0.59 % (2677170)Instructions burned: 6 (million)
% 1.19/0.59 % (2677171)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.19/0.59 % (2677171)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1134271702:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.19/0.59 % (2677160)Instruction limit reached!
% 1.19/0.59 % (2677160)------------------------------
% 1.19/0.59 % (2677160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677160)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677160)Termination reason: Instruction limit
% 1.19/0.59 % (2677160)Termination phase: Saturation
% 1.19/0.59 % (2677160)Time elapsed: 0.063 s
% 1.19/0.59 % (2677160)Peak memory usage: 13 MB
% 1.19/0.59 % (2677160)Instructions burned: 76 (million)
% 1.19/0.59 % (2677171)Instruction limit reached!
% 1.19/0.59 % (2677171)------------------------------
% 1.19/0.59 % (2677171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677171)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677171)Termination reason: Instruction limit
% 1.19/0.59 % (2677171)Termination phase: Function definition elimination
% 1.19/0.59 % (2677171)Time elapsed: 0.006 s
% 1.19/0.59 % (2677171)Peak memory usage: 10 MB
% 1.19/0.59 % (2677171)Instructions burned: 7 (million)
% 1.19/0.59 % (2677175)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
% 1.19/0.59 % (2677175)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.19/0.59 % (2677155)Instruction limit reached!
% 1.19/0.59 % (2677155)------------------------------
% 1.19/0.59 % (2677155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677155)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677155)Termination reason: Instruction limit
% 1.19/0.59 % (2677155)Termination phase: Saturation
% 1.19/0.59 % (2677155)Time elapsed: 0.071 s
% 1.19/0.59 % (2677155)Peak memory usage: 12 MB
% 1.19/0.59 % (2677155)Instructions burned: 88 (million)
% 1.19/0.59 % (2677175)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=925590226:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.19/0.59 % (2677173)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1894953757:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.19/0.59 % (2677173)Instruction limit reached!
% 1.19/0.59 % (2677173)------------------------------
% 1.19/0.59 % (2677173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677173)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677173)Termination reason: Instruction limit
% 1.19/0.59 % (2677173)Termination phase: Saturation
% 1.19/0.59 % (2677173)Time elapsed: 0.006 s
% 1.19/0.59 % (2677173)Peak memory usage: 11 MB
% 1.19/0.59 % (2677173)Instructions burned: 13 (million)
% 1.19/0.59 % (2677175)Instruction limit reached!
% 1.19/0.59 % (2677175)------------------------------
% 1.19/0.59 % (2677175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677175)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677175)Termination reason: Instruction limit
% 1.19/0.59 % (2677175)Termination phase: Saturation
% 1.19/0.59 % (2677175)Time elapsed: 0.022 s
% 1.19/0.59 % (2677175)Peak memory usage: 12 MB
% 1.19/0.59 % (2677175)Instructions burned: 28 (million)
% 1.19/0.59 % (2677177)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=1892813428:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.19/0.59 % (2677178)lrs+10_1_si=on:cs=on:random_seed=2502034923:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.19/0.59 % (2677179)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.19/0.59 % (2677179)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=940463517:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.19/0.59 % (2677178)Instruction limit reached!
% 1.19/0.59 % (2677178)------------------------------
% 1.19/0.59 % (2677178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677178)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677178)Termination reason: Instruction limit
% 1.19/0.59 % (2677178)Termination phase: Property scanning
% 1.19/0.59 % (2677178)Time elapsed: 0.008 s
% 1.19/0.59 % (2677178)Peak memory usage: 10 MB
% 1.19/0.59 % (2677178)Instructions burned: 9 (million)
% 1.19/0.59 % (2677179)Instruction limit reached!
% 1.19/0.59 % (2677179)------------------------------
% 1.19/0.59 % (2677179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677179)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677179)Termination reason: Instruction limit
% 1.19/0.59 % (2677179)Termination phase: Property scanning
% 1.19/0.59 % (2677179)Time elapsed: 0.002 s
% 1.19/0.59 % (2677179)Peak memory usage: 9 MB
% 1.19/0.59 % (2677179)Instructions burned: 2 (million)
% 1.19/0.59 % (2677182)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2478566228:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.19/0.59 % (2677182)Refutation not found, incomplete strategy
% 1.19/0.59 % (2677182)------------------------------
% 1.19/0.59 % (2677182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677182)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677182)Termination reason: Refutation not found, incomplete strategy
% 1.19/0.59 % (2677182)Time elapsed: 0.004 s
% 1.19/0.59 % (2677182)Peak memory usage: 12 MB
% 1.19/0.59 % (2677182)Instructions burned: 7 (million)
% 1.19/0.59 % (2677182)------------------------------
% 1.19/0.59 % (2677182)------------------------------
% 1.19/0.59 % (2677161)Instruction limit reached!
% 1.19/0.59 % (2677161)------------------------------
% 1.19/0.59 % (2677161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677161)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677161)Termination reason: Instruction limit
% 1.19/0.59 % (2677161)Termination phase: Saturation
% 1.19/0.59 % (2677161)Time elapsed: 0.121 s
% 1.19/0.59 % (2677161)Peak memory usage: 13 MB
% 1.19/0.59 % (2677161)Instructions burned: 158 (million)
% 1.19/0.59 % (2677183)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2286627224:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.19/0.59 % (2677183)Refutation not found, incomplete strategy
% 1.19/0.59 % (2677183)------------------------------
% 1.19/0.59 % (2677183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677183)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677183)Termination reason: Refutation not found, incomplete strategy
% 1.19/0.59 % (2677183)Time elapsed: 0.007 s
% 1.19/0.59 % (2677183)Peak memory usage: 12 MB
% 1.19/0.59 % (2677183)Instructions burned: 6 (million)
% 1.19/0.59 % (2677190)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1815803123:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.19/0.59 % (2677183)------------------------------
% 1.19/0.59 % (2677183)------------------------------
% 1.19/0.59 % (2677188)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=698694353:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.59 % (2677187)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1732671325:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.19/0.59 % (2677188)Instruction limit reached!
% 1.19/0.59 % (2677188)------------------------------
% 1.19/0.59 % (2677188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677188)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677188)Termination reason: Instruction limit
% 1.19/0.59 % (2677188)Termination phase: Saturation
% 1.19/0.59 % (2677188)Time elapsed: 0.012 s
% 1.19/0.59 % (2677188)Peak memory usage: 11 MB
% 1.19/0.59 % (2677188)Instructions burned: 15 (million)
% 1.19/0.59 % (2677177) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2677150-2677177"...
% 1.19/0.59 % (2677191)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4235140207:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.59 % (2677187)Instruction limit reached!
% 1.19/0.59 % (2677187)------------------------------
% 1.19/0.59 % (2677187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677187)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677187)Termination reason: Instruction limit
% 1.19/0.59 % (2677187)Termination phase: Saturation
% 1.19/0.59 % (2677187)Time elapsed: 0.023 s
% 1.19/0.59 % (2677187)Peak memory usage: 12 MB
% 1.19/0.59 % (2677187)Instructions burned: 25 (million)
% 1.19/0.59 % (2677191)Instruction limit reached!
% 1.19/0.59 % (2677191)------------------------------
% 1.19/0.59 % (2677191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.59 % (2677191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.59 % (2677191)CaDiCaL version: 2.1.3
% 1.19/0.59 % (2677191)Termination reason: Instruction limit
% 1.19/0.59 % (2677191)Termination phase: Saturation
% 1.19/0.59 % (2677191)Time elapsed: 0.012 s
% 1.19/0.59 % (2677191)Peak memory usage: 11 MB
% 1.19/0.59 % (2677191)Instructions burned: 14 (million)
% 1.19/0.59 % (2677194)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4120761379: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)
% 1.19/0.59 % (2677177)...printing done.
% 1.19/0.59 % (2677177)Refutation found. Thanks to Tanya!
% 1.19/0.59 % SZS status Theorem for theBenchmark
% 1.19/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.19/0.60 % (2677177)------------------------------
% 1.19/0.60 % (2677177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.60 % (2677177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.60 % (2677177)CaDiCaL version: 2.1.3
% 1.19/0.60 % (2677177)Termination reason: Refutation
% 1.19/0.60 % (2677177)Time elapsed: 0.077 s
% 1.19/0.60 % (2677177)Peak memory usage: 13 MB
% 1.19/0.60 % (2677177)Instructions burned: 91 (million)
% 1.19/0.60 % (2677150)Success in time 0.233 s
% 1.19/0.60 % Vampire exiting
%------------------------------------------------------------------------------