%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO066^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:46:28 AM UTC 2026
% Result : Theorem 0.86s 0.39s
% Output : Refutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 33
% Syntax : Number of formulae : 339 ( 131 unt; 0 typ; 21 def)
% Number of atoms : 2508 ( 388 equ; 0 cnn)
% Maximal formula atoms : 36 ( 7 avg)
% Number of connectives : 2885 ( 183 ~; 339 |; 112 &;1843 @)
% ( 21 <=>; 210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 143 ( 143 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 35 con; 0-4 aty)
% ( 177 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 505 ( 0 sgn 116 !; 0 ?; 505 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
o11: $i > $o ).
thf(func_def_22,type,
o12: $i > $o ).
thf(func_def_23,type,
o21: $i > $o ).
thf(func_def_24,type,
o22: $i > $o ).
thf(func_def_25,type,
o31: $i > $o ).
thf(func_def_26,type,
o32: $i > $o ).
thf(func_def_27,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_30,type,
vAND: $o > $o > $o ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vNOT: $o > $o ).
thf(func_def_36,type,
vIMP: $o > $o > $o ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X0 @ X1 )
& ( irel @ X1 @ X2 ) )
=> ( irel @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',trans_axiom) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f12,axiom,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(f13,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
= ior ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ior) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( ior @ ( iatom @ o21 ) @ ( iatom @ o22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(f24,axiom,
ivalid @ ( ior @ ( iatom @ o31 ) @ ( iatom @ o32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(f25,conjecture,
ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f26,negated_conjecture,
~ ( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f28,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f5]) ).
thf(f29,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f31,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f32,plain,
ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o12 ) ),
inference(rectify,[],[f22]) ).
thf(f33,plain,
( ( ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o12 ) ) )
= $true ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f35,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
ivalid @ ( ior @ ( iatom @ o31 ) @ ( iatom @ o32 ) ),
inference(rectify,[],[f24]) ).
thf(f37,plain,
( ( ivalid @ ( ior @ ( iatom @ o31 ) @ ( iatom @ o32 ) ) )
= $true ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f41,plain,
ivalid @ ( ior @ ( iatom @ o21 ) @ ( iatom @ o22 ) ),
inference(rectify,[],[f23]) ).
thf(f42,plain,
( ( ivalid @ ( ior @ ( iatom @ o21 ) @ ( iatom @ o22 ) ) )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X0 @ X1 )
& ( irel @ X1 @ X2 ) )
=> ( irel @ X0 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f44,plain,
! [X1: $i,X0: $i,X2: $i] :
( ( ( ( irel @ X1 @ X2 )
= $true )
& ( ( irel @ X0 @ X1 )
= $true ) )
=> ( ( irel @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f49,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f50,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f53,plain,
~ ( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f54,plain,
( ( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f61,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f62,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f65,plain,
( ( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f54]) ).
thf(f66,plain,
! [X1: $i,X0: $i,X2: $i] :
( ( ( irel @ X0 @ X2 )
= $true )
| ( ( irel @ X1 @ X2 )
!= $true )
| ( ( irel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f44]) ).
thf(f67,plain,
! [X2: $i,X1: $i,X0: $i] :
( ( ( irel @ X1 @ X2 )
!= $true )
| ( ( irel @ X0 @ X1 )
!= $true )
| ( ( irel @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f66]) ).
thf(f68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X1 @ X0 )
!= $true )
| ( ( irel @ X2 @ X1 )
!= $true )
| ( ( irel @ X2 @ X0 )
= $true ) ),
inference(rectify,[],[f67]) ).
thf(f70,plain,
( ( ivalid @ ( ior @ ( iatom @ o11 ) @ ( iatom @ o12 ) ) )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f73,plain,
( ( ivalid @ ( ior @ ( iatom @ o31 ) @ ( iatom @ o32 ) ) )
= $true ),
inference(cnf_transformation,[],[f37]) ).
thf(f74,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f77,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f78,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f82,plain,
( ( ivalid @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o21 ) ) @ ( ior @ ( iand @ ( iatom @ o11 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o21 ) @ ( iatom @ o31 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o22 ) ) @ ( ior @ ( iand @ ( iatom @ o12 ) @ ( iatom @ o32 ) ) @ ( iand @ ( iatom @ o22 ) @ ( iatom @ o32 ) ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f65]) ).
thf(f85,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f87,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f88,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X2 @ X1 )
!= $true )
| ( ( irel @ X1 @ X0 )
!= $true )
| ( ( irel @ X2 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f89,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f90,plain,
( ( ivalid @ ( ior @ ( iatom @ o21 ) @ ( iatom @ o22 ) ) )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f91,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f97,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f74,f91]) ).
thf(f98,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f85,f87,f77,f77]) ).
thf(f103,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ o11 )
@ ( ^ [Y0: $i > $o] : Y0
@ o12 ) ) )
= $true ),
inference(definition_unfolding,[],[f70,f78,f98,f89,f89]) ).
thf(f104,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ o31 )
@ ( ^ [Y0: $i > $o] : Y0
@ o32 ) ) ) ),
inference(definition_unfolding,[],[f73,f78,f98,f89,f89]) ).
thf(f105,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ o11 )
@ ( ^ [Y0: $i > $o] : Y0
@ o21 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ o11 )
@ ( ^ [Y0: $i > $o] : Y0
@ o31 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ o21 )
@ ( ^ [Y0: $i > $o] : Y0
@ o31 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ o12 )
@ ( ^ [Y0: $i > $o] : Y0
@ o22 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ o12 )
@ ( ^ [Y0: $i > $o] : Y0
@ o32 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ o22 )
@ ( ^ [Y0: $i > $o] : Y0
@ o32 ) ) ) ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f82,f78,f98,f97,f89,f89,f98,f97,f89,f89,f98,f97,f89,f89,f98,f97,f89,f89,f98,f97,f89,f89,f97,f89,f89]) ).
thf(f106,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ o21 )
@ ( ^ [Y0: $i > $o] : Y0
@ o22 ) ) ) ),
inference(definition_unfolding,[],[f90,f78,f98,f89,f89]) ).
thf(f107,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o21 @ Y1 )
& ( o11 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o31 @ Y2 )
& ( o11 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o31 @ Y3 )
& ( o21 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o22 @ Y4 )
& ( o12 @ Y4 ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( !! @ $i
@ ^ [Y5: $i] :
( ( irel @ Y4 @ Y5 )
=> ( ( o32 @ Y5 )
& ( o12 @ Y5 ) ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( irel @ Y4 @ Y5 )
=> ( ( o32 @ Y5 )
& ( o22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f108,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o21 @ Y1 )
& ( o11 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o31 @ Y2 )
& ( o11 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o31 @ Y3 )
& ( o21 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o22 @ Y4 )
& ( o12 @ Y4 ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( !! @ $i
@ ^ [Y5: $i] :
( ( irel @ Y4 @ Y5 )
=> ( ( o32 @ Y5 )
& ( o12 @ Y5 ) ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( irel @ Y4 @ Y5 )
=> ( ( o32 @ Y5 )
& ( o22 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( o21 @ Y0 )
& ( o11 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o31 @ Y1 )
& ( o11 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o31 @ Y2 )
& ( o21 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o22 @ Y3 )
& ( o12 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o32 @ Y4 )
& ( o12 @ Y4 ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o32 @ Y4 )
& ( o22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o31 @ Y1 )
& ( o11 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o31 @ Y2 )
& ( o21 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o22 @ Y3 )
& ( o12 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o32 @ Y4 )
& ( o12 @ Y4 ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o32 @ Y4 )
& ( o22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f109]) ).
thf(f111,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( o21 @ Y0 )
& ( o11 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f109]) ).
thf(f112,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( o21 @ Y0 )
& ( o11 @ Y0 ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f111]) ).
thf(f113,plain,
( $false
= ( ( irel @ sK0 @ sK1 )
=> ( ( o21 @ sK1 )
& ( o11 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
( $false
= ( ( o21 @ sK1 )
& ( o11 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( ( irel @ sK0 @ sK1 )
= $true ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f116,plain,
( ( ( o11 @ sK1 )
= $false )
| ( ( o21 @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f117,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o31 @ Y1 )
& ( o11 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o31 @ Y2 )
& ( o21 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o22 @ Y3 )
& ( o12 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o32 @ Y4 )
& ( o12 @ Y4 ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( ( o32 @ Y4 )
& ( o22 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f110]) ).
thf(f118,plain,
( $false
= ( ( irel @ sK0 @ sK2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o11 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o31 @ Y1 )
& ( o21 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o22 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o12 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o22 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o11 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o31 @ Y1 )
& ( o21 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o22 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o12 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o22 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f118]) ).
thf(f120,plain,
( ( irel @ sK0 @ sK2 )
= $true ),
inference(imp_proxy_clausification,[],[f118]) ).
thf(f121,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o31 @ Y1 )
& ( o21 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o22 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o12 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o22 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o11 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f119]) ).
thf(f123,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o11 @ Y0 ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ( ( irel @ sK2 @ sK3 )
=> ( ( o31 @ sK3 )
& ( o11 @ sK3 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
( ( ( o31 @ sK3 )
& ( o11 @ sK3 ) )
= $false ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( $true
= ( irel @ sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f127,plain,
( ( ( o11 @ sK3 )
= $false )
| ( ( o31 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f125]) ).
thf(f128,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o31 @ Y1 )
& ( o21 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o22 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o12 @ Y3 ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( o32 @ Y3 )
& ( o22 @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f121]) ).
thf(f129,plain,
( ( ( irel @ sK2 @ sK4 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o21 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o22 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o22 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f130,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o21 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o22 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o22 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( irel @ sK2 @ sK4 )
= $true ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o22 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o22 @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f130]) ).
thf(f133,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o21 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f130]) ).
thf(f134,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( o31 @ Y0 )
& ( o21 @ Y0 ) ) )
@ sK5 )
= $false ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( ( ( irel @ sK4 @ sK5 )
=> ( ( o31 @ sK5 )
& ( o21 @ sK5 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( ( ( o31 @ sK5 )
& ( o21 @ sK5 ) )
= $false ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( irel @ sK4 @ sK5 )
= $true ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f138,plain,
( ( ( o31 @ sK5 )
= $false )
| ( ( o21 @ sK5 )
= $false ) ),
inference(and_proxy_clausification,[],[f136]) ).
thf(f139,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o22 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o12 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( o32 @ Y2 )
& ( o22 @ Y2 ) ) ) ) ) ) ) ) )
@ sK6 )
= $false ),
inference(sigma_proxy_clausification,[],[f132]) ).
thf(f140,plain,
( ( ( irel @ sK4 @ sK6 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( o22 @ Y0 )
& ( o12 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o22 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( o22 @ Y0 )
& ( o12 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o22 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( irel @ sK4 @ sK6 )
= $true ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o22 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( o22 @ Y0 )
& ( o12 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f141]) ).
thf(f145,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( o22 @ Y0 )
& ( o12 @ Y0 ) ) )
@ sK7 )
= $false ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( irel @ sK6 @ sK7 )
=> ( ( o22 @ sK7 )
& ( o12 @ sK7 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( ( ( o22 @ sK7 )
& ( o12 @ sK7 ) )
= $false ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( irel @ sK6 @ sK7 )
= $true ),
inference(imp_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( ( ( o22 @ sK7 )
= $false )
| ( ( o12 @ sK7 )
= $false ) ),
inference(and_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK6 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o12 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( o32 @ Y1 )
& ( o22 @ Y1 ) ) ) ) ) )
@ sK8 )
= $false ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f151,plain,
( ( ( irel @ sK6 @ sK8 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o12 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o22 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o12 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o22 @ Y0 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( irel @ sK6 @ sK8 )
= $true ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o22 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o12 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f156,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o12 @ Y0 ) ) )
@ sK9 )
= $false ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( irel @ sK8 @ sK9 )
=> ( ( o32 @ sK9 )
& ( o12 @ sK9 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( ( o32 @ sK9 )
& ( o12 @ sK9 ) )
= $false ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $true
= ( irel @ sK8 @ sK9 ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( ( o32 @ sK9 )
= $false )
| ( $false
= ( o12 @ sK9 ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f161,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK8 @ Y0 )
=> ( ( o32 @ Y0 )
& ( o22 @ Y0 ) ) )
@ sK10 )
= $false ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f162,plain,
( ( ( irel @ sK8 @ sK10 )
=> ( ( o32 @ sK10 )
& ( o22 @ sK10 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( ( o32 @ sK10 )
& ( o22 @ sK10 ) )
= $false ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $true
= ( irel @ sK8 @ sK10 ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( ( o22 @ sK10 )
= $false )
| ( $false
= ( o32 @ sK10 ) ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o12 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f167,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o11 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o12 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o11 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o12 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o11 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o12 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o12 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o11 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o11 @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o12 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( o11 @ X2 ) ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( o12 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X3 )
=> ( o12 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( o11 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( o11 @ X2 ) )
| ( ( o12 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o21 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o22 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f176,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o21 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o22 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o21 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o22 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o22 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o21 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o21 @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o22 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o21 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o22 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( o22 @ X2 ) ) )
| ( ( ( irel @ X1 @ X3 )
=> ( o21 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( o22 @ X2 )
= $true )
| ( ( ( irel @ X1 @ X3 )
=> ( o21 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( ( o22 @ X2 )
= $true )
| ( $true
= ( o21 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o31 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o32 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f185,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o31 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( o32 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o31 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o32 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o31 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o32 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o31 @ Y0 ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o32 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o31 @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( o32 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X1 @ X3 )
=> ( o32 @ X3 ) )
= $true )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( o31 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( o31 @ X2 ) ) )
| ( $true
= ( o32 @ X3 ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( o32 @ X3 ) )
| ( $true
= ( o31 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f191]) ).
thf(f194,definition,
( spl11_1
<=> ( ( o11 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f196,plain,
( ( ( o11 @ sK1 )
= $false )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f198,definition,
( spl11_2
<=> ( ( o21 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f200,plain,
( ( ( o21 @ sK1 )
= $false )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f198]) ).
thf(f201,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f116,f198,f194]) ).
thf(f203,definition,
( spl11_3
<=> ( ( o31 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f205,plain,
( ( ( o31 @ sK3 )
= $false )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f207,definition,
( spl11_4
<=> ( ( o11 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f209,plain,
( ( ( o11 @ sK3 )
= $false )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f210,plain,
( spl11_3
| spl11_4 ),
inference(avatar_split_clause,[],[f127,f207,f203]) ).
thf(f212,definition,
( spl11_5
<=> ( ( o21 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f214,plain,
( ( ( o21 @ sK5 )
= $false )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f216,definition,
( spl11_6
<=> ( ( o31 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f218,plain,
( ( ( o31 @ sK5 )
= $false )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f216]) ).
thf(f219,plain,
( spl11_5
| spl11_6 ),
inference(avatar_split_clause,[],[f138,f216,f212]) ).
thf(f221,definition,
( spl11_7
<=> ( ( o22 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f223,plain,
( ( ( o22 @ sK7 )
= $false )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f225,definition,
( spl11_8
<=> ( ( o12 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f227,plain,
( ( ( o12 @ sK7 )
= $false )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f228,plain,
( spl11_7
| spl11_8 ),
inference(avatar_split_clause,[],[f149,f225,f221]) ).
thf(f230,definition,
( spl11_9
<=> ( $false
= ( o12 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f232,plain,
( ( $false
= ( o12 @ sK9 ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f230]) ).
thf(f234,definition,
( spl11_10
<=> ( ( o32 @ sK9 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f236,plain,
( ( ( o32 @ sK9 )
= $false )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f237,plain,
( spl11_9
| spl11_10 ),
inference(avatar_split_clause,[],[f160,f234,f230]) ).
thf(f239,definition,
( spl11_11
<=> ( $false
= ( o32 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f241,plain,
( ( $false
= ( o32 @ sK10 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f243,definition,
( spl11_12
<=> ( ( o22 @ sK10 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f245,plain,
( ( ( o22 @ sK10 )
= $false )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl11_11
| spl11_12 ),
inference(avatar_split_clause,[],[f165,f243,f239]) ).
thf(f257,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o22 @ X0 ) )
| ( ( o21 @ sK1 )
= $true ) ),
inference(superposition,[],[f183,f115]) ).
thf(f260,plain,
! [X0: $i] :
( ( $true
= ( o22 @ X0 ) )
| ( ( o21 @ sK1 )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f270,definition,
( spl11_14
<=> ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o31 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f271,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o31 @ X0 )
= $true ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f273,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( o22 @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl11_2 ),
inference(forward_demodulation,[],[f260,f200]) ).
thf(f274,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o22 @ X0 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f276,definition,
( spl11_15
<=> ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o11 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f277,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o11 @ X0 )
= $true ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f314,definition,
( spl11_20
<=> ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o22 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
thf(f315,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o22 @ X0 ) ) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f314]) ).
thf(f375,plain,
( spl11_20
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f274,f198,f314]) ).
thf(f391,plain,
( ( $true = $false )
| ( $true
= ( o11 @ sK1 ) )
| ~ spl11_15 ),
inference(superposition,[],[f115,f277]) ).
thf(f396,plain,
( ( $true
= ( o11 @ sK1 ) )
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f401,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_15 ),
inference(forward_demodulation,[],[f396,f196]) ).
thf(f402,plain,
( $false
| ~ spl11_1
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f403,plain,
( ~ spl11_1
| ~ spl11_15 ),
inference(avatar_contradiction_clause,[],[f402]) ).
thf(f441,definition,
( spl11_28
<=> ! [X0: $i] :
( ( ( irel @ sK2 @ X0 )
= $false )
| ( ( o11 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_28])],[avatar_definition]) ).
thf(f442,plain,
( ! [X0: $i] :
( ( ( irel @ sK2 @ X0 )
= $false )
| ( ( o11 @ X0 )
= $true ) )
| ~ spl11_28 ),
inference(avatar_component_clause,[],[f441]) ).
thf(f465,definition,
( spl11_33
<=> ( ( o11 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_33])],[avatar_definition]) ).
thf(f467,plain,
( ( ( o11 @ sK3 )
= $true )
| ~ spl11_33 ),
inference(avatar_component_clause,[],[f465]) ).
thf(f551,plain,
! [X0: $i] :
( ( ( irel @ sK4 @ X0 )
= $false )
| ( $true
= ( o22 @ X0 ) )
| ( ( o21 @ sK5 )
= $true )
| ( $true = $false ) ),
inference(superposition,[],[f183,f137]) ).
thf(f559,plain,
! [X0: $i] :
( ( $true
= ( o22 @ X0 ) )
| ( ( o21 @ sK5 )
= $true )
| ( ( irel @ sK4 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f595,plain,
( ! [X0: $i] :
( ( $true
= ( o22 @ X0 ) )
| ( $true = $false )
| ( ( irel @ sK4 @ X0 )
= $false ) )
| ~ spl11_5 ),
inference(forward_demodulation,[],[f559,f214]) ).
thf(f596,plain,
( ! [X0: $i] :
( ( $true
= ( o22 @ X0 ) )
| ( ( irel @ sK4 @ X0 )
= $false ) )
| ~ spl11_5 ),
inference(trivial_inequality_removal,[],[f595]) ).
thf(f642,definition,
( spl11_49
<=> ! [X0: $i] :
( ( ( irel @ sK4 @ X0 )
= $false )
| ( $true
= ( o22 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_49])],[avatar_definition]) ).
thf(f643,plain,
( ! [X0: $i] :
( ( ( irel @ sK4 @ X0 )
= $false )
| ( $true
= ( o22 @ X0 ) ) )
| ~ spl11_49 ),
inference(avatar_component_clause,[],[f642]) ).
thf(f666,plain,
( spl11_49
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f596,f212,f642]) ).
thf(f713,definition,
( spl11_55
<=> ( $true
= ( o12 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_55])],[avatar_definition]) ).
thf(f715,plain,
( ( $true
= ( o12 @ sK7 ) )
| ~ spl11_55 ),
inference(avatar_component_clause,[],[f713]) ).
thf(f830,plain,
( ( $true = $false )
| ~ spl11_8
| ~ spl11_55 ),
inference(superposition,[],[f227,f715]) ).
thf(f834,plain,
( $false
| ~ spl11_8
| ~ spl11_55 ),
inference(trivial_inequality_removal,[],[f830]) ).
thf(f835,plain,
( ~ spl11_8
| ~ spl11_55 ),
inference(avatar_contradiction_clause,[],[f834]) ).
thf(f892,definition,
( spl11_73
<=> ( ( o32 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_73])],[avatar_definition]) ).
thf(f894,plain,
( ( ( o32 @ sK9 )
= $true )
| ~ spl11_73 ),
inference(avatar_component_clause,[],[f892]) ).
thf(f970,definition,
( spl11_80
<=> ( $true
= ( o32 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_80])],[avatar_definition]) ).
thf(f972,plain,
( ( $true
= ( o32 @ sK10 ) )
| ~ spl11_80 ),
inference(avatar_component_clause,[],[f970]) ).
thf(f1081,plain,
! [X0: $i] :
( ( ( irel @ sK2 @ X0 )
!= $true )
| ( $true != $true )
| ( $true
= ( irel @ sK0 @ X0 ) ) ),
inference(superposition,[],[f88,f120]) ).
thf(f1083,plain,
! [X0: $i] :
( ( ( irel @ sK2 @ X0 )
= $true )
| ( ( irel @ sK4 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f88,f131]) ).
thf(f1085,plain,
! [X0: $i] :
( ( ( irel @ sK6 @ X0 )
!= $true )
| ( $true != $true )
| ( ( irel @ sK4 @ X0 )
= $true ) ),
inference(superposition,[],[f88,f142]) ).
thf(f1087,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( irel @ sK6 @ X0 )
= $true )
| ( $true
!= ( irel @ sK8 @ X0 ) ) ),
inference(superposition,[],[f88,f153]) ).
thf(f1091,plain,
! [X0: $i] :
( ( $true
!= ( irel @ sK8 @ X0 ) )
| ( ( irel @ sK6 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f1087]) ).
thf(f1094,plain,
! [X0: $i] :
( ( ( irel @ sK4 @ X0 )
!= $true )
| ( ( irel @ sK2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f1083]) ).
thf(f1099,plain,
! [X0: $i] :
( ( ( irel @ sK2 @ X0 )
!= $true )
| ( $true
= ( irel @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1081]) ).
thf(f1100,plain,
! [X0: $i] :
( ( ( irel @ sK6 @ X0 )
!= $true )
| ( ( irel @ sK4 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f1085]) ).
thf(f1110,plain,
( ( $true
= ( irel @ sK6 @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[],[f1091,f159]) ).
thf(f1111,plain,
( ( ( irel @ sK6 @ sK10 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f1091,f164]) ).
thf(f1114,plain,
( $true
= ( irel @ sK6 @ sK9 ) ),
inference(trivial_inequality_removal,[],[f1110]) ).
thf(f1116,plain,
( ( irel @ sK6 @ sK10 )
= $true ),
inference(trivial_inequality_removal,[],[f1111]) ).
thf(f1230,plain,
( ( ( irel @ sK2 @ sK5 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f1094,f137]) ).
thf(f1233,plain,
( ( irel @ sK2 @ sK5 )
= $true ),
inference(trivial_inequality_removal,[],[f1230]) ).
thf(f1335,plain,
( ( $true != $true )
| ( $true
= ( irel @ sK0 @ sK3 ) ) ),
inference(superposition,[],[f1099,f126]) ).
thf(f1337,plain,
( ( ( irel @ sK0 @ sK5 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f1099,f1233]) ).
thf(f1343,plain,
( ( irel @ sK0 @ sK5 )
= $true ),
inference(trivial_inequality_removal,[],[f1337]) ).
thf(f1345,plain,
( $true
= ( irel @ sK0 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f1335]) ).
thf(f1408,plain,
( ( $true != $true )
| ( $true
= ( irel @ sK4 @ sK7 ) ) ),
inference(superposition,[],[f1100,f148]) ).
thf(f1410,plain,
( ( $true != $true )
| ( ( irel @ sK4 @ sK9 )
= $true ) ),
inference(superposition,[],[f1100,f1114]) ).
thf(f1411,plain,
( ( $true != $true )
| ( ( irel @ sK4 @ sK10 )
= $true ) ),
inference(superposition,[],[f1100,f1116]) ).
thf(f1414,plain,
( $true
= ( irel @ sK4 @ sK7 ) ),
inference(trivial_inequality_removal,[],[f1408]) ).
thf(f1417,plain,
( ( irel @ sK4 @ sK10 )
= $true ),
inference(trivial_inequality_removal,[],[f1411]) ).
thf(f1418,plain,
( ( irel @ sK4 @ sK9 )
= $true ),
inference(trivial_inequality_removal,[],[f1410]) ).
thf(f1426,plain,
( ( $true
= ( irel @ sK2 @ sK7 ) )
| ( $true != $true ) ),
inference(superposition,[],[f1094,f1414]) ).
thf(f1427,plain,
( ( ( o22 @ sK7 )
= $true )
| ( $true = $false )
| ~ spl11_49 ),
inference(superposition,[],[f643,f1414]) ).
thf(f1437,plain,
( $true
= ( irel @ sK2 @ sK7 ) ),
inference(trivial_inequality_removal,[],[f1426]) ).
thf(f1443,plain,
( ( ( o22 @ sK7 )
= $true )
| ~ spl11_49 ),
inference(trivial_inequality_removal,[],[f1427]) ).
thf(f1454,plain,
( ( $true = $false )
| ~ spl11_7
| ~ spl11_49 ),
inference(forward_demodulation,[],[f1443,f223]) ).
thf(f1455,plain,
( $false
| ~ spl11_7
| ~ spl11_49 ),
inference(trivial_inequality_removal,[],[f1454]) ).
thf(f1456,plain,
( ~ spl11_7
| ~ spl11_49 ),
inference(avatar_contradiction_clause,[],[f1455]) ).
thf(f1563,plain,
( ( ( irel @ sK2 @ sK10 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f1094,f1417]) ).
thf(f1579,plain,
( ( irel @ sK2 @ sK10 )
= $true ),
inference(trivial_inequality_removal,[],[f1563]) ).
thf(f1591,plain,
( ( $true != $true )
| ( $true
= ( irel @ sK2 @ sK9 ) ) ),
inference(superposition,[],[f1094,f1418]) ).
thf(f1611,plain,
( $true
= ( irel @ sK2 @ sK9 ) ),
inference(trivial_inequality_removal,[],[f1591]) ).
thf(f1721,plain,
( ( $true = $false )
| ~ spl11_10
| ~ spl11_73 ),
inference(superposition,[],[f894,f236]) ).
thf(f1728,plain,
( $false
| ~ spl11_10
| ~ spl11_73 ),
inference(trivial_inequality_removal,[],[f1721]) ).
thf(f1729,plain,
( ~ spl11_10
| ~ spl11_73 ),
inference(avatar_contradiction_clause,[],[f1728]) ).
thf(f1782,plain,
( ( $true
= ( irel @ sK0 @ sK7 ) )
| ( $true != $true ) ),
inference(superposition,[],[f1099,f1437]) ).
thf(f1785,plain,
! [X0: $i] :
( ( $true
= ( o12 @ sK7 ) )
| ( ( o11 @ X0 )
= $true )
| ( $true = $false )
| ( ( irel @ sK2 @ X0 )
= $false ) ),
inference(superposition,[],[f174,f1437]) ).
thf(f1796,plain,
( $true
= ( irel @ sK0 @ sK7 ) ),
inference(trivial_inequality_removal,[],[f1782]) ).
thf(f1804,plain,
! [X0: $i] :
( ( ( o11 @ X0 )
= $true )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( $true
= ( o12 @ sK7 ) ) ),
inference(trivial_inequality_removal,[],[f1785]) ).
thf(f1814,plain,
( spl11_55
| spl11_28 ),
inference(avatar_split_clause,[],[f1804,f441,f713]) ).
thf(f1816,plain,
( ( $true = $false )
| ( ( o11 @ sK3 )
= $true )
| ~ spl11_28 ),
inference(superposition,[],[f442,f126]) ).
thf(f1830,plain,
( ( ( o11 @ sK3 )
= $true )
| ~ spl11_28 ),
inference(trivial_inequality_removal,[],[f1816]) ).
thf(f1843,plain,
( spl11_33
| ~ spl11_28 ),
inference(avatar_split_clause,[],[f1830,f441,f465]) ).
thf(f2278,plain,
( ( $true
= ( irel @ sK0 @ sK10 ) )
| ( $true != $true ) ),
inference(superposition,[],[f1099,f1579]) ).
thf(f2290,plain,
( $true
= ( irel @ sK0 @ sK10 ) ),
inference(trivial_inequality_removal,[],[f2278]) ).
thf(f2324,plain,
( ( $true = $false )
| ~ spl11_11
| ~ spl11_80 ),
inference(superposition,[],[f972,f241]) ).
thf(f2331,plain,
( $false
| ~ spl11_11
| ~ spl11_80 ),
inference(trivial_inequality_removal,[],[f2324]) ).
thf(f2332,plain,
( ~ spl11_11
| ~ spl11_80 ),
inference(avatar_contradiction_clause,[],[f2331]) ).
thf(f2453,plain,
( ( $true != $true )
| ( ( irel @ sK0 @ sK9 )
= $true ) ),
inference(superposition,[],[f1099,f1611]) ).
thf(f2470,plain,
( ( irel @ sK0 @ sK9 )
= $true ),
inference(trivial_inequality_removal,[],[f2453]) ).
thf(f2506,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o12 @ sK7 ) )
| ( ( o11 @ X0 )
= $true ) ),
inference(superposition,[],[f1796,f174]) ).
thf(f2534,plain,
! [X0: $i] :
( ( ( o11 @ X0 )
= $true )
| ( $true
= ( o12 @ sK7 ) )
| ( ( irel @ sK0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f2506]) ).
thf(f2546,plain,
( ! [X0: $i] :
( ( ( o11 @ X0 )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl11_8 ),
inference(forward_demodulation,[],[f2534,f227]) ).
thf(f2547,plain,
( ! [X0: $i] :
( ( ( o11 @ X0 )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl11_8 ),
inference(trivial_inequality_removal,[],[f2546]) ).
thf(f2550,plain,
( spl11_15
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f2547,f225,f276]) ).
thf(f2614,plain,
! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o32 @ sK10 ) )
| ( $true = $false )
| ( ( o31 @ X0 )
= $true ) ),
inference(superposition,[],[f2290,f192]) ).
thf(f2632,plain,
! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o31 @ X0 )
= $true )
| ( $true
= ( o32 @ sK10 ) ) ),
inference(trivial_inequality_removal,[],[f2614]) ).
thf(f2711,plain,
! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o12 @ sK9 ) )
| ( $true = $false )
| ( ( o11 @ X0 )
= $true ) ),
inference(superposition,[],[f2470,f174]) ).
thf(f2713,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( o31 @ X0 )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o32 @ sK9 )
= $true ) ),
inference(superposition,[],[f2470,f192]) ).
thf(f2734,plain,
! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( o12 @ sK9 ) )
| ( ( o11 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f2711]) ).
thf(f2737,plain,
! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o31 @ X0 )
= $true )
| ( ( o32 @ sK9 )
= $true ) ),
inference(trivial_inequality_removal,[],[f2713]) ).
thf(f2751,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o11 @ X0 )
= $true )
| ( $true = $false ) )
| ~ spl11_9 ),
inference(forward_demodulation,[],[f2734,f232]) ).
thf(f2752,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( o11 @ X0 )
= $true ) )
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f2751]) ).
thf(f2755,plain,
( spl11_15
| ~ spl11_9 ),
inference(avatar_split_clause,[],[f2752,f230,f276]) ).
thf(f3129,plain,
( ( $true = $false )
| ( ( o22 @ sK7 )
= $true )
| ~ spl11_20 ),
inference(superposition,[],[f1796,f315]) ).
thf(f3132,plain,
( ( ( o22 @ sK10 )
= $true )
| ( $true = $false )
| ~ spl11_20 ),
inference(superposition,[],[f2290,f315]) ).
thf(f3150,plain,
( ( ( o22 @ sK7 )
= $true )
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f3129]) ).
thf(f3155,plain,
( ( ( o22 @ sK10 )
= $true )
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f3132]) ).
thf(f3164,plain,
( ( $true = $false )
| ~ spl11_7
| ~ spl11_20 ),
inference(forward_demodulation,[],[f3150,f223]) ).
thf(f3165,plain,
( $false
| ~ spl11_7
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f3164]) ).
thf(f3166,plain,
( ~ spl11_7
| ~ spl11_20 ),
inference(avatar_contradiction_clause,[],[f3165]) ).
thf(f3167,plain,
( ( $true = $false )
| ~ spl11_12
| ~ spl11_20 ),
inference(forward_demodulation,[],[f3155,f245]) ).
thf(f3168,plain,
( $false
| ~ spl11_12
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f3167]) ).
thf(f3169,plain,
( ~ spl11_12
| ~ spl11_20 ),
inference(avatar_contradiction_clause,[],[f3168]) ).
thf(f3172,plain,
( spl11_80
| spl11_14 ),
inference(avatar_split_clause,[],[f2632,f270,f970]) ).
thf(f3183,plain,
( ( $true
= ( o31 @ sK5 ) )
| ( $true = $false )
| ~ spl11_14 ),
inference(superposition,[],[f271,f1343]) ).
thf(f3195,plain,
( ( ( o31 @ sK3 )
= $true )
| ( $true = $false )
| ~ spl11_14 ),
inference(superposition,[],[f1345,f271]) ).
thf(f3205,plain,
( ( ( o31 @ sK3 )
= $true )
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f3195]) ).
thf(f3222,plain,
( ( $true
= ( o31 @ sK5 ) )
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f3183]) ).
thf(f3229,plain,
( ( $true = $false )
| ~ spl11_3
| ~ spl11_14 ),
inference(forward_demodulation,[],[f3205,f205]) ).
thf(f3230,plain,
( $false
| ~ spl11_3
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f3229]) ).
thf(f3231,plain,
( ~ spl11_3
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f3230]) ).
thf(f3238,plain,
( ( $true = $false )
| ~ spl11_6
| ~ spl11_14 ),
inference(forward_demodulation,[],[f3222,f218]) ).
thf(f3239,plain,
( $false
| ~ spl11_6
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f3238]) ).
thf(f3240,plain,
( ~ spl11_6
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f3239]) ).
thf(f3245,plain,
( spl11_14
| spl11_73 ),
inference(avatar_split_clause,[],[f2737,f892,f270]) ).
thf(f3384,plain,
( ( $true = $false )
| ~ spl11_4
| ~ spl11_33 ),
inference(superposition,[],[f209,f467]) ).
thf(f3387,plain,
( $false
| ~ spl11_4
| ~ spl11_33 ),
inference(trivial_inequality_removal,[],[f3384]) ).
thf(f3388,plain,
( ~ spl11_4
| ~ spl11_33 ),
inference(avatar_contradiction_clause,[],[f3387]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f201]) ).
cnf(s2,plain,
( spl11_3
| spl11_4 ),
inference(sat_conversion,[],[f210]) ).
cnf(s3,plain,
( spl11_5
| spl11_6 ),
inference(sat_conversion,[],[f219]) ).
cnf(s4,plain,
( spl11_7
| spl11_8 ),
inference(sat_conversion,[],[f228]) ).
cnf(s5,plain,
( spl11_9
| spl11_10 ),
inference(sat_conversion,[],[f237]) ).
cnf(s6,plain,
( spl11_11
| spl11_12 ),
inference(sat_conversion,[],[f246]) ).
cnf(s25,plain,
( ~ spl11_2
| spl11_20 ),
inference(sat_conversion,[],[f375]) ).
cnf(s33,plain,
( ~ spl11_1
| ~ spl11_15 ),
inference(sat_conversion,[],[f403]) ).
cnf(s80,plain,
( ~ spl11_5
| spl11_49 ),
inference(sat_conversion,[],[f666]) ).
cnf(s114,plain,
( ~ spl11_8
| ~ spl11_55 ),
inference(sat_conversion,[],[f835]) ).
cnf(s152,plain,
( ~ spl11_7
| ~ spl11_49 ),
inference(sat_conversion,[],[f1456]) ).
cnf(s186,plain,
( ~ spl11_10
| ~ spl11_73 ),
inference(sat_conversion,[],[f1729]) ).
cnf(s205,plain,
( spl11_28
| spl11_55 ),
inference(sat_conversion,[],[f1814]) ).
cnf(s206,plain,
( ~ spl11_28
| spl11_33 ),
inference(sat_conversion,[],[f1843]) ).
cnf(s229,plain,
( ~ spl11_11
| ~ spl11_80 ),
inference(sat_conversion,[],[f2332]) ).
cnf(s245,plain,
( ~ spl11_8
| spl11_15 ),
inference(sat_conversion,[],[f2550]) ).
cnf(s251,plain,
( ~ spl11_9
| spl11_15 ),
inference(sat_conversion,[],[f2755]) ).
cnf(s338,plain,
( ~ spl11_7
| ~ spl11_20 ),
inference(sat_conversion,[],[f3166]) ).
cnf(s340,plain,
( ~ spl11_12
| ~ spl11_20 ),
inference(sat_conversion,[],[f3169]) ).
cnf(s343,plain,
( spl11_14
| spl11_80 ),
inference(sat_conversion,[],[f3172]) ).
cnf(s354,plain,
( ~ spl11_3
| ~ spl11_14 ),
inference(sat_conversion,[],[f3231]) ).
cnf(s362,plain,
( ~ spl11_6
| ~ spl11_14 ),
inference(sat_conversion,[],[f3240]) ).
cnf(s369,plain,
( spl11_14
| spl11_73 ),
inference(sat_conversion,[],[f3245]) ).
cnf(s420,plain,
( ~ spl11_4
| ~ spl11_33 ),
inference(sat_conversion,[],[f3388]) ).
cnf(s422,plain,
~ spl11_20,
inference(rat,[],[s420,s2,s206,s354,s205,s343,s114,s229,s4,s6,s338,s340]) ).
cnf(s425,plain,
~ spl11_2,
inference(rat,[],[s25,s422]) ).
cnf(s427,plain,
spl11_1,
inference(rat,[],[s1,s425]) ).
cnf(s429,plain,
~ spl11_15,
inference(rat,[],[s33,s427]) ).
cnf(s431,plain,
~ spl11_9,
inference(rat,[],[s251,s429]) ).
cnf(s433,plain,
~ spl11_8,
inference(rat,[],[s245,s429]) ).
cnf(s436,plain,
spl11_10,
inference(rat,[],[s5,s431]) ).
cnf(s437,plain,
spl11_7,
inference(rat,[],[s4,s433]) ).
cnf(s441,plain,
~ spl11_73,
inference(rat,[],[s186,s436]) ).
cnf(s443,plain,
~ spl11_49,
inference(rat,[],[s152,s437]) ).
cnf(s447,plain,
spl11_14,
inference(rat,[],[s369,s441]) ).
cnf(s451,plain,
~ spl11_5,
inference(rat,[],[s80,s443]) ).
cnf(s455,plain,
~ spl11_6,
inference(rat,[],[s362,s447]) ).
cnf(s464,plain,
$false,
inference(rat,[],[s3,s455,s451]) ).
thf(f3392,plain,
$false,
inference(avatar_sat_refutation,[],[s464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO066^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:28:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.35 % (1512700)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (1512709)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2922154911:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (1512711)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (1512711)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (1512710)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=765855336:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (1512705)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=228495601:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (1512706)lrs+10_16_si=on:nwc=1.5:random_seed=846746635:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (1512707)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3370849061:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (1512709)Instruction limit reached!
% 0.20/0.35 % (1512709)------------------------------
% 0.20/0.35 % (1512709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1512709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1512708)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=1462584315:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.35 % (1512709)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1512709)Termination reason: Instruction limit
% 0.20/0.35 % (1512709)Termination phase: Saturation
% 0.20/0.35 % (1512709)Time elapsed: 0.007 s
% 0.20/0.35 % (1512709)Peak memory usage: 12 MB
% 0.20/0.35 % (1512709)Instructions burned: 24 (million)
% 0.20/0.35 % (1512711)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=2940504795:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (1512707)Instruction limit reached!
% 0.20/0.35 % (1512707)------------------------------
% 0.20/0.35 % (1512707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1512707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1512707)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1512707)Termination reason: Instruction limit
% 0.20/0.35 % (1512707)Termination phase: Function definition elimination
% 0.20/0.35 % (1512707)Time elapsed: 0.002 s
% 0.20/0.35 % (1512707)Peak memory usage: 10 MB
% 0.20/0.35 % (1512707)Instructions burned: 4 (million)
% 0.20/0.35 % (1512706)Instruction limit reached!
% 0.20/0.35 % (1512706)------------------------------
% 0.20/0.35 % (1512706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1512706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1512706)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1512706)Termination reason: Instruction limit
% 0.20/0.35 % (1512706)Termination phase: Saturation
% 0.20/0.35 % (1512706)Time elapsed: 0.008 s
% 0.20/0.35 % (1512706)Peak memory usage: 12 MB
% 0.20/0.35 % (1512706)Instructions burned: 18 (million)
% 0.20/0.35 % (1512719)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1751021969:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (1512719)Instruction limit reached!
% 0.20/0.35 % (1512719)------------------------------
% 0.20/0.35 % (1512719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1512719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1512719)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1512719)Termination reason: Instruction limit
% 0.20/0.35 % (1512719)Termination phase: Function definition elimination
% 0.20/0.35 % (1512719)Time elapsed: 0.001 s
% 0.20/0.35 % (1512719)Peak memory usage: 10 MB
% 0.20/0.35 % (1512719)Instructions burned: 4 (million)
% 0.20/0.35 % (1512720)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3380799882:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.86/0.38 % (1512723)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=184242535:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.86/0.38 % (1512721)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.86/0.38 % (1512720)Instruction limit reached!
% 0.86/0.38 % (1512720)------------------------------
% 0.86/0.38 % (1512720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (1512720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (1512720)CaDiCaL version: 2.1.3
% 0.86/0.38 % (1512720)Termination reason: Instruction limit
% 0.86/0.38 % (1512720)Termination phase: Saturation
% 0.86/0.38 % (1512720)Time elapsed: 0.003 s
% 0.86/0.38 % (1512720)Peak memory usage: 11 MB
% 0.86/0.38 % (1512720)Instructions burned: 6 (million)
% 0.86/0.38 % (1512723)Instruction limit reached!
% 0.86/0.38 % (1512723)------------------------------
% 0.86/0.38 % (1512723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (1512723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (1512723)CaDiCaL version: 2.1.3
% 0.86/0.38 % (1512723)Termination reason: Instruction limit
% 0.86/0.38 % (1512723)Termination phase: Saturation
% 0.86/0.38 % (1512723)Time elapsed: 0.003 s
% 0.86/0.38 % (1512723)Peak memory usage: 12 MB
% 0.86/0.38 % (1512723)Instructions burned: 13 (million)
% 0.86/0.38 % (1512721)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2583578659:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.86/0.38 % (1512721)Instruction limit reached!
% 0.86/0.38 % (1512721)------------------------------
% 0.86/0.38 % (1512721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (1512721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (1512721)CaDiCaL version: 2.1.3
% 0.86/0.38 % (1512721)Termination reason: Instruction limit
% 0.86/0.38 % (1512721)Termination phase: Saturation
% 0.86/0.38 % (1512721)Time elapsed: 0.004 s
% 0.86/0.38 % (1512721)Peak memory usage: 11 MB
% 0.86/0.38 % (1512721)Instructions burned: 9 (million)
% 0.86/0.38 % (1512710)Instruction limit reached!
% 0.86/0.38 % (1512710)------------------------------
% 0.86/0.38 % (1512710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (1512710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (1512710)CaDiCaL version: 2.1.3
% 0.86/0.38 % (1512710)Termination reason: Instruction limit
% 0.86/0.38 % (1512710)Termination phase: Saturation
% 0.86/0.38 % (1512710)Time elapsed: 0.037 s
% 0.86/0.38 % (1512710)Peak memory usage: 12 MB
% 0.86/0.38 % (1512710)Instructions burned: 76 (million)
% 0.86/0.38 % (1512727)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=2666273180:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.86/0.38 % (1512726)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
% 0.86/0.38 % (1512726)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.86/0.38 % (1512726)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2251045827:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.86/0.38 % (1512705)Instruction limit reached!
% 0.86/0.38 % (1512705)------------------------------
% 0.86/0.38 % (1512705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (1512705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (1512705)CaDiCaL version: 2.1.3
% 0.86/0.38 % (1512705)Termination reason: Instruction limit
% 0.86/0.38 % (1512705)Termination phase: Saturation
% 0.86/0.38 % (1512705)Time elapsed: 0.044 s
% 0.86/0.38 % (1512705)Peak memory usage: 13 MB
% 0.86/0.38 % (1512705)Instructions burned: 89 (million)
% 0.86/0.38 % (1512729)lrs+10_1_si=on:cs=on:random_seed=715527881:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.86/0.38 % (1512731)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.86/0.38 % (1512729)Instruction limit reached!
% 0.86/0.38 % (1512729)------------------------------
% 0.86/0.38 % (1512729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (1512729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (1512729)CaDiCaL version: 2.1.3
% 0.86/0.38 % (1512729)Termination reason: Instruction limit
% 0.86/0.38 % (1512729)Termination phase: Saturation
% 0.86/0.38 % (1512729)Time elapsed: 0.004 s
% 0.86/0.38 % (1512729)Peak memory usage: 11 MB
% 0.86/0.38 % (1512729)Instructions burned: 9 (million)
% 0.86/0.38 % (1512731)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=1056450312:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.86/0.38 % (1512726)Instruction limit reached!
% 0.86/0.38 % (1512726)------------------------------
% 0.86/0.38 % (1512726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512726)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512726)Termination reason: Instruction limit
% 0.86/0.39 % (1512726)Termination phase: Saturation
% 0.86/0.39 % (1512726)Time elapsed: 0.013 s
% 0.86/0.39 % (1512726)Peak memory usage: 12 MB
% 0.86/0.39 % (1512726)Instructions burned: 28 (million)
% 0.86/0.39 % (1512731)Instruction limit reached!
% 0.86/0.39 % (1512731)------------------------------
% 0.86/0.39 % (1512731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512731)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512731)Termination reason: Instruction limit
% 0.86/0.39 % (1512731)Termination phase: Property scanning
% 0.86/0.39 % (1512731)Time elapsed: 0.002 s
% 0.86/0.39 % (1512731)Peak memory usage: 10 MB
% 0.86/0.39 % (1512731)Instructions burned: 4 (million)
% 0.86/0.39 % (1512727)Instruction limit reached!
% 0.86/0.39 % (1512727)------------------------------
% 0.86/0.39 % (1512727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512727)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512727)Termination reason: Instruction limit
% 0.86/0.39 % (1512727)Termination phase: Saturation
% 0.86/0.39 % (1512727)Time elapsed: 0.025 s
% 0.86/0.39 % (1512727)Peak memory usage: 13 MB
% 0.86/0.39 % (1512727)Instructions burned: 90 (million)
% 0.86/0.39 % (1512733)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3110884394:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.86/0.39 % (1512733)Refutation not found, incomplete strategy
% 0.86/0.39 % (1512733)------------------------------
% 0.86/0.39 % (1512733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512733)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512733)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.39 % (1512733)Time elapsed: 0.003 s
% 0.86/0.39 % (1512733)Peak memory usage: 12 MB
% 0.86/0.39 % (1512733)Instructions burned: 5 (million)
% 0.86/0.39 % (1512733)------------------------------
% 0.86/0.39 % (1512733)------------------------------
% 0.86/0.39 % (1512740)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3963030703:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.86/0.39 % (1512736)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2064351929:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.86/0.39 % (1512738)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3232541637:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.86/0.39 % (1512711)Instruction limit reached!
% 0.86/0.39 % (1512711)------------------------------
% 0.86/0.39 % (1512711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512711)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512711)Termination reason: Instruction limit
% 0.86/0.39 % (1512711)Termination phase: Saturation
% 0.86/0.39 % (1512711)Time elapsed: 0.077 s
% 0.86/0.39 % (1512711)Peak memory usage: 13 MB
% 0.86/0.39 % (1512711)Instructions burned: 158 (million)
% 0.86/0.39 % (1512736)Refutation not found, incomplete strategy
% 0.86/0.39 % (1512736)------------------------------
% 0.86/0.39 % (1512736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512736)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512736)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.39 % (1512736)Time elapsed: 0.004 s
% 0.86/0.39 % (1512737)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2951538506:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.86/0.39 % (1512736)Peak memory usage: 12 MB
% 0.86/0.39 % (1512736)Instructions burned: 6 (million)
% 0.86/0.39 % (1512736)------------------------------
% 0.86/0.39 % (1512736)------------------------------
% 0.86/0.39 % (1512738)Instruction limit reached!
% 0.86/0.39 % (1512738)------------------------------
% 0.86/0.39 % (1512738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512738)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512738)Termination reason: Instruction limit
% 0.86/0.39 % (1512738)Termination phase: Saturation
% 0.86/0.39 % (1512738)Time elapsed: 0.008 s
% 0.86/0.39 % (1512738)Peak memory usage: 12 MB
% 0.86/0.39 % (1512738)Instructions burned: 15 (million)
% 0.86/0.39 % (1512741)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1134688735:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.86/0.39 % (1512737)Instruction limit reached!
% 0.86/0.39 % (1512737)------------------------------
% 0.86/0.39 % (1512737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512737)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512737)Termination reason: Instruction limit
% 0.86/0.39 % (1512737)Termination phase: Saturation
% 0.86/0.39 % (1512737)Time elapsed: 0.014 s
% 0.86/0.39 % (1512737)Peak memory usage: 12 MB
% 0.86/0.39 % (1512737)Instructions burned: 25 (million)
% 0.86/0.39 % (1512741)Instruction limit reached!
% 0.86/0.39 % (1512741)------------------------------
% 0.86/0.39 % (1512741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512741)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512741)Termination reason: Instruction limit
% 0.86/0.39 % (1512741)Termination phase: Saturation
% 0.86/0.39 % (1512741)Time elapsed: 0.007 s
% 0.86/0.39 % (1512741)Peak memory usage: 12 MB
% 0.86/0.39 % (1512741)Instructions burned: 14 (million)
% 0.86/0.39 % (1512745)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=197533847:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.86/0.39 % (1512747)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3960639034:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.86/0.39 % (1512745)Instruction limit reached!
% 0.86/0.39 % (1512745)------------------------------
% 0.86/0.39 % (1512745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512745)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512745)Termination reason: Instruction limit
% 0.86/0.39 % (1512745)Termination phase: Function definition elimination
% 0.86/0.39 % (1512745)Time elapsed: 0.002 s
% 0.86/0.39 % (1512745)Peak memory usage: 11 MB
% 0.86/0.39 % (1512745)Instructions burned: 4 (million)
% 0.86/0.39 % (1512748)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1708345585:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.86/0.39 % (1512751)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.86/0.39 % (1512751)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.86/0.39 % (1512740) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1512700-1512740"...
% 0.86/0.39 % (1512750)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=322018282:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.86/0.39 % (1512747)Instruction limit reached!
% 0.86/0.39 % (1512747)------------------------------
% 0.86/0.39 % (1512747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512747)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512747)Termination reason: Instruction limit
% 0.86/0.39 % (1512747)Termination phase: Saturation
% 0.86/0.39 % (1512747)Time elapsed: 0.014 s
% 0.86/0.39 % (1512747)Peak memory usage: 12 MB
% 0.86/0.39 % (1512747)Instructions burned: 27 (million)
% 0.86/0.39 % (1512751)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3390475733:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.86/0.39 % (1512754)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.86/0.39 % (1512748)Instruction limit reached!
% 0.86/0.39 % (1512748)------------------------------
% 0.86/0.39 % (1512748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512748)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512748)Termination reason: Instruction limit
% 0.86/0.39 % (1512748)Termination phase: Saturation
% 0.86/0.39 % (1512748)Time elapsed: 0.010 s
% 0.86/0.39 % (1512748)Peak memory usage: 12 MB
% 0.86/0.39 % (1512748)Instructions burned: 23 (million)
% 0.86/0.39 % (1512740)...printing done.
% 0.86/0.39 % (1512740)Refutation found. Thanks to Tanya!
% 0.86/0.39 % SZS status Theorem for theBenchmark
% 0.86/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.86/0.39 % (1512740)------------------------------
% 0.86/0.39 % (1512740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.39 % (1512740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.39 % (1512740)CaDiCaL version: 2.1.3
% 0.86/0.39 % (1512740)Termination reason: Refutation
% 0.86/0.39 % (1512740)Time elapsed: 0.040 s
% 0.86/0.39 % (1512740)Peak memory usage: 14 MB
% 0.86/0.39 % (1512740)Instructions burned: 148 (million)
% 0.86/0.39 % (1512700)Success in time 0.15 s
% 0.86/0.39 % Vampire exiting
%------------------------------------------------------------------------------