%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN045^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:41:37 AM UTC 2026
% Result : Theorem 0.21s 0.34s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 49
% Syntax : Number of formulae : 527 ( 68 unt; 0 typ; 37 def)
% Number of atoms : 5606 ( 910 equ; 0 cnn)
% Maximal formula atoms : 21 ( 10 avg)
% Number of connectives : 6031 ( 320 ~;1327 |; 121 &;3403 @)
% ( 36 <=>; 488 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 283 ( 283 >; 0 *; 0 +; 0 <<)
% Number of symbols : 101 ( 97 usr; 55 con; 0-4 aty)
% ( 336 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 965 ( 0 sgn 174 !; 0 ?; 965 :)
% 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,
p: $i > $o ).
thf(func_def_22,type,
q: $i > $o ).
thf(func_def_23,type,
r: $i > $o ).
thf(func_def_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vOR: $o > $o > $o ).
thf(func_def_35,type,
vAND: $o > $o > $o ).
thf(func_def_36,type,
sF0: $o ).
thf(func_def_37,type,
sK1: $i > $i ).
thf(func_def_38,type,
sK2: $i > $i ).
thf(func_def_39,type,
sK3: $i > $i ).
thf(func_def_40,type,
sK4: $i > $i ).
thf(func_def_41,type,
sK5: $i > $i ).
thf(func_def_42,type,
sK6: $i > $i ).
thf(func_def_43,type,
sK7: $i > $i ).
thf(func_def_44,type,
sK8: $i > $i ).
thf(func_def_45,type,
sK9: $i > $i ).
thf(func_def_46,type,
sK10: $i > $i ).
thf(func_def_47,type,
sK11: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f12,axiom,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(f13,axiom,
( ior
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ior) ).
thf(f14,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
= iimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( iand @ ( iimplies @ X0 @ X1 ) @ ( iimplies @ X1 @ X0 ) ) )
= iequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iequiv) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel13) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f27,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f28,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f32,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f36,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f37,plain,
~ ( ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f38,plain,
( ( ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f40,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f44,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f45,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f47,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f48,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f49,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f50,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f55,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f56,plain,
( ( ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) )
!= $true ),
inference(flattening,[],[f38]) ).
thf(f61,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f62,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f69,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f70,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f71,plain,
( ( ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f72,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f75,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f76,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f77,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f84,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f64,f66,f63]) ).
thf(f87,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f70,f76]) ).
thf(f88,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,[],[f77,f66,f72,f72]) ).
thf(f89,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [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,[],[f62,f84,f72,f72]) ).
thf(f91,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f61,f87,f89,f89]) ).
thf(f93,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [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
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ q )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ 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
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ q ) )
@ ( ^ [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
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f71,f69,f91,f88,f75,f87,f75,f75,f87,f88,f75,f75,f88,f75,f75]) ).
thf(f94,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [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
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ q )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ 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
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ q ) )
@ ( ^ [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
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f95,plain,
sF0 != $true,
inference(definition_folding,[],[f93,f94]) ).
thf(f96,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [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
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ q )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ 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
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ q ) )
@ ( ^ [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
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f94]) ).
thf(f298,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( q @ Y2 )
& ( r @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( q @ Y2 )
& ( r @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f96]) ).
thf(f299,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( q @ Y2 )
& ( r @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( q @ Y2 )
& ( r @ Y2 ) ) ) ) ) ) ) ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( ( sF0 = $true )
| ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f304,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f306,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f304]) ).
thf(f307,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) )
= $true )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) )
@ X1 )
= $true )
| ( sF0 = $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK12 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) ) ) ) ) )
| ( ( ( irel @ sK12 @ X2 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( ( irel @ sK12 @ X2 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( sF0 = $true )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) ) ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
= $true )
| ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF0 = $true )
| ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( sF0 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f314]) ).
thf(f317,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $true )
| ( sF0 = $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK12 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) )
@ X5 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK12 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) )
@ X6 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) )
@ X5 ) )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( irel @ X1 @ X4 )
=> ( p @ X4 ) )
= $true )
| ( sF0 = $true )
| ( ( ( irel @ X2 @ X5 )
=> ( q @ X5 ) )
= $true )
| ( $true
= ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( q @ X3 )
& ( r @ X3 ) ) ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ sK12 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f320]) ).
thf(f322,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( q @ X3 )
& ( r @ X3 ) ) ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( p @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( ( ( irel @ X2 @ X5 )
=> ( q @ X5 ) )
= $true )
| ( sF0 = $true )
| ( $true
= ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) ) ) ),
inference(imp_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( ( p @ X4 )
= $true )
| ( ( ( q @ X3 )
& ( r @ X3 ) )
= $true )
| ( ( ( irel @ X2 @ X5 )
=> ( q @ X5 ) )
= $true )
| ( sF0 = $true )
| ( $true
= ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) ) ) ),
inference(imp_proxy_clausification,[],[f322]) ).
thf(f325,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X1 @ X4 ) )
| ( sF0 = $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( p @ X4 )
= $true )
| ( ( ( irel @ X2 @ X5 )
=> ( q @ X5 ) )
= $true )
| ( $true
= ( q @ X3 ) )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $true
= ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) ) ) ),
inference(and_proxy_clausification,[],[f323]) ).
thf(f326,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( q @ X5 )
= $true )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( q @ X3 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X2 @ X5 ) )
| ( $true
= ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) ) )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( sF0 = $true )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( ( p @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( q @ X5 )
= $true )
| ( $true
= ( q @ X3 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( p @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( sF0 = $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X2 @ X6 ) )
| ( $false
= ( irel @ X2 @ X5 ) )
| ( ( p @ X6 )
= $true ) ),
inference(imp_proxy_clausification,[],[f326]) ).
thf(f330,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK12 @ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f315]) ).
thf(f331,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( sF0 = $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) )
@ X5 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) )
@ X5 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) )
@ X6 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( sF0 = $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $true
= ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) ) )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( q @ X3 )
& ( r @ X3 ) ) ) )
| ( ( ( irel @ X1 @ X4 )
=> ( p @ X4 ) )
= $true )
| ( ( ( irel @ X2 @ X5 )
=> ( r @ X5 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( irel @ X2 @ X5 )
=> ( r @ X5 ) )
= $true )
| ( $false
= ( irel @ X2 @ X6 ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( q @ X3 )
& ( r @ X3 ) ) ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( sF0 = $true )
| ( ( ( irel @ X1 @ X4 )
=> ( p @ X4 ) )
= $true )
| ( ( p @ X6 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ X2 @ X5 ) )
| ( ( r @ X5 )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( ( p @ X6 )
= $true )
| ( ( ( irel @ X1 @ X4 )
=> ( p @ X4 ) )
= $true )
| ( $false
= ( irel @ X2 @ X6 ) )
| ( sF0 = $true )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( q @ X3 )
& ( r @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( r @ X5 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ X2 @ X6 ) )
| ( ( p @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( sF0 = $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( q @ X3 )
& ( r @ X3 ) ) ) )
| ( $false
= ( irel @ X2 @ X5 ) )
| ( ( p @ X6 )
= $true ) ),
inference(imp_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X2 @ X6 ) )
| ( ( p @ X6 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) )
| ( $false
= ( irel @ X2 @ X5 ) )
| ( ( p @ X4 )
= $true )
| ( sF0 = $true )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( ( ( q @ X3 )
& ( r @ X3 ) )
= $true )
| ( ( r @ X5 )
= $true )
| ( $false
= ( irel @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( r @ X3 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X2 @ X5 ) )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( sF0 = $true )
| ( ( p @ X6 )
= $true )
| ( $false
= ( irel @ X2 @ X6 ) )
| ( ( p @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( r @ X5 )
= $true )
| ( $false
= ( irel @ sK12 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f338]) ).
thf(f502,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) )
@ sK21 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f302]) ).
thf(f503,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) )
@ sK21 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f502]) ).
thf(f553,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) )
@ sK24 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK12 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( r @ Y1 ) ) ) ) ) )
@ sK21 ) ) ),
inference(sigma_proxy_clausification,[],[f503]) ).
thf(f554,plain,
( ( $false
= ( ( irel @ sK12 @ sK21 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( irel @ sK12 @ sK24 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f553]) ).
thf(f555,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK12 @ sK24 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f554]) ).
thf(f556,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK12 @ sK24 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f554]) ).
thf(f557,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f556]) ).
thf(f558,plain,
( ( sF0 = $true )
| ( $true
= ( irel @ sK12 @ sK24 ) )
| ( ( irel @ sK12 @ sK21 )
= $true ) ),
inference(imp_proxy_clausification,[],[f556]) ).
thf(f559,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f557]) ).
thf(f560,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f559]) ).
thf(f561,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f559]) ).
thf(f563,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f561]) ).
thf(f564,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK25 ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK25 ) ) ),
inference(sigma_proxy_clausification,[],[f563]) ).
thf(f565,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK25 ) )
| ( sF0 = $true )
| ( ( irel @ sK12 @ sK21 )
= $true ) ),
inference(duplicate_literal_removal,[],[f564]) ).
thf(f566,plain,
( ( sF0 = $true )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( ( irel @ sK24 @ sK25 )
=> ( p @ sK25 ) ) ) ),
inference(beta-eta_normalization,[],[f565]) ).
thf(f567,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( p @ sK25 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f566]) ).
thf(f568,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true )
| ( ( irel @ sK24 @ sK25 )
= $true ) ),
inference(imp_proxy_clausification,[],[f566]) ).
thf(f578,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f560]) ).
thf(f589,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( sF0 = $true )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) )
@ sK30 ) ) ),
inference(sigma_proxy_clausification,[],[f578]) ).
thf(f590,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) )
@ sK31 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) )
@ sK30 ) )
| ( sF0 = $true )
| ( ( irel @ sK12 @ sK21 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f589]) ).
thf(f591,plain,
( ( $false
= ( ( irel @ sK24 @ sK30 )
=> ( q @ sK30 ) ) )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK31 )
=> ( r @ sK31 ) ) ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
( ( $false
= ( ( irel @ sK24 @ sK31 )
=> ( r @ sK31 ) ) )
| ( sF0 = $true )
| ( $false
= ( q @ sK30 ) )
| ( ( irel @ sK12 @ sK21 )
= $true ) ),
inference(imp_proxy_clausification,[],[f591]) ).
thf(f593,plain,
( ( ( irel @ sK24 @ sK30 )
= $true )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( ( irel @ sK24 @ sK31 )
=> ( r @ sK31 ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f591]) ).
thf(f594,plain,
( ( $false
= ( r @ sK31 ) )
| ( ( irel @ sK24 @ sK30 )
= $true )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f593]) ).
thf(f595,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true )
| ( ( irel @ sK24 @ sK30 )
= $true )
| ( ( irel @ sK24 @ sK31 )
= $true ) ),
inference(imp_proxy_clausification,[],[f593]) ).
thf(f596,plain,
( ( $false
= ( q @ sK30 ) )
| ( sF0 = $true )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( $false
= ( r @ sK31 ) ) ),
inference(imp_proxy_clausification,[],[f592]) ).
thf(f597,plain,
( ( ( irel @ sK24 @ sK31 )
= $true )
| ( ( irel @ sK12 @ sK21 )
= $true )
| ( sF0 = $true )
| ( $false
= ( q @ sK30 ) ) ),
inference(imp_proxy_clausification,[],[f592]) ).
thf(f598,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK12 @ sK24 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f555]) ).
thf(f599,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( ( irel @ sK12 @ sK24 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f555]) ).
thf(f600,plain,
( ( $false
= ( ( irel @ sK12 @ sK24 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f599]) ).
thf(f601,plain,
( ( sF0 = $true )
| ( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f600]) ).
thf(f602,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f600]) ).
thf(f603,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK21 @ sK32 )
=> ( p @ sK32 ) ) ) ),
inference(beta-eta_normalization,[],[f602]) ).
thf(f604,plain,
( ( sF0 = $true )
| ( $false
= ( p @ sK32 ) )
| ( $true
= ( irel @ sK12 @ sK24 ) ) ),
inference(imp_proxy_clausification,[],[f603]) ).
thf(f605,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ( ( irel @ sK21 @ sK32 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f603]) ).
thf(f606,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f601]) ).
thf(f607,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f606]) ).
thf(f608,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f606]) ).
thf(f610,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f608]) ).
thf(f611,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK33 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK33 ) ) ),
inference(sigma_proxy_clausification,[],[f610]) ).
thf(f612,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK33 ) ) ),
inference(duplicate_literal_removal,[],[f611]) ).
thf(f613,plain,
( ( $false
= ( ( irel @ sK24 @ sK33 )
=> ( p @ sK33 ) ) )
| ( $false
= ( ( irel @ sK21 @ sK32 )
=> ( p @ sK32 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f612]) ).
thf(f614,plain,
( ( $false
= ( p @ sK33 ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK21 @ sK32 )
=> ( p @ sK32 ) ) ) ),
inference(imp_proxy_clausification,[],[f613]) ).
thf(f615,plain,
( ( sF0 = $true )
| ( $false
= ( ( irel @ sK21 @ sK32 )
=> ( p @ sK32 ) ) )
| ( ( irel @ sK24 @ sK33 )
= $true ) ),
inference(imp_proxy_clausification,[],[f613]) ).
thf(f616,plain,
( ( ( irel @ sK24 @ sK33 )
= $true )
| ( sF0 = $true )
| ( $false
= ( p @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f615]) ).
thf(f617,plain,
( ( sF0 = $true )
| ( ( irel @ sK24 @ sK33 )
= $true )
| ( ( irel @ sK21 @ sK32 )
= $true ) ),
inference(imp_proxy_clausification,[],[f615]) ).
thf(f618,plain,
( ( sF0 = $true )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( p @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f614]) ).
thf(f619,plain,
( ( sF0 = $true )
| ( $false
= ( p @ sK33 ) )
| ( ( irel @ sK21 @ sK32 )
= $true ) ),
inference(imp_proxy_clausification,[],[f614]) ).
thf(f637,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) )
@ sK36 ) ) ),
inference(sigma_proxy_clausification,[],[f607]) ).
thf(f638,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) )
@ sK36 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f637]) ).
thf(f656,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( p @ Y0 ) )
@ sK32 ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) )
@ sK38 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) )
@ sK36 ) ) ),
inference(sigma_proxy_clausification,[],[f638]) ).
thf(f657,plain,
( ( sF0 = $true )
| ( $false
= ( ( irel @ sK21 @ sK32 )
=> ( p @ sK32 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK36 )
=> ( q @ sK36 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK38 )
=> ( r @ sK38 ) ) ) ),
inference(beta-eta_normalization,[],[f656]) ).
thf(f658,plain,
( ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK38 )
=> ( r @ sK38 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK36 )
=> ( q @ sK36 ) ) )
| ( $false
= ( p @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f657]) ).
thf(f659,plain,
( ( ( irel @ sK21 @ sK32 )
= $true )
| ( $false
= ( ( irel @ sK24 @ sK36 )
=> ( q @ sK36 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK38 )
=> ( r @ sK38 ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f657]) ).
thf(f660,plain,
( ( ( q @ sK36 )
= $false )
| ( ( irel @ sK21 @ sK32 )
= $true )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK38 )
=> ( r @ sK38 ) ) ) ),
inference(imp_proxy_clausification,[],[f659]) ).
thf(f661,plain,
( ( $false
= ( ( irel @ sK24 @ sK38 )
=> ( r @ sK38 ) ) )
| ( $true
= ( irel @ sK24 @ sK36 ) )
| ( ( irel @ sK21 @ sK32 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f659]) ).
thf(f662,plain,
( ( ( irel @ sK21 @ sK32 )
= $true )
| ( $false
= ( r @ sK38 ) )
| ( $true
= ( irel @ sK24 @ sK36 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f661]) ).
thf(f663,plain,
( ( ( irel @ sK21 @ sK32 )
= $true )
| ( $true
= ( irel @ sK24 @ sK38 ) )
| ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f661]) ).
thf(f664,plain,
( ( ( irel @ sK21 @ sK32 )
= $true )
| ( ( q @ sK36 )
= $false )
| ( $false
= ( r @ sK38 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f660]) ).
thf(f665,plain,
( ( $true
= ( irel @ sK24 @ sK38 ) )
| ( sF0 = $true )
| ( ( q @ sK36 )
= $false )
| ( ( irel @ sK21 @ sK32 )
= $true ) ),
inference(imp_proxy_clausification,[],[f660]) ).
thf(f666,plain,
( ( $false
= ( ( irel @ sK24 @ sK36 )
=> ( q @ sK36 ) ) )
| ( sF0 = $true )
| ( $false
= ( r @ sK38 ) )
| ( $false
= ( p @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f658]) ).
thf(f667,plain,
( ( $true
= ( irel @ sK24 @ sK38 ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK36 )
=> ( q @ sK36 ) ) )
| ( $false
= ( p @ sK32 ) ) ),
inference(imp_proxy_clausification,[],[f658]) ).
thf(f668,plain,
( ( ( q @ sK36 )
= $false )
| ( $false
= ( p @ sK32 ) )
| ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK38 ) ) ),
inference(imp_proxy_clausification,[],[f667]) ).
thf(f669,plain,
( ( sF0 = $true )
| ( $false
= ( p @ sK32 ) )
| ( $true
= ( irel @ sK24 @ sK38 ) )
| ( $true
= ( irel @ sK24 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f667]) ).
thf(f670,plain,
( ( sF0 = $true )
| ( $false
= ( r @ sK38 ) )
| ( $false
= ( p @ sK32 ) )
| ( ( q @ sK36 )
= $false ) ),
inference(imp_proxy_clausification,[],[f666]) ).
thf(f671,plain,
( ( sF0 = $true )
| ( $false
= ( p @ sK32 ) )
| ( $false
= ( r @ sK38 ) )
| ( $true
= ( irel @ sK24 @ sK36 ) ) ),
inference(imp_proxy_clausification,[],[f666]) ).
thf(f672,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( ( irel @ sK12 @ sK24 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f598]) ).
thf(f673,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f672]) ).
thf(f674,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f672]) ).
thf(f675,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK21 @ sK39 )
=> ( ( q @ sK39 )
& ( r @ sK39 ) ) ) ) ),
inference(beta-eta_normalization,[],[f674]) ).
thf(f676,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ( sF0 = $true )
| ( $false
= ( ( q @ sK39 )
& ( r @ sK39 ) ) ) ),
inference(imp_proxy_clausification,[],[f675]) ).
thf(f677,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ( sF0 = $true )
| ( ( irel @ sK21 @ sK39 )
= $true ) ),
inference(imp_proxy_clausification,[],[f675]) ).
thf(f678,plain,
( ( $false
= ( r @ sK39 ) )
| ( $true
= ( irel @ sK12 @ sK24 ) )
| ( ( q @ sK39 )
= $false )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f676]) ).
thf(f679,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f673]) ).
thf(f680,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) ) ),
inference(or_proxy_clausification,[],[f679]) ).
thf(f681,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f679]) ).
thf(f682,plain,
( ( sF0 = $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK40 ) ) ),
inference(sigma_proxy_clausification,[],[f681]) ).
thf(f684,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) ) ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK40 ) ) ),
inference(or_proxy_clausification,[],[f682]) ).
thf(f685,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK41 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( p @ Y0 ) )
@ sK40 ) ) ),
inference(sigma_proxy_clausification,[],[f684]) ).
thf(f686,plain,
( ( sF0 = $true )
| ( $false
= ( ( irel @ sK21 @ sK39 )
=> ( ( q @ sK39 )
& ( r @ sK39 ) ) ) )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK41 )
=> ( p @ sK41 ) ) ) ),
inference(beta-eta_normalization,[],[f685]) ).
thf(f687,plain,
( ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK41 )
=> ( p @ sK41 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) )
| ( $false
= ( ( q @ sK39 )
& ( r @ sK39 ) ) ) ),
inference(imp_proxy_clausification,[],[f686]) ).
thf(f688,plain,
( ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK41 )
=> ( p @ sK41 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) )
| ( ( irel @ sK21 @ sK39 )
= $true ) ),
inference(imp_proxy_clausification,[],[f686]) ).
thf(f689,plain,
( ( sF0 = $true )
| ( $false
= ( p @ sK41 ) )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) )
| ( ( irel @ sK21 @ sK39 )
= $true ) ),
inference(imp_proxy_clausification,[],[f688]) ).
thf(f690,plain,
( ( sF0 = $true )
| ( ( irel @ sK21 @ sK39 )
= $true )
| ( ( irel @ sK24 @ sK41 )
= $true )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) ) ),
inference(imp_proxy_clausification,[],[f688]) ).
thf(f691,plain,
( ( ( irel @ sK21 @ sK39 )
= $true )
| ( ( irel @ sK24 @ sK41 )
= $true )
| ( sF0 = $true )
| ( $false
= ( p @ sK40 ) ) ),
inference(imp_proxy_clausification,[],[f690]) ).
thf(f692,plain,
( ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK40 ) )
| ( ( irel @ sK24 @ sK41 )
= $true )
| ( ( irel @ sK21 @ sK39 )
= $true ) ),
inference(imp_proxy_clausification,[],[f690]) ).
thf(f693,plain,
( ( $false
= ( p @ sK40 ) )
| ( $false
= ( p @ sK41 ) )
| ( ( irel @ sK21 @ sK39 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f689]) ).
thf(f694,plain,
( ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK40 ) )
| ( ( irel @ sK21 @ sK39 )
= $true )
| ( $false
= ( p @ sK41 ) ) ),
inference(imp_proxy_clausification,[],[f689]) ).
thf(f695,plain,
( ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) )
| ( $false
= ( p @ sK41 ) )
| ( $false
= ( ( q @ sK39 )
& ( r @ sK39 ) ) ) ),
inference(imp_proxy_clausification,[],[f687]) ).
thf(f696,plain,
( ( ( irel @ sK24 @ sK41 )
= $true )
| ( $false
= ( ( q @ sK39 )
& ( r @ sK39 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f687]) ).
thf(f697,plain,
( ( ( q @ sK39 )
= $false )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK40 )
=> ( p @ sK40 ) ) )
| ( $false
= ( r @ sK39 ) )
| ( ( irel @ sK24 @ sK41 )
= $true ) ),
inference(and_proxy_clausification,[],[f696]) ).
thf(f698,plain,
( ( ( q @ sK39 )
= $false )
| ( sF0 = $true )
| ( ( irel @ sK24 @ sK41 )
= $true )
| ( $false
= ( r @ sK39 ) )
| ( $false
= ( p @ sK40 ) ) ),
inference(imp_proxy_clausification,[],[f697]) ).
thf(f699,plain,
( ( $false
= ( r @ sK39 ) )
| ( ( irel @ sK24 @ sK41 )
= $true )
| ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK40 ) )
| ( ( q @ sK39 )
= $false ) ),
inference(imp_proxy_clausification,[],[f697]) ).
thf(f700,plain,
( ( $false
= ( ( q @ sK39 )
& ( r @ sK39 ) ) )
| ( sF0 = $true )
| ( $false
= ( p @ sK41 ) )
| ( $false
= ( p @ sK40 ) ) ),
inference(imp_proxy_clausification,[],[f695]) ).
thf(f701,plain,
( ( $false
= ( p @ sK41 ) )
| ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK40 ) )
| ( $false
= ( ( q @ sK39 )
& ( r @ sK39 ) ) ) ),
inference(imp_proxy_clausification,[],[f695]) ).
thf(f702,plain,
( ( ( q @ sK39 )
= $false )
| ( $false
= ( p @ sK41 ) )
| ( $false
= ( r @ sK39 ) )
| ( $true
= ( irel @ sK24 @ sK40 ) )
| ( sF0 = $true ) ),
inference(and_proxy_clausification,[],[f701]) ).
thf(f703,plain,
( ( $false
= ( r @ sK39 ) )
| ( sF0 = $true )
| ( ( q @ sK39 )
= $false )
| ( $false
= ( p @ sK40 ) )
| ( $false
= ( p @ sK41 ) ) ),
inference(and_proxy_clausification,[],[f700]) ).
thf(f724,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f680]) ).
thf(f747,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) )
@ sK45 ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) ) ),
inference(sigma_proxy_clausification,[],[f724]) ).
thf(f748,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK21 @ Y0 )
=> ( ( q @ Y0 )
& ( r @ Y0 ) ) )
@ sK39 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( q @ Y0 ) )
@ sK45 ) )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK24 @ Y0 )
=> ( r @ Y0 ) )
@ sK46 ) ) ),
inference(sigma_proxy_clausification,[],[f747]) ).
thf(f749,plain,
( ( $false
= ( ( irel @ sK21 @ sK39 )
=> ( ( q @ sK39 )
& ( r @ sK39 ) ) ) )
| ( $false
= ( ( irel @ sK24 @ sK45 )
=> ( q @ sK45 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f748]) ).
thf(f750,plain,
( ( $false
= ( ( q @ sK39 )
& ( r @ sK39 ) ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK45 )
=> ( q @ sK45 ) ) ) ),
inference(imp_proxy_clausification,[],[f749]) ).
thf(f751,plain,
( ( $false
= ( ( irel @ sK24 @ sK45 )
=> ( q @ sK45 ) ) )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) )
| ( sF0 = $true )
| ( ( irel @ sK21 @ sK39 )
= $true ) ),
inference(imp_proxy_clausification,[],[f749]) ).
thf(f752,plain,
( ( $false
= ( q @ sK45 ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) )
| ( ( irel @ sK21 @ sK39 )
= $true ) ),
inference(imp_proxy_clausification,[],[f751]) ).
thf(f753,plain,
( ( $true
= ( irel @ sK24 @ sK45 ) )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) )
| ( ( irel @ sK21 @ sK39 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f751]) ).
thf(f754,plain,
( ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK45 ) )
| ( ( irel @ sK21 @ sK39 )
= $true )
| ( $false
= ( r @ sK46 ) ) ),
inference(imp_proxy_clausification,[],[f753]) ).
thf(f755,plain,
( ( ( irel @ sK21 @ sK39 )
= $true )
| ( $true
= ( irel @ sK24 @ sK45 ) )
| ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK46 ) ) ),
inference(imp_proxy_clausification,[],[f753]) ).
thf(f756,plain,
( ( $false
= ( q @ sK45 ) )
| ( ( irel @ sK21 @ sK39 )
= $true )
| ( $false
= ( r @ sK46 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f752]) ).
thf(f757,plain,
( ( $false
= ( q @ sK45 ) )
| ( $true
= ( irel @ sK24 @ sK46 ) )
| ( ( irel @ sK21 @ sK39 )
= $true )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f752]) ).
thf(f758,plain,
( ( $false
= ( ( irel @ sK24 @ sK45 )
=> ( q @ sK45 ) ) )
| ( sF0 = $true )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) )
| ( ( q @ sK39 )
= $false )
| ( $false
= ( r @ sK39 ) ) ),
inference(and_proxy_clausification,[],[f750]) ).
thf(f759,plain,
( ( $false
= ( r @ sK39 ) )
| ( ( q @ sK39 )
= $false )
| ( sF0 = $true )
| ( $false
= ( q @ sK45 ) )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) ) ),
inference(imp_proxy_clausification,[],[f758]) ).
thf(f760,plain,
( ( $false
= ( r @ sK39 ) )
| ( $true
= ( irel @ sK24 @ sK45 ) )
| ( $false
= ( ( irel @ sK24 @ sK46 )
=> ( r @ sK46 ) ) )
| ( sF0 = $true )
| ( ( q @ sK39 )
= $false ) ),
inference(imp_proxy_clausification,[],[f758]) ).
thf(f761,plain,
( ( $false
= ( r @ sK39 ) )
| ( $false
= ( r @ sK46 ) )
| ( sF0 = $true )
| ( $true
= ( irel @ sK24 @ sK45 ) )
| ( ( q @ sK39 )
= $false ) ),
inference(imp_proxy_clausification,[],[f760]) ).
thf(f762,plain,
( ( $true
= ( irel @ sK24 @ sK46 ) )
| ( $true
= ( irel @ sK24 @ sK45 ) )
| ( ( q @ sK39 )
= $false )
| ( sF0 = $true )
| ( $false
= ( r @ sK39 ) ) ),
inference(imp_proxy_clausification,[],[f760]) ).
thf(f763,plain,
( ( $false
= ( q @ sK45 ) )
| ( $false
= ( r @ sK39 ) )
| ( ( q @ sK39 )
= $false )
| ( $false
= ( r @ sK46 ) )
| ( sF0 = $true ) ),
inference(imp_proxy_clausification,[],[f759]) ).
thf(f764,plain,
( ( sF0 = $true )
| ( $false
= ( r @ sK39 ) )
| ( ( q @ sK39 )
= $false )
| ( $true
= ( irel @ sK24 @ sK46 ) )
| ( $false
= ( q @ sK45 ) ) ),
inference(imp_proxy_clausification,[],[f759]) ).
thf(f946,definition,
( spl47_46
<=> ! [X4: $i,X1: $i,X3: $i] :
( ( $true
= ( q @ X3 ) )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( ( p @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl47_46])],[avatar_definition]) ).
thf(f947,plain,
( ! [X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( ( p @ X4 )
= $true )
| ( $true
= ( q @ X3 ) ) )
| ~ spl47_46 ),
inference(avatar_component_clause,[],[f946]) ).
thf(f949,definition,
( spl47_47
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl47_47])],[avatar_definition]) ).
thf(f952,plain,
( spl47_46
| spl47_46
| spl47_47 ),
inference(avatar_split_clause,[],[f327,f949,f946,f946]) ).
thf(f954,definition,
( spl47_48
<=> ! [X4: $i,X1: $i,X3: $i] :
( ( $false
= ( irel @ X1 @ X4 ) )
| ( ( p @ X4 )
= $true )
| ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( r @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl47_48])],[avatar_definition]) ).
thf(f955,plain,
( ! [X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK12 @ X1 ) )
| ( $false
= ( irel @ X1 @ X4 ) )
| ( ( p @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( r @ X3 ) ) )
| ~ spl47_48 ),
inference(avatar_component_clause,[],[f954]) ).
thf(f958,plain,
( spl47_48
| spl47_47
| spl47_48 ),
inference(avatar_split_clause,[],[f339,f954,f949,f954]) ).
thf(f1050,definition,
( spl47_64
<=> ( ( irel @ sK12 @ sK21 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_64])],[avatar_definition]) ).
thf(f1052,plain,
( ( ( irel @ sK12 @ sK21 )
= $true )
| ~ spl47_64 ),
inference(avatar_component_clause,[],[f1050]) ).
thf(f1084,definition,
( spl47_70
<=> ( $true
= ( irel @ sK12 @ sK24 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_70])],[avatar_definition]) ).
thf(f1086,plain,
( ( $true
= ( irel @ sK12 @ sK24 ) )
| ~ spl47_70 ),
inference(avatar_component_clause,[],[f1084]) ).
thf(f1087,plain,
( spl47_47
| spl47_70
| spl47_64 ),
inference(avatar_split_clause,[],[f558,f1050,f1084,f949]) ).
thf(f1089,definition,
( spl47_71
<=> ( ( irel @ sK24 @ sK25 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_71])],[avatar_definition]) ).
thf(f1091,plain,
( ( ( irel @ sK24 @ sK25 )
= $true )
| ~ spl47_71 ),
inference(avatar_component_clause,[],[f1089]) ).
thf(f1092,plain,
( spl47_64
| spl47_71
| spl47_47 ),
inference(avatar_split_clause,[],[f568,f949,f1089,f1050]) ).
thf(f1094,definition,
( spl47_72
<=> ( $false
= ( p @ sK25 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_72])],[avatar_definition]) ).
thf(f1096,plain,
( ( $false
= ( p @ sK25 ) )
| ~ spl47_72 ),
inference(avatar_component_clause,[],[f1094]) ).
thf(f1097,plain,
( spl47_47
| spl47_72
| spl47_64 ),
inference(avatar_split_clause,[],[f567,f1050,f1094,f949]) ).
thf(f1139,definition,
( spl47_81
<=> ( ( irel @ sK24 @ sK31 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_81])],[avatar_definition]) ).
thf(f1141,plain,
( ( ( irel @ sK24 @ sK31 )
= $true )
| ~ spl47_81 ),
inference(avatar_component_clause,[],[f1139]) ).
thf(f1143,definition,
( spl47_82
<=> ( ( irel @ sK24 @ sK30 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_82])],[avatar_definition]) ).
thf(f1145,plain,
( ( ( irel @ sK24 @ sK30 )
= $true )
| ~ spl47_82 ),
inference(avatar_component_clause,[],[f1143]) ).
thf(f1146,plain,
( spl47_81
| spl47_82
| spl47_64
| spl47_47 ),
inference(avatar_split_clause,[],[f595,f949,f1050,f1143,f1139]) ).
thf(f1148,definition,
( spl47_83
<=> ( $false
= ( r @ sK31 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_83])],[avatar_definition]) ).
thf(f1150,plain,
( ( $false
= ( r @ sK31 ) )
| ~ spl47_83 ),
inference(avatar_component_clause,[],[f1148]) ).
thf(f1151,plain,
( spl47_64
| spl47_47
| spl47_82
| spl47_83 ),
inference(avatar_split_clause,[],[f594,f1148,f1143,f949,f1050]) ).
thf(f1153,definition,
( spl47_84
<=> ( $false
= ( q @ sK30 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_84])],[avatar_definition]) ).
thf(f1155,plain,
( ( $false
= ( q @ sK30 ) )
| ~ spl47_84 ),
inference(avatar_component_clause,[],[f1153]) ).
thf(f1156,plain,
( spl47_47
| spl47_64
| spl47_81
| spl47_84 ),
inference(avatar_split_clause,[],[f597,f1153,f1139,f1050,f949]) ).
thf(f1157,plain,
( spl47_84
| spl47_47
| spl47_64
| spl47_83 ),
inference(avatar_split_clause,[],[f596,f1148,f1050,f949,f1153]) ).
thf(f1159,definition,
( spl47_85
<=> ( ( irel @ sK21 @ sK32 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_85])],[avatar_definition]) ).
thf(f1161,plain,
( ( ( irel @ sK21 @ sK32 )
= $true )
| ~ spl47_85 ),
inference(avatar_component_clause,[],[f1159]) ).
thf(f1162,plain,
( spl47_85
| spl47_47
| spl47_70 ),
inference(avatar_split_clause,[],[f605,f1084,f949,f1159]) ).
thf(f1164,definition,
( spl47_86
<=> ( $false
= ( p @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_86])],[avatar_definition]) ).
thf(f1166,plain,
( ( $false
= ( p @ sK32 ) )
| ~ spl47_86 ),
inference(avatar_component_clause,[],[f1164]) ).
thf(f1167,plain,
( spl47_70
| spl47_86
| spl47_47 ),
inference(avatar_split_clause,[],[f604,f949,f1164,f1084]) ).
thf(f1169,definition,
( spl47_87
<=> ( ( irel @ sK24 @ sK33 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_87])],[avatar_definition]) ).
thf(f1171,plain,
( ( ( irel @ sK24 @ sK33 )
= $true )
| ~ spl47_87 ),
inference(avatar_component_clause,[],[f1169]) ).
thf(f1172,plain,
( spl47_85
| spl47_47
| spl47_87 ),
inference(avatar_split_clause,[],[f617,f1169,f949,f1159]) ).
thf(f1173,plain,
( spl47_87
| spl47_86
| spl47_47 ),
inference(avatar_split_clause,[],[f616,f949,f1164,f1169]) ).
thf(f1175,definition,
( spl47_88
<=> ( $false
= ( p @ sK33 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_88])],[avatar_definition]) ).
thf(f1177,plain,
( ( $false
= ( p @ sK33 ) )
| ~ spl47_88 ),
inference(avatar_component_clause,[],[f1175]) ).
thf(f1178,plain,
( spl47_88
| spl47_85
| spl47_47 ),
inference(avatar_split_clause,[],[f619,f949,f1159,f1175]) ).
thf(f1179,plain,
( spl47_47
| spl47_86
| spl47_88 ),
inference(avatar_split_clause,[],[f618,f1175,f1164,f949]) ).
thf(f1205,definition,
( spl47_93
<=> ( $true
= ( irel @ sK24 @ sK36 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_93])],[avatar_definition]) ).
thf(f1207,plain,
( ( $true
= ( irel @ sK24 @ sK36 ) )
| ~ spl47_93 ),
inference(avatar_component_clause,[],[f1205]) ).
thf(f1221,definition,
( spl47_96
<=> ( ( q @ sK36 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl47_96])],[avatar_definition]) ).
thf(f1223,plain,
( ( ( q @ sK36 )
= $false )
| ~ spl47_96 ),
inference(avatar_component_clause,[],[f1221]) ).
thf(f1229,definition,
( spl47_97
<=> ( $true
= ( irel @ sK24 @ sK38 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_97])],[avatar_definition]) ).
thf(f1231,plain,
( ( $true
= ( irel @ sK24 @ sK38 ) )
| ~ spl47_97 ),
inference(avatar_component_clause,[],[f1229]) ).
thf(f1232,plain,
( spl47_47
| spl47_85
| spl47_97
| spl47_93 ),
inference(avatar_split_clause,[],[f663,f1205,f1229,f1159,f949]) ).
thf(f1234,definition,
( spl47_98
<=> ( $false
= ( r @ sK38 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_98])],[avatar_definition]) ).
thf(f1236,plain,
( ( $false
= ( r @ sK38 ) )
| ~ spl47_98 ),
inference(avatar_component_clause,[],[f1234]) ).
thf(f1237,plain,
( spl47_85
| spl47_93
| spl47_47
| spl47_98 ),
inference(avatar_split_clause,[],[f662,f1234,f949,f1205,f1159]) ).
thf(f1238,plain,
( spl47_47
| spl47_96
| spl47_85
| spl47_97 ),
inference(avatar_split_clause,[],[f665,f1229,f1159,f1221,f949]) ).
thf(f1239,plain,
( spl47_85
| spl47_47
| spl47_96
| spl47_98 ),
inference(avatar_split_clause,[],[f664,f1234,f1221,f949,f1159]) ).
thf(f1240,plain,
( spl47_93
| spl47_86
| spl47_97
| spl47_47 ),
inference(avatar_split_clause,[],[f669,f949,f1229,f1164,f1205]) ).
thf(f1241,plain,
( spl47_86
| spl47_47
| spl47_97
| spl47_96 ),
inference(avatar_split_clause,[],[f668,f1221,f1229,f949,f1164]) ).
thf(f1242,plain,
( spl47_98
| spl47_47
| spl47_86
| spl47_93 ),
inference(avatar_split_clause,[],[f671,f1205,f1164,f949,f1234]) ).
thf(f1243,plain,
( spl47_98
| spl47_86
| spl47_96
| spl47_47 ),
inference(avatar_split_clause,[],[f670,f949,f1221,f1164,f1234]) ).
thf(f1245,definition,
( spl47_99
<=> ( ( irel @ sK21 @ sK39 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_99])],[avatar_definition]) ).
thf(f1247,plain,
( ( ( irel @ sK21 @ sK39 )
= $true )
| ~ spl47_99 ),
inference(avatar_component_clause,[],[f1245]) ).
thf(f1248,plain,
( spl47_99
| spl47_47
| spl47_70 ),
inference(avatar_split_clause,[],[f677,f1084,f949,f1245]) ).
thf(f1250,definition,
( spl47_100
<=> ( ( q @ sK39 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl47_100])],[avatar_definition]) ).
thf(f1252,plain,
( ( ( q @ sK39 )
= $false )
| ~ spl47_100 ),
inference(avatar_component_clause,[],[f1250]) ).
thf(f1254,definition,
( spl47_101
<=> ( $false
= ( r @ sK39 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_101])],[avatar_definition]) ).
thf(f1256,plain,
( ( $false
= ( r @ sK39 ) )
| ~ spl47_101 ),
inference(avatar_component_clause,[],[f1254]) ).
thf(f1257,plain,
( spl47_47
| spl47_100
| spl47_70
| spl47_101 ),
inference(avatar_split_clause,[],[f678,f1254,f1084,f1250,f949]) ).
thf(f1259,definition,
( spl47_102
<=> ( $true
= ( irel @ sK24 @ sK40 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_102])],[avatar_definition]) ).
thf(f1261,plain,
( ( $true
= ( irel @ sK24 @ sK40 ) )
| ~ spl47_102 ),
inference(avatar_component_clause,[],[f1259]) ).
thf(f1263,definition,
( spl47_103
<=> ( ( irel @ sK24 @ sK41 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl47_103])],[avatar_definition]) ).
thf(f1265,plain,
( ( ( irel @ sK24 @ sK41 )
= $true )
| ~ spl47_103 ),
inference(avatar_component_clause,[],[f1263]) ).
thf(f1266,plain,
( spl47_99
| spl47_102
| spl47_103
| spl47_47 ),
inference(avatar_split_clause,[],[f692,f949,f1263,f1259,f1245]) ).
thf(f1268,definition,
( spl47_104
<=> ( $false
= ( p @ sK40 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_104])],[avatar_definition]) ).
thf(f1270,plain,
( ( $false
= ( p @ sK40 ) )
| ~ spl47_104 ),
inference(avatar_component_clause,[],[f1268]) ).
thf(f1271,plain,
( spl47_103
| spl47_47
| spl47_99
| spl47_104 ),
inference(avatar_split_clause,[],[f691,f1268,f1245,f949,f1263]) ).
thf(f1273,definition,
( spl47_105
<=> ( $false
= ( p @ sK41 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_105])],[avatar_definition]) ).
thf(f1275,plain,
( ( $false
= ( p @ sK41 ) )
| ~ spl47_105 ),
inference(avatar_component_clause,[],[f1273]) ).
thf(f1276,plain,
( spl47_47
| spl47_105
| spl47_102
| spl47_99 ),
inference(avatar_split_clause,[],[f694,f1245,f1259,f1273,f949]) ).
thf(f1277,plain,
( spl47_99
| spl47_104
| spl47_105
| spl47_47 ),
inference(avatar_split_clause,[],[f693,f949,f1273,f1268,f1245]) ).
thf(f1278,plain,
( spl47_100
| spl47_47
| spl47_103
| spl47_101
| spl47_102 ),
inference(avatar_split_clause,[],[f699,f1259,f1254,f1263,f949,f1250]) ).
thf(f1279,plain,
( spl47_101
| spl47_47
| spl47_104
| spl47_100
| spl47_103 ),
inference(avatar_split_clause,[],[f698,f1263,f1250,f1268,f949,f1254]) ).
thf(f1280,plain,
( spl47_102
| spl47_101
| spl47_105
| spl47_47
| spl47_100 ),
inference(avatar_split_clause,[],[f702,f1250,f949,f1273,f1254,f1259]) ).
thf(f1281,plain,
( spl47_105
| spl47_47
| spl47_100
| spl47_101
| spl47_104 ),
inference(avatar_split_clause,[],[f703,f1268,f1254,f1250,f949,f1273]) ).
thf(f1323,definition,
( spl47_112
<=> ( $true
= ( irel @ sK24 @ sK45 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_112])],[avatar_definition]) ).
thf(f1325,plain,
( ( $true
= ( irel @ sK24 @ sK45 ) )
| ~ spl47_112 ),
inference(avatar_component_clause,[],[f1323]) ).
thf(f1327,definition,
( spl47_113
<=> ( $true
= ( irel @ sK24 @ sK46 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_113])],[avatar_definition]) ).
thf(f1329,plain,
( ( $true
= ( irel @ sK24 @ sK46 ) )
| ~ spl47_113 ),
inference(avatar_component_clause,[],[f1327]) ).
thf(f1330,plain,
( spl47_47
| spl47_99
| spl47_112
| spl47_113 ),
inference(avatar_split_clause,[],[f755,f1327,f1323,f1245,f949]) ).
thf(f1332,definition,
( spl47_114
<=> ( $false
= ( r @ sK46 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_114])],[avatar_definition]) ).
thf(f1334,plain,
( ( $false
= ( r @ sK46 ) )
| ~ spl47_114 ),
inference(avatar_component_clause,[],[f1332]) ).
thf(f1335,plain,
( spl47_99
| spl47_114
| spl47_47
| spl47_112 ),
inference(avatar_split_clause,[],[f754,f1323,f949,f1332,f1245]) ).
thf(f1337,definition,
( spl47_115
<=> ( $false
= ( q @ sK45 ) ) ),
introduced(definition,[new_symbols(definition,[spl47_115])],[avatar_definition]) ).
thf(f1339,plain,
( ( $false
= ( q @ sK45 ) )
| ~ spl47_115 ),
inference(avatar_component_clause,[],[f1337]) ).
thf(f1340,plain,
( spl47_99
| spl47_47
| spl47_113
| spl47_115 ),
inference(avatar_split_clause,[],[f757,f1337,f1327,f949,f1245]) ).
thf(f1341,plain,
( spl47_114
| spl47_99
| spl47_47
| spl47_115 ),
inference(avatar_split_clause,[],[f756,f1337,f949,f1245,f1332]) ).
thf(f1342,plain,
( spl47_101
| spl47_47
| spl47_112
| spl47_113
| spl47_100 ),
inference(avatar_split_clause,[],[f762,f1250,f1327,f1323,f949,f1254]) ).
thf(f1343,plain,
( spl47_114
| spl47_112
| spl47_101
| spl47_100
| spl47_47 ),
inference(avatar_split_clause,[],[f761,f949,f1250,f1254,f1323,f1332]) ).
thf(f1344,plain,
( spl47_115
| spl47_113
| spl47_101
| spl47_100
| spl47_47 ),
inference(avatar_split_clause,[],[f764,f949,f1250,f1254,f1327,f1337]) ).
thf(f1345,plain,
( spl47_47
| spl47_115
| spl47_100
| spl47_114
| spl47_101 ),
inference(avatar_split_clause,[],[f763,f1254,f1332,f1250,f1337,f949]) ).
thf(f1346,plain,
~ spl47_47,
inference(avatar_split_clause,[],[f95,f949]) ).
thf(f1383,definition,
( spl47_116
<=> ! [X0: $i] :
( ( $false
= ( irel @ sK21 @ X0 ) )
| ( ( q @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl47_116])],[avatar_definition]) ).
thf(f1384,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK21 @ X0 ) )
| ( ( q @ X0 )
= $true ) )
| ~ spl47_116 ),
inference(avatar_component_clause,[],[f1383]) ).
thf(f1386,definition,
( spl47_117
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $false
= ( irel @ sK21 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl47_117])],[avatar_definition]) ).
thf(f1387,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK21 @ X1 ) )
| ( ( p @ X1 )
= $true ) )
| ~ spl47_117 ),
inference(avatar_component_clause,[],[f1386]) ).
thf(f1430,definition,
( spl47_122
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $false
= ( irel @ sK24 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl47_122])],[avatar_definition]) ).
thf(f1431,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK24 @ X1 ) )
| ( ( p @ X1 )
= $true ) )
| ~ spl47_122 ),
inference(avatar_component_clause,[],[f1430]) ).
thf(f1433,definition,
( spl47_123
<=> ! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( $false
= ( irel @ sK24 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl47_123])],[avatar_definition]) ).
thf(f1434,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK24 @ X0 ) )
| ( ( q @ X0 )
= $true ) )
| ~ spl47_123 ),
inference(avatar_component_clause,[],[f1433]) ).
thf(f1466,plain,
( ( ( q @ sK39 )
= $true )
| ( $false = $true )
| ~ spl47_99
| ~ spl47_116 ),
inference(constrained_superposition,[],[f1384,f1247]) ).
thf(f1479,plain,
( ( ( q @ sK39 )
= $true )
| ~ spl47_99
| ~ spl47_116 ),
inference(trivial_inequality_removal,[],[f1466]) ).
thf(f1495,plain,
( ( $false = $true )
| ~ spl47_99
| ~ spl47_100
| ~ spl47_116 ),
inference(forward_demodulation,[],[f1479,f1252]) ).
thf(f1496,plain,
( $false
| ~ spl47_99
| ~ spl47_100
| ~ spl47_116 ),
inference(trivial_inequality_removal,[],[f1495]) ).
thf(f1497,plain,
( ~ spl47_99
| ~ spl47_100
| ~ spl47_116 ),
inference(avatar_contradiction_clause,[],[f1496]) ).
thf(f1508,plain,
( ( $false = $true )
| ( ( p @ sK32 )
= $true )
| ~ spl47_85
| ~ spl47_117 ),
inference(constrained_superposition,[],[f1161,f1387]) ).
thf(f1520,plain,
( ( ( p @ sK32 )
= $true )
| ~ spl47_85
| ~ spl47_117 ),
inference(trivial_inequality_removal,[],[f1508]) ).
thf(f1530,plain,
( ( $false = $true )
| ~ spl47_85
| ~ spl47_86
| ~ spl47_117 ),
inference(forward_demodulation,[],[f1520,f1166]) ).
thf(f1531,plain,
( $false
| ~ spl47_85
| ~ spl47_86
| ~ spl47_117 ),
inference(trivial_inequality_removal,[],[f1530]) ).
thf(f1532,plain,
( ~ spl47_85
| ~ spl47_86
| ~ spl47_117 ),
inference(avatar_contradiction_clause,[],[f1531]) ).
thf(f1651,plain,
( ( ( p @ sK25 )
= $true )
| ( $false = $true )
| ~ spl47_71
| ~ spl47_122 ),
inference(constrained_superposition,[],[f1091,f1431]) ).
thf(f1664,plain,
( ( ( p @ sK25 )
= $true )
| ~ spl47_71
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f1651]) ).
thf(f1690,plain,
( ( $false = $true )
| ~ spl47_71
| ~ spl47_72
| ~ spl47_122 ),
inference(forward_demodulation,[],[f1664,f1096]) ).
thf(f1691,plain,
( $false
| ~ spl47_71
| ~ spl47_72
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f1690]) ).
thf(f1692,plain,
( ~ spl47_71
| ~ spl47_72
| ~ spl47_122 ),
inference(avatar_contradiction_clause,[],[f1691]) ).
thf(f1862,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ sK24 @ X0 ) )
| ( ( q @ X0 )
= $true )
| ( ( p @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( irel @ sK24 @ X1 ) ) )
| ~ spl47_46
| ~ spl47_70 ),
inference(constrained_superposition,[],[f947,f1086]) ).
thf(f1866,plain,
( ! [X0: $i,X1: $i] :
( ( ( q @ X0 )
= $true )
| ( $false
= ( irel @ sK24 @ X0 ) )
| ( $false
= ( irel @ sK24 @ X1 ) )
| ( ( p @ X1 )
= $true ) )
| ~ spl47_46
| ~ spl47_70 ),
inference(trivial_inequality_removal,[],[f1862]) ).
thf(f1868,plain,
( spl47_122
| spl47_123
| ~ spl47_46
| ~ spl47_70 ),
inference(avatar_split_clause,[],[f1866,f1084,f946,f1433,f1430]) ).
thf(f1879,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ sK24 @ X0 ) )
| ( ( r @ X1 )
= $true )
| ( $false
= ( irel @ sK24 @ X1 ) )
| ( $false = $true )
| ( $true
= ( p @ X0 ) ) )
| ~ spl47_48
| ~ spl47_70 ),
inference(constrained_superposition,[],[f1086,f955]) ).
thf(f1893,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ sK24 @ X1 ) )
| ( $true
= ( p @ X0 ) )
| ( ( r @ X1 )
= $true )
| ( $false
= ( irel @ sK24 @ X0 ) ) )
| ~ spl47_48
| ~ spl47_70 ),
inference(trivial_inequality_removal,[],[f1879]) ).
thf(f1904,definition,
( spl47_143
<=> ! [X1: $i] :
( ( $false
= ( irel @ sK24 @ X1 ) )
| ( ( r @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl47_143])],[avatar_definition]) ).
thf(f1905,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK24 @ X1 ) )
| ( ( r @ X1 )
= $true ) )
| ~ spl47_143 ),
inference(avatar_component_clause,[],[f1904]) ).
thf(f1908,definition,
( spl47_144
<=> ! [X1: $i] :
( ( $false
= ( irel @ sK21 @ X1 ) )
| ( ( r @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl47_144])],[avatar_definition]) ).
thf(f1909,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK21 @ X1 ) )
| ( ( r @ X1 )
= $true ) )
| ~ spl47_144 ),
inference(avatar_component_clause,[],[f1908]) ).
thf(f1912,plain,
( spl47_143
| spl47_122
| ~ spl47_48
| ~ spl47_70 ),
inference(avatar_split_clause,[],[f1893,f1084,f954,f1430,f1904]) ).
thf(f1968,plain,
( ( $false = $true )
| ( ( q @ sK36 )
= $true )
| ~ spl47_93
| ~ spl47_123 ),
inference(constrained_superposition,[],[f1207,f1434]) ).
thf(f1984,plain,
( ( ( q @ sK36 )
= $true )
| ~ spl47_93
| ~ spl47_123 ),
inference(trivial_inequality_removal,[],[f1968]) ).
thf(f1995,plain,
( ( $false = $true )
| ~ spl47_93
| ~ spl47_96
| ~ spl47_123 ),
inference(forward_demodulation,[],[f1984,f1223]) ).
thf(f1996,plain,
( $false
| ~ spl47_93
| ~ spl47_96
| ~ spl47_123 ),
inference(trivial_inequality_removal,[],[f1995]) ).
thf(f1997,plain,
( ~ spl47_93
| ~ spl47_96
| ~ spl47_123 ),
inference(avatar_contradiction_clause,[],[f1996]) ).
thf(f2037,plain,
( ( ( p @ sK33 )
= $true )
| ( $false = $true )
| ~ spl47_87
| ~ spl47_122 ),
inference(constrained_superposition,[],[f1171,f1431]) ).
thf(f2045,plain,
( ( ( p @ sK33 )
= $true )
| ~ spl47_87
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f2037]) ).
thf(f2064,plain,
( ( $false = $true )
| ~ spl47_87
| ~ spl47_88
| ~ spl47_122 ),
inference(forward_demodulation,[],[f2045,f1177]) ).
thf(f2065,plain,
( $false
| ~ spl47_87
| ~ spl47_88
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f2064]) ).
thf(f2066,plain,
( ~ spl47_87
| ~ spl47_88
| ~ spl47_122 ),
inference(avatar_contradiction_clause,[],[f2065]) ).
thf(f2148,plain,
( ( ( r @ sK31 )
= $true )
| ( $false = $true )
| ~ spl47_81
| ~ spl47_143 ),
inference(constrained_superposition,[],[f1905,f1141]) ).
thf(f2153,plain,
( ( ( r @ sK38 )
= $true )
| ( $false = $true )
| ~ spl47_97
| ~ spl47_143 ),
inference(constrained_superposition,[],[f1905,f1231]) ).
thf(f2174,plain,
( ( ( r @ sK31 )
= $true )
| ~ spl47_81
| ~ spl47_143 ),
inference(trivial_inequality_removal,[],[f2148]) ).
thf(f2182,plain,
( ( ( r @ sK38 )
= $true )
| ~ spl47_97
| ~ spl47_143 ),
inference(trivial_inequality_removal,[],[f2153]) ).
thf(f2197,plain,
( ( $false = $true )
| ~ spl47_81
| ~ spl47_83
| ~ spl47_143 ),
inference(forward_demodulation,[],[f2174,f1150]) ).
thf(f2198,plain,
( $false
| ~ spl47_81
| ~ spl47_83
| ~ spl47_143 ),
inference(trivial_inequality_removal,[],[f2197]) ).
thf(f2199,plain,
( ~ spl47_81
| ~ spl47_83
| ~ spl47_143 ),
inference(avatar_contradiction_clause,[],[f2198]) ).
thf(f2208,plain,
( ( $false = $true )
| ~ spl47_97
| ~ spl47_98
| ~ spl47_143 ),
inference(forward_demodulation,[],[f2182,f1236]) ).
thf(f2209,plain,
( $false
| ~ spl47_97
| ~ spl47_98
| ~ spl47_143 ),
inference(trivial_inequality_removal,[],[f2208]) ).
thf(f2210,plain,
( ~ spl47_97
| ~ spl47_98
| ~ spl47_143 ),
inference(avatar_contradiction_clause,[],[f2209]) ).
thf(f2364,plain,
( ( $false = $true )
| ( ( q @ sK30 )
= $true )
| ~ spl47_82
| ~ spl47_123 ),
inference(constrained_superposition,[],[f1434,f1145]) ).
thf(f2366,plain,
( ( ( q @ sK30 )
= $true )
| ~ spl47_82
| ~ spl47_123 ),
inference(trivial_inequality_removal,[],[f2364]) ).
thf(f2372,plain,
( ( $false = $true )
| ~ spl47_82
| ~ spl47_84
| ~ spl47_123 ),
inference(forward_demodulation,[],[f2366,f1155]) ).
thf(f2373,plain,
( $false
| ~ spl47_82
| ~ spl47_84
| ~ spl47_123 ),
inference(trivial_inequality_removal,[],[f2372]) ).
thf(f2374,plain,
( ~ spl47_82
| ~ spl47_84
| ~ spl47_123 ),
inference(avatar_contradiction_clause,[],[f2373]) ).
thf(f2376,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( irel @ sK21 @ X0 ) )
| ( $false
= ( irel @ sK21 @ X1 ) )
| ( $true
= ( p @ X0 ) )
| ( ( r @ X1 )
= $true ) )
| ~ spl47_48
| ~ spl47_64 ),
inference(constrained_superposition,[],[f1052,f955]) ).
thf(f2378,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ sK21 @ X0 ) )
| ( $false = $true )
| ( $false
= ( irel @ sK21 @ X1 ) )
| ( ( q @ X0 )
= $true )
| ( ( p @ X1 )
= $true ) )
| ~ spl47_46
| ~ spl47_64 ),
inference(constrained_superposition,[],[f1052,f947]) ).
thf(f2387,plain,
( ! [X0: $i,X1: $i] :
( ( ( q @ X0 )
= $true )
| ( $false
= ( irel @ sK21 @ X1 ) )
| ( ( p @ X1 )
= $true )
| ( $false
= ( irel @ sK21 @ X0 ) ) )
| ~ spl47_46
| ~ spl47_64 ),
inference(trivial_inequality_removal,[],[f2378]) ).
thf(f2389,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ sK21 @ X0 ) )
| ( ( r @ X1 )
= $true )
| ( $false
= ( irel @ sK21 @ X1 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl47_48
| ~ spl47_64 ),
inference(trivial_inequality_removal,[],[f2376]) ).
thf(f2393,plain,
( spl47_116
| spl47_117
| ~ spl47_46
| ~ spl47_64 ),
inference(avatar_split_clause,[],[f2387,f1050,f946,f1386,f1383]) ).
thf(f2394,plain,
( spl47_144
| spl47_117
| ~ spl47_48
| ~ spl47_64 ),
inference(avatar_split_clause,[],[f2389,f1050,f954,f1386,f1908]) ).
thf(f2430,plain,
( ( $false = $true )
| ( ( r @ sK39 )
= $true )
| ~ spl47_99
| ~ spl47_144 ),
inference(constrained_superposition,[],[f1909,f1247]) ).
thf(f2447,plain,
( ( ( r @ sK39 )
= $true )
| ~ spl47_99
| ~ spl47_144 ),
inference(trivial_inequality_removal,[],[f2430]) ).
thf(f2457,plain,
( ( $false = $true )
| ~ spl47_99
| ~ spl47_101
| ~ spl47_144 ),
inference(forward_demodulation,[],[f2447,f1256]) ).
thf(f2458,plain,
( $false
| ~ spl47_99
| ~ spl47_101
| ~ spl47_144 ),
inference(trivial_inequality_removal,[],[f2457]) ).
thf(f2459,plain,
( ~ spl47_99
| ~ spl47_101
| ~ spl47_144 ),
inference(avatar_contradiction_clause,[],[f2458]) ).
thf(f2688,plain,
( ( $false = $true )
| ( $true
= ( r @ sK46 ) )
| ~ spl47_113
| ~ spl47_143 ),
inference(constrained_superposition,[],[f1905,f1329]) ).
thf(f2697,plain,
( ( $true
= ( r @ sK46 ) )
| ~ spl47_113
| ~ spl47_143 ),
inference(trivial_inequality_removal,[],[f2688]) ).
thf(f2703,plain,
( ( $false = $true )
| ~ spl47_113
| ~ spl47_114
| ~ spl47_143 ),
inference(forward_demodulation,[],[f2697,f1334]) ).
thf(f2704,plain,
( $false
| ~ spl47_113
| ~ spl47_114
| ~ spl47_143 ),
inference(trivial_inequality_removal,[],[f2703]) ).
thf(f2705,plain,
( ~ spl47_113
| ~ spl47_114
| ~ spl47_143 ),
inference(avatar_contradiction_clause,[],[f2704]) ).
thf(f2709,plain,
( ( $false = $true )
| ( $true
= ( q @ sK45 ) )
| ~ spl47_112
| ~ spl47_123 ),
inference(constrained_superposition,[],[f1325,f1434]) ).
thf(f2721,plain,
( ( $true
= ( q @ sK45 ) )
| ~ spl47_112
| ~ spl47_123 ),
inference(trivial_inequality_removal,[],[f2709]) ).
thf(f2727,plain,
( ( $false = $true )
| ~ spl47_112
| ~ spl47_115
| ~ spl47_123 ),
inference(forward_demodulation,[],[f2721,f1339]) ).
thf(f2728,plain,
( $false
| ~ spl47_112
| ~ spl47_115
| ~ spl47_123 ),
inference(trivial_inequality_removal,[],[f2727]) ).
thf(f2729,plain,
( ~ spl47_112
| ~ spl47_115
| ~ spl47_123 ),
inference(avatar_contradiction_clause,[],[f2728]) ).
thf(f2812,plain,
( ( $false = $true )
| ( $true
= ( p @ sK40 ) )
| ~ spl47_102
| ~ spl47_122 ),
inference(constrained_superposition,[],[f1261,f1431]) ).
thf(f2834,plain,
( ( $true
= ( p @ sK40 ) )
| ~ spl47_102
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f2812]) ).
thf(f2862,plain,
( ( $false = $true )
| ~ spl47_102
| ~ spl47_104
| ~ spl47_122 ),
inference(forward_demodulation,[],[f2834,f1270]) ).
thf(f2863,plain,
( $false
| ~ spl47_102
| ~ spl47_104
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f2862]) ).
thf(f2864,plain,
( ~ spl47_102
| ~ spl47_104
| ~ spl47_122 ),
inference(avatar_contradiction_clause,[],[f2863]) ).
thf(f3030,plain,
( ( $true
= ( p @ sK41 ) )
| ( $false = $true )
| ~ spl47_103
| ~ spl47_122 ),
inference(constrained_superposition,[],[f1265,f1431]) ).
thf(f3046,plain,
( ( $true
= ( p @ sK41 ) )
| ~ spl47_103
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f3030]) ).
thf(f3055,plain,
( ( $false = $true )
| ~ spl47_103
| ~ spl47_105
| ~ spl47_122 ),
inference(forward_demodulation,[],[f3046,f1275]) ).
thf(f3056,plain,
( $false
| ~ spl47_103
| ~ spl47_105
| ~ spl47_122 ),
inference(trivial_inequality_removal,[],[f3055]) ).
thf(f3057,plain,
( ~ spl47_103
| ~ spl47_105
| ~ spl47_122 ),
inference(avatar_contradiction_clause,[],[f3056]) ).
cnf(s45,plain,
( spl47_46
| spl47_46
| spl47_47 ),
inference(sat_conversion,[],[f952]) ).
cnf(s46,plain,
( spl47_46
| spl47_47 ),
inference(rat,[],[s45]) ).
cnf(s49,plain,
( spl47_48
| spl47_47
| spl47_48 ),
inference(sat_conversion,[],[f958]) ).
cnf(s50,plain,
( spl47_47
| spl47_48 ),
inference(rat,[],[s49]) ).
cnf(s91,plain,
( spl47_47
| spl47_64
| spl47_70 ),
inference(sat_conversion,[],[f1087]) ).
cnf(s92,plain,
( spl47_47
| spl47_64
| spl47_71 ),
inference(sat_conversion,[],[f1092]) ).
cnf(s93,plain,
( spl47_47
| spl47_64
| spl47_72 ),
inference(sat_conversion,[],[f1097]) ).
cnf(s102,plain,
( spl47_47
| spl47_64
| spl47_81
| spl47_82 ),
inference(sat_conversion,[],[f1146]) ).
cnf(s103,plain,
( spl47_47
| spl47_64
| spl47_82
| spl47_83 ),
inference(sat_conversion,[],[f1151]) ).
cnf(s104,plain,
( spl47_47
| spl47_64
| spl47_81
| spl47_84 ),
inference(sat_conversion,[],[f1156]) ).
cnf(s105,plain,
( spl47_47
| spl47_64
| spl47_83
| spl47_84 ),
inference(sat_conversion,[],[f1157]) ).
cnf(s106,plain,
( spl47_47
| spl47_70
| spl47_85 ),
inference(sat_conversion,[],[f1162]) ).
cnf(s107,plain,
( spl47_47
| spl47_70
| spl47_86 ),
inference(sat_conversion,[],[f1167]) ).
cnf(s108,plain,
( spl47_47
| spl47_85
| spl47_87 ),
inference(sat_conversion,[],[f1172]) ).
cnf(s109,plain,
( spl47_47
| spl47_86
| spl47_87 ),
inference(sat_conversion,[],[f1173]) ).
cnf(s110,plain,
( spl47_47
| spl47_85
| spl47_88 ),
inference(sat_conversion,[],[f1178]) ).
cnf(s111,plain,
( spl47_47
| spl47_86
| spl47_88 ),
inference(sat_conversion,[],[f1179]) ).
cnf(s128,plain,
( spl47_47
| spl47_85
| spl47_93
| spl47_97 ),
inference(sat_conversion,[],[f1232]) ).
cnf(s129,plain,
( spl47_47
| spl47_85
| spl47_93
| spl47_98 ),
inference(sat_conversion,[],[f1237]) ).
cnf(s130,plain,
( spl47_47
| spl47_85
| spl47_96
| spl47_97 ),
inference(sat_conversion,[],[f1238]) ).
cnf(s131,plain,
( spl47_47
| spl47_85
| spl47_96
| spl47_98 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s132,plain,
( spl47_47
| spl47_86
| spl47_93
| spl47_97 ),
inference(sat_conversion,[],[f1240]) ).
cnf(s133,plain,
( spl47_47
| spl47_86
| spl47_96
| spl47_97 ),
inference(sat_conversion,[],[f1241]) ).
cnf(s134,plain,
( spl47_47
| spl47_86
| spl47_93
| spl47_98 ),
inference(sat_conversion,[],[f1242]) ).
cnf(s135,plain,
( spl47_47
| spl47_86
| spl47_96
| spl47_98 ),
inference(sat_conversion,[],[f1243]) ).
cnf(s136,plain,
( spl47_47
| spl47_70
| spl47_99 ),
inference(sat_conversion,[],[f1248]) ).
cnf(s137,plain,
( spl47_47
| spl47_70
| spl47_100
| spl47_101 ),
inference(sat_conversion,[],[f1257]) ).
cnf(s138,plain,
( spl47_47
| spl47_99
| spl47_102
| spl47_103 ),
inference(sat_conversion,[],[f1266]) ).
cnf(s139,plain,
( spl47_47
| spl47_99
| spl47_103
| spl47_104 ),
inference(sat_conversion,[],[f1271]) ).
cnf(s140,plain,
( spl47_47
| spl47_99
| spl47_102
| spl47_105 ),
inference(sat_conversion,[],[f1276]) ).
cnf(s141,plain,
( spl47_47
| spl47_99
| spl47_104
| spl47_105 ),
inference(sat_conversion,[],[f1277]) ).
cnf(s142,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_102
| spl47_103 ),
inference(sat_conversion,[],[f1278]) ).
cnf(s143,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_103
| spl47_104 ),
inference(sat_conversion,[],[f1279]) ).
cnf(s144,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_102
| spl47_105 ),
inference(sat_conversion,[],[f1280]) ).
cnf(s145,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_104
| spl47_105 ),
inference(sat_conversion,[],[f1281]) ).
cnf(s162,plain,
( spl47_47
| spl47_99
| spl47_112
| spl47_113 ),
inference(sat_conversion,[],[f1330]) ).
cnf(s163,plain,
( spl47_47
| spl47_99
| spl47_112
| spl47_114 ),
inference(sat_conversion,[],[f1335]) ).
cnf(s164,plain,
( spl47_47
| spl47_99
| spl47_113
| spl47_115 ),
inference(sat_conversion,[],[f1340]) ).
cnf(s165,plain,
( spl47_47
| spl47_99
| spl47_114
| spl47_115 ),
inference(sat_conversion,[],[f1341]) ).
cnf(s166,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_112
| spl47_113 ),
inference(sat_conversion,[],[f1342]) ).
cnf(s167,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_112
| spl47_114 ),
inference(sat_conversion,[],[f1343]) ).
cnf(s168,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_113
| spl47_115 ),
inference(sat_conversion,[],[f1344]) ).
cnf(s169,plain,
( spl47_47
| spl47_100
| spl47_101
| spl47_114
| spl47_115 ),
inference(sat_conversion,[],[f1345]) ).
cnf(s170,plain,
~ spl47_47,
inference(sat_conversion,[],[f1346]) ).
cnf(s184,plain,
( ~ spl47_99
| ~ spl47_100
| ~ spl47_116 ),
inference(sat_conversion,[],[f1497]) ).
cnf(s189,plain,
( ~ spl47_85
| ~ spl47_86
| ~ spl47_117 ),
inference(sat_conversion,[],[f1532]) ).
cnf(s204,plain,
( ~ spl47_71
| ~ spl47_72
| ~ spl47_122 ),
inference(sat_conversion,[],[f1692]) ).
cnf(s229,plain,
( ~ spl47_46
| ~ spl47_70
| spl47_122
| spl47_123 ),
inference(sat_conversion,[],[f1868]) ).
cnf(s234,plain,
( ~ spl47_48
| ~ spl47_70
| spl47_122
| spl47_143 ),
inference(sat_conversion,[],[f1912]) ).
cnf(s243,plain,
( ~ spl47_93
| ~ spl47_96
| ~ spl47_123 ),
inference(sat_conversion,[],[f1997]) ).
cnf(s247,plain,
( ~ spl47_87
| ~ spl47_88
| ~ spl47_122 ),
inference(sat_conversion,[],[f2066]) ).
cnf(s255,plain,
( ~ spl47_81
| ~ spl47_83
| ~ spl47_143 ),
inference(sat_conversion,[],[f2199]) ).
cnf(s258,plain,
( ~ spl47_97
| ~ spl47_98
| ~ spl47_143 ),
inference(sat_conversion,[],[f2210]) ).
cnf(s265,plain,
( ~ spl47_82
| ~ spl47_84
| ~ spl47_123 ),
inference(sat_conversion,[],[f2374]) ).
cnf(s268,plain,
( ~ spl47_46
| ~ spl47_64
| spl47_116
| spl47_117 ),
inference(sat_conversion,[],[f2393]) ).
cnf(s269,plain,
( ~ spl47_48
| ~ spl47_64
| spl47_117
| spl47_144 ),
inference(sat_conversion,[],[f2394]) ).
cnf(s275,plain,
( ~ spl47_99
| ~ spl47_101
| ~ spl47_144 ),
inference(sat_conversion,[],[f2459]) ).
cnf(s279,plain,
( ~ spl47_113
| ~ spl47_114
| ~ spl47_143 ),
inference(sat_conversion,[],[f2705]) ).
cnf(s281,plain,
( ~ spl47_112
| ~ spl47_115
| ~ spl47_123 ),
inference(sat_conversion,[],[f2729]) ).
cnf(s313,plain,
( ~ spl47_102
| ~ spl47_104
| ~ spl47_122 ),
inference(sat_conversion,[],[f2864]) ).
cnf(s325,plain,
( ~ spl47_103
| ~ spl47_105
| ~ spl47_122 ),
inference(sat_conversion,[],[f3057]) ).
cnf(s329,plain,
( spl47_100
| spl47_101
| spl47_114
| spl47_115 ),
inference(rat,[],[s169,s170]) ).
cnf(s330,plain,
( spl47_100
| spl47_101
| spl47_113
| spl47_115 ),
inference(rat,[],[s168,s170]) ).
cnf(s331,plain,
( spl47_100
| spl47_101
| spl47_112
| spl47_114 ),
inference(rat,[],[s167,s170]) ).
cnf(s332,plain,
( spl47_100
| spl47_101
| spl47_112
| spl47_113 ),
inference(rat,[],[s166,s170]) ).
cnf(s333,plain,
( spl47_99
| spl47_114
| spl47_115 ),
inference(rat,[],[s165,s170]) ).
cnf(s334,plain,
( spl47_99
| spl47_113
| spl47_115 ),
inference(rat,[],[s164,s170]) ).
cnf(s335,plain,
( spl47_99
| spl47_112
| spl47_114 ),
inference(rat,[],[s163,s170]) ).
cnf(s336,plain,
( spl47_99
| spl47_112
| spl47_113 ),
inference(rat,[],[s162,s170]) ).
cnf(s353,plain,
( spl47_100
| spl47_101
| spl47_104
| spl47_105 ),
inference(rat,[],[s145,s170]) ).
cnf(s354,plain,
( spl47_100
| spl47_101
| spl47_102
| spl47_105 ),
inference(rat,[],[s144,s170]) ).
cnf(s355,plain,
( spl47_100
| spl47_101
| spl47_103
| spl47_104 ),
inference(rat,[],[s143,s170]) ).
cnf(s356,plain,
( spl47_100
| spl47_101
| spl47_102
| spl47_103 ),
inference(rat,[],[s142,s170]) ).
cnf(s357,plain,
( spl47_99
| spl47_104
| spl47_105 ),
inference(rat,[],[s141,s170]) ).
cnf(s358,plain,
( spl47_99
| spl47_102
| spl47_105 ),
inference(rat,[],[s140,s170]) ).
cnf(s359,plain,
( spl47_99
| spl47_103
| spl47_104 ),
inference(rat,[],[s139,s170]) ).
cnf(s360,plain,
( spl47_99
| spl47_102
| spl47_103 ),
inference(rat,[],[s138,s170]) ).
cnf(s361,plain,
( spl47_70
| spl47_100
| spl47_101 ),
inference(rat,[],[s137,s170]) ).
cnf(s362,plain,
( spl47_70
| spl47_99 ),
inference(rat,[],[s136,s170]) ).
cnf(s363,plain,
( spl47_86
| spl47_96
| spl47_98 ),
inference(rat,[],[s135,s170]) ).
cnf(s364,plain,
( spl47_86
| spl47_93
| spl47_98 ),
inference(rat,[],[s134,s170]) ).
cnf(s365,plain,
( spl47_86
| spl47_96
| spl47_97 ),
inference(rat,[],[s133,s170]) ).
cnf(s366,plain,
( spl47_86
| spl47_93
| spl47_97 ),
inference(rat,[],[s132,s170]) ).
cnf(s367,plain,
( spl47_85
| spl47_96
| spl47_98 ),
inference(rat,[],[s131,s170]) ).
cnf(s368,plain,
( spl47_85
| spl47_96
| spl47_97 ),
inference(rat,[],[s130,s170]) ).
cnf(s369,plain,
( spl47_85
| spl47_93
| spl47_98 ),
inference(rat,[],[s129,s170]) ).
cnf(s370,plain,
( spl47_85
| spl47_93
| spl47_97 ),
inference(rat,[],[s128,s170]) ).
cnf(s387,plain,
( spl47_86
| spl47_88 ),
inference(rat,[],[s111,s170]) ).
cnf(s388,plain,
( spl47_85
| spl47_88 ),
inference(rat,[],[s110,s170]) ).
cnf(s389,plain,
( spl47_86
| spl47_87 ),
inference(rat,[],[s109,s170]) ).
cnf(s390,plain,
( spl47_85
| spl47_87 ),
inference(rat,[],[s108,s170]) ).
cnf(s391,plain,
( spl47_70
| spl47_86 ),
inference(rat,[],[s107,s170]) ).
cnf(s392,plain,
( spl47_70
| spl47_85 ),
inference(rat,[],[s106,s170]) ).
cnf(s393,plain,
( spl47_64
| spl47_83
| spl47_84 ),
inference(rat,[],[s105,s170]) ).
cnf(s394,plain,
( spl47_64
| spl47_81
| spl47_84 ),
inference(rat,[],[s104,s170]) ).
cnf(s395,plain,
( spl47_64
| spl47_82
| spl47_83 ),
inference(rat,[],[s103,s170]) ).
cnf(s396,plain,
( spl47_64
| spl47_81
| spl47_82 ),
inference(rat,[],[s102,s170]) ).
cnf(s405,plain,
( spl47_64
| spl47_72 ),
inference(rat,[],[s93,s170]) ).
cnf(s406,plain,
( spl47_64
| spl47_71 ),
inference(rat,[],[s92,s170]) ).
cnf(s407,plain,
( spl47_64
| spl47_70 ),
inference(rat,[],[s91,s170]) ).
cnf(s448,plain,
spl47_48,
inference(rat,[],[s50,s170]) ).
cnf(s449,plain,
spl47_46,
inference(rat,[],[s46,s170]) ).
cnf(s451,plain,
( spl47_81
| spl47_64 ),
inference(rat,[],[s265,s396,s394,s229,s407,s204,s406,s405,s449]) ).
cnf(s452,plain,
spl47_64,
inference(rat,[],[s265,s395,s393,s255,s451,s229,s234,s204,s407,s406,s405,s449,s448]) ).
cnf(s453,plain,
( spl47_85
| ~ spl47_122 ),
inference(rat,[],[s247,s390,s388]) ).
cnf(s454,plain,
( spl47_102
| spl47_99
| ~ spl47_122 ),
inference(rat,[],[s325,s358,s360]) ).
cnf(s455,plain,
( spl47_99
| ~ spl47_122 ),
inference(rat,[],[s359,s325,s357,s313,s454]) ).
cnf(s456,plain,
( spl47_102
| spl47_117
| ~ spl47_122 ),
inference(rat,[],[s325,s356,s354,s275,s269,s184,s455,s268,s452,s449,s448]) ).
cnf(s457,plain,
( spl47_117
| ~ spl47_122 ),
inference(rat,[],[s325,s355,s353,s313,s456,s184,s275,s268,s269,s455,s449,s452,s448]) ).
cnf(s458,plain,
~ spl47_122,
inference(rat,[],[s247,s389,s387,s189,s457,s453]) ).
cnf(s459,plain,
spl47_70,
inference(rat,[],[s361,s184,s275,s268,s269,s189,s392,s391,s362,s449,s452,s448]) ).
cnf(s460,plain,
spl47_143,
inference(rat,[],[s234,s458,s448,s459]) ).
cnf(s461,plain,
spl47_123,
inference(rat,[],[s229,s458,s449,s459]) ).
cnf(s463,plain,
( spl47_112
| spl47_99 ),
inference(rat,[],[s279,s336,s335,s460]) ).
cnf(s464,plain,
( spl47_115
| spl47_99 ),
inference(rat,[],[s279,s334,s333,s460]) ).
cnf(s465,plain,
spl47_99,
inference(rat,[],[s464,s281,s463,s461]) ).
cnf(s466,plain,
( spl47_114
| spl47_100
| spl47_101 ),
inference(rat,[],[s281,s331,s329,s461]) ).
cnf(s467,plain,
( spl47_113
| spl47_101
| spl47_100 ),
inference(rat,[],[s281,s330,s332,s461]) ).
cnf(s468,plain,
( spl47_100
| spl47_101 ),
inference(rat,[],[s467,s279,s466,s460]) ).
cnf(s469,plain,
spl47_117,
inference(rat,[],[s468,s184,s275,s268,s269,s465,s449,s452,s448]) ).
cnf(s470,plain,
( spl47_93
| spl47_86 ),
inference(rat,[],[s258,s366,s364,s460]) ).
cnf(s471,plain,
( spl47_96
| spl47_86 ),
inference(rat,[],[s258,s365,s363,s460]) ).
cnf(s472,plain,
spl47_86,
inference(rat,[],[s471,s243,s470,s461]) ).
cnf(s473,plain,
~ spl47_85,
inference(rat,[],[s189,s469,s472]) ).
cnf(s476,plain,
spl47_97,
inference(rat,[],[s243,s370,s368,s461,s473]) ).
cnf(s477,plain,
~ spl47_98,
inference(rat,[],[s258,s460,s476]) ).
cnf(s478,plain,
spl47_96,
inference(rat,[],[s367,s473,s477]) ).
cnf(s479,plain,
spl47_93,
inference(rat,[],[s369,s473,s477]) ).
cnf(s480,plain,
$false,
inference(rat,[],[s243,s461,s478,s479]) ).
thf(f3062,plain,
$false,
inference(avatar_sat_refutation,[],[s480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN045^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:15:09 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.34 % (3353105)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.34 % (3353112)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2205219954:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.34 % (3353111)lrs+10_16_si=on:nwc=1.5:random_seed=3722112669:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.34 % (3353110)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2758494851:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.34 % (3353116)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.34 % (3353116)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.34 % (3353112)Instruction limit reached!
% 0.21/0.34 % (3353112)------------------------------
% 0.21/0.34 % (3353112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353116)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=3086044240:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.34 % (3353112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353112)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353112)Termination reason: Instruction limit
% 0.21/0.34 % (3353112)Termination phase: Property scanning
% 0.21/0.34 % (3353112)Time elapsed: 0.002 s
% 0.21/0.34 % (3353112)Peak memory usage: 10 MB
% 0.21/0.34 % (3353112)Instructions burned: 3 (million)
% 0.21/0.34 % (3353111)Instruction limit reached!
% 0.21/0.34 % (3353111)------------------------------
% 0.21/0.34 % (3353111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353111)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353111)Termination reason: Instruction limit
% 0.21/0.34 % (3353111)Termination phase: Saturation
% 0.21/0.34 % (3353111)Time elapsed: 0.009 s
% 0.21/0.34 % (3353111)Peak memory usage: 11 MB
% 0.21/0.34 % (3353111)Instructions burned: 19 (million)
% 0.21/0.34 % (3353113)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=1914275997:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.34 % (3353114)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=36919036:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.34 % (3353115)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4082258197:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.34 % (3353121)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3252649921:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.34 % (3353121)Instruction limit reached!
% 0.21/0.34 % (3353121)------------------------------
% 0.21/0.34 % (3353121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353121)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353121)Termination reason: Instruction limit
% 0.21/0.34 % (3353121)Termination phase: Property scanning
% 0.21/0.34 % (3353121)Time elapsed: 0.002 s
% 0.21/0.34 % (3353121)Peak memory usage: 10 MB
% 0.21/0.34 % (3353121)Instructions burned: 4 (million)
% 0.21/0.34 % (3353122)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2506092516:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.34 % (3353122)Instruction limit reached!
% 0.21/0.34 % (3353122)------------------------------
% 0.21/0.34 % (3353122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353122)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353122)Termination reason: Instruction limit
% 0.21/0.34 % (3353122)Termination phase: Saturation
% 0.21/0.34 % (3353122)Time elapsed: 0.003 s
% 0.21/0.34 % (3353122)Peak memory usage: 11 MB
% 0.21/0.34 % (3353122)Instructions burned: 6 (million)
% 0.21/0.34 % (3353114)Instruction limit reached!
% 0.21/0.34 % (3353114)------------------------------
% 0.21/0.34 % (3353114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353114)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353114)Termination reason: Instruction limit
% 0.21/0.34 % (3353114)Termination phase: Saturation
% 0.21/0.34 % (3353114)Time elapsed: 0.023 s
% 0.21/0.34 % (3353114)Peak memory usage: 11 MB
% 0.21/0.34 % (3353114)Instructions burned: 24 (million)
% 0.21/0.34 % (3353127)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (3353110)Instruction limit reached!
% 0.21/0.34 % (3353110)------------------------------
% 0.21/0.34 % (3353110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353110)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353110)Termination reason: Instruction limit
% 0.21/0.34 % (3353110)Termination phase: Saturation
% 0.21/0.34 % (3353110)Time elapsed: 0.042 s
% 0.21/0.34 % (3353110)Peak memory usage: 13 MB
% 0.21/0.34 % (3353110)Instructions burned: 87 (million)
% 0.21/0.34 % (3353116) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3353105-3353116"...
% 0.21/0.34 % (3353127)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2607480167:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.34 % (3353127)Instruction limit reached!
% 0.21/0.34 % (3353127)------------------------------
% 0.21/0.34 % (3353127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353127)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353127)Termination reason: Instruction limit
% 0.21/0.34 % (3353127)Termination phase: Saturation
% 0.21/0.34 % (3353127)Time elapsed: 0.004 s
% 0.21/0.34 % (3353127)Peak memory usage: 11 MB
% 0.21/0.34 % (3353127)Instructions burned: 9 (million)
% 0.21/0.34 % (3353116)...printing done.
% 0.21/0.34 % (3353129)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2977036655:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.34 % (3353116)Refutation found. Thanks to Tanya!
% 0.21/0.34 % SZS status Theorem for theBenchmark
% 0.21/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.34 % (3353116)------------------------------
% 0.21/0.34 % (3353116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3353116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3353116)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3353116)Termination reason: Refutation
% 0.21/0.34 % (3353116)Time elapsed: 0.048 s
% 0.21/0.34 % (3353116)Peak memory usage: 14 MB
% 0.21/0.34 % (3353116)Instructions burned: 174 (million)
% 0.21/0.34 % (3353105)Success in time 0.086 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------