%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV426^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:39:56 AM UTC 2026
% Result : Theorem 0.20s 0.35s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 25
% Syntax : Number of formulae : 217 ( 72 unt; 0 typ; 12 def)
% Number of atoms : 1965 ( 365 equ; 0 cnn)
% Maximal formula atoms : 21 ( 9 avg)
% Number of connectives : 2742 ( 169 ~; 409 |; 0 &;1786 @)
% ( 11 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 351 ( 351 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 74 usr; 20 con; 0-4 aty)
% ( 171 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 712 ( 0 sgn 163 !; 0 ?; 712 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
rel: $i > $i > $o ).
thf(func_def_21,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
icl_true: $i > $o ).
thf(func_def_27,type,
icl_false: $i > $o ).
thf(func_def_28,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_29,type,
iclval: ( $i > $o ) > $o ).
thf(func_def_30,type,
s: $i > $o ).
thf(func_def_31,type,
a: $i > $o ).
thf(func_def_32,type,
b: $i > $o ).
thf(func_def_35,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
sF0: $o ).
thf(func_def_47,type,
sK1: $i > ( $i > $o ) > $i ).
thf(func_def_48,type,
sK2: $i > $i ).
thf(func_def_49,type,
sK3: $i > $i ).
thf(func_def_50,type,
sK4: $i > $i ).
thf(func_def_51,type,
sK5: $i > $i ).
thf(func_def_52,type,
sK6: $i > $i ).
thf(func_def_53,type,
sK7: $i > $i ).
thf(func_def_54,type,
sK8: $i > $i ).
thf(func_def_55,type,
sK9: $i > $i ).
thf(func_def_56,type,
sK10: $i > $i ).
thf(func_def_57,type,
sK11: $i > $i ).
thf(func_def_58,type,
sK12: $i > $i ).
thf(func_def_59,type,
sK13: $i > $i ).
thf(func_def_65,type,
sK19: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( icl_atom
= ( ^ [X0: $i > $o] : ( mbox @ rel @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_atom) ).
thf(f17,axiom,
( icl_princ
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_princ) ).
thf(f20,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) )
= icl_impl ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_impl) ).
thf(f23,axiom,
( icl_says
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_says) ).
thf(f24,axiom,
( iclval
= ( ^ [X0: $i > $o] : ( mvalid @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^1.ax',refl_axiom) ).
thf(f26,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^1.ax',trans_axiom) ).
thf(f27,conjecture,
iclval @ ( icl_impl @ ( icl_says @ ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_atom @ s ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cuc) ).
thf(f28,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_atom @ s ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
thf(f29,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f30,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(fool_elimination,[],[f29]) ).
thf(f33,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f35,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f36,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f45,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f48,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f49,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f51,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f52,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f55,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f56,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f59,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f60,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f62,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f65,plain,
~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_atom @ s ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f66,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_atom @ s ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f65]) ).
thf(f68,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_atom @ s ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )
!= $true ),
inference(flattening,[],[f66]) ).
thf(f70,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f71,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f75,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f77,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f81,plain,
( icl_atom
= ( ^ [Y0: $i > $o] : ( mbox @ rel @ Y0 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f82,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_atom @ s ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f68]) ).
thf(f83,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f30]) ).
thf(f84,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f87,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f90,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ ( mbox @ rel @ ( mbox @ rel @ X0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f60]) ).
thf(f91,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f92,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f93,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f98,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f77,f92,f75]) ).
thf(f100,plain,
( icl_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 ) ) ),
inference(definition_unfolding,[],[f81,f70]) ).
thf(f103,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f84,f70,f98]) ).
thf(f106,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f93,f70,f92]) ).
thf(f107,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f91,f87]) ).
thf(f108,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) ) ),
inference(definition_unfolding,[],[f82,f107,f103,f106,f103,f71,f71,f100,f103,f106,f71,f100,f106,f71,f100]) ).
thf(f109,plain,
! [X0: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 )
@ X0 ) ) ),
inference(definition_unfolding,[],[f83,f87,f98,f70]) ).
thf(f110,plain,
! [X0: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 ) ) ) ) ),
inference(definition_unfolding,[],[f90,f87,f98,f70,f70,f70]) ).
thf(f111,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f112,plain,
$true != sF0,
inference(definition_folding,[],[f108,f111]) ).
thf(f113,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f114,plain,
! [X0: $i > $o,X1: $i] :
( ( ^ [Y0: $i] :
( ( X0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ( X0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK1 @ X1 @ X0 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( ( rel @ X1 @ ( sK1 @ X1 @ X0 ) )
=> ( X0 @ ( sK1 @ X1 @ X0 ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK1 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK1 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ rel
@ Y0 )
@ s ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f111]) ).
thf(f278,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) )
| ( b @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) )
| ( a @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( b @ Y3 )
| ~ ( a @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f279,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) )
| ( b @ Y3 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( !! @ $i
@ ^ [Y4: $i] :
( ( rel @ Y3 @ Y4 )
=> ( s @ Y4 ) ) )
| ( a @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ( b @ Y3 )
| ~ ( a @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK14 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f278]) ).
thf(f280,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK14 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( b @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( a @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ~ ( a @ Y2 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( rel @ sK14 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( b @ Y2 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( s @ Y3 ) ) )
| ( a @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ~ ( a @ Y2 ) ) ) ) ) ) ) ) )
@ sK15 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f280]) ).
thf(f282,plain,
( ( ( ( rel @ sK14 @ sK15 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( b @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( a @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) ) ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( b @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( a @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f282]) ).
thf(f285,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f286,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( b @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( a @ Y1 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f287,plain,
( ( ( ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( b @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( s @ Y2 ) ) )
| ( a @ Y1 ) ) ) ) ) )
@ sK16 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f286]) ).
thf(f288,plain,
( ( $false
= ( ( rel @ sK15 @ sK16 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( b @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( b @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) ) ) )
= $false )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f288]) ).
thf(f290,plain,
( ( $true = sF0 )
| ( $true
= ( rel @ sK15 @ sK16 ) ) ),
inference(imp_proxy_clausification,[],[f288]) ).
thf(f291,plain,
( ( $true = sF0 )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f292,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( b @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f293,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( b @ Y0 ) ) )
@ sK17 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f292]) ).
thf(f294,plain,
( ( $true = sF0 )
| ( ( ( rel @ sK16 @ sK17 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK17 @ Y0 )
=> ( s @ Y0 ) ) )
| ( b @ sK17 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f295,plain,
( ( $true = sF0 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK17 @ Y0 )
=> ( s @ Y0 ) ) )
| ( b @ sK17 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( ( $true
= ( rel @ sK16 @ sK17 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f294]) ).
thf(f297,plain,
( ( $true = sF0 )
| ( $false
= ( b @ sK17 ) ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f298,plain,
( ( $true = sF0 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK17 @ Y0 )
=> ( s @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f299,plain,
( ( ( ^ [Y0: $i] :
( ( rel @ sK17 @ Y0 )
=> ( s @ Y0 ) )
@ sK18 )
= $false )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( ( $true = sF0 )
| ( ( ( rel @ sK17 @ sK18 )
=> ( s @ sK18 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
( ( $true = sF0 )
| ( ( s @ sK18 )
= $false ) ),
inference(imp_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ( $true
= ( rel @ sK17 @ sK18 ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f300]) ).
thf(f303,plain,
( ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f304,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ sK16 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( a @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ( rel @ sK16 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) )
| ( a @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f304]) ).
thf(f306,plain,
! [X1: $i] :
( ( ( rel @ sK16 @ X1 )
= $false )
| ( $true = sF0 )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) )
| ( a @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X1: $i] :
( ( $true
= ( a @ X1 ) )
| ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) ) )
| ( ( rel @ sK16 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) )
@ X2 ) )
| ( ( rel @ sK16 @ X1 )
= $false )
| ( $true
= ( a @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ sK16 @ X1 )
= $false )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( s @ X2 ) ) )
| ( $true
= ( a @ X1 ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f308]) ).
thf(f310,plain,
! [X2: $i,X1: $i] :
( ( ( rel @ sK16 @ X1 )
= $false )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true = sF0 )
| ( $true
= ( s @ X2 ) )
| ( $true
= ( a @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f309]) ).
thf(f311,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f312,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ sK15 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( s @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ~ ( a @ Y1 ) ) ) ) ) )
@ X1 ) )
| ( $true = sF0 ) ),
inference(pi_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ( rel @ sK15 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f312]) ).
thf(f314,plain,
! [X1: $i] :
( ( ( rel @ sK15 @ X1 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(imp_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) ) ) )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) ) ) )
| ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) )
@ X2 ) )
| ( ( rel @ sK15 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( s @ Y0 ) )
@ X3 ) )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ( b @ Y0 )
| ~ ( a @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel @ X1 @ X2 )
=> ( ( b @ X2 )
| ~ ( a @ X2 ) ) )
= $true )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( $true
= ( ( rel @ X1 @ X3 )
=> ( s @ X3 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel @ sK15 @ X1 )
= $false )
| ( $true
= ( ( rel @ X1 @ X3 )
=> ( s @ X3 ) ) )
| ( $true = sF0 )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ( b @ X2 )
| ~ ( a @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( s @ X3 ) )
| ( $true
= ( ( b @ X2 )
| ~ ( a @ X2 ) ) )
| ( $true = sF0 )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( $false
= ( rel @ X1 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( $true = sF0 )
| ( $true
= ( s @ X3 ) )
| ( $true
= ( ~ ( a @ X2 ) ) )
| ( $true
= ( b @ X2 ) )
| ( $false
= ( rel @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( b @ X2 ) )
| ( $false
= ( rel @ X1 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( ( a @ X2 )
= $false )
| ( $true = sF0 )
| ( $true
= ( s @ X3 ) ) ),
inference(not_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f324,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( X0 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f324]) ).
thf(f326,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK19 @ X1 @ X0 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( ( rel @ X1 @ ( sK19 @ X1 @ X0 ) )
=> ( X0 @ ( sK19 @ X1 @ X0 ) ) )
= $false )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK19 @ X1 @ X0 ) )
= $false )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( rel @ X1 @ ( sK19 @ X1 @ X0 ) )
= $true )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f330]) ).
thf(f333,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( ( rel @ X1 @ ( sK19 @ X1 @ X0 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) )
| ( ( rel @ X1 @ ( sK19 @ X1 @ X0 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) ) )
| ( ( rel @ X1 @ ( sK19 @ X1 @ X0 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( rel @ X1 @ ( sK19 @ X1 @ X0 ) )
= $true )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( ( rel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK19 @ X1 @ X0 ) )
= $false )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f331]) ).
thf(f338,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK19 @ X1 @ X0 ) )
= $false )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( ( rel @ X2 @ X3 )
=> ( X0 @ X3 ) ) )
| ( ( X0 @ ( sK19 @ X1 @ X0 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f338]) ).
thf(f340,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ ( sK19 @ X1 @ X0 ) )
= $false )
| ( $true
= ( X0 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( ( rel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f339]) ).
thf(f446,definition,
( spl20_27
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl20_27])],[avatar_definition]) ).
thf(f451,definition,
( spl20_28
<=> ( $true
= ( rel @ sK15 @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
thf(f453,plain,
( ( $true
= ( rel @ sK15 @ sK16 ) )
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f451]) ).
thf(f454,plain,
( spl20_28
| spl20_27 ),
inference(avatar_split_clause,[],[f290,f446,f451]) ).
thf(f456,definition,
( spl20_29
<=> ( $true
= ( rel @ sK16 @ sK17 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_29])],[avatar_definition]) ).
thf(f458,plain,
( ( $true
= ( rel @ sK16 @ sK17 ) )
| ~ spl20_29 ),
inference(avatar_component_clause,[],[f456]) ).
thf(f459,plain,
( spl20_29
| spl20_27 ),
inference(avatar_split_clause,[],[f296,f446,f456]) ).
thf(f461,definition,
( spl20_30
<=> ( $true
= ( rel @ sK17 @ sK18 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_30])],[avatar_definition]) ).
thf(f463,plain,
( ( $true
= ( rel @ sK17 @ sK18 ) )
| ~ spl20_30 ),
inference(avatar_component_clause,[],[f461]) ).
thf(f464,plain,
( spl20_30
| spl20_27 ),
inference(avatar_split_clause,[],[f302,f446,f461]) ).
thf(f466,definition,
( spl20_31
<=> ( ( s @ sK18 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_31])],[avatar_definition]) ).
thf(f468,plain,
( ( ( s @ sK18 )
= $false )
| ~ spl20_31 ),
inference(avatar_component_clause,[],[f466]) ).
thf(f469,plain,
( spl20_31
| spl20_27 ),
inference(avatar_split_clause,[],[f301,f446,f466]) ).
thf(f471,definition,
( spl20_32
<=> ( $false
= ( b @ sK17 ) ) ),
introduced(definition,[new_symbols(definition,[spl20_32])],[avatar_definition]) ).
thf(f473,plain,
( ( $false
= ( b @ sK17 ) )
| ~ spl20_32 ),
inference(avatar_component_clause,[],[f471]) ).
thf(f474,plain,
( spl20_32
| spl20_27 ),
inference(avatar_split_clause,[],[f297,f446,f471]) ).
thf(f476,definition,
( spl20_33
<=> ! [X2: $i,X1: $i] :
( ( ( rel @ sK16 @ X1 )
= $false )
| ( $true
= ( a @ X1 ) )
| ( $true
= ( s @ X2 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_33])],[avatar_definition]) ).
thf(f477,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( rel @ X1 @ X2 ) )
| ( ( rel @ sK16 @ X1 )
= $false )
| ( $true
= ( a @ X1 ) )
| ( $true
= ( s @ X2 ) ) )
| ~ spl20_33 ),
inference(avatar_component_clause,[],[f476]) ).
thf(f478,plain,
( spl20_33
| spl20_27 ),
inference(avatar_split_clause,[],[f310,f446,f476]) ).
thf(f480,definition,
( spl20_34
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $true
= ( b @ X2 ) )
| ( $true
= ( s @ X3 ) )
| ( ( a @ X2 )
= $false )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( $false
= ( rel @ X1 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl20_34])],[avatar_definition]) ).
thf(f481,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel @ X1 @ X3 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( ( rel @ sK15 @ X1 )
= $false )
| ( $true
= ( s @ X3 ) )
| ( $true
= ( b @ X2 ) )
| ( ( a @ X2 )
= $false ) )
| ~ spl20_34 ),
inference(avatar_component_clause,[],[f480]) ).
thf(f482,plain,
( spl20_34
| spl20_27 ),
inference(avatar_split_clause,[],[f322,f446,f480]) ).
thf(f483,plain,
~ spl20_27,
inference(avatar_split_clause,[],[f112,f446]) ).
thf(f503,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel @ X0 @ X0 ) )
| ( $true
= ( rel @ X0 @ X0 ) ) ),
inference(constrained_superposition,[],[f121,f120]) ).
thf(f505,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel @ X0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f503]) ).
thf(f506,plain,
! [X0: $i] :
( $true
= ( rel @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f505]) ).
thf(f514,plain,
( ( ( rel @ sK16 @ sK17 )
= $false )
| ( $true
= ( s @ sK18 ) )
| ( $true = $false )
| ( $true
= ( a @ sK17 ) )
| ~ spl20_30
| ~ spl20_33 ),
inference(constrained_superposition,[],[f477,f463]) ).
thf(f527,plain,
( ( ( rel @ sK16 @ sK17 )
= $false )
| ( $true
= ( s @ sK18 ) )
| ( $true
= ( a @ sK17 ) )
| ~ spl20_30
| ~ spl20_33 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f553,plain,
( ( $true
= ( a @ sK17 ) )
| ( $true = $false )
| ( $true
= ( s @ sK18 ) )
| ~ spl20_29
| ~ spl20_30
| ~ spl20_33 ),
inference(forward_demodulation,[],[f527,f458]) ).
thf(f554,plain,
( ( $true
= ( a @ sK17 ) )
| ( $true
= ( s @ sK18 ) )
| ~ spl20_29
| ~ spl20_30
| ~ spl20_33 ),
inference(trivial_inequality_removal,[],[f553]) ).
thf(f584,plain,
( ( $true = $false )
| ( $true
= ( a @ sK17 ) )
| ~ spl20_29
| ~ spl20_30
| ~ spl20_31
| ~ spl20_33 ),
inference(forward_demodulation,[],[f554,f468]) ).
thf(f585,plain,
( ( $true
= ( a @ sK17 ) )
| ~ spl20_29
| ~ spl20_30
| ~ spl20_31
| ~ spl20_33 ),
inference(trivial_inequality_removal,[],[f584]) ).
thf(f625,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( rel @ X0 @ X2 )
= $false )
| ( $true
= ( rel @ X0 @ X1 ) )
| ( $true
= ( rel @ X0 @ X3 ) )
| ( ( rel @ X2 @ X1 )
= $false )
| ( $true = $false )
| ( ( rel @ X0 @ X4 )
= $false )
| ( $false
= ( rel @ X4 @ X3 ) ) ),
inference(constrained_superposition,[],[f336,f340]) ).
thf(f637,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( rel @ X0 @ X3 ) )
| ( ( rel @ X0 @ X2 )
= $false )
| ( $true
= ( rel @ X0 @ X1 ) )
| ( ( rel @ X2 @ X1 )
= $false )
| ( $false
= ( rel @ X4 @ X3 ) )
| ( ( rel @ X0 @ X4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f625]) ).
thf(f648,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( rel @ X0 @ X2 )
= $false )
| ( $false
= ( rel @ X0 @ X3 ) )
| ( $true != $true )
| ( $true
= ( rel @ X0 @ X1 ) )
| ( ( rel @ X3 @ X1 )
= $false )
| ( ( rel @ X2 @ X1 )
= $false ) ),
inference(equality_factoring,[],[f637]) ).
thf(f652,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( rel @ X0 @ X1 ) )
| ( ( rel @ X2 @ X1 )
= $false )
| ( ( rel @ X0 @ X2 )
= $false )
| ( $false
= ( rel @ X0 @ X3 ) )
| ( ( rel @ X3 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f648]) ).
thf(f1242,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( rel @ sK15 @ sK17 )
= $false )
| ( ( rel @ sK17 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) )
| ( ( a @ X0 )
= $false )
| ( $true
= ( s @ sK18 ) ) )
| ~ spl20_30
| ~ spl20_34 ),
inference(constrained_superposition,[],[f481,f463]) ).
thf(f1279,plain,
( ! [X0: $i] :
( ( $true
= ( b @ X0 ) )
| ( $true
= ( s @ sK18 ) )
| ( ( rel @ sK17 @ X0 )
= $false )
| ( ( a @ X0 )
= $false )
| ( ( rel @ sK15 @ sK17 )
= $false ) )
| ~ spl20_30
| ~ spl20_34 ),
inference(trivial_inequality_removal,[],[f1242]) ).
thf(f1298,definition,
( spl20_65
<=> ! [X2: $i] :
( ( $true
= ( b @ X2 ) )
| ( $false
= ( rel @ sK17 @ X2 ) )
| ( ( a @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_65])],[avatar_definition]) ).
thf(f1299,plain,
( ! [X2: $i] :
( ( $false
= ( rel @ sK17 @ X2 ) )
| ( $true
= ( b @ X2 ) )
| ( ( a @ X2 )
= $false ) )
| ~ spl20_65 ),
inference(avatar_component_clause,[],[f1298]) ).
thf(f1301,definition,
( spl20_66
<=> ( ( rel @ sK15 @ sK17 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl20_66])],[avatar_definition]) ).
thf(f1303,plain,
( ( ( rel @ sK15 @ sK17 )
= $false )
| ~ spl20_66 ),
inference(avatar_component_clause,[],[f1301]) ).
thf(f1313,plain,
( ! [X0: $i] :
( ( ( a @ X0 )
= $false )
| ( ( rel @ sK15 @ sK17 )
= $false )
| ( ( rel @ sK17 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) )
| ( $true = $false ) )
| ~ spl20_30
| ~ spl20_31
| ~ spl20_34 ),
inference(forward_demodulation,[],[f1279,f468]) ).
thf(f1314,plain,
( ! [X0: $i] :
( ( ( rel @ sK17 @ X0 )
= $false )
| ( ( rel @ sK15 @ sK17 )
= $false )
| ( $true
= ( b @ X0 ) )
| ( ( a @ X0 )
= $false ) )
| ~ spl20_30
| ~ spl20_31
| ~ spl20_34 ),
inference(trivial_inequality_removal,[],[f1313]) ).
thf(f1328,plain,
( spl20_65
| spl20_66
| ~ spl20_30
| ~ spl20_31
| ~ spl20_34 ),
inference(avatar_split_clause,[],[f1314,f480,f466,f461,f1301,f1298]) ).
thf(f1386,plain,
( ( $true = $false )
| ( $true
= ( b @ sK17 ) )
| ( ( a @ sK17 )
= $false )
| ~ spl20_65 ),
inference(constrained_superposition,[],[f506,f1299]) ).
thf(f1399,plain,
( ( $true
= ( b @ sK17 ) )
| ( ( a @ sK17 )
= $false )
| ~ spl20_65 ),
inference(trivial_inequality_removal,[],[f1386]) ).
thf(f1411,plain,
( ( ( a @ sK17 )
= $false )
| ( $true = $false )
| ~ spl20_32
| ~ spl20_65 ),
inference(forward_demodulation,[],[f1399,f473]) ).
thf(f1412,plain,
( ( ( a @ sK17 )
= $false )
| ~ spl20_32
| ~ spl20_65 ),
inference(trivial_inequality_removal,[],[f1411]) ).
thf(f1428,plain,
( ( $true = $false )
| ~ spl20_29
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32
| ~ spl20_33
| ~ spl20_65 ),
inference(forward_demodulation,[],[f1412,f585]) ).
thf(f1429,plain,
( $false
| ~ spl20_29
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32
| ~ spl20_33
| ~ spl20_65 ),
inference(trivial_inequality_removal,[],[f1428]) ).
thf(f1430,plain,
( ~ spl20_29
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32
| ~ spl20_33
| ~ spl20_65 ),
inference(avatar_contradiction_clause,[],[f1429]) ).
thf(f1441,definition,
( spl20_73
<=> ! [X2: $i] :
( ( $false
= ( rel @ X2 @ sK17 ) )
| ( ( rel @ sK15 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl20_73])],[avatar_definition]) ).
thf(f1442,plain,
( ! [X2: $i] :
( ( $false
= ( rel @ X2 @ sK17 ) )
| ( ( rel @ sK15 @ X2 )
= $false ) )
| ~ spl20_73 ),
inference(avatar_component_clause,[],[f1441]) ).
thf(f1579,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel @ sK15 @ X1 )
= $false )
| ( ( rel @ sK15 @ X0 )
= $false )
| ( $true = $false )
| ( $false
= ( rel @ X0 @ sK17 ) )
| ( ( rel @ X1 @ sK17 )
= $false ) )
| ~ spl20_66 ),
inference(constrained_superposition,[],[f652,f1303]) ).
thf(f1622,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel @ sK15 @ X1 )
= $false )
| ( $false
= ( rel @ X0 @ sK17 ) )
| ( ( rel @ X1 @ sK17 )
= $false )
| ( ( rel @ sK15 @ X0 )
= $false ) )
| ~ spl20_66 ),
inference(trivial_inequality_removal,[],[f1579]) ).
thf(f1632,plain,
( spl20_73
| spl20_73
| ~ spl20_66 ),
inference(avatar_split_clause,[],[f1622,f1301,f1441,f1441]) ).
thf(f1640,plain,
( ( $false
= ( rel @ sK15 @ sK16 ) )
| ( $true = $false )
| ~ spl20_29
| ~ spl20_73 ),
inference(constrained_superposition,[],[f458,f1442]) ).
thf(f1655,plain,
( ( $false
= ( rel @ sK15 @ sK16 ) )
| ~ spl20_29
| ~ spl20_73 ),
inference(trivial_inequality_removal,[],[f1640]) ).
thf(f1662,plain,
( ( $true = $false )
| ~ spl20_28
| ~ spl20_29
| ~ spl20_73 ),
inference(forward_demodulation,[],[f1655,f453]) ).
thf(f1663,plain,
( $false
| ~ spl20_28
| ~ spl20_29
| ~ spl20_73 ),
inference(trivial_inequality_removal,[],[f1662]) ).
thf(f1664,plain,
( ~ spl20_28
| ~ spl20_29
| ~ spl20_73 ),
inference(avatar_contradiction_clause,[],[f1663]) ).
cnf(s26,plain,
( spl20_27
| spl20_28 ),
inference(sat_conversion,[],[f454]) ).
cnf(s27,plain,
( spl20_27
| spl20_29 ),
inference(sat_conversion,[],[f459]) ).
cnf(s28,plain,
( spl20_27
| spl20_30 ),
inference(sat_conversion,[],[f464]) ).
cnf(s29,plain,
( spl20_27
| spl20_31 ),
inference(sat_conversion,[],[f469]) ).
cnf(s30,plain,
( spl20_27
| spl20_32 ),
inference(sat_conversion,[],[f474]) ).
cnf(s31,plain,
( spl20_27
| spl20_33 ),
inference(sat_conversion,[],[f478]) ).
cnf(s32,plain,
( spl20_27
| spl20_34 ),
inference(sat_conversion,[],[f482]) ).
cnf(s33,plain,
~ spl20_27,
inference(sat_conversion,[],[f483]) ).
cnf(s87,plain,
( ~ spl20_30
| ~ spl20_31
| ~ spl20_34
| spl20_65
| spl20_66 ),
inference(sat_conversion,[],[f1328]) ).
cnf(s94,plain,
( ~ spl20_29
| ~ spl20_30
| ~ spl20_31
| ~ spl20_32
| ~ spl20_33
| ~ spl20_65 ),
inference(sat_conversion,[],[f1430]) ).
cnf(s119,plain,
( spl20_73
| ~ spl20_66
| spl20_73 ),
inference(sat_conversion,[],[f1632]) ).
cnf(s120,plain,
( ~ spl20_66
| spl20_73 ),
inference(rat,[],[s119]) ).
cnf(s122,plain,
( ~ spl20_28
| ~ spl20_29
| ~ spl20_73 ),
inference(sat_conversion,[],[f1664]) ).
cnf(s124,plain,
spl20_34,
inference(rat,[],[s32,s33]) ).
cnf(s125,plain,
spl20_33,
inference(rat,[],[s31,s33]) ).
cnf(s126,plain,
spl20_32,
inference(rat,[],[s30,s33]) ).
cnf(s127,plain,
spl20_31,
inference(rat,[],[s29,s33]) ).
cnf(s128,plain,
spl20_30,
inference(rat,[],[s28,s33]) ).
cnf(s129,plain,
spl20_29,
inference(rat,[],[s27,s33]) ).
cnf(s131,plain,
~ spl20_65,
inference(rat,[],[s94,s128,s125,s126,s127,s129]) ).
cnf(s133,plain,
spl20_66,
inference(rat,[],[s87,s128,s127,s124,s131]) ).
cnf(s134,plain,
spl20_73,
inference(rat,[],[s120,s133]) ).
cnf(s135,plain,
~ spl20_28,
inference(rat,[],[s122,s129,s134]) ).
cnf(s136,plain,
$false,
inference(rat,[],[s26,s135,s33]) ).
thf(f1665,plain,
$false,
inference(avatar_sat_refutation,[],[s136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV426^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:59:52 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % (3549644)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (3549649)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1341790383:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (3549655)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (3549655)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (3549650)lrs+10_16_si=on:nwc=1.5:random_seed=384958352:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (3549651)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1794832182:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (3549654)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1229218552:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (3549652)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=3145205539:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.35 % (3549655)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=3862762389:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (3549653)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=945550701:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (3549651)Instruction limit reached!
% 0.20/0.35 % (3549651)------------------------------
% 0.20/0.35 % (3549651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549651)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549651)Termination reason: Instruction limit
% 0.20/0.35 % (3549651)Termination phase: Function definition elimination
% 0.20/0.35 % (3549651)Time elapsed: 0.002 s
% 0.20/0.35 % (3549651)Peak memory usage: 10 MB
% 0.20/0.35 % (3549651)Instructions burned: 4 (million)
% 0.20/0.35 % (3549650)Instruction limit reached!
% 0.20/0.35 % (3549650)------------------------------
% 0.20/0.35 % (3549650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549650)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549650)Termination reason: Instruction limit
% 0.20/0.35 % (3549650)Termination phase: Saturation
% 0.20/0.35 % (3549650)Time elapsed: 0.010 s
% 0.20/0.35 % (3549650)Peak memory usage: 12 MB
% 0.20/0.35 % (3549650)Instructions burned: 19 (million)
% 0.20/0.35 % (3549649)Instruction limit reached!
% 0.20/0.35 % (3549649)------------------------------
% 0.20/0.35 % (3549649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549653)Instruction limit reached!
% 0.20/0.35 % (3549653)------------------------------
% 0.20/0.35 % (3549653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549649)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549653)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549649)Termination reason: Instruction limit
% 0.20/0.35 % (3549649)Termination phase: Saturation
% 0.20/0.35 % (3549653)Termination reason: Instruction limit
% 0.20/0.35 % (3549653)Termination phase: Saturation
% 0.20/0.35 % (3549649)Time elapsed: 0.023 s
% 0.20/0.35 % (3549653)Time elapsed: 0.015 s
% 0.20/0.35 % (3549649)Peak memory usage: 12 MB
% 0.20/0.35 % (3549653)Peak memory usage: 12 MB
% 0.20/0.35 % (3549649)Instructions burned: 88 (million)
% 0.20/0.35 % (3549653)Instructions burned: 26 (million)
% 0.20/0.35 % (3549663)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=374077241:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (3549663)Instruction limit reached!
% 0.20/0.35 % (3549663)------------------------------
% 0.20/0.35 % (3549663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549663)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549663)Termination reason: Instruction limit
% 0.20/0.35 % (3549663)Termination phase: Property scanning
% 0.20/0.35 % (3549663)Time elapsed: 0.002 s
% 0.20/0.35 % (3549663)Peak memory usage: 10 MB
% 0.20/0.35 % (3549663)Instructions burned: 4 (million)
% 0.20/0.35 % (3549666)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2436819132:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.35 % (3549664)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2815704649:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.35 % (3549666)Instruction limit reached!
% 0.20/0.35 % (3549666)------------------------------
% 0.20/0.35 % (3549666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549666)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549666)Termination reason: Instruction limit
% 0.20/0.35 % (3549666)Termination phase: Saturation
% 0.20/0.35 % (3549666)Time elapsed: 0.003 s
% 0.20/0.35 % (3549666)Peak memory usage: 12 MB
% 0.20/0.35 % (3549666)Instructions burned: 12 (million)
% 0.20/0.35 % (3549665)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (3549664)Instruction limit reached!
% 0.20/0.35 % (3549664)------------------------------
% 0.20/0.35 % (3549664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549664)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549664)Termination reason: Instruction limit
% 0.20/0.35 % (3549664)Termination phase: Saturation
% 0.20/0.35 % (3549664)Time elapsed: 0.003 s
% 0.20/0.35 % (3549664)Peak memory usage: 11 MB
% 0.20/0.35 % (3549664)Instructions burned: 6 (million)
% 0.20/0.35 % (3549665)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2602111636:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.35 % (3549668)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (3549668)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (3549665)Instruction limit reached!
% 0.20/0.35 % (3549665)------------------------------
% 0.20/0.35 % (3549665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549665)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549665)Termination reason: Instruction limit
% 0.20/0.35 % (3549665)Termination phase: Saturation
% 0.20/0.35 % (3549665)Time elapsed: 0.004 s
% 0.20/0.35 % (3549665)Peak memory usage: 11 MB
% 0.20/0.35 % (3549665)Instructions burned: 9 (million)
% 0.20/0.35 % (3549654)Instruction limit reached!
% 0.20/0.35 % (3549654)------------------------------
% 0.20/0.35 % (3549654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549654)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549654)Termination reason: Instruction limit
% 0.20/0.35 % (3549654)Termination phase: Saturation
% 0.20/0.35 % (3549654)Time elapsed: 0.039 s
% 0.20/0.35 % (3549654)Peak memory usage: 13 MB
% 0.20/0.35 % (3549654)Instructions burned: 77 (million)
% 0.20/0.35 % (3549668)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2248355208:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.35 % (3549671)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2036411659:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.35 % (3549672)lrs+10_1_si=on:cs=on:random_seed=819153595:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.35 % (3549674)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.20/0.35 % (3549672)Instruction limit reached!
% 0.20/0.35 % (3549672)------------------------------
% 0.20/0.35 % (3549672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549672)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549672)Termination reason: Instruction limit
% 0.20/0.35 % (3549672)Termination phase: Saturation
% 0.20/0.35 % (3549672)Time elapsed: 0.005 s
% 0.20/0.35 % (3549672)Peak memory usage: 11 MB
% 0.20/0.35 % (3549672)Instructions burned: 10 (million)
% 0.20/0.35 % (3549668)Instruction limit reached!
% 0.20/0.35 % (3549668)------------------------------
% 0.20/0.35 % (3549668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549668)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549668)Termination reason: Instruction limit
% 0.20/0.35 % (3549668)Termination phase: Saturation
% 0.20/0.35 % (3549668)Time elapsed: 0.014 s
% 0.20/0.35 % (3549668)Peak memory usage: 12 MB
% 0.20/0.35 % (3549668)Instructions burned: 32 (million)
% 0.20/0.35 % (3549674)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3663127087:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (3549675)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2948754102:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.20/0.35 % (3549655) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3549644-3549655"...
% 0.20/0.35 % (3549674)Instruction limit reached!
% 0.20/0.35 % (3549674)------------------------------
% 0.20/0.35 % (3549674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549674)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549674)Termination reason: Instruction limit
% 0.20/0.35 % (3549674)Termination phase: Property scanning
% 0.20/0.35 % (3549674)Time elapsed: 0.001 s
% 0.20/0.35 % (3549674)Peak memory usage: 10 MB
% 0.20/0.35 % (3549674)Instructions burned: 2 (million)
% 0.20/0.35 % (3549675)Refutation not found, incomplete strategy
% 0.20/0.35 % (3549675)------------------------------
% 0.20/0.35 % (3549675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549675)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549675)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.35 % (3549675)Time elapsed: 0.003 s
% 0.20/0.35 % (3549675)Peak memory usage: 12 MB
% 0.20/0.35 % (3549675)Instructions burned: 5 (million)
% 0.20/0.35 % (3549675)------------------------------
% 0.20/0.35 % (3549675)------------------------------
% 0.20/0.35 % (3549679)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2251257477:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.20/0.35 % (3549655)...printing done.
% 0.20/0.35 % (3549655)Refutation found. Thanks to Tanya!
% 0.20/0.35 % SZS status Theorem for theBenchmark
% 0.20/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.35 % (3549655)------------------------------
% 0.20/0.35 % (3549655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3549655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3549655)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3549655)Termination reason: Refutation
% 0.20/0.35 % (3549655)Time elapsed: 0.065 s
% 0.20/0.35 % (3549655)Peak memory usage: 13 MB
% 0.20/0.35 % (3549655)Instructions burned: 131 (million)
% 0.20/0.35 % (3549644)Success in time 0.102 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------