%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN393^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:41:53 AM UTC 2026
% Result : Theorem 88.07s 12.74s
% Output : Refutation 88.07s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% 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,
a1: $i > $o ).
thf(func_def_22,type,
a2: $i > $o ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_29,type,
vOR: $o > $o > $o ).
thf(func_def_30,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
sK1: $i > $i ).
thf(func_def_37,type,
sK2: $i > $i ).
thf(func_def_38,type,
sK3: $i > $i ).
thf(func_def_39,type,
sK4: $i > $i ).
thf(func_def_40,type,
sK5: $i > $i ).
thf(func_def_41,type,
sK6: $i > $i ).
thf(func_def_42,type,
sK7: $i > $i ).
thf(func_def_43,type,
sK8: $i > $i ).
thf(func_def_45,type,
sK10: $i > $i ).
thf(func_def_46,type,
sK11: $i > $i ).
thf(func_def_47,type,
sK12: $i > $i ).
thf(func_def_49,type,
sK14: $i > $i ).
thf(func_def_50,type,
sK15: $i > $i ).
thf(func_def_52,type,
sK17: $i > $i ).
thf(func_def_54,type,
sK19: $i > $i ).
thf(func_def_56,type,
sK21: $i > $i ).
thf(func_def_57,type,
sK22: $i > $i ).
thf(func_def_59,type,
sK24: $i > $i ).
thf(func_def_61,type,
sK26: $i > $i ).
thf(func_def_62,type,
sK27: $i > $i ).
thf(func_def_63,type,
sK28: $i > $i ).
thf(func_def_64,type,
sK29: $i > $i ).
thf(func_def_66,type,
sK31: $i > $i ).
thf(func_def_67,type,
sK32: $i > $i ).
thf(func_def_69,type,
sK34: $i > $i ).
thf(func_def_70,type,
sK35: $i > $i ).
thf(func_def_72,type,
sK37: $i > $i ).
thf(func_def_73,type,
sK38: $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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
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,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
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(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f16,axiom,
( iequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( iand @ ( iimplies @ X0 @ X1 ) @ ( iimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iequiv) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f28,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f29,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f31,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f33,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f35,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f36,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f40,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f42,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f44,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f46,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f47,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f54,plain,
~ ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f55,plain,
( ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) )
!= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) )
!= $true ),
inference(flattening,[],[f55]) ).
thf(f61,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f62,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f63,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f65,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f66,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f70,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f72,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f74,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f76,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f80,plain,
( ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f83,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,f62,f61]) ).
thf(f86,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,f63]) ).
thf(f88,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,[],[f72,f83,f65,f65]) ).
thf(f90,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,[],[f74,f86,f88,f88]) ).
thf(f92,plain,
( $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 > $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] : Y0
@ a1 )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 ) )
@ ( ^ [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] : Y0
@ a2 )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) ) ) ) ),
inference(definition_unfolding,[],[f80,f76,f90,f90,f66,f66,f90,f66,f66]) ).
thf(f93,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
( $false
= ( ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f102,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f100]) ).
thf(f103,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f107]) ).
thf(f110,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f114,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK2 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( a2 @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a1 @ ( sK2 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( a2 @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a1 @ ( sK2 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( a2 @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a1 @ ( sK2 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a2 @ ( sK1 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a1 @ ( sK2 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a1 @ ( sK2 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f122]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( a1 @ ( sK2 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( irel @ X2 @ ( sK2 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a2 @ ( sK1 @ X1 ) ) )
| ( $false
= ( a1 @ ( sK2 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a2 @ ( sK1 @ X1 ) ) )
| ( $true
= ( irel @ X2 @ ( sK2 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f112]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK4 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( a2 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( a2 @ ( sK4 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( a2 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( a2 @ ( sK4 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( a2 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( a2 @ ( sK4 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a2 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( a2 @ ( sK4 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( a2 @ ( sK4 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f140,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( a2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f142,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a2 @ ( sK3 @ X1 ) ) )
| ( $false
= ( a2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f143,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a2 @ ( sK3 @ X1 ) ) )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f108]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f147,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f148,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK6 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( a1 @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( a1 @ ( sK6 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( a1 @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( a1 @ ( sK6 @ X2 ) ) ) )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( a1 @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( a1 @ ( sK6 @ X2 ) ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( a1 @ ( sK6 @ X2 ) ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( a1 @ ( sK6 @ X2 ) ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( a1 @ ( sK6 @ X2 ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( a1 @ ( sK6 @ X2 ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f341,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ sK25 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f342,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ sK25 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f341]) ).
thf(f343,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ sK25 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f341]) ).
thf(f344,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ sK25 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ sK25 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ sK0 @ sK25 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f348,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f349,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f349]) ).
thf(f360,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f350]) ).
thf(f361,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK27 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK27 @ X1 ) )
=> ( a2 @ ( sK27 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f363]) ).
thf(f365,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK27 @ X1 ) )
=> ( a2 @ ( sK27 @ X1 ) ) ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( a2 @ ( sK27 @ X1 ) ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK27 @ X1 ) ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f365]) ).
thf(f518,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ sK25 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
@ sK39 ) ) ),
inference(sigma_proxy_clausification,[],[f342]) ).
thf(f519,plain,
( ( $false
= ( ( irel @ sK0 @ sK25 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f518]) ).
thf(f520,plain,
( ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f519]) ).
thf(f521,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f519]) ).
thf(f522,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f521]) ).
thf(f523,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) ) ),
inference(imp_proxy_clausification,[],[f521]) ).
thf(f524,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f522]) ).
thf(f525,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f524]) ).
thf(f526,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f524]) ).
thf(f527,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f526]) ).
thf(f528,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f527]) ).
thf(f529,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f528]) ).
thf(f530,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f528]) ).
thf(f531,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f530]) ).
thf(f532,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f531]) ).
thf(f533,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f532]) ).
thf(f534,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f533]) ).
thf(f535,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f534]) ).
thf(f536,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK40 ) ) ),
inference(sigma_proxy_clausification,[],[f529]) ).
thf(f537,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK40 )
=> ( a1 @ sK40 ) ) ) ),
inference(beta-eta_normalization,[],[f536]) ).
thf(f538,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK40 )
=> ( a1 @ sK40 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f537]) ).
thf(f539,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( a1 @ sK40 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f538]) ).
thf(f540,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK40 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f538]) ).
thf(f541,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK41 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f525]) ).
thf(f542,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK41 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f541]) ).
thf(f551,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK41 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK42 ) ) ),
inference(sigma_proxy_clausification,[],[f542]) ).
thf(f552,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( ( irel @ sK39 @ sK41 )
=> ( a2 @ sK41 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK42 )
=> ( a1 @ sK42 ) ) ) ),
inference(beta-eta_normalization,[],[f551]) ).
thf(f553,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ sK41 ) )
| ( $false
= ( ( irel @ sK39 @ sK42 )
=> ( a1 @ sK42 ) ) ) ),
inference(imp_proxy_clausification,[],[f552]) ).
thf(f554,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( irel @ sK39 @ sK41 ) )
| ( $false
= ( ( irel @ sK39 @ sK42 )
=> ( a1 @ sK42 ) ) ) ),
inference(imp_proxy_clausification,[],[f552]) ).
thf(f555,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( irel @ sK39 @ sK41 ) )
| ( $false
= ( a1 @ sK42 ) ) ),
inference(imp_proxy_clausification,[],[f554]) ).
thf(f556,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( irel @ sK39 @ sK41 ) )
| ( $true
= ( irel @ sK39 @ sK42 ) ) ),
inference(imp_proxy_clausification,[],[f554]) ).
thf(f557,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ sK41 ) )
| ( $false
= ( a1 @ sK42 ) ) ),
inference(imp_proxy_clausification,[],[f553]) ).
thf(f558,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ sK41 ) )
| ( $true
= ( irel @ sK39 @ sK42 ) ) ),
inference(imp_proxy_clausification,[],[f553]) ).
thf(f559,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f520]) ).
thf(f560,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f559]) ).
thf(f561,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f559]) ).
thf(f562,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f561]) ).
thf(f563,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f562]) ).
thf(f564,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f563]) ).
thf(f565,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f563]) ).
thf(f566,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f565]) ).
thf(f567,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f565]) ).
thf(f568,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f567]) ).
thf(f569,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f568]) ).
thf(f570,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f569]) ).
thf(f571,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f570]) ).
thf(f572,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f571]) ).
thf(f573,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK43 ) ) ),
inference(sigma_proxy_clausification,[],[f566]) ).
thf(f574,plain,
! [X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ( irel @ sK25 @ sK43 )
=> ( a2 @ sK43 ) ) ) ),
inference(beta-eta_normalization,[],[f573]) ).
thf(f575,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ( irel @ sK25 @ sK43 )
=> ( a2 @ sK43 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f574]) ).
thf(f576,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ sK43 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f575]) ).
thf(f577,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( irel @ sK25 @ sK43 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f575]) ).
thf(f578,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f564]) ).
thf(f579,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f578]) ).
thf(f580,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f578]) ).
thf(f581,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f580]) ).
thf(f582,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f581]) ).
thf(f583,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f582]) ).
thf(f584,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f582]) ).
thf(f585,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f584]) ).
thf(f586,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f585]) ).
thf(f587,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f586]) ).
thf(f588,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f586]) ).
thf(f589,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f588]) ).
thf(f590,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f589]) ).
thf(f591,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK25 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $true
= ( ( irel @ sK39 @ X4 )
=> ( a2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK25 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $true
= ( ( irel @ sK39 @ X4 )
=> ( a2 @ X4 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f591]) ).
thf(f593,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( ( irel @ sK25 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $true
= ( ( irel @ sK39 @ X4 )
=> ( a2 @ X4 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f592]) ).
thf(f594,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( irel @ sK25 @ X3 ) )
| ( $true
= ( ( irel @ sK39 @ X4 )
=> ( a2 @ X4 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f593]) ).
thf(f595,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( irel @ sK25 @ X3 ) )
| ( $false
= ( irel @ sK39 @ X4 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f594]) ).
thf(f596,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK44 ) ) ),
inference(sigma_proxy_clausification,[],[f587]) ).
thf(f597,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK25 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK44 )
=> ( a1 @ sK44 ) ) ) ),
inference(beta-eta_normalization,[],[f596]) ).
thf(f598,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK25 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK44 )
=> ( a1 @ sK44 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f597]) ).
thf(f599,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( ( irel @ sK25 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK44 )
=> ( a1 @ sK44 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f598]) ).
thf(f600,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( irel @ sK25 @ X3 ) )
| ( $false
= ( ( irel @ sK39 @ sK44 )
=> ( a1 @ sK44 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f599]) ).
thf(f601,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( irel @ sK25 @ X3 ) )
| ( $false
= ( a1 @ sK44 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f600]) ).
thf(f602,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( irel @ sK25 @ X3 ) )
| ( $true
= ( irel @ sK39 @ sK44 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f600]) ).
thf(f603,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK45 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f583]) ).
thf(f605,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK45 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f603]) ).
thf(f606,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK45 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f605]) ).
thf(f607,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK45 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f606]) ).
thf(f608,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK45 )
=> ( a2 @ sK45 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f607]) ).
thf(f609,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK45 )
=> ( a2 @ sK45 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f608]) ).
thf(f610,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( ( irel @ sK25 @ sK45 )
=> ( a2 @ sK45 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f609]) ).
thf(f611,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( a2 @ sK45 ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f610]) ).
thf(f612,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( irel @ sK25 @ sK45 ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f610]) ).
thf(f613,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( irel @ sK25 @ sK45 ) )
| ( $false
= ( irel @ sK39 @ X3 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f612]) ).
thf(f614,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $false
= ( a2 @ sK45 ) )
| ( $false
= ( irel @ sK39 @ X3 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f611]) ).
thf(f625,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f579]) ).
thf(f626,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f625]) ).
thf(f627,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f625]) ).
thf(f628,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f627]) ).
thf(f629,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f628]) ).
thf(f630,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f629]) ).
thf(f631,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f629]) ).
thf(f632,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f631]) ).
thf(f633,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f632]) ).
thf(f634,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f633]) ).
thf(f635,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f634]) ).
thf(f636,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f635]) ).
thf(f640,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f636]) ).
thf(f641,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( irel @ sK39 @ X3 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f640]) ).
thf(f642,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK48 ) ) ),
inference(sigma_proxy_clausification,[],[f630]) ).
thf(f643,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK48 )
=> ( a1 @ sK48 ) ) ) ),
inference(beta-eta_normalization,[],[f642]) ).
thf(f644,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK48 )
=> ( a1 @ sK48 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f643]) ).
thf(f645,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK48 )
=> ( a1 @ sK48 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f644]) ).
thf(f646,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK48 )
=> ( a1 @ sK48 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f644]) ).
thf(f647,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( ( irel @ sK39 @ sK48 )
=> ( a1 @ sK48 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f646]) ).
thf(f648,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( a1 @ sK48 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f647]) ).
thf(f649,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( irel @ sK39 @ sK48 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f647]) ).
thf(f650,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( ( irel @ sK39 @ sK48 )
=> ( a1 @ sK48 ) ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f645]) ).
thf(f651,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( a1 @ sK48 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f650]) ).
thf(f652,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( irel @ sK39 @ sK48 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f650]) ).
thf(f653,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK49 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f626]) ).
thf(f654,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK49 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f653]) ).
thf(f655,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK49 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f653]) ).
thf(f656,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK49 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f655]) ).
thf(f657,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK49 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f656]) ).
thf(f658,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK49 )
=> ( a2 @ sK49 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f657]) ).
thf(f659,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK49 )
=> ( a2 @ sK49 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f658]) ).
thf(f661,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( ( irel @ sK25 @ sK49 )
=> ( a2 @ sK49 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f659]) ).
thf(f662,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f661]) ).
thf(f663,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f661]) ).
thf(f664,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f663]) ).
thf(f665,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a2 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f662]) ).
thf(f670,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK47 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK49 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK50 ) ) ),
inference(sigma_proxy_clausification,[],[f654]) ).
thf(f671,plain,
! [X1: $i] :
( ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a2 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK49 )
=> ( a2 @ sK49 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) ) ),
inference(beta-eta_normalization,[],[f670]) ).
thf(f672,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK47 )
=> ( a2 @ sK47 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK49 )
=> ( a2 @ sK49 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f671]) ).
thf(f673,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( ( irel @ sK25 @ sK49 )
=> ( a2 @ sK49 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f672]) ).
thf(f674,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( ( irel @ sK25 @ sK49 )
=> ( a2 @ sK49 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f672]) ).
thf(f675,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f674]) ).
thf(f676,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f674]) ).
thf(f677,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $false
= ( a1 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f676]) ).
thf(f678,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $true
= ( irel @ sK39 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f676]) ).
thf(f679,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $false
= ( a1 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f675]) ).
thf(f680,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $true
= ( irel @ sK39 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f675]) ).
thf(f681,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f673]) ).
thf(f682,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $false
= ( ( irel @ sK39 @ sK50 )
=> ( a1 @ sK50 ) ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f673]) ).
thf(f683,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $false
= ( a1 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f682]) ).
thf(f684,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $true
= ( irel @ sK25 @ sK49 ) )
| ( $true
= ( irel @ sK39 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f682]) ).
thf(f685,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $false
= ( a1 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f681]) ).
thf(f686,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a2 @ sK47 ) )
| ( $false
= ( a2 @ sK49 ) )
| ( $true
= ( irel @ sK39 @ sK50 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f681]) ).
thf(f687,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ( irel @ sK0 @ sK39 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f560]) ).
thf(f688,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f687]) ).
thf(f689,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f687]) ).
thf(f690,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f689]) ).
thf(f691,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f689]) ).
thf(f692,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f691]) ).
thf(f693,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f692]) ).
thf(f694,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f693]) ).
thf(f695,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f694]) ).
thf(f696,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f694]) ).
thf(f697,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f696]) ).
thf(f698,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f695]) ).
thf(f699,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK52 ) ) ),
inference(sigma_proxy_clausification,[],[f690]) ).
thf(f700,plain,
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ( irel @ sK25 @ sK52 )
=> ( a2 @ sK52 ) ) ) ),
inference(beta-eta_normalization,[],[f699]) ).
thf(f701,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ( irel @ sK25 @ sK52 )
=> ( a2 @ sK52 ) ) ) ),
inference(imp_proxy_clausification,[],[f700]) ).
thf(f702,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( ( irel @ sK25 @ sK52 )
=> ( a2 @ sK52 ) ) ) ),
inference(imp_proxy_clausification,[],[f700]) ).
thf(f703,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ sK52 ) ) ),
inference(imp_proxy_clausification,[],[f702]) ).
thf(f704,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( irel @ sK25 @ sK52 ) ) ),
inference(imp_proxy_clausification,[],[f702]) ).
thf(f705,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ sK52 ) ) ),
inference(imp_proxy_clausification,[],[f701]) ).
thf(f706,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( irel @ sK25 @ sK52 ) ) ),
inference(imp_proxy_clausification,[],[f701]) ).
thf(f707,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f688]) ).
thf(f708,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f707]) ).
thf(f709,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f707]) ).
thf(f710,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f709]) ).
thf(f711,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f710]) ).
thf(f712,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f711]) ).
thf(f713,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f711]) ).
thf(f714,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f713]) ).
thf(f715,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f714]) ).
thf(f716,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f715]) ).
thf(f717,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f715]) ).
thf(f718,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f717]) ).
thf(f719,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f718]) ).
thf(f720,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f719]) ).
thf(f721,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f720]) ).
thf(f722,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f720]) ).
thf(f723,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f722]) ).
thf(f724,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f723]) ).
thf(f725,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( irel @ sK39 @ X3 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f724]) ).
thf(f726,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f721]) ).
thf(f727,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( ( irel @ sK39 @ X3 )
=> ( a2 @ X3 ) ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f726]) ).
thf(f728,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( irel @ sK39 @ X3 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f727]) ).
thf(f729,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK53 ) ) ),
inference(sigma_proxy_clausification,[],[f716]) ).
thf(f730,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK53 )
=> ( a1 @ sK53 ) ) ) ),
inference(beta-eta_normalization,[],[f729]) ).
thf(f731,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK53 )
=> ( a1 @ sK53 ) ) ) ),
inference(imp_proxy_clausification,[],[f730]) ).
thf(f732,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK53 )
=> ( a1 @ sK53 ) ) ) ),
inference(imp_proxy_clausification,[],[f730]) ).
thf(f733,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK53 )
=> ( a1 @ sK53 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f732]) ).
thf(f734,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( ( irel @ sK39 @ sK53 )
=> ( a1 @ sK53 ) ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f733]) ).
thf(f735,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( a1 @ sK53 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f734]) ).
thf(f736,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( irel @ sK39 @ sK53 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f734]) ).
thf(f737,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( ( irel @ sK25 @ X2 )
=> ( a1 @ X2 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK53 )
=> ( a1 @ sK53 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f731]) ).
thf(f738,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( ( irel @ sK39 @ sK53 )
=> ( a1 @ sK53 ) ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f737]) ).
thf(f739,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $false
= ( a1 @ sK53 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f738]) ).
thf(f740,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( irel @ sK39 @ sK53 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f738]) ).
thf(f741,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK54 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f712]) ).
thf(f743,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK54 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f741]) ).
thf(f744,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK54 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f743]) ).
thf(f745,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK54 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f744]) ).
thf(f746,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK54 )
=> ( a2 @ sK54 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f745]) ).
thf(f747,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK54 )
=> ( a2 @ sK54 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f746]) ).
thf(f748,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK54 )
=> ( a2 @ sK54 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f746]) ).
thf(f749,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( ( irel @ sK25 @ sK54 )
=> ( a2 @ sK54 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f748]) ).
thf(f750,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( a2 @ sK54 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f749]) ).
thf(f751,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( irel @ sK25 @ sK54 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f749]) ).
thf(f752,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( irel @ sK25 @ sK54 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f751]) ).
thf(f753,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( a2 @ sK54 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f750]) ).
thf(f754,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( ( irel @ sK25 @ sK54 )
=> ( a2 @ sK54 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f747]) ).
thf(f755,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( a2 @ sK54 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f754]) ).
thf(f756,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( irel @ sK25 @ sK54 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f754]) ).
thf(f757,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( irel @ sK25 @ sK54 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f756]) ).
thf(f758,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $false
= ( a2 @ sK54 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f755]) ).
thf(f777,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f708]) ).
thf(f778,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f777]) ).
thf(f779,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f777]) ).
thf(f780,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f779]) ).
thf(f781,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f780]) ).
thf(f782,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f781]) ).
thf(f783,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f781]) ).
thf(f784,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f783]) ).
thf(f785,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f784]) ).
thf(f786,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f785]) ).
thf(f787,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f786]) ).
thf(f788,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f786]) ).
thf(f789,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f788]) ).
thf(f790,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f788]) ).
thf(f791,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f790]) ).
thf(f792,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f791]) ).
thf(f793,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f789]) ).
thf(f794,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f793]) ).
thf(f795,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f787]) ).
thf(f796,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f787]) ).
thf(f797,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f796]) ).
thf(f798,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f797]) ).
thf(f799,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( ( irel @ sK39 @ X2 )
=> ( a2 @ X2 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f795]) ).
thf(f800,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a1 @ X1 ) )
| ( $true
= ( a2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f799]) ).
thf(f801,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK57 ) ) ),
inference(sigma_proxy_clausification,[],[f782]) ).
thf(f802,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) ) ),
inference(beta-eta_normalization,[],[f801]) ).
thf(f803,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) ) ),
inference(imp_proxy_clausification,[],[f802]) ).
thf(f804,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) ) ),
inference(imp_proxy_clausification,[],[f802]) ).
thf(f805,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) ) ),
inference(imp_proxy_clausification,[],[f804]) ).
thf(f806,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) ) ),
inference(imp_proxy_clausification,[],[f804]) ).
thf(f807,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f806]) ).
thf(f808,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a1 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f807]) ).
thf(f809,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f807]) ).
thf(f810,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f805]) ).
thf(f811,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a1 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f810]) ).
thf(f812,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f810]) ).
thf(f813,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) ) ),
inference(imp_proxy_clausification,[],[f803]) ).
thf(f814,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( ( irel @ sK25 @ X1 )
=> ( a1 @ X1 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) ) ),
inference(imp_proxy_clausification,[],[f803]) ).
thf(f815,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f814]) ).
thf(f816,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a1 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f815]) ).
thf(f817,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f815]) ).
thf(f818,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( ( irel @ sK39 @ sK57 )
=> ( a1 @ sK57 ) ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f813]) ).
thf(f819,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $false
= ( a1 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f818]) ).
thf(f820,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( irel @ sK25 @ X1 ) )
| ( $true
= ( irel @ sK39 @ sK57 ) )
| ( $true
= ( a1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f818]) ).
thf(f821,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK58 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f778]) ).
thf(f822,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK58 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f821]) ).
thf(f823,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK58 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f821]) ).
thf(f824,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK58 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f823]) ).
thf(f825,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK58 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f824]) ).
thf(f826,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f825]) ).
thf(f827,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f826]) ).
thf(f828,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f826]) ).
thf(f830,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f828]) ).
thf(f831,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f830]) ).
thf(f832,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f830]) ).
thf(f833,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f832]) ).
thf(f834,plain,
! [X1: $i] :
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f831]) ).
thf(f840,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f827]) ).
thf(f841,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f840]) ).
thf(f842,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $true
= ( ( irel @ sK39 @ X1 )
=> ( a2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f840]) ).
thf(f843,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f842]) ).
thf(f844,plain,
! [X1: $i] :
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( a2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f841]) ).
thf(f849,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK51 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK56 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK25 @ Y0 )
=> ( a2 @ Y0 ) )
@ sK58 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK39 @ Y0 )
=> ( a1 @ Y0 ) )
@ sK59 ) ) ),
inference(sigma_proxy_clausification,[],[f822]) ).
thf(f850,plain,
( ( $false
= ( ( irel @ sK25 @ sK51 )
=> ( a1 @ sK51 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(beta-eta_normalization,[],[f849]) ).
thf(f851,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f850]) ).
thf(f852,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( ( irel @ sK39 @ sK56 )
=> ( a2 @ sK56 ) ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f850]) ).
thf(f853,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f852]) ).
thf(f854,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f852]) ).
thf(f855,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f854]) ).
thf(f856,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f854]) ).
thf(f857,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f856]) ).
thf(f858,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f856]) ).
thf(f859,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f855]) ).
thf(f860,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f855]) ).
thf(f861,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f853]) ).
thf(f862,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f853]) ).
thf(f863,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f862]) ).
thf(f864,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f862]) ).
thf(f865,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f861]) ).
thf(f866,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f861]) ).
thf(f867,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f851]) ).
thf(f868,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( ( irel @ sK25 @ sK58 )
=> ( a2 @ sK58 ) ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f851]) ).
thf(f869,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f868]) ).
thf(f870,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f868]) ).
thf(f871,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f870]) ).
thf(f872,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f870]) ).
thf(f873,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f869]) ).
thf(f874,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $true
= ( irel @ sK39 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f869]) ).
thf(f875,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f867]) ).
thf(f876,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( ( irel @ sK39 @ sK59 )
=> ( a1 @ sK59 ) ) ) ),
inference(imp_proxy_clausification,[],[f867]) ).
thf(f877,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f876]) ).
thf(f878,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $true
= ( irel @ sK25 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f876]) ).
thf(f879,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $false
= ( a1 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f875]) ).
thf(f880,plain,
( ( $false
= ( a1 @ sK51 ) )
| ( $false
= ( a2 @ sK56 ) )
| ( $false
= ( a2 @ sK58 ) )
| ( $true
= ( irel @ sK39 @ sK59 ) ) ),
inference(imp_proxy_clausification,[],[f875]) ).
thf(f882,definition,
( spl60_1
<=> ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( a2 @ X4 ) )
| ( $true
= ( irel @ X2 @ ( sK2 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_1])],[avatar_definition]) ).
thf(f883,plain,
( ! [X2: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK2 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( a2 @ X4 ) )
| ( $false
= ( irel @ sK0 @ X2 ) ) )
| ~ spl60_1 ),
inference(avatar_component_clause,[],[f882]) ).
thf(f885,definition,
( spl60_2
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_2])],[avatar_definition]) ).
thf(f886,plain,
( ! [X3: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( a1 @ X3 ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) )
| ~ spl60_2 ),
inference(avatar_component_clause,[],[f885]) ).
thf(f887,plain,
( spl60_1
| spl60_2 ),
inference(avatar_split_clause,[],[f126,f885,f882]) ).
thf(f889,definition,
( spl60_3
<=> ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( a2 @ X4 ) )
| ( $false
= ( a1 @ ( sK2 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_3])],[avatar_definition]) ).
thf(f890,plain,
( ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a1 @ ( sK2 @ X2 ) ) )
| ( $true
= ( a2 @ X4 ) ) )
| ~ spl60_3 ),
inference(avatar_component_clause,[],[f889]) ).
thf(f891,plain,
( spl60_3
| spl60_2 ),
inference(avatar_split_clause,[],[f125,f885,f889]) ).
thf(f893,definition,
( spl60_4
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a1 @ X3 ) )
| ( $false
= ( a2 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_4])],[avatar_definition]) ).
thf(f894,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( a2 @ ( sK1 @ X1 ) ) )
| ( $true
= ( a1 @ X3 ) ) )
| ~ spl60_4 ),
inference(avatar_component_clause,[],[f893]) ).
thf(f895,plain,
( spl60_1
| spl60_4 ),
inference(avatar_split_clause,[],[f128,f893,f882]) ).
thf(f896,plain,
( spl60_3
| spl60_4 ),
inference(avatar_split_clause,[],[f127,f893,f889]) ).
thf(f898,definition,
( spl60_5
<=> ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( a1 @ X4 ) )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_5])],[avatar_definition]) ).
thf(f899,plain,
( ! [X2: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( a1 @ X4 ) )
| ( $false
= ( irel @ sK0 @ X2 ) ) )
| ~ spl60_5 ),
inference(avatar_component_clause,[],[f898]) ).
thf(f901,definition,
( spl60_6
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_6])],[avatar_definition]) ).
thf(f902,plain,
( ! [X3: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( a1 @ X3 ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) )
| ~ spl60_6 ),
inference(avatar_component_clause,[],[f901]) ).
thf(f903,plain,
( spl60_5
| spl60_6 ),
inference(avatar_split_clause,[],[f141,f901,f898]) ).
thf(f905,definition,
( spl60_7
<=> ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( a1 @ X4 ) )
| ( $false
= ( a2 @ ( sK4 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_7])],[avatar_definition]) ).
thf(f906,plain,
( ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a1 @ X4 ) ) )
| ~ spl60_7 ),
inference(avatar_component_clause,[],[f905]) ).
thf(f907,plain,
( spl60_7
| spl60_6 ),
inference(avatar_split_clause,[],[f140,f901,f905]) ).
thf(f909,definition,
( spl60_8
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a1 @ X3 ) )
| ( $false
= ( a2 @ ( sK3 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_8])],[avatar_definition]) ).
thf(f910,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( a2 @ ( sK3 @ X1 ) ) )
| ( $true
= ( a1 @ X3 ) ) )
| ~ spl60_8 ),
inference(avatar_component_clause,[],[f909]) ).
thf(f911,plain,
( spl60_5
| spl60_8 ),
inference(avatar_split_clause,[],[f143,f909,f898]) ).
thf(f912,plain,
( spl60_7
| spl60_8 ),
inference(avatar_split_clause,[],[f142,f909,f905]) ).
thf(f914,definition,
( spl60_9
<=> ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( a2 @ X4 ) )
| ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_9])],[avatar_definition]) ).
thf(f915,plain,
( ! [X2: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $true
= ( a2 @ X4 ) )
| ( $false
= ( irel @ sK0 @ X2 ) ) )
| ~ spl60_9 ),
inference(avatar_component_clause,[],[f914]) ).
thf(f917,definition,
( spl60_10
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_10])],[avatar_definition]) ).
thf(f918,plain,
( ! [X3: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( a2 @ X3 ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) )
| ~ spl60_10 ),
inference(avatar_component_clause,[],[f917]) ).
thf(f919,plain,
( spl60_9
| spl60_10 ),
inference(avatar_split_clause,[],[f160,f917,f914]) ).
thf(f921,definition,
( spl60_11
<=> ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $true
= ( a2 @ X4 ) )
| ( $false
= ( a1 @ ( sK6 @ X2 ) ) )
| ( $false
= ( irel @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_11])],[avatar_definition]) ).
thf(f922,plain,
( ! [X2: $i,X4: $i] :
( ( $false
= ( irel @ sK0 @ X2 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( a1 @ ( sK6 @ X2 ) ) )
| ( $true
= ( a2 @ X4 ) ) )
| ~ spl60_11 ),
inference(avatar_component_clause,[],[f921]) ).
thf(f923,plain,
( spl60_11
| spl60_10 ),
inference(avatar_split_clause,[],[f159,f917,f921]) ).
thf(f925,definition,
( spl60_12
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a2 @ X3 ) )
| ( $false
= ( a1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_12])],[avatar_definition]) ).
thf(f926,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( a1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( a2 @ X3 ) ) )
| ~ spl60_12 ),
inference(avatar_component_clause,[],[f925]) ).
thf(f927,plain,
( spl60_9
| spl60_12 ),
inference(avatar_split_clause,[],[f162,f925,f914]) ).
thf(f928,plain,
( spl60_11
| spl60_12 ),
inference(avatar_split_clause,[],[f161,f925,f921]) ).
thf(f1099,definition,
( spl60_51
<=> ( $true
= ( irel @ sK0 @ sK25 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_51])],[avatar_definition]) ).
thf(f1101,plain,
( ( $true
= ( irel @ sK0 @ sK25 ) )
| ~ spl60_51 ),
inference(avatar_component_clause,[],[f1099]) ).
thf(f1108,definition,
( spl60_53
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $true
= ( irel @ X1 @ ( sK27 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl60_53])],[avatar_definition]) ).
thf(f1109,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK27 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( a1 @ X2 ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) )
| ~ spl60_53 ),
inference(avatar_component_clause,[],[f1108]) ).
thf(f1110,plain,
( spl60_53
| spl60_51 ),
inference(avatar_split_clause,[],[f367,f1099,f1108]) ).
thf(f1112,definition,
( spl60_54
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( a1 @ X2 ) )
| ( $false
= ( a2 @ ( sK27 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl60_54])],[avatar_definition]) ).
thf(f1113,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( a2 @ ( sK27 @ X1 ) ) )
| ( $true
= ( a1 @ X2 ) ) )
| ~ spl60_54 ),
inference(avatar_component_clause,[],[f1112]) ).
thf(f1114,plain,
( spl60_54
| spl60_51 ),
inference(avatar_split_clause,[],[f366,f1099,f1112]) ).
thf(f1116,definition,
( spl60_55
<=> ! [X3: $i] :
( ( $false
= ( irel @ sK25 @ X3 ) )
| ( $true
= ( a1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_55])],[avatar_definition]) ).
thf(f1117,plain,
( ! [X3: $i] :
( ( $false
= ( irel @ sK25 @ X3 ) )
| ( $true
= ( a1 @ X3 ) ) )
| ~ spl60_55 ),
inference(avatar_component_clause,[],[f1116]) ).
thf(f1122,definition,
( spl60_57
<=> ! [X2: $i] :
( ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( a2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_57])],[avatar_definition]) ).
thf(f1123,plain,
( ! [X2: $i] :
( ( $false
= ( irel @ sK25 @ X2 ) )
| ( $true
= ( a2 @ X2 ) ) )
| ~ spl60_57 ),
inference(avatar_component_clause,[],[f1122]) ).
thf(f1230,definition,
( spl60_79
<=> ( $true
= ( irel @ sK0 @ sK39 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_79])],[avatar_definition]) ).
thf(f1232,plain,
( ( $true
= ( irel @ sK0 @ sK39 ) )
| ~ spl60_79 ),
inference(avatar_component_clause,[],[f1230]) ).
thf(f1233,plain,
( spl60_79
| spl60_51 ),
inference(avatar_split_clause,[],[f523,f1099,f1230]) ).
thf(f1235,definition,
( spl60_80
<=> ! [X2: $i] :
( ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_80])],[avatar_definition]) ).
thf(f1236,plain,
( ! [X2: $i] :
( ( $false
= ( irel @ sK39 @ X2 ) )
| ( $true
= ( a2 @ X2 ) ) )
| ~ spl60_80 ),
inference(avatar_component_clause,[],[f1235]) ).
thf(f1238,definition,
( spl60_81
<=> ! [X1: $i] :
( ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_81])],[avatar_definition]) ).
thf(f1239,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK39 @ X1 ) )
| ( $true
= ( a1 @ X1 ) ) )
| ~ spl60_81 ),
inference(avatar_component_clause,[],[f1238]) ).
thf(f1240,plain,
( spl60_80
| spl60_81
| spl60_51 ),
inference(avatar_split_clause,[],[f535,f1099,f1238,f1235]) ).
thf(f1242,definition,
( spl60_82
<=> ( $true
= ( irel @ sK39 @ sK40 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_82])],[avatar_definition]) ).
thf(f1244,plain,
( ( $true
= ( irel @ sK39 @ sK40 ) )
| ~ spl60_82 ),
inference(avatar_component_clause,[],[f1242]) ).
thf(f1245,plain,
( spl60_82
| spl60_81
| spl60_51 ),
inference(avatar_split_clause,[],[f540,f1099,f1238,f1242]) ).
thf(f1247,definition,
( spl60_83
<=> ( $false
= ( a1 @ sK40 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_83])],[avatar_definition]) ).
thf(f1249,plain,
( ( $false
= ( a1 @ sK40 ) )
| ~ spl60_83 ),
inference(avatar_component_clause,[],[f1247]) ).
thf(f1250,plain,
( spl60_83
| spl60_81
| spl60_51 ),
inference(avatar_split_clause,[],[f539,f1099,f1238,f1247]) ).
thf(f1252,definition,
( spl60_84
<=> ( $true
= ( irel @ sK39 @ sK41 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_84])],[avatar_definition]) ).
thf(f1254,plain,
( ( $true
= ( irel @ sK39 @ sK41 ) )
| ~ spl60_84 ),
inference(avatar_component_clause,[],[f1252]) ).
thf(f1257,definition,
( spl60_85
<=> ( $false
= ( a2 @ sK41 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_85])],[avatar_definition]) ).
thf(f1259,plain,
( ( $false
= ( a2 @ sK41 ) )
| ~ spl60_85 ),
inference(avatar_component_clause,[],[f1257]) ).
thf(f1262,definition,
( spl60_86
<=> ( $true
= ( irel @ sK39 @ sK42 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_86])],[avatar_definition]) ).
thf(f1264,plain,
( ( $true
= ( irel @ sK39 @ sK42 ) )
| ~ spl60_86 ),
inference(avatar_component_clause,[],[f1262]) ).
thf(f1265,plain,
( spl60_86
| spl60_84
| spl60_51 ),
inference(avatar_split_clause,[],[f556,f1099,f1252,f1262]) ).
thf(f1267,definition,
( spl60_87
<=> ( $false
= ( a1 @ sK42 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_87])],[avatar_definition]) ).
thf(f1269,plain,
( ( $false
= ( a1 @ sK42 ) )
| ~ spl60_87 ),
inference(avatar_component_clause,[],[f1267]) ).
thf(f1270,plain,
( spl60_87
| spl60_84
| spl60_51 ),
inference(avatar_split_clause,[],[f555,f1099,f1252,f1267]) ).
thf(f1271,plain,
( spl60_86
| spl60_85
| spl60_51 ),
inference(avatar_split_clause,[],[f558,f1099,f1257,f1262]) ).
thf(f1272,plain,
( spl60_87
| spl60_85
| spl60_51 ),
inference(avatar_split_clause,[],[f557,f1099,f1257,f1267]) ).
thf(f1273,plain,
( spl60_55
| spl60_79
| spl60_57 ),
inference(avatar_split_clause,[],[f572,f1122,f1230,f1116]) ).
thf(f1275,definition,
( spl60_88
<=> ( $true
= ( irel @ sK25 @ sK43 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_88])],[avatar_definition]) ).
thf(f1277,plain,
( ( $true
= ( irel @ sK25 @ sK43 ) )
| ~ spl60_88 ),
inference(avatar_component_clause,[],[f1275]) ).
thf(f1278,plain,
( spl60_88
| spl60_79
| spl60_57 ),
inference(avatar_split_clause,[],[f577,f1122,f1230,f1275]) ).
thf(f1280,definition,
( spl60_89
<=> ( $false
= ( a2 @ sK43 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_89])],[avatar_definition]) ).
thf(f1282,plain,
( ( $false
= ( a2 @ sK43 ) )
| ~ spl60_89 ),
inference(avatar_component_clause,[],[f1280]) ).
thf(f1283,plain,
( spl60_89
| spl60_79
| spl60_57 ),
inference(avatar_split_clause,[],[f576,f1122,f1230,f1280]) ).
thf(f1284,plain,
( spl60_80
| spl60_55
| spl60_81
| spl60_57 ),
inference(avatar_split_clause,[],[f595,f1122,f1238,f1116,f1235]) ).
thf(f1286,definition,
( spl60_90
<=> ( $true
= ( irel @ sK39 @ sK44 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_90])],[avatar_definition]) ).
thf(f1288,plain,
( ( $true
= ( irel @ sK39 @ sK44 ) )
| ~ spl60_90 ),
inference(avatar_component_clause,[],[f1286]) ).
thf(f1289,plain,
( spl60_90
| spl60_55
| spl60_81
| spl60_57 ),
inference(avatar_split_clause,[],[f602,f1122,f1238,f1116,f1286]) ).
thf(f1291,definition,
( spl60_91
<=> ( $false
= ( a1 @ sK44 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_91])],[avatar_definition]) ).
thf(f1293,plain,
( ( $false
= ( a1 @ sK44 ) )
| ~ spl60_91 ),
inference(avatar_component_clause,[],[f1291]) ).
thf(f1294,plain,
( spl60_91
| spl60_55
| spl60_81
| spl60_57 ),
inference(avatar_split_clause,[],[f601,f1122,f1238,f1116,f1291]) ).
thf(f1296,definition,
( spl60_92
<=> ( $true
= ( irel @ sK25 @ sK45 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_92])],[avatar_definition]) ).
thf(f1298,plain,
( ( $true
= ( irel @ sK25 @ sK45 ) )
| ~ spl60_92 ),
inference(avatar_component_clause,[],[f1296]) ).
thf(f1299,plain,
( spl60_80
| spl60_92
| spl60_81
| spl60_57 ),
inference(avatar_split_clause,[],[f613,f1122,f1238,f1296,f1235]) ).
thf(f1301,definition,
( spl60_93
<=> ( $false
= ( a2 @ sK45 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_93])],[avatar_definition]) ).
thf(f1303,plain,
( ( $false
= ( a2 @ sK45 ) )
| ~ spl60_93 ),
inference(avatar_component_clause,[],[f1301]) ).
thf(f1304,plain,
( spl60_80
| spl60_93
| spl60_81
| spl60_57 ),
inference(avatar_split_clause,[],[f614,f1122,f1238,f1301,f1235]) ).
thf(f1318,definition,
( spl60_96
<=> ( $true
= ( irel @ sK39 @ sK47 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_96])],[avatar_definition]) ).
thf(f1320,plain,
( ( $true
= ( irel @ sK39 @ sK47 ) )
| ~ spl60_96 ),
inference(avatar_component_clause,[],[f1318]) ).
thf(f1323,definition,
( spl60_97
<=> ( $false
= ( a2 @ sK47 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_97])],[avatar_definition]) ).
thf(f1325,plain,
( ( $false
= ( a2 @ sK47 ) )
| ~ spl60_97 ),
inference(avatar_component_clause,[],[f1323]) ).
thf(f1326,plain,
( spl60_80
| spl60_55
| spl60_97
| spl60_57 ),
inference(avatar_split_clause,[],[f641,f1122,f1323,f1116,f1235]) ).
thf(f1328,definition,
( spl60_98
<=> ( $true
= ( irel @ sK39 @ sK48 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_98])],[avatar_definition]) ).
thf(f1330,plain,
( ( $true
= ( irel @ sK39 @ sK48 ) )
| ~ spl60_98 ),
inference(avatar_component_clause,[],[f1328]) ).
thf(f1331,plain,
( spl60_98
| spl60_55
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f649,f1122,f1318,f1116,f1328]) ).
thf(f1333,definition,
( spl60_99
<=> ( $false
= ( a1 @ sK48 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_99])],[avatar_definition]) ).
thf(f1335,plain,
( ( $false
= ( a1 @ sK48 ) )
| ~ spl60_99 ),
inference(avatar_component_clause,[],[f1333]) ).
thf(f1336,plain,
( spl60_99
| spl60_55
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f648,f1122,f1318,f1116,f1333]) ).
thf(f1337,plain,
( spl60_98
| spl60_55
| spl60_97
| spl60_57 ),
inference(avatar_split_clause,[],[f652,f1122,f1323,f1116,f1328]) ).
thf(f1338,plain,
( spl60_99
| spl60_55
| spl60_97
| spl60_57 ),
inference(avatar_split_clause,[],[f651,f1122,f1323,f1116,f1333]) ).
thf(f1340,definition,
( spl60_100
<=> ( $true
= ( irel @ sK25 @ sK49 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_100])],[avatar_definition]) ).
thf(f1342,plain,
( ( $true
= ( irel @ sK25 @ sK49 ) )
| ~ spl60_100 ),
inference(avatar_component_clause,[],[f1340]) ).
thf(f1343,plain,
( spl60_80
| spl60_100
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f664,f1122,f1318,f1340,f1235]) ).
thf(f1345,definition,
( spl60_101
<=> ( $false
= ( a2 @ sK49 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_101])],[avatar_definition]) ).
thf(f1347,plain,
( ( $false
= ( a2 @ sK49 ) )
| ~ spl60_101 ),
inference(avatar_component_clause,[],[f1345]) ).
thf(f1348,plain,
( spl60_80
| spl60_101
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f665,f1122,f1318,f1345,f1235]) ).
thf(f1352,definition,
( spl60_102
<=> ( $true
= ( irel @ sK39 @ sK50 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_102])],[avatar_definition]) ).
thf(f1354,plain,
( ( $true
= ( irel @ sK39 @ sK50 ) )
| ~ spl60_102 ),
inference(avatar_component_clause,[],[f1352]) ).
thf(f1355,plain,
( spl60_102
| spl60_100
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f678,f1122,f1318,f1340,f1352]) ).
thf(f1357,definition,
( spl60_103
<=> ( $false
= ( a1 @ sK50 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_103])],[avatar_definition]) ).
thf(f1359,plain,
( ( $false
= ( a1 @ sK50 ) )
| ~ spl60_103 ),
inference(avatar_component_clause,[],[f1357]) ).
thf(f1360,plain,
( spl60_103
| spl60_100
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f677,f1122,f1318,f1340,f1357]) ).
thf(f1361,plain,
( spl60_102
| spl60_101
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f680,f1122,f1318,f1345,f1352]) ).
thf(f1362,plain,
( spl60_103
| spl60_101
| spl60_96
| spl60_57 ),
inference(avatar_split_clause,[],[f679,f1122,f1318,f1345,f1357]) ).
thf(f1363,plain,
( spl60_102
| spl60_100
| spl60_97
| spl60_57 ),
inference(avatar_split_clause,[],[f684,f1122,f1323,f1340,f1352]) ).
thf(f1364,plain,
( spl60_103
| spl60_100
| spl60_97
| spl60_57 ),
inference(avatar_split_clause,[],[f683,f1122,f1323,f1340,f1357]) ).
thf(f1365,plain,
( spl60_102
| spl60_101
| spl60_97
| spl60_57 ),
inference(avatar_split_clause,[],[f686,f1122,f1323,f1345,f1352]) ).
thf(f1366,plain,
( spl60_103
| spl60_101
| spl60_97
| spl60_57 ),
inference(avatar_split_clause,[],[f685,f1122,f1323,f1345,f1357]) ).
thf(f1368,definition,
( spl60_104
<=> ( $true
= ( irel @ sK25 @ sK51 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_104])],[avatar_definition]) ).
thf(f1370,plain,
( ( $true
= ( irel @ sK25 @ sK51 ) )
| ~ spl60_104 ),
inference(avatar_component_clause,[],[f1368]) ).
thf(f1371,plain,
( spl60_55
| spl60_79
| spl60_104 ),
inference(avatar_split_clause,[],[f697,f1368,f1230,f1116]) ).
thf(f1373,definition,
( spl60_105
<=> ( $false
= ( a1 @ sK51 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_105])],[avatar_definition]) ).
thf(f1375,plain,
( ( $false
= ( a1 @ sK51 ) )
| ~ spl60_105 ),
inference(avatar_component_clause,[],[f1373]) ).
thf(f1376,plain,
( spl60_55
| spl60_79
| spl60_105 ),
inference(avatar_split_clause,[],[f698,f1373,f1230,f1116]) ).
thf(f1378,definition,
( spl60_106
<=> ( $true
= ( irel @ sK25 @ sK52 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_106])],[avatar_definition]) ).
thf(f1380,plain,
( ( $true
= ( irel @ sK25 @ sK52 ) )
| ~ spl60_106 ),
inference(avatar_component_clause,[],[f1378]) ).
thf(f1381,plain,
( spl60_106
| spl60_79
| spl60_104 ),
inference(avatar_split_clause,[],[f704,f1368,f1230,f1378]) ).
thf(f1383,definition,
( spl60_107
<=> ( $false
= ( a2 @ sK52 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_107])],[avatar_definition]) ).
thf(f1385,plain,
( ( $false
= ( a2 @ sK52 ) )
| ~ spl60_107 ),
inference(avatar_component_clause,[],[f1383]) ).
thf(f1386,plain,
( spl60_107
| spl60_79
| spl60_104 ),
inference(avatar_split_clause,[],[f703,f1368,f1230,f1383]) ).
thf(f1387,plain,
( spl60_106
| spl60_79
| spl60_105 ),
inference(avatar_split_clause,[],[f706,f1373,f1230,f1378]) ).
thf(f1388,plain,
( spl60_107
| spl60_79
| spl60_105 ),
inference(avatar_split_clause,[],[f705,f1373,f1230,f1383]) ).
thf(f1389,plain,
( spl60_80
| spl60_55
| spl60_81
| spl60_104 ),
inference(avatar_split_clause,[],[f725,f1368,f1238,f1116,f1235]) ).
thf(f1390,plain,
( spl60_80
| spl60_55
| spl60_81
| spl60_105 ),
inference(avatar_split_clause,[],[f728,f1373,f1238,f1116,f1235]) ).
thf(f1392,definition,
( spl60_108
<=> ( $true
= ( irel @ sK39 @ sK53 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_108])],[avatar_definition]) ).
thf(f1394,plain,
( ( $true
= ( irel @ sK39 @ sK53 ) )
| ~ spl60_108 ),
inference(avatar_component_clause,[],[f1392]) ).
thf(f1395,plain,
( spl60_108
| spl60_55
| spl60_81
| spl60_104 ),
inference(avatar_split_clause,[],[f736,f1368,f1238,f1116,f1392]) ).
thf(f1397,definition,
( spl60_109
<=> ( $false
= ( a1 @ sK53 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_109])],[avatar_definition]) ).
thf(f1399,plain,
( ( $false
= ( a1 @ sK53 ) )
| ~ spl60_109 ),
inference(avatar_component_clause,[],[f1397]) ).
thf(f1400,plain,
( spl60_109
| spl60_55
| spl60_81
| spl60_104 ),
inference(avatar_split_clause,[],[f735,f1368,f1238,f1116,f1397]) ).
thf(f1401,plain,
( spl60_108
| spl60_55
| spl60_81
| spl60_105 ),
inference(avatar_split_clause,[],[f740,f1373,f1238,f1116,f1392]) ).
thf(f1402,plain,
( spl60_109
| spl60_55
| spl60_81
| spl60_105 ),
inference(avatar_split_clause,[],[f739,f1373,f1238,f1116,f1397]) ).
thf(f1404,definition,
( spl60_110
<=> ( $true
= ( irel @ sK25 @ sK54 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_110])],[avatar_definition]) ).
thf(f1406,plain,
( ( $true
= ( irel @ sK25 @ sK54 ) )
| ~ spl60_110 ),
inference(avatar_component_clause,[],[f1404]) ).
thf(f1407,plain,
( spl60_80
| spl60_110
| spl60_81
| spl60_104 ),
inference(avatar_split_clause,[],[f752,f1368,f1238,f1404,f1235]) ).
thf(f1409,definition,
( spl60_111
<=> ( $false
= ( a2 @ sK54 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_111])],[avatar_definition]) ).
thf(f1411,plain,
( ( $false
= ( a2 @ sK54 ) )
| ~ spl60_111 ),
inference(avatar_component_clause,[],[f1409]) ).
thf(f1412,plain,
( spl60_80
| spl60_111
| spl60_81
| spl60_104 ),
inference(avatar_split_clause,[],[f753,f1368,f1238,f1409,f1235]) ).
thf(f1413,plain,
( spl60_80
| spl60_110
| spl60_81
| spl60_105 ),
inference(avatar_split_clause,[],[f757,f1373,f1238,f1404,f1235]) ).
thf(f1414,plain,
( spl60_80
| spl60_111
| spl60_81
| spl60_105 ),
inference(avatar_split_clause,[],[f758,f1373,f1238,f1409,f1235]) ).
thf(f1432,definition,
( spl60_114
<=> ( $true
= ( irel @ sK39 @ sK56 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_114])],[avatar_definition]) ).
thf(f1434,plain,
( ( $true
= ( irel @ sK39 @ sK56 ) )
| ~ spl60_114 ),
inference(avatar_component_clause,[],[f1432]) ).
thf(f1435,plain,
( spl60_80
| spl60_55
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f792,f1368,f1432,f1116,f1235]) ).
thf(f1437,definition,
( spl60_115
<=> ( $false
= ( a2 @ sK56 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_115])],[avatar_definition]) ).
thf(f1439,plain,
( ( $false
= ( a2 @ sK56 ) )
| ~ spl60_115 ),
inference(avatar_component_clause,[],[f1437]) ).
thf(f1440,plain,
( spl60_80
| spl60_55
| spl60_115
| spl60_104 ),
inference(avatar_split_clause,[],[f794,f1368,f1437,f1116,f1235]) ).
thf(f1441,plain,
( spl60_80
| spl60_55
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f798,f1373,f1432,f1116,f1235]) ).
thf(f1442,plain,
( spl60_80
| spl60_55
| spl60_115
| spl60_105 ),
inference(avatar_split_clause,[],[f800,f1373,f1437,f1116,f1235]) ).
thf(f1444,definition,
( spl60_116
<=> ( $true
= ( irel @ sK39 @ sK57 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_116])],[avatar_definition]) ).
thf(f1446,plain,
( ( $true
= ( irel @ sK39 @ sK57 ) )
| ~ spl60_116 ),
inference(avatar_component_clause,[],[f1444]) ).
thf(f1447,plain,
( spl60_116
| spl60_55
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f809,f1368,f1432,f1116,f1444]) ).
thf(f1449,definition,
( spl60_117
<=> ( $false
= ( a1 @ sK57 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_117])],[avatar_definition]) ).
thf(f1451,plain,
( ( $false
= ( a1 @ sK57 ) )
| ~ spl60_117 ),
inference(avatar_component_clause,[],[f1449]) ).
thf(f1452,plain,
( spl60_117
| spl60_55
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f808,f1368,f1432,f1116,f1449]) ).
thf(f1453,plain,
( spl60_116
| spl60_55
| spl60_115
| spl60_104 ),
inference(avatar_split_clause,[],[f812,f1368,f1437,f1116,f1444]) ).
thf(f1454,plain,
( spl60_117
| spl60_55
| spl60_115
| spl60_104 ),
inference(avatar_split_clause,[],[f811,f1368,f1437,f1116,f1449]) ).
thf(f1455,plain,
( spl60_116
| spl60_55
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f817,f1373,f1432,f1116,f1444]) ).
thf(f1456,plain,
( spl60_117
| spl60_55
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f816,f1373,f1432,f1116,f1449]) ).
thf(f1457,plain,
( spl60_116
| spl60_55
| spl60_115
| spl60_105 ),
inference(avatar_split_clause,[],[f820,f1373,f1437,f1116,f1444]) ).
thf(f1458,plain,
( spl60_117
| spl60_55
| spl60_115
| spl60_105 ),
inference(avatar_split_clause,[],[f819,f1373,f1437,f1116,f1449]) ).
thf(f1460,definition,
( spl60_118
<=> ( $true
= ( irel @ sK25 @ sK58 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_118])],[avatar_definition]) ).
thf(f1462,plain,
( ( $true
= ( irel @ sK25 @ sK58 ) )
| ~ spl60_118 ),
inference(avatar_component_clause,[],[f1460]) ).
thf(f1463,plain,
( spl60_80
| spl60_118
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f833,f1368,f1432,f1460,f1235]) ).
thf(f1465,definition,
( spl60_119
<=> ( $false
= ( a2 @ sK58 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_119])],[avatar_definition]) ).
thf(f1467,plain,
( ( $false
= ( a2 @ sK58 ) )
| ~ spl60_119 ),
inference(avatar_component_clause,[],[f1465]) ).
thf(f1468,plain,
( spl60_80
| spl60_119
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f834,f1368,f1432,f1465,f1235]) ).
thf(f1471,plain,
( spl60_80
| spl60_118
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f843,f1373,f1432,f1460,f1235]) ).
thf(f1472,plain,
( spl60_80
| spl60_119
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f844,f1373,f1432,f1465,f1235]) ).
thf(f1476,definition,
( spl60_120
<=> ( $true
= ( irel @ sK39 @ sK59 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_120])],[avatar_definition]) ).
thf(f1478,plain,
( ( $true
= ( irel @ sK39 @ sK59 ) )
| ~ spl60_120 ),
inference(avatar_component_clause,[],[f1476]) ).
thf(f1479,plain,
( spl60_120
| spl60_118
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f858,f1368,f1432,f1460,f1476]) ).
thf(f1481,definition,
( spl60_121
<=> ( $false
= ( a1 @ sK59 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_121])],[avatar_definition]) ).
thf(f1483,plain,
( ( $false
= ( a1 @ sK59 ) )
| ~ spl60_121 ),
inference(avatar_component_clause,[],[f1481]) ).
thf(f1484,plain,
( spl60_121
| spl60_118
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f857,f1368,f1432,f1460,f1481]) ).
thf(f1485,plain,
( spl60_120
| spl60_119
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f860,f1368,f1432,f1465,f1476]) ).
thf(f1486,plain,
( spl60_121
| spl60_119
| spl60_114
| spl60_104 ),
inference(avatar_split_clause,[],[f859,f1368,f1432,f1465,f1481]) ).
thf(f1487,plain,
( spl60_120
| spl60_118
| spl60_115
| spl60_104 ),
inference(avatar_split_clause,[],[f864,f1368,f1437,f1460,f1476]) ).
thf(f1488,plain,
( spl60_121
| spl60_118
| spl60_115
| spl60_104 ),
inference(avatar_split_clause,[],[f863,f1368,f1437,f1460,f1481]) ).
thf(f1489,plain,
( spl60_120
| spl60_119
| spl60_115
| spl60_104 ),
inference(avatar_split_clause,[],[f866,f1368,f1437,f1465,f1476]) ).
thf(f1490,plain,
( spl60_121
| spl60_119
| spl60_115
| spl60_104 ),
inference(avatar_split_clause,[],[f865,f1368,f1437,f1465,f1481]) ).
thf(f1491,plain,
( spl60_120
| spl60_118
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f872,f1373,f1432,f1460,f1476]) ).
thf(f1492,plain,
( spl60_121
| spl60_118
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f871,f1373,f1432,f1460,f1481]) ).
thf(f1493,plain,
( spl60_120
| spl60_119
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f874,f1373,f1432,f1465,f1476]) ).
thf(f1494,plain,
( spl60_121
| spl60_119
| spl60_114
| spl60_105 ),
inference(avatar_split_clause,[],[f873,f1373,f1432,f1465,f1481]) ).
thf(f1495,plain,
( spl60_120
| spl60_118
| spl60_115
| spl60_105 ),
inference(avatar_split_clause,[],[f878,f1373,f1437,f1460,f1476]) ).
thf(f1496,plain,
( spl60_121
| spl60_118
| spl60_115
| spl60_105 ),
inference(avatar_split_clause,[],[f877,f1373,f1437,f1460,f1481]) ).
thf(f1497,plain,
( spl60_120
| spl60_119
| spl60_115
| spl60_105 ),
inference(avatar_split_clause,[],[f880,f1373,f1437,f1465,f1476]) ).
thf(f1498,plain,
( spl60_121
| spl60_119
| spl60_115
| spl60_105 ),
inference(avatar_split_clause,[],[f879,f1373,f1437,f1465,f1481]) ).
thf(f1701,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK1 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_4
| ~ spl60_104 ),
inference(constrained_superposition,[],[f894,f1370]) ).
thf(f1742,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK1 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_4
| ~ spl60_104 ),
inference(trivial_inequality_removal,[],[f1701]) ).
thf(f1809,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK1 @ sK25 ) ) )
| ~ spl60_4
| ~ spl60_104
| ~ spl60_105 ),
inference(forward_demodulation,[],[f1742,f1375]) ).
thf(f1810,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK1 @ sK25 ) ) )
| ~ spl60_4
| ~ spl60_104
| ~ spl60_105 ),
inference(trivial_inequality_removal,[],[f1809]) ).
thf(f1820,definition,
( spl60_130
<=> ( $false
= ( a2 @ ( sK1 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_130])],[avatar_definition]) ).
thf(f1822,plain,
( ( $false
= ( a2 @ ( sK1 @ sK25 ) ) )
| ~ spl60_130 ),
inference(avatar_component_clause,[],[f1820]) ).
thf(f1824,definition,
( spl60_131
<=> ( $false
= ( irel @ sK0 @ sK25 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_131])],[avatar_definition]) ).
thf(f1826,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ~ spl60_131 ),
inference(avatar_component_clause,[],[f1824]) ).
thf(f1829,plain,
( spl60_130
| spl60_131
| ~ spl60_4
| ~ spl60_104
| ~ spl60_105 ),
inference(avatar_split_clause,[],[f1810,f1373,f1368,f893,f1824,f1820]) ).
thf(f1894,definition,
( spl60_134
<=> ( $false
= ( a2 @ ( sK1 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_134])],[avatar_definition]) ).
thf(f1896,plain,
( ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ~ spl60_134 ),
inference(avatar_component_clause,[],[f1894]) ).
thf(f3207,definition,
( spl60_150
<=> ( $false
= ( a1 @ ( sK5 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_150])],[avatar_definition]) ).
thf(f3208,plain,
( ( $false
!= ( a1 @ ( sK5 @ sK25 ) ) )
| spl60_150 ),
inference(avatar_component_clause,[],[f3207]) ).
thf(f3209,plain,
( ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ~ spl60_150 ),
inference(avatar_component_clause,[],[f3207]) ).
thf(f3283,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK50 ) )
| ~ spl60_81
| ~ spl60_102 ),
inference(constrained_superposition,[],[f1354,f1239]) ).
thf(f3284,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $true
= ( a1 @ sK50 ) )
| ~ spl60_4
| ~ spl60_102 ),
inference(constrained_superposition,[],[f894,f1354]) ).
thf(f3303,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $true
= ( a1 @ sK50 ) )
| ~ spl60_4
| ~ spl60_102 ),
inference(trivial_inequality_removal,[],[f3284]) ).
thf(f3304,plain,
( ( $true
= ( a1 @ sK50 ) )
| ~ spl60_81
| ~ spl60_102 ),
inference(trivial_inequality_removal,[],[f3283]) ).
thf(f3326,plain,
( ( $true = $false )
| ~ spl60_81
| ~ spl60_102
| ~ spl60_103 ),
inference(forward_demodulation,[],[f3304,f1359]) ).
thf(f3327,plain,
( $false
| ~ spl60_81
| ~ spl60_102
| ~ spl60_103 ),
inference(trivial_inequality_removal,[],[f3326]) ).
thf(f3328,plain,
( ~ spl60_81
| ~ spl60_102
| ~ spl60_103 ),
inference(avatar_contradiction_clause,[],[f3327]) ).
thf(f3384,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $true
= ( a1 @ sK50 ) )
| ~ spl60_4
| ~ spl60_79
| ~ spl60_102 ),
inference(forward_demodulation,[],[f3303,f1232]) ).
thf(f3385,plain,
( ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $true
= ( a1 @ sK50 ) )
| ~ spl60_4
| ~ spl60_79
| ~ spl60_102 ),
inference(trivial_inequality_removal,[],[f3384]) ).
thf(f3401,definition,
( spl60_155
<=> ( $false
= ( a2 @ ( sK4 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_155])],[avatar_definition]) ).
thf(f3403,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_155 ),
inference(avatar_component_clause,[],[f3401]) ).
thf(f3418,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ~ spl60_4
| ~ spl60_79
| ~ spl60_102
| ~ spl60_103 ),
inference(forward_demodulation,[],[f3385,f1359]) ).
thf(f3419,plain,
( ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ~ spl60_4
| ~ spl60_79
| ~ spl60_102
| ~ spl60_103 ),
inference(trivial_inequality_removal,[],[f3418]) ).
thf(f3422,plain,
( spl60_134
| ~ spl60_4
| ~ spl60_79
| ~ spl60_102
| ~ spl60_103 ),
inference(avatar_split_clause,[],[f3419,f1357,f1352,f1230,f893,f1894]) ).
thf(f3603,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_80
| ~ spl60_84 ),
inference(constrained_superposition,[],[f1236,f1254]) ).
thf(f3607,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_80
| ~ spl60_114 ),
inference(constrained_superposition,[],[f1236,f1434]) ).
thf(f3630,plain,
( ( $true
= ( a2 @ sK56 ) )
| ~ spl60_80
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f3607]) ).
thf(f3634,plain,
( ( $true
= ( a2 @ sK41 ) )
| ~ spl60_80
| ~ spl60_84 ),
inference(trivial_inequality_removal,[],[f3603]) ).
thf(f3646,plain,
( ( $true = $false )
| ~ spl60_80
| ~ spl60_114
| ~ spl60_115 ),
inference(forward_demodulation,[],[f3630,f1439]) ).
thf(f3647,plain,
( $false
| ~ spl60_80
| ~ spl60_114
| ~ spl60_115 ),
inference(trivial_inequality_removal,[],[f3646]) ).
thf(f3648,plain,
( ~ spl60_80
| ~ spl60_114
| ~ spl60_115 ),
inference(avatar_contradiction_clause,[],[f3647]) ).
thf(f3649,plain,
( ( $true = $false )
| ~ spl60_80
| ~ spl60_84
| ~ spl60_85 ),
inference(forward_demodulation,[],[f3634,f1259]) ).
thf(f3650,plain,
( $false
| ~ spl60_80
| ~ spl60_84
| ~ spl60_85 ),
inference(trivial_inequality_removal,[],[f3649]) ).
thf(f3651,plain,
( ~ spl60_80
| ~ spl60_84
| ~ spl60_85 ),
inference(avatar_contradiction_clause,[],[f3650]) ).
thf(f3730,definition,
( spl60_162
<=> ( $false
= ( a1 @ ( sK5 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_162])],[avatar_definition]) ).
thf(f3732,plain,
( ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_162 ),
inference(avatar_component_clause,[],[f3730]) ).
thf(f3846,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_4
| ~ spl60_120 ),
inference(constrained_superposition,[],[f1478,f894]) ).
thf(f3857,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_7
| ~ spl60_120 ),
inference(constrained_superposition,[],[f906,f1478]) ).
thf(f3874,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_7
| ~ spl60_120 ),
inference(trivial_inequality_removal,[],[f3857]) ).
thf(f3885,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_4
| ~ spl60_120 ),
inference(trivial_inequality_removal,[],[f3846]) ).
thf(f4384,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( a2 @ ( sK27 @ sK39 ) ) ) )
| ~ spl60_53
| ~ spl60_80 ),
inference(constrained_superposition,[],[f1109,f1236]) ).
thf(f4438,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( a2 @ ( sK27 @ sK39 ) ) ) )
| ~ spl60_53
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f4384]) ).
thf(f4472,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK27 @ sK39 ) ) ) )
| ~ spl60_53
| ~ spl60_79
| ~ spl60_80 ),
inference(forward_demodulation,[],[f4438,f1232]) ).
thf(f4473,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK27 @ sK39 ) ) ) )
| ~ spl60_53
| ~ spl60_79
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f4472]) ).
thf(f4475,definition,
( spl60_168
<=> ( $true
= ( a2 @ ( sK27 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_168])],[avatar_definition]) ).
thf(f4477,plain,
( ( $true
= ( a2 @ ( sK27 @ sK39 ) ) )
| ~ spl60_168 ),
inference(avatar_component_clause,[],[f4475]) ).
thf(f4479,plain,
( spl60_168
| spl60_81
| ~ spl60_53
| ~ spl60_79
| ~ spl60_80 ),
inference(avatar_split_clause,[],[f4473,f1235,f1230,f1108,f1238,f4475]) ).
thf(f4520,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_2
| ~ spl60_80 ),
inference(constrained_superposition,[],[f1236,f886]) ).
thf(f4525,plain,
( ! [X0: $i] :
( ( $true
= ( a2 @ ( sK1 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_2
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f4520]) ).
thf(f4588,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_2
| ~ spl60_80
| ~ spl60_134 ),
inference(forward_demodulation,[],[f4525,f1896]) ).
thf(f4589,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_2
| ~ spl60_80
| ~ spl60_134 ),
inference(trivial_inequality_removal,[],[f4588]) ).
thf(f4592,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_2
| ~ spl60_79
| ~ spl60_80
| ~ spl60_134 ),
inference(forward_demodulation,[],[f4589,f1232]) ).
thf(f4593,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_2
| ~ spl60_79
| ~ spl60_80
| ~ spl60_134 ),
inference(trivial_inequality_removal,[],[f4592]) ).
thf(f4596,plain,
( spl60_81
| ~ spl60_2
| ~ spl60_79
| ~ spl60_80
| ~ spl60_134 ),
inference(avatar_split_clause,[],[f4593,f1894,f1235,f1230,f885,f1238]) ).
thf(f4682,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ ( sK2 @ sK25 ) ) ) )
| ~ spl60_1
| ~ spl60_55 ),
inference(constrained_superposition,[],[f883,f1117]) ).
thf(f4744,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ ( sK2 @ sK25 ) ) ) )
| ~ spl60_1
| ~ spl60_55 ),
inference(trivial_inequality_removal,[],[f4682]) ).
thf(f4777,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK2 @ sK25 ) ) ) )
| ~ spl60_1
| ~ spl60_51
| ~ spl60_55 ),
inference(forward_demodulation,[],[f4744,f1101]) ).
thf(f4778,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK2 @ sK25 ) ) ) )
| ~ spl60_1
| ~ spl60_51
| ~ spl60_55 ),
inference(trivial_inequality_removal,[],[f4777]) ).
thf(f4780,definition,
( spl60_169
<=> ( $true
= ( a1 @ ( sK2 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_169])],[avatar_definition]) ).
thf(f4782,plain,
( ( $true
= ( a1 @ ( sK2 @ sK25 ) ) )
| ~ spl60_169 ),
inference(avatar_component_clause,[],[f4780]) ).
thf(f4784,plain,
( spl60_169
| spl60_57
| ~ spl60_1
| ~ spl60_51
| ~ spl60_55 ),
inference(avatar_split_clause,[],[f4778,f1116,f1099,f882,f1122,f4780]) ).
thf(f4824,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_5
| ~ spl60_80 ),
inference(constrained_superposition,[],[f1236,f899]) ).
thf(f4829,plain,
( ! [X0: $i] :
( ( $true
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_5
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f4824]) ).
thf(f4900,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_5
| ~ spl60_80
| ~ spl60_155 ),
inference(forward_demodulation,[],[f4829,f3403]) ).
thf(f4901,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_5
| ~ spl60_80
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4900]) ).
thf(f4904,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_5
| ~ spl60_79
| ~ spl60_80
| ~ spl60_155 ),
inference(forward_demodulation,[],[f4901,f1232]) ).
thf(f4905,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_5
| ~ spl60_79
| ~ spl60_80
| ~ spl60_155 ),
inference(trivial_inequality_removal,[],[f4904]) ).
thf(f4908,plain,
( spl60_81
| ~ spl60_5
| ~ spl60_79
| ~ spl60_80
| ~ spl60_155 ),
inference(avatar_split_clause,[],[f4905,f3401,f1235,f1230,f898,f1238]) ).
thf(f4914,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_120 ),
inference(forward_demodulation,[],[f3874,f1232]) ).
thf(f4915,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_120 ),
inference(trivial_inequality_removal,[],[f4914]) ).
thf(f4918,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_5
| ~ spl60_79
| ~ spl60_80 ),
inference(forward_demodulation,[],[f4829,f1232]) ).
thf(f4919,plain,
( ! [X0: $i] :
( ( $true
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_5
| ~ spl60_79
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f4918]) ).
thf(f4921,definition,
( spl60_170
<=> ( $true
= ( a2 @ ( sK4 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_170])],[avatar_definition]) ).
thf(f4923,plain,
( ( $true
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_170 ),
inference(avatar_component_clause,[],[f4921]) ).
thf(f4929,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_120
| ~ spl60_121 ),
inference(forward_demodulation,[],[f4915,f1483]) ).
thf(f4930,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_120
| ~ spl60_121 ),
inference(trivial_inequality_removal,[],[f4929]) ).
thf(f4933,plain,
( spl60_81
| spl60_170
| ~ spl60_5
| ~ spl60_79
| ~ spl60_80 ),
inference(avatar_split_clause,[],[f4919,f1235,f1230,f898,f4921,f1238]) ).
thf(f4935,plain,
( spl60_155
| ~ spl60_7
| ~ spl60_79
| ~ spl60_120
| ~ spl60_121 ),
inference(avatar_split_clause,[],[f4930,f1481,f1476,f1230,f905,f3401]) ).
thf(f4995,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK45 ) )
| ~ spl60_12
| ~ spl60_92 ),
inference(constrained_superposition,[],[f1298,f926]) ).
thf(f5048,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK45 ) )
| ~ spl60_12
| ~ spl60_92 ),
inference(trivial_inequality_removal,[],[f4995]) ).
thf(f5092,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a2 @ sK45 ) )
| ~ spl60_12
| ~ spl60_92
| spl60_150 ),
inference(forward_subsumption_resolution,[],[f5048,f3208]) ).
thf(f5138,definition,
( spl60_182
<=> ( $false
= ( a2 @ ( sK4 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_182])],[avatar_definition]) ).
thf(f5140,plain,
( ( $false
= ( a2 @ ( sK4 @ sK25 ) ) )
| ~ spl60_182 ),
inference(avatar_component_clause,[],[f5138]) ).
thf(f5159,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK45 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_92
| spl60_150 ),
inference(forward_demodulation,[],[f5092,f1101]) ).
thf(f5160,plain,
( ( $true
= ( a2 @ sK45 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_92
| spl60_150 ),
inference(trivial_inequality_removal,[],[f5159]) ).
thf(f5185,plain,
( ( $true = $false )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_92
| ~ spl60_93
| spl60_150 ),
inference(forward_demodulation,[],[f5160,f1303]) ).
thf(f5186,plain,
( $false
| ~ spl60_12
| ~ spl60_51
| ~ spl60_92
| ~ spl60_93
| spl60_150 ),
inference(trivial_inequality_removal,[],[f5185]) ).
thf(f5187,plain,
( ~ spl60_12
| ~ spl60_51
| ~ spl60_92
| ~ spl60_93
| spl60_150 ),
inference(avatar_contradiction_clause,[],[f5186]) ).
thf(f5953,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK54 ) )
| ~ spl60_11
| ~ spl60_110 ),
inference(constrained_superposition,[],[f922,f1406]) ).
thf(f5983,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_11
| ~ spl60_96 ),
inference(constrained_superposition,[],[f1320,f922]) ).
thf(f5999,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_11
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f5983]) ).
thf(f6016,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK54 ) )
| ~ spl60_11
| ~ spl60_110 ),
inference(trivial_inequality_removal,[],[f5953]) ).
thf(f6031,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_96 ),
inference(forward_demodulation,[],[f5999,f1232]) ).
thf(f6032,plain,
( ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f6031]) ).
thf(f6041,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK54 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_110 ),
inference(forward_demodulation,[],[f6016,f1101]) ).
thf(f6042,plain,
( ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK54 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_110 ),
inference(trivial_inequality_removal,[],[f6041]) ).
thf(f6050,definition,
( spl60_192
<=> ( $true
= ( a2 @ sK54 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_192])],[avatar_definition]) ).
thf(f6052,plain,
( ( $true
= ( a2 @ sK54 ) )
| ~ spl60_192 ),
inference(avatar_component_clause,[],[f6050]) ).
thf(f6054,definition,
( spl60_193
<=> ( $false
= ( a1 @ ( sK6 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_193])],[avatar_definition]) ).
thf(f6055,plain,
( ( $false
!= ( a1 @ ( sK6 @ sK25 ) ) )
| spl60_193 ),
inference(avatar_component_clause,[],[f6054]) ).
thf(f6056,plain,
( ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ~ spl60_193 ),
inference(avatar_component_clause,[],[f6054]) ).
thf(f6064,plain,
( spl60_192
| spl60_193
| ~ spl60_11
| ~ spl60_51
| ~ spl60_110 ),
inference(avatar_split_clause,[],[f6042,f1404,f1099,f921,f6054,f6050]) ).
thf(f6412,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( a1 @ ( sK6 @ sK39 ) ) ) )
| ~ spl60_9
| ~ spl60_81 ),
inference(constrained_superposition,[],[f915,f1239]) ).
thf(f6430,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) ) )
| ~ spl60_9
| ~ spl60_55 ),
inference(constrained_superposition,[],[f1117,f915]) ).
thf(f6434,plain,
( ! [X0: $i] :
( ( $true
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) ) )
| ~ spl60_9
| ~ spl60_55 ),
inference(trivial_inequality_removal,[],[f6430]) ).
thf(f6468,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( a1 @ ( sK6 @ sK39 ) ) ) )
| ~ spl60_9
| ~ spl60_81 ),
inference(trivial_inequality_removal,[],[f6412]) ).
thf(f6504,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) ) )
| ~ spl60_9
| ~ spl60_55
| ~ spl60_193 ),
inference(forward_demodulation,[],[f6434,f6056]) ).
thf(f6505,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) ) )
| ~ spl60_9
| ~ spl60_55
| ~ spl60_193 ),
inference(trivial_inequality_removal,[],[f6504]) ).
thf(f6506,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK6 @ sK39 ) ) ) )
| ~ spl60_9
| ~ spl60_79
| ~ spl60_81 ),
inference(forward_demodulation,[],[f6468,f1232]) ).
thf(f6507,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK6 @ sK39 ) ) ) )
| ~ spl60_9
| ~ spl60_79
| ~ spl60_81 ),
inference(trivial_inequality_removal,[],[f6506]) ).
thf(f6511,definition,
( spl60_194
<=> ( $true
= ( a1 @ ( sK6 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_194])],[avatar_definition]) ).
thf(f6513,plain,
( ( $true
= ( a1 @ ( sK6 @ sK39 ) ) )
| ~ spl60_194 ),
inference(avatar_component_clause,[],[f6511]) ).
thf(f6515,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) ) )
| ~ spl60_9
| ~ spl60_51
| ~ spl60_55
| ~ spl60_193 ),
inference(forward_demodulation,[],[f6505,f1101]) ).
thf(f6516,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) ) )
| ~ spl60_9
| ~ spl60_51
| ~ spl60_55
| ~ spl60_193 ),
inference(trivial_inequality_removal,[],[f6515]) ).
thf(f6517,plain,
( spl60_194
| spl60_80
| ~ spl60_9
| ~ spl60_79
| ~ spl60_81 ),
inference(avatar_split_clause,[],[f6507,f1238,f1230,f914,f1235,f6511]) ).
thf(f6520,plain,
( spl60_57
| ~ spl60_9
| ~ spl60_51
| ~ spl60_55
| ~ spl60_193 ),
inference(avatar_split_clause,[],[f6516,f6054,f1116,f1099,f914,f1122]) ).
thf(f6569,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_12
| ~ spl60_96 ),
inference(constrained_superposition,[],[f1320,f926]) ).
thf(f6574,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_114 ),
inference(constrained_superposition,[],[f1434,f926]) ).
thf(f6582,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f6574]) ).
thf(f6585,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_12
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f6569]) ).
thf(f6644,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ ( sK5 @ sK25 ) ) ) )
| ~ spl60_10
| ~ spl60_55 ),
inference(constrained_superposition,[],[f918,f1117]) ).
thf(f6665,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_10
| ~ spl60_81 ),
inference(constrained_superposition,[],[f1239,f918]) ).
thf(f6667,plain,
( ! [X0: $i] :
( ( $true
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_10
| ~ spl60_81 ),
inference(trivial_inequality_removal,[],[f6665]) ).
thf(f6705,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ ( sK5 @ sK25 ) ) ) )
| ~ spl60_10
| ~ spl60_55 ),
inference(trivial_inequality_removal,[],[f6644]) ).
thf(f6740,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_10
| ~ spl60_81
| ~ spl60_162 ),
inference(forward_demodulation,[],[f6667,f3732]) ).
thf(f6741,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) ) )
| ~ spl60_10
| ~ spl60_81
| ~ spl60_162 ),
inference(trivial_inequality_removal,[],[f6740]) ).
thf(f6746,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK5 @ sK25 ) ) ) )
| ~ spl60_10
| ~ spl60_51
| ~ spl60_55 ),
inference(forward_demodulation,[],[f6705,f1101]) ).
thf(f6747,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK5 @ sK25 ) ) ) )
| ~ spl60_10
| ~ spl60_51
| ~ spl60_55 ),
inference(trivial_inequality_removal,[],[f6746]) ).
thf(f6748,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) ) )
| ~ spl60_10
| ~ spl60_79
| ~ spl60_81
| ~ spl60_162 ),
inference(forward_demodulation,[],[f6741,f1232]) ).
thf(f6749,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) ) )
| ~ spl60_10
| ~ spl60_79
| ~ spl60_81
| ~ spl60_162 ),
inference(trivial_inequality_removal,[],[f6748]) ).
thf(f6751,definition,
( spl60_195
<=> ( $true
= ( a1 @ ( sK5 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_195])],[avatar_definition]) ).
thf(f6753,plain,
( ( $true
= ( a1 @ ( sK5 @ sK25 ) ) )
| ~ spl60_195 ),
inference(avatar_component_clause,[],[f6751]) ).
thf(f6757,plain,
( spl60_195
| spl60_57
| ~ spl60_10
| ~ spl60_51
| ~ spl60_55 ),
inference(avatar_split_clause,[],[f6747,f1116,f1099,f917,f1122,f6751]) ).
thf(f6758,plain,
( spl60_80
| ~ spl60_10
| ~ spl60_79
| ~ spl60_81
| ~ spl60_162 ),
inference(avatar_split_clause,[],[f6749,f3730,f1238,f1230,f917,f1235]) ).
thf(f6759,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114 ),
inference(forward_demodulation,[],[f6582,f1232]) ).
thf(f6760,plain,
( ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f6759]) ).
thf(f6761,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_96 ),
inference(forward_demodulation,[],[f6585,f1232]) ).
thf(f6762,plain,
( ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f6761]) ).
thf(f6767,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) ) )
| ~ spl60_10
| ~ spl60_79
| ~ spl60_81 ),
inference(forward_demodulation,[],[f6667,f1232]) ).
thf(f6768,plain,
( ! [X0: $i] :
( ( $true
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a2 @ X0 ) ) )
| ~ spl60_10
| ~ spl60_79
| ~ spl60_81 ),
inference(trivial_inequality_removal,[],[f6767]) ).
thf(f6770,definition,
( spl60_196
<=> ( $true
= ( a1 @ ( sK5 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_196])],[avatar_definition]) ).
thf(f6772,plain,
( ( $true
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_196 ),
inference(avatar_component_clause,[],[f6770]) ).
thf(f6774,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115 ),
inference(forward_demodulation,[],[f6760,f1439]) ).
thf(f6775,plain,
( ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115 ),
inference(trivial_inequality_removal,[],[f6774]) ).
thf(f6776,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_96
| ~ spl60_97 ),
inference(forward_demodulation,[],[f6762,f1325]) ).
thf(f6777,plain,
( ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_96
| ~ spl60_97 ),
inference(trivial_inequality_removal,[],[f6776]) ).
thf(f6782,plain,
( spl60_80
| spl60_196
| ~ spl60_10
| ~ spl60_79
| ~ spl60_81 ),
inference(avatar_split_clause,[],[f6768,f1238,f1230,f917,f6770,f1235]) ).
thf(f6783,plain,
( spl60_162
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115 ),
inference(avatar_split_clause,[],[f6775,f1437,f1432,f1230,f925,f3730]) ).
thf(f6784,plain,
( spl60_162
| ~ spl60_12
| ~ spl60_79
| ~ spl60_96
| ~ spl60_97 ),
inference(avatar_split_clause,[],[f6777,f1323,f1318,f1230,f925,f3730]) ).
thf(f6805,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ ( sK6 @ sK25 ) ) ) )
| ~ spl60_9
| ~ spl60_55 ),
inference(constrained_superposition,[],[f915,f1117]) ).
thf(f6866,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ ( sK6 @ sK25 ) ) ) )
| ~ spl60_9
| ~ spl60_55 ),
inference(trivial_inequality_removal,[],[f6805]) ).
thf(f6903,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK6 @ sK25 ) ) ) )
| ~ spl60_9
| ~ spl60_51
| ~ spl60_55 ),
inference(forward_demodulation,[],[f6866,f1101]) ).
thf(f6904,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a2 @ X0 ) )
| ( $true
= ( a1 @ ( sK6 @ sK25 ) ) ) )
| ~ spl60_9
| ~ spl60_51
| ~ spl60_55 ),
inference(trivial_inequality_removal,[],[f6903]) ).
thf(f6906,definition,
( spl60_197
<=> ( $true
= ( a1 @ ( sK6 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_197])],[avatar_definition]) ).
thf(f6908,plain,
( ( $true
= ( a1 @ ( sK6 @ sK25 ) ) )
| ~ spl60_197 ),
inference(avatar_component_clause,[],[f6906]) ).
thf(f6910,plain,
( spl60_197
| spl60_57
| ~ spl60_9
| ~ spl60_51
| ~ spl60_55 ),
inference(avatar_split_clause,[],[f6904,f1116,f1099,f914,f1122,f6906]) ).
thf(f7479,definition,
( spl60_201
<=> ( $true
= ( a2 @ sK47 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_201])],[avatar_definition]) ).
thf(f7481,plain,
( ( $true
= ( a2 @ sK47 ) )
| ~ spl60_201 ),
inference(avatar_component_clause,[],[f7479]) ).
thf(f7490,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_96
| ~ spl60_194 ),
inference(forward_demodulation,[],[f6032,f6513]) ).
thf(f7491,plain,
( ( $true
= ( a2 @ sK47 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_96
| ~ spl60_194 ),
inference(trivial_inequality_removal,[],[f7490]) ).
thf(f7502,plain,
( spl60_201
| ~ spl60_11
| ~ spl60_79
| ~ spl60_96
| ~ spl60_194 ),
inference(avatar_split_clause,[],[f7491,f6511,f1318,f1230,f921,f7479]) ).
thf(f7539,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK49 ) )
| ~ spl60_11
| ~ spl60_100 ),
inference(constrained_superposition,[],[f1342,f922]) ).
thf(f7594,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK49 ) )
| ~ spl60_11
| ~ spl60_100 ),
inference(trivial_inequality_removal,[],[f7539]) ).
thf(f7622,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a2 @ sK49 ) )
| ~ spl60_11
| ~ spl60_100
| spl60_193 ),
inference(forward_subsumption_resolution,[],[f7594,f6055]) ).
thf(f7673,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK49 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_100
| spl60_193 ),
inference(forward_demodulation,[],[f7622,f1101]) ).
thf(f7674,plain,
( ( $true
= ( a2 @ sK49 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_100
| spl60_193 ),
inference(trivial_inequality_removal,[],[f7673]) ).
thf(f7707,plain,
( ( $true = $false )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_100
| ~ spl60_101
| spl60_193 ),
inference(forward_demodulation,[],[f7674,f1347]) ).
thf(f7708,plain,
( $false
| ~ spl60_11
| ~ spl60_51
| ~ spl60_100
| ~ spl60_101
| spl60_193 ),
inference(trivial_inequality_removal,[],[f7707]) ).
thf(f7709,plain,
( ~ spl60_11
| ~ spl60_51
| ~ spl60_100
| ~ spl60_101
| spl60_193 ),
inference(avatar_contradiction_clause,[],[f7708]) ).
thf(f7904,plain,
( ( $true = $false )
| ~ spl60_150
| ~ spl60_195 ),
inference(constrained_superposition,[],[f6753,f3209]) ).
thf(f7905,plain,
( $false
| ~ spl60_150
| ~ spl60_195 ),
inference(trivial_inequality_removal,[],[f7904]) ).
thf(f7906,plain,
( ~ spl60_150
| ~ spl60_195 ),
inference(avatar_contradiction_clause,[],[f7905]) ).
thf(f7922,plain,
( ( $true = $false )
| ~ spl60_97
| ~ spl60_201 ),
inference(constrained_superposition,[],[f1325,f7481]) ).
thf(f7926,plain,
( $false
| ~ spl60_97
| ~ spl60_201 ),
inference(trivial_inequality_removal,[],[f7922]) ).
thf(f7927,plain,
( ~ spl60_97
| ~ spl60_201 ),
inference(avatar_contradiction_clause,[],[f7926]) ).
thf(f7941,plain,
( ( $true = $false )
| ~ spl60_111
| ~ spl60_192 ),
inference(constrained_superposition,[],[f1411,f6052]) ).
thf(f7945,plain,
( $false
| ~ spl60_111
| ~ spl60_192 ),
inference(trivial_inequality_removal,[],[f7941]) ).
thf(f7946,plain,
( ~ spl60_111
| ~ spl60_192 ),
inference(avatar_contradiction_clause,[],[f7945]) ).
thf(f8041,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK4 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_7
| ~ spl60_104 ),
inference(constrained_superposition,[],[f906,f1370]) ).
thf(f8058,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK4 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_7
| ~ spl60_104 ),
inference(trivial_inequality_removal,[],[f8041]) ).
thf(f8142,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_7
| ~ spl60_51
| ~ spl60_104 ),
inference(forward_demodulation,[],[f8058,f1101]) ).
thf(f8143,plain,
( ( $false
= ( a2 @ ( sK4 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_7
| ~ spl60_51
| ~ spl60_104 ),
inference(trivial_inequality_removal,[],[f8142]) ).
thf(f8162,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK25 ) ) )
| ~ spl60_7
| ~ spl60_51
| ~ spl60_104
| ~ spl60_105 ),
inference(forward_demodulation,[],[f8143,f1375]) ).
thf(f8163,plain,
( ( $false
= ( a2 @ ( sK4 @ sK25 ) ) )
| ~ spl60_7
| ~ spl60_51
| ~ spl60_104
| ~ spl60_105 ),
inference(trivial_inequality_removal,[],[f8162]) ).
thf(f8182,plain,
( spl60_182
| ~ spl60_7
| ~ spl60_51
| ~ spl60_104
| ~ spl60_105 ),
inference(avatar_split_clause,[],[f8163,f1373,f1368,f1099,f905,f5138]) ).
thf(f8373,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_55
| ~ spl60_104 ),
inference(constrained_superposition,[],[f1117,f1370]) ).
thf(f8403,plain,
( ( $true
= ( a1 @ sK51 ) )
| ~ spl60_55
| ~ spl60_104 ),
inference(trivial_inequality_removal,[],[f8373]) ).
thf(f8415,plain,
( ( $true = $false )
| ~ spl60_55
| ~ spl60_104
| ~ spl60_105 ),
inference(forward_demodulation,[],[f8403,f1375]) ).
thf(f8416,plain,
( $false
| ~ spl60_55
| ~ spl60_104
| ~ spl60_105 ),
inference(trivial_inequality_removal,[],[f8415]) ).
thf(f8417,plain,
( ~ spl60_55
| ~ spl60_104
| ~ spl60_105 ),
inference(avatar_contradiction_clause,[],[f8416]) ).
thf(f8453,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK54 ) )
| ~ spl60_57
| ~ spl60_110 ),
inference(constrained_superposition,[],[f1123,f1406]) ).
thf(f8454,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_57
| ~ spl60_118 ),
inference(constrained_superposition,[],[f1123,f1462]) ).
thf(f8455,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a2 @ ( sK1 @ sK25 ) ) ) )
| ~ spl60_2
| ~ spl60_57 ),
inference(constrained_superposition,[],[f886,f1123]) ).
thf(f8456,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a2 @ ( sK4 @ sK25 ) ) ) )
| ~ spl60_5
| ~ spl60_57 ),
inference(constrained_superposition,[],[f899,f1123]) ).
thf(f8477,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a2 @ ( sK4 @ sK25 ) ) ) )
| ~ spl60_5
| ~ spl60_57 ),
inference(trivial_inequality_removal,[],[f8456]) ).
thf(f8478,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a2 @ ( sK1 @ sK25 ) ) ) )
| ~ spl60_2
| ~ spl60_57 ),
inference(trivial_inequality_removal,[],[f8455]) ).
thf(f8479,plain,
( ( $true
= ( a2 @ sK58 ) )
| ~ spl60_57
| ~ spl60_118 ),
inference(trivial_inequality_removal,[],[f8454]) ).
thf(f8480,plain,
( ( $true
= ( a2 @ sK54 ) )
| ~ spl60_57
| ~ spl60_110 ),
inference(trivial_inequality_removal,[],[f8453]) ).
thf(f8495,plain,
( ( $true = $false )
| ~ spl60_57
| ~ spl60_118
| ~ spl60_119 ),
inference(forward_demodulation,[],[f8479,f1467]) ).
thf(f8496,plain,
( $false
| ~ spl60_57
| ~ spl60_118
| ~ spl60_119 ),
inference(trivial_inequality_removal,[],[f8495]) ).
thf(f8497,plain,
( ~ spl60_57
| ~ spl60_118
| ~ spl60_119 ),
inference(avatar_contradiction_clause,[],[f8496]) ).
thf(f8498,plain,
( ( $true = $false )
| ~ spl60_57
| ~ spl60_110
| ~ spl60_111 ),
inference(forward_demodulation,[],[f8480,f1411]) ).
thf(f8499,plain,
( $false
| ~ spl60_57
| ~ spl60_110
| ~ spl60_111 ),
inference(trivial_inequality_removal,[],[f8498]) ).
thf(f8500,plain,
( ~ spl60_57
| ~ spl60_110
| ~ spl60_111 ),
inference(avatar_contradiction_clause,[],[f8499]) ).
thf(f8505,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK4 @ sK25 ) ) ) )
| ~ spl60_5
| ~ spl60_51
| ~ spl60_57 ),
inference(forward_demodulation,[],[f8477,f1101]) ).
thf(f8506,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK4 @ sK25 ) ) ) )
| ~ spl60_5
| ~ spl60_51
| ~ spl60_57 ),
inference(trivial_inequality_removal,[],[f8505]) ).
thf(f8507,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK1 @ sK25 ) ) ) )
| ~ spl60_2
| ~ spl60_51
| ~ spl60_57 ),
inference(forward_demodulation,[],[f8478,f1101]) ).
thf(f8508,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK1 @ sK25 ) ) ) )
| ~ spl60_2
| ~ spl60_51
| ~ spl60_57 ),
inference(trivial_inequality_removal,[],[f8507]) ).
thf(f8527,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_5
| ~ spl60_51
| ~ spl60_57
| ~ spl60_182 ),
inference(forward_demodulation,[],[f8506,f5140]) ).
thf(f8528,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_5
| ~ spl60_51
| ~ spl60_57
| ~ spl60_182 ),
inference(trivial_inequality_removal,[],[f8527]) ).
thf(f8529,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_2
| ~ spl60_51
| ~ spl60_57
| ~ spl60_130 ),
inference(forward_demodulation,[],[f8508,f1822]) ).
thf(f8530,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_2
| ~ spl60_51
| ~ spl60_57
| ~ spl60_130 ),
inference(trivial_inequality_removal,[],[f8529]) ).
thf(f8537,plain,
( spl60_55
| ~ spl60_5
| ~ spl60_51
| ~ spl60_57
| ~ spl60_182 ),
inference(avatar_split_clause,[],[f8528,f5138,f1122,f1099,f898,f1116]) ).
thf(f8538,plain,
( spl60_55
| ~ spl60_2
| ~ spl60_51
| ~ spl60_57
| ~ spl60_130 ),
inference(avatar_split_clause,[],[f8530,f1820,f1122,f1099,f885,f1116]) ).
thf(f8640,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK2 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_3
| ~ spl60_118 ),
inference(constrained_superposition,[],[f1462,f890]) ).
thf(f8663,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK2 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_3
| ~ spl60_118 ),
inference(trivial_inequality_removal,[],[f8640]) ).
thf(f8726,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104 ),
inference(constrained_superposition,[],[f910,f1370]) ).
thf(f8732,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_8
| ~ spl60_120 ),
inference(constrained_superposition,[],[f910,f1478]) ).
thf(f8749,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104 ),
inference(constrained_superposition,[],[f1370,f910]) ).
thf(f8776,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104 ),
inference(trivial_inequality_removal,[],[f8749]) ).
thf(f8789,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_8
| ~ spl60_120 ),
inference(trivial_inequality_removal,[],[f8732]) ).
thf(f8795,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104 ),
inference(trivial_inequality_removal,[],[f8726]) ).
thf(f8872,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_114 ),
inference(constrained_superposition,[],[f926,f1434]) ).
thf(f8893,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_12
| ~ spl60_118 ),
inference(constrained_superposition,[],[f1462,f926]) ).
thf(f8916,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_12
| ~ spl60_118 ),
inference(trivial_inequality_removal,[],[f8893]) ).
thf(f8931,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f8872]) ).
thf(f9076,definition,
( spl60_224
<=> ( $true
= ( a2 @ sK56 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_224])],[avatar_definition]) ).
thf(f9078,plain,
( ( $true
= ( a2 @ sK56 ) )
| ~ spl60_224 ),
inference(avatar_component_clause,[],[f9076]) ).
thf(f10267,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) ) )
| ~ spl60_6
| ~ spl60_57 ),
inference(constrained_superposition,[],[f1123,f902]) ).
thf(f10275,plain,
( ! [X0: $i] :
( ( $true
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK25 ) ) )
| ~ spl60_6
| ~ spl60_57 ),
inference(trivial_inequality_removal,[],[f10267]) ).
thf(f10393,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_6
| ~ spl60_51
| ~ spl60_57 ),
inference(forward_demodulation,[],[f10275,f1101]) ).
thf(f10394,plain,
( ! [X0: $i] :
( ( $true
= ( a2 @ ( sK3 @ sK25 ) ) )
| ( $false
= ( irel @ sK25 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_6
| ~ spl60_51
| ~ spl60_57 ),
inference(trivial_inequality_removal,[],[f10393]) ).
thf(f10396,definition,
( spl60_232
<=> ( $true
= ( a2 @ ( sK3 @ sK25 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_232])],[avatar_definition]) ).
thf(f10398,plain,
( ( $true
= ( a2 @ ( sK3 @ sK25 ) ) )
| ~ spl60_232 ),
inference(avatar_component_clause,[],[f10396]) ).
thf(f10413,definition,
( spl60_233
<=> ( $true
= ( a1 @ sK51 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_233])],[avatar_definition]) ).
thf(f10415,plain,
( ( $true
= ( a1 @ sK51 ) )
| ~ spl60_233 ),
inference(avatar_component_clause,[],[f10413]) ).
thf(f10442,plain,
( spl60_55
| spl60_232
| ~ spl60_6
| ~ spl60_51
| ~ spl60_57 ),
inference(avatar_split_clause,[],[f10394,f1122,f1099,f901,f10396,f1116]) ).
thf(f10452,plain,
( ( $true = $false )
| ~ spl60_115
| ~ spl60_224 ),
inference(constrained_superposition,[],[f1439,f9078]) ).
thf(f10456,plain,
( $false
| ~ spl60_115
| ~ spl60_224 ),
inference(trivial_inequality_removal,[],[f10452]) ).
thf(f10457,plain,
( ~ spl60_115
| ~ spl60_224 ),
inference(avatar_contradiction_clause,[],[f10456]) ).
thf(f10534,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK59 ) )
| ~ spl60_81
| ~ spl60_120 ),
inference(constrained_superposition,[],[f1239,f1478]) ).
thf(f10560,plain,
( ( $true
= ( a1 @ sK59 ) )
| ~ spl60_81
| ~ spl60_120 ),
inference(trivial_inequality_removal,[],[f10534]) ).
thf(f10588,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_11
| ~ spl60_114 ),
inference(constrained_superposition,[],[f922,f1434]) ).
thf(f10651,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_11
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f10588]) ).
thf(f10675,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_114 ),
inference(forward_demodulation,[],[f10651,f1232]) ).
thf(f10676,plain,
( ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f10675]) ).
thf(f10679,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_114
| ~ spl60_194 ),
inference(forward_demodulation,[],[f10676,f6513]) ).
thf(f10680,plain,
( ( $true
= ( a2 @ sK56 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_114
| ~ spl60_194 ),
inference(trivial_inequality_removal,[],[f10679]) ).
thf(f10684,plain,
( ( $true = $false )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115
| ~ spl60_194 ),
inference(forward_demodulation,[],[f10680,f1439]) ).
thf(f10685,plain,
( $false
| ~ spl60_11
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115
| ~ spl60_194 ),
inference(trivial_inequality_removal,[],[f10684]) ).
thf(f10686,plain,
( ~ spl60_11
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115
| ~ spl60_194 ),
inference(avatar_contradiction_clause,[],[f10685]) ).
thf(f10689,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114 ),
inference(forward_demodulation,[],[f8931,f1232]) ).
thf(f10690,plain,
( ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK56 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114 ),
inference(trivial_inequality_removal,[],[f10689]) ).
thf(f10714,plain,
( spl60_224
| spl60_162
| ~ spl60_12
| ~ spl60_79
| ~ spl60_114 ),
inference(avatar_split_clause,[],[f10690,f1432,f1230,f925,f3730,f9076]) ).
thf(f10717,plain,
( ( $true = $false )
| ~ spl60_105
| ~ spl60_233 ),
inference(constrained_superposition,[],[f1375,f10415]) ).
thf(f10721,plain,
( $false
| ~ spl60_105
| ~ spl60_233 ),
inference(trivial_inequality_removal,[],[f10717]) ).
thf(f10722,plain,
( ~ spl60_105
| ~ spl60_233 ),
inference(avatar_contradiction_clause,[],[f10721]) ).
thf(f10725,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104
| ~ spl60_232 ),
inference(forward_demodulation,[],[f8776,f10398]) ).
thf(f10726,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104
| ~ spl60_232 ),
inference(trivial_inequality_removal,[],[f10725]) ).
thf(f10727,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104
| ~ spl60_232 ),
inference(forward_demodulation,[],[f8795,f10398]) ).
thf(f10728,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $true
= ( a1 @ sK51 ) )
| ~ spl60_8
| ~ spl60_104
| ~ spl60_232 ),
inference(trivial_inequality_removal,[],[f10727]) ).
thf(f10735,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ~ spl60_8
| ~ spl60_104
| ~ spl60_105
| ~ spl60_232 ),
inference(forward_demodulation,[],[f10726,f1375]) ).
thf(f10736,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ~ spl60_8
| ~ spl60_104
| ~ spl60_105
| ~ spl60_232 ),
inference(trivial_inequality_removal,[],[f10735]) ).
thf(f10751,plain,
( spl60_131
| ~ spl60_8
| ~ spl60_104
| ~ spl60_105
| ~ spl60_232 ),
inference(avatar_split_clause,[],[f10736,f10396,f1373,f1368,f909,f1824]) ).
thf(f10786,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_12
| ~ spl60_84 ),
inference(constrained_superposition,[],[f1254,f926]) ).
thf(f10863,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_12
| ~ spl60_84 ),
inference(trivial_inequality_removal,[],[f10786]) ).
thf(f10877,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_84 ),
inference(forward_demodulation,[],[f10863,f1232]) ).
thf(f10878,plain,
( ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_84 ),
inference(trivial_inequality_removal,[],[f10877]) ).
thf(f10897,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_84
| ~ spl60_196 ),
inference(forward_demodulation,[],[f10878,f6772]) ).
thf(f10898,plain,
( ( $true
= ( a2 @ sK41 ) )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_84
| ~ spl60_196 ),
inference(trivial_inequality_removal,[],[f10897]) ).
thf(f10925,plain,
( ( $true = $false )
| ~ spl60_12
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_196 ),
inference(forward_demodulation,[],[f10898,f1259]) ).
thf(f10926,plain,
( $false
| ~ spl60_12
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_196 ),
inference(trivial_inequality_removal,[],[f10925]) ).
thf(f10927,plain,
( ~ spl60_12
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_196 ),
inference(avatar_contradiction_clause,[],[f10926]) ).
thf(f11085,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_11
| ~ spl60_84 ),
inference(constrained_superposition,[],[f922,f1254]) ).
thf(f11151,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_11
| ~ spl60_84 ),
inference(trivial_inequality_removal,[],[f11085]) ).
thf(f11170,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_84 ),
inference(forward_demodulation,[],[f11151,f1232]) ).
thf(f11171,plain,
( ( $false
= ( a1 @ ( sK6 @ sK39 ) ) )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_84 ),
inference(trivial_inequality_removal,[],[f11170]) ).
thf(f11174,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK41 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_84
| ~ spl60_194 ),
inference(forward_demodulation,[],[f11171,f6513]) ).
thf(f11175,plain,
( ( $true
= ( a2 @ sK41 ) )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_84
| ~ spl60_194 ),
inference(trivial_inequality_removal,[],[f11174]) ).
thf(f11179,plain,
( ( $true = $false )
| ~ spl60_11
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_194 ),
inference(forward_demodulation,[],[f11175,f1259]) ).
thf(f11180,plain,
( $false
| ~ spl60_11
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_194 ),
inference(trivial_inequality_removal,[],[f11179]) ).
thf(f11181,plain,
( ~ spl60_11
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_194 ),
inference(avatar_contradiction_clause,[],[f11180]) ).
thf(f11182,plain,
( ( $true = $false )
| ~ spl60_51
| ~ spl60_131 ),
inference(forward_demodulation,[],[f1101,f1826]) ).
thf(f11183,plain,
( $false
| ~ spl60_51
| ~ spl60_131 ),
inference(trivial_inequality_removal,[],[f11182]) ).
thf(f11184,plain,
( ~ spl60_51
| ~ spl60_131 ),
inference(avatar_contradiction_clause,[],[f11183]) ).
thf(f11190,definition,
( spl60_241
<=> ( $false
= ( irel @ sK0 @ sK39 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_241])],[avatar_definition]) ).
thf(f11192,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ~ spl60_241 ),
inference(avatar_component_clause,[],[f11190]) ).
thf(f11207,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_12
| ~ spl60_84
| ~ spl60_85 ),
inference(forward_demodulation,[],[f10863,f1259]) ).
thf(f11208,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a1 @ ( sK5 @ sK39 ) ) )
| ~ spl60_12
| ~ spl60_84
| ~ spl60_85 ),
inference(trivial_inequality_removal,[],[f11207]) ).
thf(f11218,plain,
( spl60_162
| spl60_241
| ~ spl60_12
| ~ spl60_84
| ~ spl60_85 ),
inference(avatar_split_clause,[],[f11208,f1257,f1252,f925,f11190,f3730]) ).
thf(f11229,plain,
( spl60_233
| spl60_131
| ~ spl60_8
| ~ spl60_104
| ~ spl60_232 ),
inference(avatar_split_clause,[],[f10728,f10396,f1368,f909,f1824,f10413]) ).
thf(f11365,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK52 ) )
| ~ spl60_11
| ~ spl60_106 ),
inference(constrained_superposition,[],[f1380,f922]) ).
thf(f11383,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK52 ) )
| ~ spl60_57
| ~ spl60_106 ),
inference(constrained_superposition,[],[f1380,f1123]) ).
thf(f11428,plain,
( ( $true
= ( a2 @ sK52 ) )
| ~ spl60_57
| ~ spl60_106 ),
inference(trivial_inequality_removal,[],[f11383]) ).
thf(f11446,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK52 ) )
| ~ spl60_11
| ~ spl60_106 ),
inference(trivial_inequality_removal,[],[f11365]) ).
thf(f11472,plain,
( ( $true = $false )
| ~ spl60_57
| ~ spl60_106
| ~ spl60_107 ),
inference(forward_demodulation,[],[f11428,f1385]) ).
thf(f11473,plain,
( $false
| ~ spl60_57
| ~ spl60_106
| ~ spl60_107 ),
inference(trivial_inequality_removal,[],[f11472]) ).
thf(f11474,plain,
( ~ spl60_57
| ~ spl60_106
| ~ spl60_107 ),
inference(avatar_contradiction_clause,[],[f11473]) ).
thf(f11488,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK52 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_106 ),
inference(forward_demodulation,[],[f11446,f1101]) ).
thf(f11489,plain,
( ( $false
= ( a1 @ ( sK6 @ sK25 ) ) )
| ( $true
= ( a2 @ sK52 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_106 ),
inference(trivial_inequality_removal,[],[f11488]) ).
thf(f11536,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK52 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_106
| ~ spl60_197 ),
inference(forward_demodulation,[],[f11489,f6908]) ).
thf(f11537,plain,
( ( $true
= ( a2 @ sK52 ) )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_106
| ~ spl60_197 ),
inference(trivial_inequality_removal,[],[f11536]) ).
thf(f11560,plain,
( ( $true = $false )
| ~ spl60_11
| ~ spl60_51
| ~ spl60_106
| ~ spl60_107
| ~ spl60_197 ),
inference(forward_demodulation,[],[f11537,f1385]) ).
thf(f11561,plain,
( $false
| ~ spl60_11
| ~ spl60_51
| ~ spl60_106
| ~ spl60_107
| ~ spl60_197 ),
inference(trivial_inequality_removal,[],[f11560]) ).
thf(f11562,plain,
( ~ spl60_11
| ~ spl60_51
| ~ spl60_106
| ~ spl60_107
| ~ spl60_197 ),
inference(avatar_contradiction_clause,[],[f11561]) ).
thf(f11572,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK2 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_3
| ~ spl60_51
| ~ spl60_118 ),
inference(forward_demodulation,[],[f8663,f1101]) ).
thf(f11573,plain,
( ( $false
= ( a1 @ ( sK2 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_3
| ~ spl60_51
| ~ spl60_118 ),
inference(trivial_inequality_removal,[],[f11572]) ).
thf(f11580,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_118 ),
inference(forward_demodulation,[],[f8916,f1101]) ).
thf(f11581,plain,
( ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_118 ),
inference(trivial_inequality_removal,[],[f11580]) ).
thf(f11616,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_3
| ~ spl60_51
| ~ spl60_118
| ~ spl60_169 ),
inference(forward_demodulation,[],[f11573,f4782]) ).
thf(f11617,plain,
( ( $true
= ( a2 @ sK58 ) )
| ~ spl60_3
| ~ spl60_51
| ~ spl60_118
| ~ spl60_169 ),
inference(trivial_inequality_removal,[],[f11616]) ).
thf(f11624,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK58 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_118
| ~ spl60_195 ),
inference(forward_demodulation,[],[f11581,f6753]) ).
thf(f11625,plain,
( ( $true
= ( a2 @ sK58 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_118
| ~ spl60_195 ),
inference(trivial_inequality_removal,[],[f11624]) ).
thf(f11633,definition,
( spl60_244
<=> ( $true
= ( a2 @ sK58 ) ) ),
introduced(definition,[new_symbols(definition,[spl60_244])],[avatar_definition]) ).
thf(f11635,plain,
( ( $true
= ( a2 @ sK58 ) )
| ~ spl60_244 ),
inference(avatar_component_clause,[],[f11633]) ).
thf(f11672,plain,
( spl60_244
| ~ spl60_3
| ~ spl60_51
| ~ spl60_118
| ~ spl60_169 ),
inference(avatar_split_clause,[],[f11617,f4780,f1460,f1099,f889,f11633]) ).
thf(f11674,plain,
( spl60_244
| ~ spl60_12
| ~ spl60_51
| ~ spl60_118
| ~ spl60_195 ),
inference(avatar_split_clause,[],[f11625,f6751,f1460,f1099,f925,f11633]) ).
thf(f11696,plain,
( ( $true = $false )
| ~ spl60_119
| ~ spl60_244 ),
inference(forward_demodulation,[],[f11635,f1467]) ).
thf(f11697,plain,
( $false
| ~ spl60_119
| ~ spl60_244 ),
inference(trivial_inequality_removal,[],[f11696]) ).
thf(f11698,plain,
( ~ spl60_119
| ~ spl60_244 ),
inference(avatar_contradiction_clause,[],[f11697]) ).
thf(f11711,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_120
| ~ spl60_121 ),
inference(forward_demodulation,[],[f8789,f1483]) ).
thf(f11712,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_120
| ~ spl60_121 ),
inference(trivial_inequality_removal,[],[f11711]) ).
thf(f11728,plain,
( ( $true = $false )
| ~ spl60_81
| ~ spl60_120
| ~ spl60_121 ),
inference(forward_demodulation,[],[f10560,f1483]) ).
thf(f11729,plain,
( $false
| ~ spl60_81
| ~ spl60_120
| ~ spl60_121 ),
inference(trivial_inequality_removal,[],[f11728]) ).
thf(f11730,plain,
( ~ spl60_81
| ~ spl60_120
| ~ spl60_121 ),
inference(avatar_contradiction_clause,[],[f11729]) ).
thf(f11740,definition,
( spl60_249
<=> ( $false
= ( a2 @ ( sK3 @ sK39 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl60_249])],[avatar_definition]) ).
thf(f11742,plain,
( ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_249 ),
inference(avatar_component_clause,[],[f11740]) ).
thf(f11744,plain,
( spl60_249
| spl60_241
| ~ spl60_8
| ~ spl60_120
| ~ spl60_121 ),
inference(avatar_split_clause,[],[f11712,f1481,f1476,f909,f11190,f11740]) ).
thf(f11773,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ~ spl60_4
| ~ spl60_120
| ~ spl60_121 ),
inference(forward_demodulation,[],[f3885,f1483]) ).
thf(f11774,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK1 @ sK39 ) ) )
| ~ spl60_4
| ~ spl60_120
| ~ spl60_121 ),
inference(trivial_inequality_removal,[],[f11773]) ).
thf(f11782,plain,
( spl60_134
| spl60_241
| ~ spl60_4
| ~ spl60_120
| ~ spl60_121 ),
inference(avatar_split_clause,[],[f11774,f1481,f1476,f893,f11190,f1894]) ).
thf(f11975,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK43 ) )
| ~ spl60_12
| ~ spl60_88 ),
inference(constrained_superposition,[],[f1277,f926]) ).
thf(f12048,plain,
( ( $false
= ( irel @ sK0 @ sK25 ) )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK43 ) )
| ~ spl60_12
| ~ spl60_88 ),
inference(trivial_inequality_removal,[],[f11975]) ).
thf(f12078,plain,
( ( $true = $false )
| ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK43 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_88 ),
inference(forward_demodulation,[],[f12048,f1101]) ).
thf(f12079,plain,
( ( $false
= ( a1 @ ( sK5 @ sK25 ) ) )
| ( $true
= ( a2 @ sK43 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_88 ),
inference(trivial_inequality_removal,[],[f12078]) ).
thf(f12126,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK43 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_88
| ~ spl60_195 ),
inference(forward_demodulation,[],[f12079,f6753]) ).
thf(f12127,plain,
( ( $true
= ( a2 @ sK43 ) )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_88
| ~ spl60_195 ),
inference(trivial_inequality_removal,[],[f12126]) ).
thf(f12168,plain,
( ( $true = $false )
| ~ spl60_12
| ~ spl60_51
| ~ spl60_88
| ~ spl60_89
| ~ spl60_195 ),
inference(forward_demodulation,[],[f12127,f1282]) ).
thf(f12169,plain,
( $false
| ~ spl60_12
| ~ spl60_51
| ~ spl60_88
| ~ spl60_89
| ~ spl60_195 ),
inference(trivial_inequality_removal,[],[f12168]) ).
thf(f12170,plain,
( ~ spl60_12
| ~ spl60_51
| ~ spl60_88
| ~ spl60_89
| ~ spl60_195 ),
inference(avatar_contradiction_clause,[],[f12169]) ).
thf(f12598,plain,
( ( $true = $false )
| ~ spl60_79
| ~ spl60_241 ),
inference(constrained_superposition,[],[f11192,f1232]) ).
thf(f12602,plain,
( $false
| ~ spl60_79
| ~ spl60_241 ),
inference(trivial_inequality_removal,[],[f12598]) ).
thf(f12603,plain,
( ~ spl60_79
| ~ spl60_241 ),
inference(avatar_contradiction_clause,[],[f12602]) ).
thf(f12613,plain,
( ( $true = $false )
| ( $true
= ( a2 @ sK47 ) )
| ~ spl60_80
| ~ spl60_96 ),
inference(constrained_superposition,[],[f1236,f1320]) ).
thf(f12617,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( a2 @ ( sK3 @ sK39 ) ) ) )
| ~ spl60_6
| ~ spl60_80 ),
inference(constrained_superposition,[],[f902,f1236]) ).
thf(f12638,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $true
= ( a2 @ ( sK3 @ sK39 ) ) ) )
| ~ spl60_6
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f12617]) ).
thf(f12642,plain,
( ( $true
= ( a2 @ sK47 ) )
| ~ spl60_80
| ~ spl60_96 ),
inference(trivial_inequality_removal,[],[f12613]) ).
thf(f12652,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK3 @ sK39 ) ) ) )
| ~ spl60_6
| ~ spl60_79
| ~ spl60_80 ),
inference(forward_demodulation,[],[f12638,f1232]) ).
thf(f12653,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) )
| ( $true
= ( a2 @ ( sK3 @ sK39 ) ) ) )
| ~ spl60_6
| ~ spl60_79
| ~ spl60_80 ),
inference(trivial_inequality_removal,[],[f12652]) ).
thf(f12654,plain,
( ( $true = $false )
| ~ spl60_80
| ~ spl60_96
| ~ spl60_97 ),
inference(forward_demodulation,[],[f12642,f1325]) ).
thf(f12655,plain,
( $false
| ~ spl60_80
| ~ spl60_96
| ~ spl60_97 ),
inference(trivial_inequality_removal,[],[f12654]) ).
thf(f12656,plain,
( ~ spl60_80
| ~ spl60_96
| ~ spl60_97 ),
inference(avatar_contradiction_clause,[],[f12655]) ).
thf(f12666,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_6
| ~ spl60_79
| ~ spl60_80
| ~ spl60_249 ),
inference(forward_demodulation,[],[f12653,f11742]) ).
thf(f12667,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK39 @ X0 ) )
| ( $true
= ( a1 @ X0 ) ) )
| ~ spl60_6
| ~ spl60_79
| ~ spl60_80
| ~ spl60_249 ),
inference(trivial_inequality_removal,[],[f12666]) ).
thf(f12671,plain,
( spl60_81
| ~ spl60_6
| ~ spl60_79
| ~ spl60_80
| ~ spl60_249 ),
inference(avatar_split_clause,[],[f12667,f11740,f1235,f1230,f901,f1238]) ).
thf(f12901,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK48 ) )
| ~ spl60_8
| ~ spl60_98 ),
inference(constrained_superposition,[],[f910,f1330]) ).
thf(f12932,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK48 ) )
| ~ spl60_8
| ~ spl60_98 ),
inference(trivial_inequality_removal,[],[f12901]) ).
thf(f13041,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_8
| ~ spl60_108 ),
inference(constrained_superposition,[],[f910,f1394]) ).
thf(f13072,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_8
| ~ spl60_108 ),
inference(trivial_inequality_removal,[],[f13041]) ).
thf(f13364,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_90 ),
inference(constrained_superposition,[],[f906,f1288]) ).
thf(f13393,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_90 ),
inference(constrained_superposition,[],[f1288,f906]) ).
thf(f13398,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_7
| ~ spl60_108 ),
inference(constrained_superposition,[],[f1394,f906]) ).
thf(f13409,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_7
| ~ spl60_108 ),
inference(trivial_inequality_removal,[],[f13398]) ).
thf(f13414,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_90 ),
inference(trivial_inequality_removal,[],[f13393]) ).
thf(f13433,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_90 ),
inference(trivial_inequality_removal,[],[f13364]) ).
thf(f13449,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_108 ),
inference(forward_demodulation,[],[f13409,f1232]) ).
thf(f13450,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_108 ),
inference(trivial_inequality_removal,[],[f13449]) ).
thf(f13456,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90 ),
inference(forward_demodulation,[],[f13414,f1232]) ).
thf(f13457,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90 ),
inference(trivial_inequality_removal,[],[f13456]) ).
thf(f13467,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90 ),
inference(forward_demodulation,[],[f13433,f1232]) ).
thf(f13468,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90 ),
inference(trivial_inequality_removal,[],[f13467]) ).
thf(f13491,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_170 ),
inference(forward_demodulation,[],[f13468,f4923]) ).
thf(f13492,plain,
( ( $true
= ( a1 @ sK44 ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_170 ),
inference(trivial_inequality_removal,[],[f13491]) ).
thf(f13515,plain,
( ( $true = $false )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91
| ~ spl60_170 ),
inference(forward_demodulation,[],[f13492,f1293]) ).
thf(f13516,plain,
( $false
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91
| ~ spl60_170 ),
inference(trivial_inequality_removal,[],[f13515]) ).
thf(f13517,plain,
( ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91
| ~ spl60_170 ),
inference(avatar_contradiction_clause,[],[f13516]) ).
thf(f13532,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK48 ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_98 ),
inference(forward_demodulation,[],[f12932,f1232]) ).
thf(f13533,plain,
( ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK48 ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_98 ),
inference(trivial_inequality_removal,[],[f13532]) ).
thf(f13536,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_108 ),
inference(forward_demodulation,[],[f13072,f1232]) ).
thf(f13537,plain,
( ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK53 ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_108 ),
inference(trivial_inequality_removal,[],[f13536]) ).
thf(f13546,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109 ),
inference(forward_demodulation,[],[f13450,f1399]) ).
thf(f13547,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109 ),
inference(trivial_inequality_removal,[],[f13546]) ).
thf(f13551,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91 ),
inference(forward_demodulation,[],[f13457,f1293]) ).
thf(f13552,plain,
( ( $false
= ( a2 @ ( sK4 @ sK39 ) ) )
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91 ),
inference(trivial_inequality_removal,[],[f13551]) ).
thf(f13568,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_98
| ~ spl60_99 ),
inference(forward_demodulation,[],[f13533,f1335]) ).
thf(f13569,plain,
( ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_98
| ~ spl60_99 ),
inference(trivial_inequality_removal,[],[f13568]) ).
thf(f13572,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109 ),
inference(forward_demodulation,[],[f13537,f1399]) ).
thf(f13573,plain,
( ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109 ),
inference(trivial_inequality_removal,[],[f13572]) ).
thf(f13581,plain,
( spl60_155
| ~ spl60_7
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109 ),
inference(avatar_split_clause,[],[f13547,f1397,f1392,f1230,f905,f3401]) ).
thf(f13583,plain,
( spl60_155
| ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91 ),
inference(avatar_split_clause,[],[f13552,f1291,f1286,f1230,f905,f3401]) ).
thf(f13585,plain,
( spl60_249
| ~ spl60_8
| ~ spl60_79
| ~ spl60_98
| ~ spl60_99 ),
inference(avatar_split_clause,[],[f13569,f1333,f1328,f1230,f909,f11740]) ).
thf(f13586,plain,
( spl60_249
| ~ spl60_8
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109 ),
inference(avatar_split_clause,[],[f13573,f1397,f1392,f1230,f909,f11740]) ).
thf(f13664,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_8
| ~ spl60_82 ),
inference(constrained_superposition,[],[f910,f1244]) ).
thf(f13693,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_8
| ~ spl60_82 ),
inference(trivial_inequality_removal,[],[f13664]) ).
thf(f13725,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_82 ),
inference(forward_demodulation,[],[f13693,f1232]) ).
thf(f13726,plain,
( ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_82 ),
inference(trivial_inequality_removal,[],[f13725]) ).
thf(f13729,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83 ),
inference(forward_demodulation,[],[f13726,f1249]) ).
thf(f13730,plain,
( ( $false
= ( a2 @ ( sK3 @ sK39 ) ) )
| ~ spl60_8
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83 ),
inference(trivial_inequality_removal,[],[f13729]) ).
thf(f13733,plain,
( spl60_249
| ~ spl60_8
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83 ),
inference(avatar_split_clause,[],[f13730,f1247,f1242,f1230,f909,f11740]) ).
thf(f13939,plain,
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK27 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_54
| ~ spl60_82 ),
inference(constrained_superposition,[],[f1113,f1244]) ).
thf(f14013,plain,
( ( $false
= ( irel @ sK0 @ sK39 ) )
| ( $false
= ( a2 @ ( sK27 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_54
| ~ spl60_82 ),
inference(trivial_inequality_removal,[],[f13939]) ).
thf(f14032,plain,
( ( $true = $false )
| ( $false
= ( a2 @ ( sK27 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_54
| ~ spl60_79
| ~ spl60_82 ),
inference(forward_demodulation,[],[f14013,f1232]) ).
thf(f14033,plain,
( ( $false
= ( a2 @ ( sK27 @ sK39 ) ) )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_54
| ~ spl60_79
| ~ spl60_82 ),
inference(trivial_inequality_removal,[],[f14032]) ).
thf(f14040,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK40 ) )
| ~ spl60_54
| ~ spl60_79
| ~ spl60_82
| ~ spl60_168 ),
inference(forward_demodulation,[],[f14033,f4477]) ).
thf(f14041,plain,
( ( $true
= ( a1 @ sK40 ) )
| ~ spl60_54
| ~ spl60_79
| ~ spl60_82
| ~ spl60_168 ),
inference(trivial_inequality_removal,[],[f14040]) ).
thf(f14051,plain,
( ( $true = $false )
| ~ spl60_54
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83
| ~ spl60_168 ),
inference(forward_demodulation,[],[f14041,f1249]) ).
thf(f14052,plain,
( $false
| ~ spl60_54
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83
| ~ spl60_168 ),
inference(trivial_inequality_removal,[],[f14051]) ).
thf(f14053,plain,
( ~ spl60_54
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83
| ~ spl60_168 ),
inference(avatar_contradiction_clause,[],[f14052]) ).
thf(f14314,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK42 ) )
| ~ spl60_81
| ~ spl60_86 ),
inference(constrained_superposition,[],[f1239,f1264]) ).
thf(f14318,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK48 ) )
| ~ spl60_81
| ~ spl60_98 ),
inference(constrained_superposition,[],[f1239,f1330]) ).
thf(f14322,plain,
( ( $true = $false )
| ( $true
= ( a1 @ sK57 ) )
| ~ spl60_81
| ~ spl60_116 ),
inference(constrained_superposition,[],[f1239,f1446]) ).
thf(f14349,plain,
( ( $true
= ( a1 @ sK57 ) )
| ~ spl60_81
| ~ spl60_116 ),
inference(trivial_inequality_removal,[],[f14322]) ).
thf(f14353,plain,
( ( $true
= ( a1 @ sK48 ) )
| ~ spl60_81
| ~ spl60_98 ),
inference(trivial_inequality_removal,[],[f14318]) ).
thf(f14357,plain,
( ( $true
= ( a1 @ sK42 ) )
| ~ spl60_81
| ~ spl60_86 ),
inference(trivial_inequality_removal,[],[f14314]) ).
thf(f14375,plain,
( ( $true = $false )
| ~ spl60_81
| ~ spl60_116
| ~ spl60_117 ),
inference(forward_demodulation,[],[f14349,f1451]) ).
thf(f14376,plain,
( $false
| ~ spl60_81
| ~ spl60_116
| ~ spl60_117 ),
inference(trivial_inequality_removal,[],[f14375]) ).
thf(f14377,plain,
( ~ spl60_81
| ~ spl60_116
| ~ spl60_117 ),
inference(avatar_contradiction_clause,[],[f14376]) ).
thf(f14384,plain,
( ( $true = $false )
| ~ spl60_81
| ~ spl60_86
| ~ spl60_87 ),
inference(forward_demodulation,[],[f14357,f1269]) ).
thf(f14385,plain,
( $false
| ~ spl60_81
| ~ spl60_86
| ~ spl60_87 ),
inference(trivial_inequality_removal,[],[f14384]) ).
thf(f14386,plain,
( ~ spl60_81
| ~ spl60_86
| ~ spl60_87 ),
inference(avatar_contradiction_clause,[],[f14385]) ).
thf(f14423,plain,
( ( $true = $false )
| ~ spl60_81
| ~ spl60_98
| ~ spl60_99 ),
inference(forward_demodulation,[],[f14353,f1335]) ).
thf(f14424,plain,
( $false
| ~ spl60_81
| ~ spl60_98
| ~ spl60_99 ),
inference(trivial_inequality_removal,[],[f14423]) ).
thf(f14425,plain,
( ~ spl60_81
| ~ spl60_98
| ~ spl60_99 ),
inference(avatar_contradiction_clause,[],[f14424]) ).
cnf(s2,plain,
( spl60_1
| spl60_2 ),
inference(sat_conversion,[],[f887]) ).
cnf(s4,plain,
( spl60_2
| spl60_3 ),
inference(sat_conversion,[],[f891]) ).
cnf(s6,plain,
( spl60_1
| spl60_4 ),
inference(sat_conversion,[],[f895]) ).
cnf(s8,plain,
( spl60_3
| spl60_4 ),
inference(sat_conversion,[],[f896]) ).
cnf(s10,plain,
( spl60_5
| spl60_6 ),
inference(sat_conversion,[],[f903]) ).
cnf(s12,plain,
( spl60_6
| spl60_7 ),
inference(sat_conversion,[],[f907]) ).
cnf(s14,plain,
( spl60_5
| spl60_8 ),
inference(sat_conversion,[],[f911]) ).
cnf(s16,plain,
( spl60_7
| spl60_8 ),
inference(sat_conversion,[],[f912]) ).
cnf(s18,plain,
( spl60_9
| spl60_10 ),
inference(sat_conversion,[],[f919]) ).
cnf(s20,plain,
( spl60_10
| spl60_11 ),
inference(sat_conversion,[],[f923]) ).
cnf(s22,plain,
( spl60_9
| spl60_12 ),
inference(sat_conversion,[],[f927]) ).
cnf(s24,plain,
( spl60_11
| spl60_12 ),
inference(sat_conversion,[],[f928]) ).
cnf(s118,plain,
( spl60_51
| spl60_53 ),
inference(sat_conversion,[],[f1110]) ).
cnf(s120,plain,
( spl60_51
| spl60_54 ),
inference(sat_conversion,[],[f1114]) ).
cnf(s194,plain,
( spl60_51
| spl60_79 ),
inference(sat_conversion,[],[f1233]) ).
cnf(s196,plain,
( spl60_51
| spl60_80
| spl60_81 ),
inference(sat_conversion,[],[f1240]) ).
cnf(s198,plain,
( spl60_51
| spl60_81
| spl60_82 ),
inference(sat_conversion,[],[f1245]) ).
cnf(s200,plain,
( spl60_51
| spl60_81
| spl60_83 ),
inference(sat_conversion,[],[f1250]) ).
cnf(s206,plain,
( spl60_51
| spl60_84
| spl60_86 ),
inference(sat_conversion,[],[f1265]) ).
cnf(s208,plain,
( spl60_51
| spl60_84
| spl60_87 ),
inference(sat_conversion,[],[f1270]) ).
cnf(s210,plain,
( spl60_51
| spl60_85
| spl60_86 ),
inference(sat_conversion,[],[f1271]) ).
cnf(s212,plain,
( spl60_51
| spl60_85
| spl60_87 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s214,plain,
( spl60_55
| spl60_57
| spl60_79 ),
inference(sat_conversion,[],[f1273]) ).
cnf(s216,plain,
( spl60_57
| spl60_79
| spl60_88 ),
inference(sat_conversion,[],[f1278]) ).
cnf(s218,plain,
( spl60_57
| spl60_79
| spl60_89 ),
inference(sat_conversion,[],[f1283]) ).
cnf(s220,plain,
( spl60_55
| spl60_57
| spl60_80
| spl60_81 ),
inference(sat_conversion,[],[f1284]) ).
cnf(s222,plain,
( spl60_55
| spl60_57
| spl60_81
| spl60_90 ),
inference(sat_conversion,[],[f1289]) ).
cnf(s224,plain,
( spl60_55
| spl60_57
| spl60_81
| spl60_91 ),
inference(sat_conversion,[],[f1294]) ).
cnf(s226,plain,
( spl60_57
| spl60_80
| spl60_81
| spl60_92 ),
inference(sat_conversion,[],[f1299]) ).
cnf(s228,plain,
( spl60_57
| spl60_80
| spl60_81
| spl60_93 ),
inference(sat_conversion,[],[f1304]) ).
cnf(s240,plain,
( spl60_55
| spl60_57
| spl60_80
| spl60_97 ),
inference(sat_conversion,[],[f1326]) ).
cnf(s242,plain,
( spl60_55
| spl60_57
| spl60_96
| spl60_98 ),
inference(sat_conversion,[],[f1331]) ).
cnf(s244,plain,
( spl60_55
| spl60_57
| spl60_96
| spl60_99 ),
inference(sat_conversion,[],[f1336]) ).
cnf(s246,plain,
( spl60_55
| spl60_57
| spl60_97
| spl60_98 ),
inference(sat_conversion,[],[f1337]) ).
cnf(s248,plain,
( spl60_55
| spl60_57
| spl60_97
| spl60_99 ),
inference(sat_conversion,[],[f1338]) ).
cnf(s250,plain,
( spl60_57
| spl60_80
| spl60_96
| spl60_100 ),
inference(sat_conversion,[],[f1343]) ).
cnf(s252,plain,
( spl60_57
| spl60_80
| spl60_96
| spl60_101 ),
inference(sat_conversion,[],[f1348]) ).
cnf(s258,plain,
( spl60_57
| spl60_96
| spl60_100
| spl60_102 ),
inference(sat_conversion,[],[f1355]) ).
cnf(s260,plain,
( spl60_57
| spl60_96
| spl60_100
| spl60_103 ),
inference(sat_conversion,[],[f1360]) ).
cnf(s262,plain,
( spl60_57
| spl60_96
| spl60_101
| spl60_102 ),
inference(sat_conversion,[],[f1361]) ).
cnf(s264,plain,
( spl60_57
| spl60_96
| spl60_101
| spl60_103 ),
inference(sat_conversion,[],[f1362]) ).
cnf(s266,plain,
( spl60_57
| spl60_97
| spl60_100
| spl60_102 ),
inference(sat_conversion,[],[f1363]) ).
cnf(s268,plain,
( spl60_57
| spl60_97
| spl60_100
| spl60_103 ),
inference(sat_conversion,[],[f1364]) ).
cnf(s270,plain,
( spl60_57
| spl60_97
| spl60_101
| spl60_102 ),
inference(sat_conversion,[],[f1365]) ).
cnf(s272,plain,
( spl60_57
| spl60_97
| spl60_101
| spl60_103 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s274,plain,
( spl60_55
| spl60_79
| spl60_104 ),
inference(sat_conversion,[],[f1371]) ).
cnf(s276,plain,
( spl60_55
| spl60_79
| spl60_105 ),
inference(sat_conversion,[],[f1376]) ).
cnf(s278,plain,
( spl60_79
| spl60_104
| spl60_106 ),
inference(sat_conversion,[],[f1381]) ).
cnf(s280,plain,
( spl60_79
| spl60_104
| spl60_107 ),
inference(sat_conversion,[],[f1386]) ).
cnf(s282,plain,
( spl60_79
| spl60_105
| spl60_106 ),
inference(sat_conversion,[],[f1387]) ).
cnf(s284,plain,
( spl60_79
| spl60_105
| spl60_107 ),
inference(sat_conversion,[],[f1388]) ).
cnf(s286,plain,
( spl60_55
| spl60_80
| spl60_81
| spl60_104 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s288,plain,
( spl60_55
| spl60_80
| spl60_81
| spl60_105 ),
inference(sat_conversion,[],[f1390]) ).
cnf(s290,plain,
( spl60_55
| spl60_81
| spl60_104
| spl60_108 ),
inference(sat_conversion,[],[f1395]) ).
cnf(s292,plain,
( spl60_55
| spl60_81
| spl60_104
| spl60_109 ),
inference(sat_conversion,[],[f1400]) ).
cnf(s294,plain,
( spl60_55
| spl60_81
| spl60_105
| spl60_108 ),
inference(sat_conversion,[],[f1401]) ).
cnf(s296,plain,
( spl60_55
| spl60_81
| spl60_105
| spl60_109 ),
inference(sat_conversion,[],[f1402]) ).
cnf(s298,plain,
( spl60_80
| spl60_81
| spl60_104
| spl60_110 ),
inference(sat_conversion,[],[f1407]) ).
cnf(s300,plain,
( spl60_80
| spl60_81
| spl60_104
| spl60_111 ),
inference(sat_conversion,[],[f1412]) ).
cnf(s302,plain,
( spl60_80
| spl60_81
| spl60_105
| spl60_110 ),
inference(sat_conversion,[],[f1413]) ).
cnf(s304,plain,
( spl60_80
| spl60_81
| spl60_105
| spl60_111 ),
inference(sat_conversion,[],[f1414]) ).
cnf(s322,plain,
( spl60_55
| spl60_80
| spl60_104
| spl60_114 ),
inference(sat_conversion,[],[f1435]) ).
cnf(s324,plain,
( spl60_55
| spl60_80
| spl60_104
| spl60_115 ),
inference(sat_conversion,[],[f1440]) ).
cnf(s326,plain,
( spl60_55
| spl60_80
| spl60_105
| spl60_114 ),
inference(sat_conversion,[],[f1441]) ).
cnf(s328,plain,
( spl60_55
| spl60_80
| spl60_105
| spl60_115 ),
inference(sat_conversion,[],[f1442]) ).
cnf(s330,plain,
( spl60_55
| spl60_104
| spl60_114
| spl60_116 ),
inference(sat_conversion,[],[f1447]) ).
cnf(s332,plain,
( spl60_55
| spl60_104
| spl60_114
| spl60_117 ),
inference(sat_conversion,[],[f1452]) ).
cnf(s334,plain,
( spl60_55
| spl60_104
| spl60_115
| spl60_116 ),
inference(sat_conversion,[],[f1453]) ).
cnf(s336,plain,
( spl60_55
| spl60_104
| spl60_115
| spl60_117 ),
inference(sat_conversion,[],[f1454]) ).
cnf(s338,plain,
( spl60_55
| spl60_105
| spl60_114
| spl60_116 ),
inference(sat_conversion,[],[f1455]) ).
cnf(s340,plain,
( spl60_55
| spl60_105
| spl60_114
| spl60_117 ),
inference(sat_conversion,[],[f1456]) ).
cnf(s342,plain,
( spl60_55
| spl60_105
| spl60_115
| spl60_116 ),
inference(sat_conversion,[],[f1457]) ).
cnf(s344,plain,
( spl60_55
| spl60_105
| spl60_115
| spl60_117 ),
inference(sat_conversion,[],[f1458]) ).
cnf(s346,plain,
( spl60_80
| spl60_104
| spl60_114
| spl60_118 ),
inference(sat_conversion,[],[f1463]) ).
cnf(s348,plain,
( spl60_80
| spl60_104
| spl60_114
| spl60_119 ),
inference(sat_conversion,[],[f1468]) ).
cnf(s354,plain,
( spl60_80
| spl60_105
| spl60_114
| spl60_118 ),
inference(sat_conversion,[],[f1471]) ).
cnf(s356,plain,
( spl60_80
| spl60_105
| spl60_114
| spl60_119 ),
inference(sat_conversion,[],[f1472]) ).
cnf(s362,plain,
( spl60_104
| spl60_114
| spl60_118
| spl60_120 ),
inference(sat_conversion,[],[f1479]) ).
cnf(s364,plain,
( spl60_104
| spl60_114
| spl60_118
| spl60_121 ),
inference(sat_conversion,[],[f1484]) ).
cnf(s366,plain,
( spl60_104
| spl60_114
| spl60_119
| spl60_120 ),
inference(sat_conversion,[],[f1485]) ).
cnf(s368,plain,
( spl60_104
| spl60_114
| spl60_119
| spl60_121 ),
inference(sat_conversion,[],[f1486]) ).
cnf(s370,plain,
( spl60_104
| spl60_115
| spl60_118
| spl60_120 ),
inference(sat_conversion,[],[f1487]) ).
cnf(s372,plain,
( spl60_104
| spl60_115
| spl60_118
| spl60_121 ),
inference(sat_conversion,[],[f1488]) ).
cnf(s374,plain,
( spl60_104
| spl60_115
| spl60_119
| spl60_120 ),
inference(sat_conversion,[],[f1489]) ).
cnf(s376,plain,
( spl60_104
| spl60_115
| spl60_119
| spl60_121 ),
inference(sat_conversion,[],[f1490]) ).
cnf(s378,plain,
( spl60_105
| spl60_114
| spl60_118
| spl60_120 ),
inference(sat_conversion,[],[f1491]) ).
cnf(s380,plain,
( spl60_105
| spl60_114
| spl60_118
| spl60_121 ),
inference(sat_conversion,[],[f1492]) ).
cnf(s382,plain,
( spl60_105
| spl60_114
| spl60_119
| spl60_120 ),
inference(sat_conversion,[],[f1493]) ).
cnf(s384,plain,
( spl60_105
| spl60_114
| spl60_119
| spl60_121 ),
inference(sat_conversion,[],[f1494]) ).
cnf(s386,plain,
( spl60_105
| spl60_115
| spl60_118
| spl60_120 ),
inference(sat_conversion,[],[f1495]) ).
cnf(s388,plain,
( spl60_105
| spl60_115
| spl60_118
| spl60_121 ),
inference(sat_conversion,[],[f1496]) ).
cnf(s390,plain,
( spl60_105
| spl60_115
| spl60_119
| spl60_120 ),
inference(sat_conversion,[],[f1497]) ).
cnf(s392,plain,
( spl60_105
| spl60_115
| spl60_119
| spl60_121 ),
inference(sat_conversion,[],[f1498]) ).
cnf(s639,plain,
( ~ spl60_4
| ~ spl60_104
| ~ spl60_105
| spl60_130
| spl60_131 ),
inference(sat_conversion,[],[f1829]) ).
cnf(s1015,plain,
( ~ spl60_81
| ~ spl60_102
| ~ spl60_103 ),
inference(sat_conversion,[],[f3328]) ).
cnf(s1052,plain,
( ~ spl60_4
| ~ spl60_79
| ~ spl60_102
| ~ spl60_103
| spl60_134 ),
inference(sat_conversion,[],[f3422]) ).
cnf(s1109,plain,
( ~ spl60_80
| ~ spl60_114
| ~ spl60_115 ),
inference(sat_conversion,[],[f3648]) ).
cnf(s1113,plain,
( ~ spl60_80
| ~ spl60_84
| ~ spl60_85 ),
inference(sat_conversion,[],[f3651]) ).
cnf(s1292,plain,
( ~ spl60_53
| ~ spl60_79
| ~ spl60_80
| spl60_81
| spl60_168 ),
inference(sat_conversion,[],[f4479]) ).
cnf(s1313,plain,
( ~ spl60_2
| ~ spl60_79
| ~ spl60_80
| spl60_81
| ~ spl60_134 ),
inference(sat_conversion,[],[f4596]) ).
cnf(s1337,plain,
( ~ spl60_1
| ~ spl60_51
| ~ spl60_55
| spl60_57
| spl60_169 ),
inference(sat_conversion,[],[f4784]) ).
cnf(s1360,plain,
( ~ spl60_5
| ~ spl60_79
| ~ spl60_80
| spl60_81
| ~ spl60_155 ),
inference(sat_conversion,[],[f4908]) ).
cnf(s1376,plain,
( ~ spl60_5
| ~ spl60_79
| ~ spl60_80
| spl60_81
| spl60_170 ),
inference(sat_conversion,[],[f4933]) ).
cnf(s1382,plain,
( ~ spl60_7
| ~ spl60_79
| ~ spl60_120
| ~ spl60_121
| spl60_155 ),
inference(sat_conversion,[],[f4935]) ).
cnf(s1490,plain,
( ~ spl60_12
| ~ spl60_51
| ~ spl60_92
| ~ spl60_93
| spl60_150 ),
inference(sat_conversion,[],[f5187]) ).
cnf(s1718,plain,
( ~ spl60_11
| ~ spl60_51
| ~ spl60_110
| spl60_192
| spl60_193 ),
inference(sat_conversion,[],[f6064]) ).
cnf(s1785,plain,
( ~ spl60_9
| ~ spl60_79
| spl60_80
| ~ spl60_81
| spl60_194 ),
inference(sat_conversion,[],[f6517]) ).
cnf(s1787,plain,
( ~ spl60_9
| ~ spl60_51
| ~ spl60_55
| spl60_57
| ~ spl60_193 ),
inference(sat_conversion,[],[f6520]) ).
cnf(s1826,plain,
( ~ spl60_10
| ~ spl60_51
| ~ spl60_55
| spl60_57
| spl60_195 ),
inference(sat_conversion,[],[f6757]) ).
cnf(s1828,plain,
( ~ spl60_10
| ~ spl60_79
| spl60_80
| ~ spl60_81
| ~ spl60_162 ),
inference(sat_conversion,[],[f6758]) ).
cnf(s1836,plain,
( ~ spl60_10
| ~ spl60_79
| spl60_80
| ~ spl60_81
| spl60_196 ),
inference(sat_conversion,[],[f6782]) ).
cnf(s1838,plain,
( ~ spl60_12
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115
| spl60_162 ),
inference(sat_conversion,[],[f6783]) ).
cnf(s1840,plain,
( ~ spl60_12
| ~ spl60_79
| ~ spl60_96
| ~ spl60_97
| spl60_162 ),
inference(sat_conversion,[],[f6784]) ).
cnf(s1877,plain,
( ~ spl60_9
| ~ spl60_51
| ~ spl60_55
| spl60_57
| spl60_197 ),
inference(sat_conversion,[],[f6910]) ).
cnf(s2007,plain,
( ~ spl60_11
| ~ spl60_79
| ~ spl60_96
| ~ spl60_194
| spl60_201 ),
inference(sat_conversion,[],[f7502]) ).
cnf(s2074,plain,
( ~ spl60_11
| ~ spl60_51
| ~ spl60_100
| ~ spl60_101
| spl60_193 ),
inference(sat_conversion,[],[f7709]) ).
cnf(s2217,plain,
( ~ spl60_150
| ~ spl60_195 ),
inference(sat_conversion,[],[f7906]) ).
cnf(s2252,plain,
( ~ spl60_97
| ~ spl60_201 ),
inference(sat_conversion,[],[f7927]) ).
cnf(s2272,plain,
( ~ spl60_111
| ~ spl60_192 ),
inference(sat_conversion,[],[f7946]) ).
cnf(s2363,plain,
( ~ spl60_7
| ~ spl60_51
| ~ spl60_104
| ~ spl60_105
| spl60_182 ),
inference(sat_conversion,[],[f8182]) ).
cnf(s2405,plain,
( ~ spl60_55
| ~ spl60_104
| ~ spl60_105 ),
inference(sat_conversion,[],[f8417]) ).
cnf(s2435,plain,
( ~ spl60_57
| ~ spl60_118
| ~ spl60_119 ),
inference(sat_conversion,[],[f8497]) ).
cnf(s2436,plain,
( ~ spl60_57
| ~ spl60_110
| ~ spl60_111 ),
inference(sat_conversion,[],[f8500]) ).
cnf(s2451,plain,
( ~ spl60_5
| ~ spl60_51
| spl60_55
| ~ spl60_57
| ~ spl60_182 ),
inference(sat_conversion,[],[f8537]) ).
cnf(s2453,plain,
( ~ spl60_2
| ~ spl60_51
| spl60_55
| ~ spl60_57
| ~ spl60_130 ),
inference(sat_conversion,[],[f8538]) ).
cnf(s2760,plain,
( ~ spl60_6
| ~ spl60_51
| spl60_55
| ~ spl60_57
| spl60_232 ),
inference(sat_conversion,[],[f10442]) ).
cnf(s2783,plain,
( ~ spl60_115
| ~ spl60_224 ),
inference(sat_conversion,[],[f10457]) ).
cnf(s2813,plain,
( ~ spl60_11
| ~ spl60_79
| ~ spl60_114
| ~ spl60_115
| ~ spl60_194 ),
inference(sat_conversion,[],[f10686]) ).
cnf(s2841,plain,
( ~ spl60_12
| ~ spl60_79
| ~ spl60_114
| spl60_162
| spl60_224 ),
inference(sat_conversion,[],[f10714]) ).
cnf(s2851,plain,
( ~ spl60_105
| ~ spl60_233 ),
inference(sat_conversion,[],[f10722]) ).
cnf(s2853,plain,
( ~ spl60_8
| ~ spl60_104
| ~ spl60_105
| spl60_131
| ~ spl60_232 ),
inference(sat_conversion,[],[f10751]) ).
cnf(s2886,plain,
( ~ spl60_12
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_196 ),
inference(sat_conversion,[],[f10927]) ).
cnf(s2929,plain,
( ~ spl60_11
| ~ spl60_79
| ~ spl60_84
| ~ spl60_85
| ~ spl60_194 ),
inference(sat_conversion,[],[f11181]) ).
cnf(s2931,plain,
( ~ spl60_51
| ~ spl60_131 ),
inference(sat_conversion,[],[f11184]) ).
cnf(s2962,plain,
( ~ spl60_12
| ~ spl60_84
| ~ spl60_85
| spl60_162
| spl60_241 ),
inference(sat_conversion,[],[f11218]) ).
cnf(s2981,plain,
( ~ spl60_8
| ~ spl60_104
| spl60_131
| ~ spl60_232
| spl60_233 ),
inference(sat_conversion,[],[f11229]) ).
cnf(s3013,plain,
( ~ spl60_57
| ~ spl60_106
| ~ spl60_107 ),
inference(sat_conversion,[],[f11474]) ).
cnf(s3035,plain,
( ~ spl60_11
| ~ spl60_51
| ~ spl60_106
| ~ spl60_107
| ~ spl60_197 ),
inference(sat_conversion,[],[f11562]) ).
cnf(s3080,plain,
( ~ spl60_3
| ~ spl60_51
| ~ spl60_118
| ~ spl60_169
| spl60_244 ),
inference(sat_conversion,[],[f11672]) ).
cnf(s3088,plain,
( ~ spl60_12
| ~ spl60_51
| ~ spl60_118
| ~ spl60_195
| spl60_244 ),
inference(sat_conversion,[],[f11674]) ).
cnf(s3125,plain,
( ~ spl60_119
| ~ spl60_244 ),
inference(sat_conversion,[],[f11698]) ).
cnf(s3136,plain,
( ~ spl60_81
| ~ spl60_120
| ~ spl60_121 ),
inference(sat_conversion,[],[f11730]) ).
cnf(s3140,plain,
( ~ spl60_8
| ~ spl60_120
| ~ spl60_121
| spl60_241
| spl60_249 ),
inference(sat_conversion,[],[f11744]) ).
cnf(s3179,plain,
( ~ spl60_4
| ~ spl60_120
| ~ spl60_121
| spl60_134
| spl60_241 ),
inference(sat_conversion,[],[f11782]) ).
cnf(s3265,plain,
( ~ spl60_12
| ~ spl60_51
| ~ spl60_88
| ~ spl60_89
| ~ spl60_195 ),
inference(sat_conversion,[],[f12170]) ).
cnf(s3352,plain,
( ~ spl60_79
| ~ spl60_241 ),
inference(sat_conversion,[],[f12603]) ).
cnf(s3356,plain,
( ~ spl60_80
| ~ spl60_96
| ~ spl60_97 ),
inference(sat_conversion,[],[f12656]) ).
cnf(s3362,plain,
( ~ spl60_6
| ~ spl60_79
| ~ spl60_80
| spl60_81
| ~ spl60_249 ),
inference(sat_conversion,[],[f12671]) ).
cnf(s3534,plain,
( ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91
| ~ spl60_170 ),
inference(sat_conversion,[],[f13517]) ).
cnf(s3560,plain,
( ~ spl60_7
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109
| spl60_155 ),
inference(sat_conversion,[],[f13581]) ).
cnf(s3564,plain,
( ~ spl60_7
| ~ spl60_79
| ~ spl60_90
| ~ spl60_91
| spl60_155 ),
inference(sat_conversion,[],[f13583]) ).
cnf(s3578,plain,
( ~ spl60_8
| ~ spl60_79
| ~ spl60_98
| ~ spl60_99
| spl60_249 ),
inference(sat_conversion,[],[f13585]) ).
cnf(s3582,plain,
( ~ spl60_8
| ~ spl60_79
| ~ spl60_108
| ~ spl60_109
| spl60_249 ),
inference(sat_conversion,[],[f13586]) ).
cnf(s3653,plain,
( ~ spl60_8
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83
| spl60_249 ),
inference(sat_conversion,[],[f13733]) ).
cnf(s3672,plain,
( ~ spl60_54
| ~ spl60_79
| ~ spl60_82
| ~ spl60_83
| ~ spl60_168 ),
inference(sat_conversion,[],[f14053]) ).
cnf(s3769,plain,
( ~ spl60_81
| ~ spl60_116
| ~ spl60_117 ),
inference(sat_conversion,[],[f14377]) ).
cnf(s3772,plain,
( ~ spl60_81
| ~ spl60_86
| ~ spl60_87 ),
inference(sat_conversion,[],[f14386]) ).
cnf(s3815,plain,
( ~ spl60_81
| ~ spl60_98
| ~ spl60_99 ),
inference(sat_conversion,[],[f14425]) ).
cnf(s3817,plain,
( spl60_79
| spl60_130
| spl60_55
| spl60_131
| ~ spl60_4 ),
inference(rat,[],[s639,s274,s276]) ).
cnf(s3818,plain,
( spl60_80
| spl60_105
| ~ spl60_79
| spl60_55
| spl60_9 ),
inference(rat,[],[s1828,s1838,s288,s326,s328,s22,s18]) ).
cnf(s3819,plain,
( spl60_115
| ~ spl60_81
| spl60_105
| spl60_55 ),
inference(rat,[],[s3769,s342,s344]) ).
cnf(s3820,plain,
( ~ spl60_81
| ~ spl60_80
| spl60_105
| spl60_55 ),
inference(rat,[],[s3769,s338,s340,s1109,s3819]) ).
cnf(s3821,plain,
( spl60_105
| ~ spl60_79
| spl60_55
| spl60_9
| spl60_5 ),
inference(rat,[],[s3582,s3362,s294,s296,s3820,s3818,s14,s10]) ).
cnf(s3822,plain,
( spl60_115
| ~ spl60_81
| spl60_104
| spl60_55 ),
inference(rat,[],[s3769,s334,s336]) ).
cnf(s3823,plain,
( ~ spl60_81
| ~ spl60_80
| spl60_104
| spl60_55 ),
inference(rat,[],[s3769,s330,s332,s1109,s3822]) ).
cnf(s3824,plain,
( ~ spl60_80
| spl60_104
| ~ spl60_79
| spl60_55
| spl60_5 ),
inference(rat,[],[s3582,s3362,s290,s292,s3823,s14,s10]) ).
cnf(s3825,plain,
( spl60_130
| spl60_55
| spl60_131
| spl60_9
| spl60_5
| ~ spl60_4 ),
inference(rat,[],[s1828,s1838,s286,s322,s324,s3824,s639,s3821,s3817,s22,s18]) ).
cnf(s3826,plain,
( spl60_96
| spl60_249
| spl60_57
| spl60_55
| ~ spl60_8 ),
inference(rat,[],[s3578,s242,s244,s214]) ).
cnf(s3827,plain,
( spl60_249
| ~ spl60_80
| spl60_57
| spl60_55
| ~ spl60_8 ),
inference(rat,[],[s3578,s246,s248,s3356,s3826,s214]) ).
cnf(s3828,plain,
( spl60_96
| ~ spl60_81
| spl60_57
| spl60_55 ),
inference(rat,[],[s3815,s242,s244]) ).
cnf(s3829,plain,
( ~ spl60_81
| ~ spl60_80
| spl60_57
| spl60_55 ),
inference(rat,[],[s3815,s246,s248,s3356,s3828]) ).
cnf(s3830,plain,
( ~ spl60_80
| spl60_57
| spl60_55
| spl60_5 ),
inference(rat,[],[s3362,s3829,s3827,s14,s10,s214]) ).
cnf(s3832,plain,
( spl60_100
| spl60_97
| ~ spl60_81
| spl60_57 ),
inference(rat,[],[s1015,s266,s268]) ).
cnf(s3834,plain,
( spl60_100
| spl60_96
| ~ spl60_81
| spl60_57 ),
inference(rat,[],[s1015,s258,s260]) ).
cnf(s3837,plain,
( spl60_100
| spl60_97
| spl60_134
| ~ spl60_79
| spl60_57
| ~ spl60_4 ),
inference(rat,[],[s1052,s266,s268]) ).
cnf(s3839,plain,
( spl60_100
| spl60_96
| spl60_134
| ~ spl60_79
| spl60_57
| ~ spl60_4 ),
inference(rat,[],[s1052,s258,s260]) ).
cnf(s3843,plain,
( spl60_118
| spl60_115
| spl60_105
| ~ spl60_81 ),
inference(rat,[],[s3136,s386,s388]) ).
cnf(s3844,plain,
( spl60_115
| spl60_105
| ~ spl60_81
| ~ spl60_57 ),
inference(rat,[],[s3136,s390,s392,s2435,s3843]) ).
cnf(s3845,plain,
( spl60_118
| spl60_114
| spl60_105
| ~ spl60_81 ),
inference(rat,[],[s3136,s378,s380]) ).
cnf(s3846,plain,
( spl60_105
| ~ spl60_80
| ~ spl60_81
| ~ spl60_57 ),
inference(rat,[],[s3136,s382,s384,s2435,s3845,s1109,s3844]) ).
cnf(s3847,plain,
( spl60_118
| spl60_115
| spl60_104
| ~ spl60_81 ),
inference(rat,[],[s3136,s370,s372]) ).
cnf(s3848,plain,
( spl60_115
| spl60_104
| ~ spl60_81
| ~ spl60_57 ),
inference(rat,[],[s3136,s374,s376,s2435,s3847]) ).
cnf(s3849,plain,
( spl60_118
| spl60_114
| spl60_104
| ~ spl60_81 ),
inference(rat,[],[s3136,s362,s364]) ).
cnf(s3850,plain,
( ~ spl60_80
| ~ spl60_81
| ~ spl60_57
| ~ spl60_55 ),
inference(rat,[],[s3136,s366,s368,s2435,s3849,s1109,s3848,s2405,s3846]) ).
cnf(s3851,plain,
( ~ spl60_79
| ~ spl60_114
| ~ spl60_115
| spl60_80
| ~ spl60_81
| spl60_9 ),
inference(rat,[],[s1838,s1828,s22,s18]) ).
cnf(s3852,plain,
( spl60_79
| spl60_105
| ~ spl60_57 ),
inference(rat,[],[s3013,s282,s284]) ).
cnf(s3853,plain,
( spl60_105
| spl60_80
| ~ spl60_81
| ~ spl60_57
| spl60_9 ),
inference(rat,[],[s2435,s354,s356,s3851,s3852,s3844]) ).
cnf(s3854,plain,
( spl60_79
| spl60_104
| ~ spl60_57 ),
inference(rat,[],[s3013,s278,s280]) ).
cnf(s3855,plain,
( ~ spl60_81
| ~ spl60_57
| ~ spl60_55
| spl60_9 ),
inference(rat,[],[s2435,s346,s348,s3851,s3854,s3848,s2405,s3853,s3850]) ).
cnf(s3856,plain,
( spl60_118
| spl60_115
| spl60_249
| spl60_241
| spl60_105
| ~ spl60_8 ),
inference(rat,[],[s3140,s386,s388]) ).
cnf(s3857,plain,
( spl60_115
| spl60_249
| spl60_105
| ~ spl60_57
| ~ spl60_8 ),
inference(rat,[],[s3140,s390,s392,s2435,s3856,s3352,s3852]) ).
cnf(s3858,plain,
( spl60_118
| spl60_114
| spl60_249
| spl60_241
| spl60_105
| ~ spl60_8 ),
inference(rat,[],[s3140,s378,s380]) ).
cnf(s3859,plain,
( spl60_105
| ~ spl60_80
| spl60_81
| ~ spl60_57
| spl60_5 ),
inference(rat,[],[s3140,s382,s384,s2435,s3858,s1109,s3857,s3362,s3352,s3852,s14,s10]) ).
cnf(s3860,plain,
( spl60_118
| spl60_115
| spl60_249
| spl60_241
| spl60_104
| ~ spl60_8 ),
inference(rat,[],[s3140,s370,s372]) ).
cnf(s3861,plain,
( spl60_115
| spl60_249
| spl60_104
| ~ spl60_57
| ~ spl60_8 ),
inference(rat,[],[s3140,s374,s376,s2435,s3860,s3352,s3854]) ).
cnf(s3862,plain,
( spl60_118
| spl60_114
| spl60_249
| spl60_241
| spl60_104
| ~ spl60_8 ),
inference(rat,[],[s3140,s362,s364]) ).
cnf(s3863,plain,
( ~ spl60_80
| spl60_81
| ~ spl60_57
| ~ spl60_55
| spl60_5 ),
inference(rat,[],[s3140,s366,s368,s2435,s3862,s1109,s3861,s3362,s3352,s3854,s2405,s3859,s14,s10]) ).
cnf(s3864,plain,
( spl60_105
| spl60_80
| spl60_81
| ~ spl60_57 ),
inference(rat,[],[s2436,s302,s304]) ).
cnf(s3865,plain,
( spl60_81
| ~ spl60_57
| spl60_5
| ~ spl60_55 ),
inference(rat,[],[s2436,s298,s300,s2405,s3864,s3863]) ).
cnf(s3867,plain,
( spl60_84
| ~ spl60_81
| spl60_51 ),
inference(rat,[],[s3772,s206,s208]) ).
cnf(s3868,plain,
( spl60_85
| ~ spl60_81
| spl60_51 ),
inference(rat,[],[s3772,s210,s212]) ).
cnf(s3871,plain,
( ~ spl60_57
| ~ spl60_81
| ~ spl60_51
| spl60_9
| spl60_5
| spl60_1 ),
inference(rat,[],[s2453,s3825,s3855,s6,s2,s2931]) ).
cnf(s3873,plain,
( ~ spl60_79
| ~ spl60_96
| ~ spl60_97
| spl60_80
| ~ spl60_81
| spl60_9 ),
inference(rat,[],[s1840,s1828,s22,s18]) ).
cnf(s3880,plain,
( spl60_115
| spl60_105
| ~ spl60_195
| ~ spl60_51
| ~ spl60_81
| ~ spl60_12 ),
inference(rat,[],[s3136,s390,s392,s3125,s3088,s3843]) ).
cnf(s3881,plain,
( spl60_105
| ~ spl60_195
| ~ spl60_80
| ~ spl60_51
| ~ spl60_81
| ~ spl60_12 ),
inference(rat,[],[s3136,s382,s384,s3125,s3088,s3845,s1109,s3880]) ).
cnf(s3882,plain,
( spl60_115
| spl60_104
| ~ spl60_195
| ~ spl60_51
| ~ spl60_81
| ~ spl60_12 ),
inference(rat,[],[s3136,s374,s376,s3125,s3088,s3847]) ).
cnf(s3883,plain,
( ~ spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| spl60_9
| spl60_5 ),
inference(rat,[],[s3136,s366,s368,s3125,s3088,s3849,s1109,s3882,s2405,s3881,s1826,s3830,s22,s18]) ).
cnf(s3884,plain,
( spl60_79
| ~ spl60_195
| spl60_57
| ~ spl60_51
| ~ spl60_12 ),
inference(rat,[],[s3265,s216,s218]) ).
cnf(s3885,plain,
( spl60_105
| ~ spl60_79
| ~ spl60_195
| spl60_80
| ~ spl60_51
| ~ spl60_81
| spl60_9 ),
inference(rat,[],[s3088,s3125,s354,s356,s3851,s3880,s22]) ).
cnf(s3886,plain,
( ~ spl60_55
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| spl60_9 ),
inference(rat,[],[s3088,s3125,s346,s348,s3851,s3882,s2405,s3885,s3884,s1826,s22,s18]) ).
cnf(s3887,plain,
( spl60_80
| spl60_57
| spl60_9
| ~ spl60_51
| ~ spl60_81 ),
inference(rat,[],[s3873,s240,s214,s3828,s3886]) ).
cnf(s3888,plain,
( spl60_57
| ~ spl60_51
| spl60_5
| ~ spl60_81
| spl60_9 ),
inference(rat,[],[s3887,s3883]) ).
cnf(s3889,plain,
( ~ spl60_51
| ~ spl60_81
| spl60_1
| spl60_9
| spl60_5 ),
inference(rat,[],[s3888,s3871]) ).
cnf(s3890,plain,
( ~ spl60_81
| spl60_9
| spl60_5
| spl60_1 ),
inference(rat,[],[s1828,s1113,s2962,s3352,s3868,s3867,s194,s3889,s22,s18]) ).
cnf(s3891,plain,
( ~ spl60_57
| ~ spl60_51
| spl60_9
| spl60_5
| spl60_1 ),
inference(rat,[],[s2453,s3825,s3865,s6,s2,s3890,s2931]) ).
cnf(s3892,plain,
( spl60_115
| spl60_105
| spl60_249
| spl60_241
| ~ spl60_195
| ~ spl60_51
| ~ spl60_12
| ~ spl60_8 ),
inference(rat,[],[s3140,s390,s392,s3125,s3088,s3856]) ).
cnf(s3893,plain,
( spl60_105
| spl60_249
| spl60_241
| ~ spl60_195
| ~ spl60_80
| ~ spl60_51
| ~ spl60_12
| ~ spl60_8 ),
inference(rat,[],[s3140,s382,s384,s3125,s3088,s3858,s1109,s3892]) ).
cnf(s3894,plain,
( spl60_115
| spl60_104
| spl60_249
| spl60_241
| ~ spl60_195
| ~ spl60_51
| ~ spl60_12
| ~ spl60_8 ),
inference(rat,[],[s3140,s374,s376,s3125,s3088,s3860]) ).
cnf(s3895,plain,
( ~ spl60_80
| spl60_57
| ~ spl60_51
| spl60_81
| ~ spl60_10
| ~ spl60_12
| spl60_5 ),
inference(rat,[],[s3140,s366,s368,s3125,s3088,s3862,s1109,s3894,s2405,s3893,s3362,s3352,s3884,s1826,s3830,s14,s10]) ).
cnf(s3896,plain,
( spl60_57
| ~ spl60_51
| spl60_5
| spl60_81
| ~ spl60_10
| ~ spl60_12 ),
inference(rat,[],[s2217,s1490,s1826,s226,s228,s220,s3895]) ).
cnf(s3897,plain,
( ~ spl60_51
| spl60_9
| spl60_5
| spl60_1 ),
inference(rat,[],[s3896,s3891,s22,s18,s3890]) ).
cnf(s3898,plain,
( spl60_9
| spl60_5
| spl60_1 ),
inference(rat,[],[s3653,s3362,s196,s198,s200,s194,s3897,s3890,s14,s10]) ).
cnf(s3899,plain,
( ~ spl60_80
| ~ spl60_57
| ~ spl60_51
| ~ spl60_81
| spl60_5 ),
inference(rat,[],[s2981,s3823,s2760,s2851,s3850,s3846,s14,s10,s2931]) ).
cnf(s3900,plain,
( spl60_114
| spl60_105
| spl60_80
| ~ spl60_57 ),
inference(rat,[],[s2435,s354,s356]) ).
cnf(s3901,plain,
( spl60_105
| ~ spl60_194
| ~ spl60_79
| spl60_80
| ~ spl60_57
| ~ spl60_81 ),
inference(rat,[],[s1828,s2841,s20,s24,s2813,s3900,s2783,s3844]) ).
cnf(s3902,plain,
( spl60_114
| spl60_104
| spl60_80
| ~ spl60_57 ),
inference(rat,[],[s2435,s346,s348]) ).
cnf(s3903,plain,
( ~ spl60_79
| ~ spl60_55
| spl60_80
| ~ spl60_57
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s1828,s2841,s20,s24,s2813,s3902,s2783,s3848,s2405,s3901,s1785]) ).
cnf(s3904,plain,
( ~ spl60_55
| spl60_80
| ~ spl60_9
| ~ spl60_57
| ~ spl60_81 ),
inference(rat,[],[s2405,s3854,s3852,s3903]) ).
cnf(s3905,plain,
( ~ spl60_57
| ~ spl60_51
| ~ spl60_81
| spl60_5
| spl60_1 ),
inference(rat,[],[s1828,s2841,s20,s24,s2813,s2783,s322,s3822,s2853,s3901,s1785,s3817,s2453,s2760,s3904,s3899,s6,s2,s14,s10,s3898,s2931]) ).
cnf(s3909,plain,
( spl60_97
| ~ spl60_11
| spl60_193
| spl60_57
| ~ spl60_51
| ~ spl60_81 ),
inference(rat,[],[s1015,s270,s272,s2074,s3832]) ).
cnf(s3910,plain,
( ~ spl60_11
| spl60_193
| ~ spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81 ),
inference(rat,[],[s1015,s262,s264,s2074,s3834,s3356,s3909]) ).
cnf(s3911,plain,
( ~ spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9
| spl60_5 ),
inference(rat,[],[s3136,s366,s368,s3125,s3088,s3849,s1109,s3882,s2405,s3881,s1826,s20,s24,s3910,s1787,s3830]) ).
cnf(s3912,plain,
( ~ spl60_11
| ~ spl60_194
| ~ spl60_79
| spl60_193
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81 ),
inference(rat,[],[s2074,s250,s252,s2007,s2252,s3909]) ).
cnf(s3913,plain,
( ~ spl60_79
| ~ spl60_12
| spl60_105
| ~ spl60_55
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s3088,s3125,s354,s356,s1838,s3880,s1826,s1828,s20,s3912,s1785,s1787]) ).
cnf(s3914,plain,
( ~ spl60_12
| spl60_105
| ~ spl60_55
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s20,s1826,s3035,s3884,s282,s284,s3913,s1877]) ).
cnf(s3915,plain,
( ~ spl60_79
| ~ spl60_11
| spl60_193
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s3912,s1785]) ).
cnf(s3916,plain,
( spl60_105
| ~ spl60_55
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s3035,s282,s284,s3915,s24,s3914,s1877,s1787]) ).
cnf(s3917,plain,
( ~ spl60_79
| ~ spl60_12
| ~ spl60_55
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s3088,s3125,s346,s348,s1838,s3882,s1826,s1828,s20,s3915,s1787,s2405,s3916]) ).
cnf(s3918,plain,
( ~ spl60_12
| ~ spl60_55
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s20,s3035,s1826,s278,s280,s3884,s3917,s1877,s2405,s3916]) ).
cnf(s3919,plain,
( ~ spl60_55
| spl60_80
| spl60_57
| ~ spl60_51
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s3035,s278,s280,s3915,s24,s3918,s2405,s3916,s1787,s1877]) ).
cnf(s3920,plain,
( spl60_80
| spl60_57
| ~ spl60_9
| ~ spl60_51
| ~ spl60_81 ),
inference(rat,[],[s1828,s1840,s20,s24,s2007,s2252,s1785,s240,s214,s3828,s3919]) ).
cnf(s3921,plain,
( spl60_57
| ~ spl60_51
| spl60_5
| ~ spl60_81
| ~ spl60_9 ),
inference(rat,[],[s3920,s3911]) ).
cnf(s3922,plain,
( ~ spl60_51
| ~ spl60_81
| spl60_5
| spl60_1 ),
inference(rat,[],[s3921,s3905,s3898]) ).
cnf(s3923,plain,
( ~ spl60_81
| spl60_5
| spl60_1 ),
inference(rat,[],[s1836,s2886,s20,s24,s2929,s1785,s1113,s3868,s3867,s194,s3922,s3898]) ).
cnf(s3924,plain,
( ~ spl60_57
| ~ spl60_80
| ~ spl60_51
| spl60_5
| spl60_1 ),
inference(rat,[],[s3824,s3817,s2853,s2453,s2760,s3859,s3865,s6,s2,s14,s10,s3923,s2931]) ).
cnf(s3925,plain,
( spl60_119
| spl60_115
| spl60_105
| spl60_249
| spl60_241
| ~ spl60_8 ),
inference(rat,[],[s3140,s390,s392]) ).
cnf(s3926,plain,
( spl60_97
| ~ spl60_11
| spl60_134
| ~ spl60_79
| spl60_193
| spl60_57
| ~ spl60_51
| ~ spl60_4 ),
inference(rat,[],[s1052,s270,s272,s2074,s3837]) ).
cnf(s3927,plain,
( ~ spl60_11
| spl60_134
| ~ spl60_79
| spl60_193
| spl60_57
| ~ spl60_80
| ~ spl60_51
| ~ spl60_4 ),
inference(rat,[],[s1052,s262,s264,s2074,s3839,s3356,s3926]) ).
cnf(s3928,plain,
( spl60_11
| spl60_57
| ~ spl60_51
| spl60_81
| spl60_5 ),
inference(rat,[],[s3896,s20,s24]) ).
cnf(s3929,plain,
( ~ spl60_79
| ~ spl60_11
| spl60_193
| spl60_57
| ~ spl60_80
| ~ spl60_51
| spl60_81
| spl60_1 ),
inference(rat,[],[s3927,s1313,s6,s2]) ).
cnf(s3930,plain,
( spl60_105
| spl60_79
| ~ spl60_11
| ~ spl60_197
| ~ spl60_51 ),
inference(rat,[],[s3035,s282,s284]) ).
cnf(s3931,plain,
( ~ spl60_80
| ~ spl60_51
| spl60_5
| spl60_1 ),
inference(rat,[],[s3035,s278,s280,s2405,s3930,s3929,s3928,s1787,s1877,s3830,s3924,s3898,s3923]) ).
cnf(s3932,plain,
( ~ spl60_57
| spl60_80
| ~ spl60_51
| spl60_81
| spl60_5 ),
inference(rat,[],[s2853,s286,s2760,s3864,s3865,s14,s10,s2931]) ).
cnf(s3933,plain,
( spl60_105
| spl60_193
| ~ spl60_11
| spl60_80
| ~ spl60_51
| spl60_81 ),
inference(rat,[],[s1718,s2272,s302,s304]) ).
cnf(s3934,plain,
( ~ spl60_51
| spl60_5
| spl60_1 ),
inference(rat,[],[s1718,s2272,s298,s300,s2405,s3933,s1787,s220,s3928,s3932,s3931,s3898,s3923]) ).
cnf(s3935,plain,
( spl60_5
| spl60_1 ),
inference(rat,[],[s3653,s3362,s196,s198,s200,s194,s3934,s3923,s10,s14]) ).
cnf(s3936,plain,
( ~ spl60_57
| ~ spl60_80
| ~ spl60_51
| ~ spl60_81
| spl60_1 ),
inference(rat,[],[s639,s3823,s2453,s3850,s3846,s6,s2,s2931]) ).
cnf(s3937,plain,
( spl60_9
| spl60_57
| ~ spl60_80
| ~ spl60_51
| ~ spl60_81 ),
inference(rat,[],[s3136,s366,s368,s3125,s3088,s3849,s1109,s3882,s2405,s3881,s1826,s18,s22,s3829]) ).
cnf(s3938,plain,
( ~ spl60_80
| ~ spl60_51
| spl60_1
| ~ spl60_81 ),
inference(rat,[],[s3136,s366,s368,s3125,s3088,s3849,s1109,s3882,s2405,s3881,s1826,s20,s24,s3910,s1787,s3937,s3829,s3936]) ).
cnf(s3939,plain,
( ~ spl60_55
| ~ spl60_57
| spl60_80
| ~ spl60_81 ),
inference(rat,[],[s3904,s3855]) ).
cnf(s3940,plain,
( spl60_9
| spl60_130
| ~ spl60_57
| spl60_80
| spl60_131
| ~ spl60_81
| ~ spl60_4 ),
inference(rat,[],[s3851,s322,s3822,s639,s3853,s3817,s3939]) ).
cnf(s3941,plain,
( ~ spl60_57
| ~ spl60_51
| ~ spl60_81
| spl60_1 ),
inference(rat,[],[s1828,s1838,s20,s24,s2813,s322,s3822,s639,s3901,s1785,s3940,s3817,s2453,s3939,s6,s2,s2931,s3938]) ).
cnf(s3942,plain,
( spl60_57
| spl60_80
| ~ spl60_81
| ~ spl60_51 ),
inference(rat,[],[s3920,s3887]) ).
cnf(s3943,plain,
( ~ spl60_51
| ~ spl60_81
| spl60_1 ),
inference(rat,[],[s3942,s3941,s3938]) ).
cnf(s3944,plain,
( spl60_9
| ~ spl60_85
| ~ spl60_84
| ~ spl60_79
| ~ spl60_81 ),
inference(rat,[],[s1836,s2886,s18,s22,s1113]) ).
cnf(s3945,plain,
( ~ spl60_81
| spl60_1 ),
inference(rat,[],[s1836,s2886,s20,s24,s2929,s1785,s3944,s1113,s3868,s3867,s194,s3943]) ).
cnf(s3946,plain,
( spl60_119
| spl60_115
| spl60_105
| spl60_134
| spl60_241
| ~ spl60_4 ),
inference(rat,[],[s3179,s390,s392]) ).
cnf(s3947,plain,
( spl60_115
| spl60_105
| spl60_134
| spl60_241
| ~ spl60_57
| ~ spl60_4 ),
inference(rat,[],[s3179,s386,s388,s2435,s3946]) ).
cnf(s3948,plain,
( spl60_119
| spl60_114
| spl60_105
| spl60_134
| spl60_241
| ~ spl60_4 ),
inference(rat,[],[s3179,s382,s384]) ).
cnf(s3949,plain,
( spl60_105
| spl60_134
| spl60_241
| ~ spl60_57
| ~ spl60_80
| ~ spl60_4 ),
inference(rat,[],[s3179,s378,s380,s2435,s3948,s1109,s3947]) ).
cnf(s3950,plain,
( spl60_119
| spl60_115
| spl60_104
| spl60_134
| spl60_241
| ~ spl60_4 ),
inference(rat,[],[s3179,s374,s376]) ).
cnf(s3951,plain,
( spl60_115
| spl60_104
| spl60_134
| spl60_241
| ~ spl60_57
| ~ spl60_4 ),
inference(rat,[],[s3179,s370,s372,s2435,s3950]) ).
cnf(s3952,plain,
( spl60_119
| spl60_114
| spl60_104
| spl60_134
| spl60_241
| ~ spl60_4 ),
inference(rat,[],[s3179,s366,s368]) ).
cnf(s3953,plain,
( ~ spl60_79
| ~ spl60_55
| ~ spl60_57
| ~ spl60_80
| spl60_1 ),
inference(rat,[],[s3179,s362,s364,s2435,s3952,s1109,s3951,s2405,s3949,s1313,s3352,s6,s2,s3945]) ).
cnf(s3954,plain,
( ~ spl60_55
| ~ spl60_57
| spl60_1
| ~ spl60_80 ),
inference(rat,[],[s2405,s3854,s3852,s3953]) ).
cnf(s3955,plain,
( ~ spl60_57
| ~ spl60_80
| ~ spl60_51
| spl60_1 ),
inference(rat,[],[s3362,s3582,s12,s16,s3560,s290,s292,s639,s3949,s1360,s1313,s3352,s3817,s2453,s3954,s6,s2,s3935,s3945,s2931]) ).
cnf(s3956,plain,
( spl60_115
| ~ spl60_195
| ~ spl60_12
| spl60_105
| spl60_134
| spl60_241
| ~ spl60_51
| ~ spl60_4 ),
inference(rat,[],[s3179,s386,s388,s3088,s3125,s3946]) ).
cnf(s3957,plain,
( spl60_9
| ~ spl60_55
| spl60_105
| spl60_134
| spl60_241
| spl60_57
| ~ spl60_80
| ~ spl60_51
| ~ spl60_4 ),
inference(rat,[],[s3179,s378,s380,s3088,s3125,s3948,s1109,s3956,s1826,s18,s22]) ).
cnf(s3958,plain,
( ~ spl60_55
| spl60_105
| ~ spl60_79
| ~ spl60_80
| ~ spl60_51
| spl60_1 ),
inference(rat,[],[s3179,s378,s380,s3088,s3125,s3948,s1109,s3956,s1826,s20,s24,s3929,s1787,s3957,s6,s3955,s3352,s1313,s2,s3945]) ).
cnf(s3959,plain,
( spl60_105
| ~ spl60_79
| ~ spl60_80
| ~ spl60_51
| spl60_1 ),
inference(rat,[],[s3362,s3582,s12,s16,s3564,s294,s296,s222,s224,s3958,s3955,s1360,s3935,s3945]) ).
cnf(s3960,plain,
( spl60_115
| ~ spl60_195
| ~ spl60_12
| spl60_104
| spl60_134
| spl60_241
| ~ spl60_51
| ~ spl60_4 ),
inference(rat,[],[s3179,s370,s372,s3088,s3125,s3950]) ).
cnf(s3961,plain,
( spl60_9
| spl60_104
| ~ spl60_55
| spl60_134
| spl60_241
| spl60_57
| ~ spl60_80
| ~ spl60_51
| ~ spl60_4 ),
inference(rat,[],[s3179,s362,s364,s3088,s3125,s3952,s1109,s3960,s1826,s18,s22]) ).
cnf(s3962,plain,
( ~ spl60_55
| ~ spl60_79
| ~ spl60_80
| ~ spl60_51
| spl60_1 ),
inference(rat,[],[s3179,s362,s364,s3088,s3125,s3952,s1109,s3960,s1826,s20,s24,s3929,s1787,s3961,s2405,s6,s3955,s3352,s1313,s2,s3945,s3959]) ).
cnf(s3963,plain,
( ~ spl60_79
| ~ spl60_80
| ~ spl60_51
| spl60_1 ),
inference(rat,[],[s3362,s3827,s12,s16,s3564,s222,s224,s3962,s1360,s3935,s3945,s3955]) ).
cnf(s3964,plain,
( spl60_9
| spl60_79
| spl60_57
| ~ spl60_51 ),
inference(rat,[],[s1826,s3884,s18,s22,s214]) ).
cnf(s3965,plain,
( spl60_11
| spl60_79
| spl60_57
| ~ spl60_51 ),
inference(rat,[],[s1826,s3884,s20,s24,s214]) ).
cnf(s3966,plain,
( ~ spl60_80
| ~ spl60_51
| spl60_1 ),
inference(rat,[],[s3035,s278,s280,s2405,s3930,s3965,s1877,s3964,s214,s3963,s3955]) ).
cnf(s3967,plain,
( spl60_104
| ~ spl60_57
| spl60_80
| spl60_81 ),
inference(rat,[],[s2436,s298,s300]) ).
cnf(s3968,plain,
( ~ spl60_57
| ~ spl60_51
| spl60_1 ),
inference(rat,[],[s2453,s639,s2405,s3967,s3864,s6,s2,s3945,s2931,s3966]) ).
cnf(s3969,plain,
( spl60_9
| ~ spl60_92
| ~ spl60_93
| ~ spl60_55
| spl60_57
| ~ spl60_51 ),
inference(rat,[],[s2217,s1826,s1490,s18,s22]) ).
cnf(s3970,plain,
( spl60_11
| ~ spl60_92
| ~ spl60_93
| ~ spl60_55
| spl60_57
| ~ spl60_51 ),
inference(rat,[],[s2217,s1826,s1490,s20,s24]) ).
cnf(s3971,plain,
( ~ spl60_51
| spl60_1 ),
inference(rat,[],[s1718,s2272,s298,s300,s2405,s3933,s3970,s1787,s3969,s226,s228,s220,s3968,s3966,s3945]) ).
cnf(s3972,plain,
spl60_1,
inference(rat,[],[s3672,s1292,s196,s198,s200,s118,s120,s194,s3971,s3945]) ).
cnf(s3973,plain,
( ~ spl60_51
| ~ spl60_81
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s2760,s2853,s12,s16,s2363,s2451,s3899,s2931,s3846,s3823,s3850]) ).
cnf(s3974,plain,
( ~ spl60_81
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s1113,s3868,s3867,s3973]) ).
cnf(s3976,plain,
( spl60_119
| spl60_115
| ~ spl60_7
| spl60_155
| ~ spl60_79
| spl60_105 ),
inference(rat,[],[s1382,s390,s392]) ).
cnf(s3977,plain,
( spl60_115
| ~ spl60_7
| spl60_155
| spl60_105
| ~ spl60_57 ),
inference(rat,[],[s1382,s386,s388,s2435,s3976,s3852]) ).
cnf(s3978,plain,
( spl60_119
| spl60_114
| ~ spl60_7
| spl60_155
| ~ spl60_79
| spl60_105 ),
inference(rat,[],[s1382,s382,s384]) ).
cnf(s3979,plain,
( ~ spl60_7
| spl60_155
| spl60_105
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s1382,s378,s380,s2435,s3978,s1109,s3977,s3852]) ).
cnf(s3980,plain,
( spl60_105
| ~ spl60_5
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s3140,s382,s384,s2435,s3858,s1109,s3857,s3362,s12,s16,s3979,s1360,s3352,s3852,s3974]) ).
cnf(s3981,plain,
( spl60_7
| spl60_115
| spl60_104
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s3362,s3861,s12,s16,s3974,s3854]) ).
cnf(s3982,plain,
( spl60_119
| ~ spl60_7
| spl60_115
| spl60_155
| ~ spl60_79
| spl60_104 ),
inference(rat,[],[s1382,s374,s376]) ).
cnf(s3983,plain,
( spl60_115
| ~ spl60_55
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s1382,s370,s372,s2435,s3982,s3981,s1360,s3854,s2405,s3980,s3865,s3974]) ).
cnf(s3984,plain,
( spl60_119
| spl60_114
| spl60_155
| ~ spl60_79
| spl60_104
| spl60_81
| ~ spl60_80 ),
inference(rat,[],[s3362,s3140,s12,s16,s1382,s366,s368,s3352]) ).
cnf(s3985,plain,
( ~ spl60_55
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s3362,s3140,s12,s16,s1382,s362,s364,s2435,s3984,s1109,s3983,s1360,s3352,s3854,s2405,s3980,s3865,s3974]) ).
cnf(s3986,plain,
( spl60_105
| ~ spl60_57
| spl60_81
| ~ spl60_80 ),
inference(rat,[],[s3980,s3859]) ).
cnf(s3987,plain,
( spl60_5
| ~ spl60_79
| ~ spl60_51
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s2760,s2853,s3824,s10,s14,s3985,s3986,s3974,s2931]) ).
cnf(s3988,plain,
( spl60_7
| spl60_115
| ~ spl60_51
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s2760,s2853,s3981,s12,s16,s3985,s3986,s3974,s2931]) ).
cnf(s3989,plain,
( ~ spl60_7
| spl60_155
| spl60_182
| ~ spl60_79
| ~ spl60_51
| ~ spl60_105
| spl60_55
| spl60_81 ),
inference(rat,[],[s3560,s290,s292,s2363]) ).
cnf(s3990,plain,
( ~ spl60_79
| ~ spl60_51
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s2435,s3984,s3862,s2981,s1109,s3362,s2760,s3988,s12,s16,s3989,s1360,s2451,s3987,s3352,s3985,s2851,s3986,s3974,s2931]) ).
cnf(s3991,plain,
( spl60_5
| ~ spl60_104
| ~ spl60_51
| ~ spl60_105
| spl60_55
| ~ spl60_57 ),
inference(rat,[],[s2760,s2853,s10,s14,s2931]) ).
cnf(s3992,plain,
( ~ spl60_51
| ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s2760,s2853,s12,s16,s2363,s2451,s3991,s3854,s3990,s2931,s3985,s3986,s3974]) ).
cnf(s3993,plain,
( ~ spl60_57
| ~ spl60_80 ),
inference(rat,[],[s3672,s1292,s198,s200,s118,s120,s194,s3992,s3974]) ).
cnf(s3994,plain,
( ~ spl60_51
| spl60_105
| ~ spl60_81
| ~ spl60_80 ),
inference(rat,[],[s1826,s3881,s20,s24,s3910,s1787,s3937,s3829,s3993]) ).
cnf(s3995,plain,
( spl60_51
| ~ spl60_81
| ~ spl60_80 ),
inference(rat,[],[s1113,s3868,s3867]) ).
cnf(s3996,plain,
( ~ spl60_81
| spl60_57
| ~ spl60_80 ),
inference(rat,[],[s3136,s366,s368,s3125,s3088,s3849,s1109,s3882,s1826,s20,s24,s3910,s2405,s1787,s3994,s3937,s3995,s3829]) ).
cnf(s3997,plain,
( spl60_3
| ~ spl60_11
| ~ spl60_79
| ~ spl60_51
| ~ spl60_55
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s1787,s3927,s3957,s1313,s4,s8,s3996,s3993,s3352]) ).
cnf(s3998,plain,
( spl60_115
| ~ spl60_3
| spl60_249
| ~ spl60_8
| spl60_241
| ~ spl60_169
| ~ spl60_51
| spl60_105 ),
inference(rat,[],[s3080,s3125,s3856,s3925]) ).
cnf(s3999,plain,
( spl60_5
| ~ spl60_79
| ~ spl60_51
| ~ spl60_55
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s3140,s382,s384,s3125,s3080,s3858,s1109,s3998,s3997,s3362,s3928,s10,s14,s3996,s1337,s3993,s3352,s3972]) ).
cnf(s4000,plain,
( spl60_119
| spl60_115
| spl60_155
| ~ spl60_79
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s3362,s3925,s12,s16,s3976,s3996,s3993,s3352]) ).
cnf(s4001,plain,
( spl60_249
| ~ spl60_8
| spl60_115
| ~ spl60_79
| ~ spl60_51
| ~ spl60_55
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s1826,s3893,s20,s24,s3997,s3998,s1337,s3993,s3352,s3972]) ).
cnf(s4002,plain,
( ~ spl60_118
| spl60_244
| ~ spl60_79
| ~ spl60_51
| ~ spl60_55
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s1826,s3088,s20,s24,s3997,s3080,s1337,s3993,s3972]) ).
cnf(s4003,plain,
( spl60_115
| ~ spl60_79
| ~ spl60_51
| ~ spl60_55
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s3362,s4001,s12,s16,s1382,s386,s388,s4002,s3125,s4000,s1360,s3999,s3996,s3993]) ).
cnf(s4004,plain,
( spl60_119
| spl60_114
| spl60_155
| ~ spl60_79
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s3362,s3140,s12,s16,s3978,s382,s384,s3996,s3993,s3352]) ).
cnf(s4005,plain,
( ~ spl60_79
| ~ spl60_51
| ~ spl60_55
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s3362,s3140,s12,s16,s1382,s378,s380,s4002,s3125,s4004,s1109,s4003,s1360,s3999,s3352,s3996,s3993]) ).
cnf(s4006,plain,
( ~ spl60_51
| ~ spl60_55
| spl60_105
| ~ spl60_80 ),
inference(rat,[],[s3930,s1877,s3965,s3964,s4005,s3993]) ).
cnf(s4007,plain,
( spl60_51
| ~ spl60_80 ),
inference(rat,[],[s3672,s1292,s198,s200,s118,s120,s194,s3996,s3993]) ).
cnf(s4008,plain,
( spl60_105
| ~ spl60_80 ),
inference(rat,[],[s3362,s3827,s12,s16,s3560,s1360,s294,s296,s214,s3830,s4006,s3996,s3993,s4007]) ).
cnf(s4009,plain,
( spl60_119
| spl60_249
| ~ spl60_8
| spl60_115
| spl60_241
| spl60_104 ),
inference(rat,[],[s3140,s374,s376]) ).
cnf(s4010,plain,
( spl60_5
| spl60_115
| ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s1787,s3927,s3961,s1313,s4,s8,s3080,s3125,s4009,s3860,s3362,s3928,s10,s14,s3996,s1337,s3993,s4007,s2405,s4008,s3352,s3972]) ).
cnf(s4011,plain,
( spl60_119
| ~ spl60_8
| spl60_155
| spl60_115
| ~ spl60_79
| spl60_104
| ~ spl60_80 ),
inference(rat,[],[s12,s3362,s3982,s4009,s3996,s3993,s3352]) ).
cnf(s4012,plain,
( spl60_249
| ~ spl60_8
| spl60_115
| ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s1826,s3894,s20,s24,s3927,s1787,s3961,s1313,s4,s8,s3080,s3860,s1337,s4007,s3352,s3125,s4011,s1360,s4010,s3996,s3993,s2405,s4008,s3972]) ).
cnf(s4013,plain,
( spl60_118
| ~ spl60_7
| spl60_155
| spl60_115
| ~ spl60_79
| spl60_104 ),
inference(rat,[],[s1382,s370,s372]) ).
cnf(s4014,plain,
( ~ spl60_8
| spl60_115
| ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s1826,s3088,s20,s24,s3927,s1787,s3961,s1313,s4,s8,s3080,s4013,s12,s3362,s4012,s3125,s4011,s1337,s4007,s2405,s4008,s3352,s1360,s4010,s3996,s3993,s3972]) ).
cnf(s4015,plain,
( spl60_115
| ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s1826,s3088,s20,s24,s3927,s1787,s3961,s1313,s4,s8,s3080,s3125,s4013,s3982,s16,s4014,s1360,s4010,s3996,s1337,s3993,s4007,s2405,s4008,s3352,s3972]) ).
cnf(s4016,plain,
( spl60_119
| spl60_249
| ~ spl60_8
| spl60_114
| spl60_241
| spl60_104 ),
inference(rat,[],[s3140,s366,s368]) ).
cnf(s4017,plain,
( spl60_5
| ~ spl60_8
| ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s1787,s3927,s3961,s1313,s4,s8,s3080,s3125,s4016,s3862,s3362,s3928,s10,s3996,s1337,s3993,s4007,s2405,s4008,s3352,s1109,s4015,s3972]) ).
cnf(s4018,plain,
( ~ spl60_118
| spl60_244
| ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s1826,s3088,s20,s24,s3927,s1787,s3961,s1313,s4,s8,s3080,s3996,s1337,s3993,s4007,s2405,s4008,s3352,s3972]) ).
cnf(s4019,plain,
( ~ spl60_8
| ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s12,s3362,s1382,s3862,s362,s364,s4018,s3125,s3984,s1360,s4017,s3996,s3993,s2405,s4008,s3352,s1109,s4015]) ).
cnf(s4020,plain,
( ~ spl60_79
| ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s1382,s362,s364,s4018,s3125,s3984,s1360,s14,s16,s4019,s1109,s4015,s3996,s3993,s2405,s4008]) ).
cnf(s4021,plain,
( ~ spl60_55
| ~ spl60_80 ),
inference(rat,[],[s3035,s1877,s278,s280,s3965,s3964,s4020,s2405,s3993,s4007,s4008]) ).
cnf(s4022,plain,
( spl60_57
| ~ spl60_80 ),
inference(rat,[],[s3362,s3827,s12,s16,s3534,s1376,s214,s3830,s222,s224,s4021,s3996]) ).
cnf(s4023,plain,
~ spl60_80,
inference(rat,[],[s4022,s3993]) ).
cnf(s4024,plain,
( ~ spl60_85
| ~ spl60_81
| ~ spl60_84
| ~ spl60_79 ),
inference(rat,[],[s1836,s2886,s20,s24,s2929,s1785,s3944,s4023]) ).
cnf(s4025,plain,
( ~ spl60_81
| ~ spl60_79
| ~ spl60_55 ),
inference(rat,[],[s4024,s3868,s3867,s3942,s3939,s4023]) ).
cnf(s4026,plain,
( ~ spl60_57
| spl60_81
| ~ spl60_55 ),
inference(rat,[],[s2405,s3967,s3864,s4023]) ).
cnf(s4027,plain,
( spl60_81
| ~ spl60_55 ),
inference(rat,[],[s1718,s2272,s298,s300,s2405,s3933,s1787,s3970,s3969,s226,s228,s4026,s196,s4023]) ).
cnf(s4028,plain,
( ~ spl60_81
| ~ spl60_55 ),
inference(rat,[],[s194,s3942,s4025,s3939,s4023]) ).
cnf(s4029,plain,
~ spl60_55,
inference(rat,[],[s4028,s4027]) ).
cnf(s4030,plain,
( spl60_105
| ~ spl60_57
| ~ spl60_81
| ~ spl60_79 ),
inference(rat,[],[s1785,s3901,s3818,s4023,s4029]) ).
cnf(s4031,plain,
( ~ spl60_104
| ~ spl60_51
| ~ spl60_105
| ~ spl60_57 ),
inference(rat,[],[s2760,s2853,s12,s16,s2363,s2451,s3991,s2931,s4029]) ).
cnf(s4032,plain,
( ~ spl60_114
| ~ spl60_115
| ~ spl60_79
| ~ spl60_81 ),
inference(rat,[],[s1828,s1838,s20,s24,s2813,s1785,s3851,s4023]) ).
cnf(s4033,plain,
( spl60_104
| ~ spl60_81
| ~ spl60_79 ),
inference(rat,[],[s4032,s322,s3822,s4029,s4023]) ).
cnf(s4034,plain,
( spl60_51
| ~ spl60_81
| ~ spl60_79 ),
inference(rat,[],[s4024,s3868,s3867]) ).
cnf(s4035,plain,
( ~ spl60_81
| ~ spl60_79 ),
inference(rat,[],[s4030,s4031,s3942,s4034,s4033,s4023]) ).
cnf(s4036,plain,
spl60_81,
inference(rat,[],[s4031,s286,s288,s220,s196,s4023,s4029]) ).
cnf(s4037,plain,
~ spl60_79,
inference(rat,[],[s4035,s4036]) ).
cnf(s4039,plain,
spl60_51,
inference(rat,[],[s194,s4037]) ).
cnf(s4040,plain,
spl60_57,
inference(rat,[],[s214,s4029,s4037]) ).
cnf(s4041,plain,
spl60_105,
inference(rat,[],[s3852,s4040,s4037]) ).
cnf(s4042,plain,
spl60_104,
inference(rat,[],[s3854,s4040,s4037]) ).
cnf(s4044,plain,
$false,
inference(rat,[],[s4031,s4040,s4042,s4041,s4039]) ).
thf(f14426,plain,
$false,
inference(avatar_sat_refutation,[],[s4044]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN393^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:19:18 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.71/1.21 % (3725516)Will run a generic schedule for satisfiability detection.
% 6.71/1.21 % (3725522)% WARNING: option uhcvi not known.
% 6.71/1.21 % (3725522)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3804768978:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.71/1.21 % (3725521)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3373747512_2999 on theBenchmark for (2999ds/0Mi)
% 6.71/1.21 % (3725526)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=550426259:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.71/1.21 % (3725522)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.71/1.21 % (3725527)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3182967204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.71/1.21 % Exception at run slice level
% 6.71/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.71/1.21 % (3725522)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.71/1.21 % (3725524)dis+10_1_sil=32000:sp=arity:random_seed=1945302570:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.71/1.21 % (3725523)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2372162529:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.71/1.21 % (3725525)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3323776411:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.71/1.21 % (3725525)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.71/1.21 % (3725533)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2992667243:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.71/1.21 % Exception at run slice level
% 6.71/1.21 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.71/1.21 % (3725537)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2723160875:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.71/1.21 % (3725524)Instruction limit reached!
% 6.71/1.21 % (3725524)------------------------------
% 6.71/1.21 % (3725524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.71/1.21 % (3725524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.21 % (3725524)CaDiCaL version: 2.1.3
% 6.71/1.21 % (3725524)Termination reason: Instruction limit
% 6.71/1.21 % (3725524)Termination phase: Saturation
% 6.71/1.21 % (3725524)Time elapsed: 0.053 s
% 6.71/1.21 % (3725524)Peak memory usage: 12 MB
% 6.71/1.21 % (3725524)Instructions burned: 103 (million)
% 6.71/1.21 % (3725526)Instruction limit reached!
% 6.71/1.21 % (3725526)------------------------------
% 6.71/1.21 % (3725526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.71/1.21 % (3725526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.21 % (3725526)CaDiCaL version: 2.1.3
% 6.71/1.21 % (3725526)Termination reason: Instruction limit
% 6.71/1.21 % (3725526)Termination phase: Saturation
% 6.71/1.21 % (3725526)Time elapsed: 0.069 s
% 6.71/1.21 % (3725526)Peak memory usage: 12 MB
% 6.71/1.21 % (3725526)Instructions burned: 132 (million)
% 6.71/1.21 % (3725527)Instruction limit reached!
% 6.71/1.21 % (3725527)------------------------------
% 6.71/1.21 % (3725527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.71/1.21 % (3725527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.21 % (3725527)CaDiCaL version: 2.1.3
% 6.71/1.21 % (3725527)Termination reason: Instruction limit
% 6.71/1.21 % (3725527)Termination phase: Saturation
% 6.71/1.21 % (3725527)Time elapsed: 0.074 s
% 6.71/1.21 % (3725527)Peak memory usage: 13 MB
% 6.71/1.21 % (3725527)Instructions burned: 159 (million)
% 6.71/1.21 % (3725539)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3257165105:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.71/1.21 % (3725539)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.71/1.21 % (3725539)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.71/1.21 % (3725540)ott-21_1_sil=16000:fs=off:random_seed=227861785:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.71/1.21 % (3725542)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3301288600:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 18.07/3.00 % (3725525)Instruction limit reached!
% 18.07/3.00 % (3725525)------------------------------
% 18.07/3.00 % (3725525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.07/3.00 % (3725525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.07/3.00 % (3725525)CaDiCaL version: 2.1.3
% 18.07/3.00 % (3725525)Termination reason: Instruction limit
% 18.07/3.00 % (3725525)Termination phase: Saturation
% 18.07/3.00 % (3725525)Time elapsed: 0.093 s
% 18.07/3.00 % (3725525)Peak memory usage: 12 MB
% 18.07/3.00 % (3725525)Instructions burned: 116 (million)
% 18.07/3.00 % (3725537)Instruction limit reached!
% 18.07/3.00 % (3725537)------------------------------
% 18.07/3.00 % (3725537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.07/3.00 % (3725537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.07/3.00 % (3725537)CaDiCaL version: 2.1.3
% 18.07/3.00 % (3725537)Termination reason: Instruction limit
% 18.07/3.00 % (3725537)Termination phase: Saturation
% 18.07/3.00 % (3725537)Time elapsed: 0.067 s
% 18.07/3.00 % (3725537)Peak memory usage: 13 MB
% 18.07/3.00 % (3725537)Instructions burned: 134 (million)
% 18.07/3.00 % (3725545)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2028262262:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 18.07/3.00 % Exception at run slice level
% 18.07/3.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 18.07/3.00 % (3725546)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2197133367:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 18.07/3.00 % (3725548)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1105377440:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 18.07/3.00 % Exception at run slice level
% 18.07/3.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 18.07/3.00 % (3725551)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=757943246:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 18.07/3.00 % (3725551)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 18.07/3.00 % (3725540)Instruction limit reached!
% 18.07/3.00 % (3725540)------------------------------
% 18.07/3.00 % (3725540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.07/3.00 % (3725540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.07/3.00 % (3725540)CaDiCaL version: 2.1.3
% 18.07/3.00 % (3725540)Termination reason: Instruction limit
% 18.07/3.00 % (3725540)Termination phase: Saturation
% 18.07/3.00 % (3725540)Time elapsed: 0.110 s
% 18.07/3.00 % (3725540)Peak memory usage: 13 MB
% 18.07/3.00 % (3725540)Instructions burned: 180 (million)
% 18.07/3.00 % (3725553)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3004817447:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 18.07/3.00 % (3725553)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 18.07/3.00 % (3725539)Instruction limit reached!
% 18.07/3.00 % (3725539)------------------------------
% 18.07/3.00 % (3725539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 18.07/3.00 % (3725539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.07/3.00 % (3725539)CaDiCaL version: 2.1.3
% 18.07/3.00 % (3725539)Termination reason: Instruction limit
% 18.07/3.00 % (3725539)Termination phase: Saturation
% 18.07/3.00 % (3725539)Time elapsed: 0.241 s
% 18.07/3.00 % (3725539)Peak memory usage: 15 MB
% 18.07/3.00 % (3725539)Instructions burned: 686 (million)
% 18.07/3.00 % (3725560)fmb+10_1_sil=64000:random_seed=1480754149:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 18.07/3.00 % (3725560)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 18.07/3.00 % Exception at run slice level
% 18.07/3.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 18.07/3.00 % (3725562)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1203643820:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 18.07/3.00 % Exception at run slice level
% 18.07/3.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.39/5.91 % (3725564)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2043992407:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 39.39/5.91 % Exception at run slice level
% 39.39/5.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.39/5.91 % (3725566)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2673171194:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 39.39/5.91 % (3725566)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 39.39/5.91 % (3725551)Instruction limit reached!
% 39.39/5.91 % (3725551)------------------------------
% 39.39/5.91 % (3725551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.39/5.91 % (3725551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.39/5.91 % (3725551)CaDiCaL version: 2.1.3
% 39.39/5.91 % (3725551)Termination reason: Instruction limit
% 39.39/5.91 % (3725551)Termination phase: Saturation
% 39.39/5.91 % (3725551)Time elapsed: 0.285 s
% 39.39/5.91 % (3725551)Peak memory usage: 14 MB
% 39.39/5.91 % (3725551)Instructions burned: 693 (million)
% 39.39/5.91 % (3725542)Instruction limit reached!
% 39.39/5.91 % (3725542)------------------------------
% 39.39/5.91 % (3725542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.39/5.91 % (3725542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.39/5.91 % (3725542)CaDiCaL version: 2.1.3
% 39.39/5.91 % (3725542)Termination reason: Instruction limit
% 39.39/5.91 % (3725542)Termination phase: Saturation
% 39.39/5.91 % (3725542)Time elapsed: 0.376 s
% 39.39/5.91 % (3725542)Peak memory usage: 13 MB
% 39.39/5.91 % (3725542)Instructions burned: 477 (million)
% 39.39/5.91 % (3725568)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1381551326:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 39.39/5.91 % (3725568)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 39.39/5.91 % (3725568)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 39.39/5.91 % (3725569)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1118904077:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 39.39/5.91 % Exception at run slice level
% 39.39/5.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.39/5.91 % (3725572)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4062905767:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 39.39/5.91 % Exception at run slice level
% 39.39/5.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.39/5.91 % (3725574)ott-2_1_sil=16000:newcnf=on:random_seed=894598856:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 39.39/5.91 % (3725574)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 39.39/5.91 % (3725553)Instruction limit reached!
% 39.39/5.91 % (3725553)------------------------------
% 39.39/5.91 % (3725553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.39/5.91 % (3725553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.39/5.91 % (3725553)CaDiCaL version: 2.1.3
% 39.39/5.91 % (3725553)Termination reason: Instruction limit
% 39.39/5.91 % (3725553)Termination phase: Saturation
% 39.39/5.91 % (3725553)Time elapsed: 0.379 s
% 39.39/5.91 % (3725553)Peak memory usage: 14 MB
% 39.39/5.91 % (3725553)Instructions burned: 879 (million)
% 39.39/5.91 % (3725576)ott+10_1_sil=32000:tgt=ground:random_seed=2206389408:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 39.39/5.91 % (3725546)Instruction limit reached!
% 39.39/5.91 % (3725546)------------------------------
% 39.39/5.91 % (3725546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.39/5.91 % (3725546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.39/5.91 % (3725546)CaDiCaL version: 2.1.3
% 39.39/5.91 % (3725546)Termination reason: Instruction limit
% 39.39/5.91 % (3725546)Termination phase: Saturation
% 39.39/5.91 % (3725546)Time elapsed: 0.752 s
% 39.39/5.91 % (3725546)Peak memory usage: 14 MB
% 39.39/5.91 % (3725546)Instructions burned: 1180 (million)
% 39.39/5.91 % (3725585)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3119870458:i=54282_2990 on theBenchmark for (2990ds/54282Mi)
% 39.39/5.91 % Exception at run slice level
% 88.07/12.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 88.07/12.74 % (3725587)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3971330355:i=3512:aac=none_2990 on theBenchmark for (2990ds/3512Mi)
% 88.07/12.74 % (3725587)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 88.07/12.74 % (3725568)Instruction limit reached!
% 88.07/12.74 % (3725568)------------------------------
% 88.07/12.74 % (3725568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725568)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725568)Termination reason: Instruction limit
% 88.07/12.74 % (3725568)Termination phase: Saturation
% 88.07/12.74 % (3725568)Time elapsed: 0.726 s
% 88.07/12.74 % (3725568)Peak memory usage: 19 MB
% 88.07/12.74 % (3725568)Instructions burned: 1474 (million)
% 88.07/12.74 % (3725590)dis+21_1_sil=32000:sas=cadical:random_seed=4214394259:i=3773:amm=off_2987 on theBenchmark for (2987ds/3773Mi)
% 88.07/12.74 % (3725574)Instruction limit reached!
% 88.07/12.74 % (3725574)------------------------------
% 88.07/12.74 % (3725574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725574)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725574)Termination reason: Instruction limit
% 88.07/12.74 % (3725574)Termination phase: Saturation
% 88.07/12.74 % (3725574)Time elapsed: 0.695 s
% 88.07/12.74 % (3725574)Peak memory usage: 15 MB
% 88.07/12.74 % (3725574)Instructions burned: 870 (million)
% 88.07/12.74 % (3725592)ott+11_1_sil=16000:gs=on:random_seed=3792046659:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2986 on theBenchmark for (2986ds/2251Mi)
% 88.07/12.74 % (3725592)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 88.07/12.74 % (3725566)Instruction limit reached!
% 88.07/12.74 % (3725566)------------------------------
% 88.07/12.74 % (3725566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725566)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725566)Termination reason: Instruction limit
% 88.07/12.74 % (3725566)Termination phase: Saturation
% 88.07/12.74 % (3725566)Time elapsed: 1.651 s
% 88.07/12.74 % (3725566)Peak memory usage: 17 MB
% 88.07/12.74 % (3725566)Instructions burned: 5132 (million)
% 88.07/12.74 % (3725595)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3646504573:fmbsr=1.6:i=67534_2979 on theBenchmark for (2979ds/67534Mi)
% 88.07/12.74 % Exception at run slice level
% 88.07/12.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 88.07/12.74 % (3725597)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=3555169260:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2979 on theBenchmark for (2979ds/4591Mi)
% 88.07/12.74 % (3725587)Instruction limit reached!
% 88.07/12.74 % (3725587)------------------------------
% 88.07/12.74 % (3725587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725587)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725587)Termination reason: Instruction limit
% 88.07/12.74 % (3725587)Termination phase: Saturation
% 88.07/12.74 % (3725587)Time elapsed: 1.505 s
% 88.07/12.74 % (3725587)Peak memory usage: 17 MB
% 88.07/12.74 % (3725587)Instructions burned: 3513 (million)
% 88.07/12.74 % (3725599)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3367669150:i=29340_2975 on theBenchmark for (2975ds/29340Mi)
% 88.07/12.74 % (3725590)Instruction limit reached!
% 88.07/12.74 % (3725590)------------------------------
% 88.07/12.74 % (3725590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725590)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725590)Termination reason: Instruction limit
% 88.07/12.74 % (3725590)Termination phase: Saturation
% 88.07/12.74 % (3725590)Time elapsed: 1.468 s
% 88.07/12.74 % (3725590)Peak memory usage: 17 MB
% 88.07/12.74 % (3725590)Instructions burned: 3775 (million)
% 88.07/12.74 % (3725602)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=2247531995:i=5211_2972 on theBenchmark for (2972ds/5211Mi)
% 88.07/12.74 % (3725592)Instruction limit reached!
% 88.07/12.74 % (3725592)------------------------------
% 88.07/12.74 % (3725592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725592)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725592)Termination reason: Instruction limit
% 88.07/12.74 % (3725592)Termination phase: Saturation
% 88.07/12.74 % (3725592)Time elapsed: 1.719 s
% 88.07/12.74 % (3725592)Peak memory usage: 17 MB
% 88.07/12.74 % (3725592)Instructions burned: 2251 (million)
% 88.07/12.74 % (3725576)Instruction limit reached!
% 88.07/12.74 % (3725576)------------------------------
% 88.07/12.74 % (3725576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725576)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725576)Termination reason: Instruction limit
% 88.07/12.74 % (3725576)Termination phase: Saturation
% 88.07/12.74 % (3725576)Time elapsed: 2.388 s
% 88.07/12.74 % (3725576)Peak memory usage: 16 MB
% 88.07/12.74 % (3725576)Instructions burned: 5114 (million)
% 88.07/12.74 % (3725609)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=1968448442:i=5497:nm=2_2969 on theBenchmark for (2969ds/5497Mi)
% 88.07/12.74 % Exception at run slice level
% 88.07/12.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 88.07/12.74 % (3725610)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=428485659:fmbsr=2:i=46332_2969 on theBenchmark for (2969ds/46332Mi)
% 88.07/12.74 % Exception at run slice level
% 88.07/12.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 88.07/12.74 % (3725612)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=3336311210:i=14071_2969 on theBenchmark for (2969ds/14071Mi)
% 88.07/12.74 % Exception at run slice level
% 88.07/12.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 88.07/12.74 % (3725616)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=28494737:i=8173:av=off_2968 on theBenchmark for (2968ds/8173Mi)
% 88.07/12.74 % (3725614)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3308201009:i=22565:add=on:rawr=on_2968 on theBenchmark for (2968ds/22565Mi)
% 88.07/12.74 % (3725597)Instruction limit reached!
% 88.07/12.74 % (3725597)------------------------------
% 88.07/12.74 % (3725597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725597)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725597)Termination reason: Instruction limit
% 88.07/12.74 % (3725597)Termination phase: Saturation
% 88.07/12.74 % (3725597)Time elapsed: 2.496 s
% 88.07/12.74 % (3725597)Peak memory usage: 20 MB
% 88.07/12.74 % (3725597)Instructions burned: 4592 (million)
% 88.07/12.74 % (3725619)dis+10_16:1_sil=16000:random_seed=2085365575:i=9155:fsr=off_2953 on theBenchmark for (2953ds/9155Mi)
% 88.07/12.74 % (3725602)Instruction limit reached!
% 88.07/12.74 % (3725602)------------------------------
% 88.07/12.74 % (3725602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725602)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725602)Termination reason: Instruction limit
% 88.07/12.74 % (3725602)Termination phase: Saturation
% 88.07/12.74 % (3725602)Time elapsed: 2.215 s
% 88.07/12.74 % (3725602)Peak memory usage: 21 MB
% 88.07/12.74 % (3725602)Instructions burned: 5213 (million)
% 88.07/12.74 % (3725621)ott-3_8_sil=64000:random_seed=2271098460:i=20139:bs=on_2950 on theBenchmark for (2950ds/20139Mi)
% 88.07/12.74 % (3725616)Instruction limit reached!
% 88.07/12.74 % (3725616)------------------------------
% 88.07/12.74 % (3725616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725616)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725616)Termination reason: Instruction limit
% 88.07/12.74 % (3725616)Termination phase: Saturation
% 88.07/12.74 % (3725616)Time elapsed: 2.515 s
% 88.07/12.74 % (3725616)Peak memory usage: 18 MB
% 88.07/12.74 % (3725616)Instructions burned: 8176 (million)
% 88.07/12.74 % (3725623)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=922342586:fmbsr=2:i=32576_2943 on theBenchmark for (2943ds/32576Mi)
% 88.07/12.74 % Exception at run slice level
% 88.07/12.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 88.07/12.74 % (3725625)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=948269084:i=11404_2943 on theBenchmark for (2943ds/11404Mi)
% 88.07/12.74 % (3725625)Instruction limit reached!
% 88.07/12.74 % (3725625)------------------------------
% 88.07/12.74 % (3725625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725625)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725625)Termination reason: Instruction limit
% 88.07/12.74 % (3725625)Termination phase: Saturation
% 88.07/12.74 % (3725625)Time elapsed: 2.737 s
% 88.07/12.74 % (3725625)Peak memory usage: 19 MB
% 88.07/12.74 % (3725625)Instructions burned: 11408 (million)
% 88.07/12.74 % (3725630)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=2121866181:i=14134_2915 on theBenchmark for (2915ds/14134Mi)
% 88.07/12.74 % (3725630)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 88.07/12.74 % (3725619)Instruction limit reached!
% 88.07/12.74 % (3725619)------------------------------
% 88.07/12.74 % (3725619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725619)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725619)Termination reason: Instruction limit
% 88.07/12.74 % (3725619)Termination phase: Saturation
% 88.07/12.74 % (3725619)Time elapsed: 5.238 s
% 88.07/12.74 % (3725619)Peak memory usage: 23 MB
% 88.07/12.74 % (3725619)Instructions burned: 9157 (million)
% 88.07/12.74 % (3725633)dis+33_16_sil=32000:sac=on:random_seed=2193734601:i=15851:nm=0_2901 on theBenchmark for (2901ds/15851Mi)
% 88.07/12.74 % (3725630)Instruction limit reached!
% 88.07/12.74 % (3725630)------------------------------
% 88.07/12.74 % (3725630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.74 % (3725630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.74 % (3725630)CaDiCaL version: 2.1.3
% 88.07/12.74 % (3725630)Termination reason: Instruction limit
% 88.07/12.74 % (3725630)Termination phase: Saturation
% 88.07/12.74 % (3725630)Time elapsed: 3.716 s
% 88.07/12.74 % (3725630)Peak memory usage: 18 MB
% 88.07/12.74 % (3725630)Instructions burned: 14137 (million)
% 88.07/12.74 % (3725638)dis+4_1024_sil=32000:avsql=on:sp=occurrence:gs=on:avsqc=1:random_seed=246599521:avsq=on:i=17627:add=on:amm=off_2878 on theBenchmark for (2878ds/17627Mi)
% 88.07/12.74 % (3725638) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3725516-3725638"...
% 88.07/12.74 % (3725638)...printing done.
% 88.07/12.74 % (3725638)Refutation found. Thanks to Tanya!
% 88.07/12.74 % SZS status Theorem for theBenchmark
% 88.07/12.74 % SZS output start Proof for theBenchmark
% See solution above
% 88.07/12.76 % (3725638)------------------------------
% 88.07/12.76 % (3725638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.07/12.76 % (3725638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.07/12.76 % (3725638)CaDiCaL version: 2.1.3
% 88.07/12.76 % (3725638)Termination reason: Refutation
% 88.07/12.76 % (3725638)Time elapsed: 0.313 s
% 88.07/12.76 % (3725638)Peak memory usage: 16 MB
% 88.07/12.76 % (3725638)Instructions burned: 1253 (million)
% 88.07/12.76 % (3725516)Success in time 12.493 s
% 88.07/12.76 % Vampire exiting
%------------------------------------------------------------------------------