%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO069^4.004 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:46:31 AM UTC 2026
% Result : Theorem 92.65s 13.54s
% Output : Refutation 92.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 53
% Syntax : Number of formulae : 652 ( 102 unt; 0 typ; 41 def)
% Number of atoms : 15674 (2373 equ; 0 cnn)
% Maximal formula atoms : 108 ( 24 avg)
% Number of connectives : 27647 (1509 ~;3352 |; 384 &;17224 @)
% ( 41 <=>;2671 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 364 ( 364 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 98 usr; 46 con; 0-6 aty)
% (2466 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 4162 ( 0 sgn1137 !; 0 ?;4162 :)
% 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,
a0: $i > $o ).
thf(func_def_22,type,
a1: $i > $o ).
thf(func_def_23,type,
a2: $i > $o ).
thf(func_def_24,type,
a3: $i > $o ).
thf(func_def_25,type,
a4: $i > $o ).
thf(func_def_26,type,
b0: $i > $o ).
thf(func_def_27,type,
b1: $i > $o ).
thf(func_def_28,type,
b2: $i > $o ).
thf(func_def_29,type,
b3: $i > $o ).
thf(func_def_30,type,
b4: $i > $o ).
thf(func_def_31,type,
f: $i > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
sK2: $i > $i ).
thf(func_def_47,type,
sK3: $i > $i ).
thf(func_def_48,type,
sK4: $i > $i ).
thf(func_def_49,type,
sK5: $i > $i ).
thf(func_def_50,type,
sK6: $i > $i ).
thf(func_def_51,type,
sK7: $i > $i ).
thf(func_def_52,type,
sK8: $i > $i ).
thf(func_def_53,type,
sK9: $i > $i ).
thf(func_def_54,type,
sK10: $i > $i ).
thf(func_def_56,type,
sK12: $i > $i ).
thf(func_def_57,type,
sK13: $i > $i ).
thf(func_def_58,type,
sF14:
!>[X0: $tType] : ( $i > ( $i > X0 ) > X0 ) ).
thf(func_def_59,type,
sF15:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X0 > X1 > X2 ) ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X0 @ X1 ) )
=> ( irel @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',trans_axiom) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f12,axiom,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(f14,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
= iimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) ) ) @ ( iatom @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) ) ) @ ( iatom @ f ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f24,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f27,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f28,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f29,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f32,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f33,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X2 @ X0 )
& ( irel @ X1 @ X2 ) )
=> ( irel @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y0 @ Y2 ) )
=> ( irel @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f34]) ).
thf(f37,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f40,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) ) ) @ ( iatom @ f ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f45,plain,
( $true
= ( ~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) ) ) @ ( iatom @ f ) ) ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f53,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f55,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f56,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f58,plain,
( $true
= ( ~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ a4 ) ) @ ( iatom @ a3 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b4 ) @ ( iatom @ b0 ) ) @ ( iatom @ a4 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) ) ) @ ( iatom @ f ) ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f62,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f66,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f67,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f71,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f72,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f73,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f74,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y0 @ Y2 ) )
=> ( irel @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f35]) ).
thf(f75,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f76,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f77,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f81,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,[],[f62,f67,f57]) ).
thf(f84,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,[],[f76,f66]) ).
thf(f86,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,f81,f75,f75]) ).
thf(f90,plain,
( $true
= ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ 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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a0 )
@ ( ^ [Y0: $i > $o] : Y0
@ f ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b4 )
@ ( ^ [Y0: $i > $o] : Y0
@ b0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a4 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b0 )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b1 )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b2 )
@ ( ^ [Y0: $i > $o] : Y0
@ a3 ) )
@ ( ^ [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 ) )
@ ( ^ [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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b3 )
@ ( ^ [Y0: $i > $o] : Y0
@ a4 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a3 ) ) ) ) ) ) )
@ ( ^ [Y0: $i > $o] : Y0
@ f ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b3 )
@ ( ^ [Y0: $i > $o] : Y0
@ a4 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b2 )
@ ( ^ [Y0: $i > $o] : Y0
@ a3 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b1 )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b0 )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $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 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b4 )
@ ( ^ [Y0: $i > $o] : Y0
@ b0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a4 ) )
@ ( ^ [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 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a0 )
@ ( ^ [Y0: $i > $o] : Y0
@ f ) ) ) ) ) ) )
@ ( ^ [Y0: $i > $o] : Y0
@ f ) ) ) ) ) ),
inference(definition_unfolding,[],[f58,f73,f84,f86,f84,f86,f71,f71,f84,f86,f86,f71,f71,f71,f84,f86,f86,f71,f71,f71,f84,f86,f86,f71,f71,f71,f84,f86,f86,f71,f71,f71,f86,f86,f71,f71,f71,f71,f86,f84,f86,f86,f71,f71,f71,f84,f86,f86,f71,f71,f71,f84,f86,f86,f71,f71,f71,f84,f86,f86,f71,f71,f71,f84,f86,f86,f71,f71,f71,f86,f71,f71,f71]) ).
thf(f91,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b4 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a4 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a4 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b4 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y0 @ Y2 ) )
=> ( irel @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f93,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( irel @ Y0 @ X1 )
& ( irel @ X1 @ Y1 ) )
=> ( irel @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( irel @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f95,plain,
! [X1: $i] :
( $true
= ( irel @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b4 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a4 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a4 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b4 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f91]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( irel @ Y0 @ X1 )
& ( irel @ X1 @ Y1 ) )
=> ( irel @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f98,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( irel @ X2 @ X1 )
& ( irel @ X1 @ Y0 ) )
=> ( irel @ X2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
( $false
= ( ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b4 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a4 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a4 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b4 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f96]) ).
thf(f100,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( irel @ X2 @ X1 )
& ( irel @ X1 @ Y0 ) )
=> ( irel @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f98]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ X1 )
& ( irel @ X1 @ X3 ) )
=> ( irel @ X2 @ X3 ) )
= $true ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f103,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f100]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ X1 )
& ( irel @ X1 @ X3 ) )
= $false )
| ( $true
= ( irel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f105,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f106,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f103]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f104]) ).
thf(f109,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f106]) ).
thf(f110,plain,
( ( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) )
@ sK1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f111,plain,
( ( ( ( irel @ sK0 @ sK1 )
=> ( f @ sK1 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f109]) ).
thf(f114,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false )
| ( ( f @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f115,plain,
( ( $true
= ( irel @ sK0 @ sK1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f116,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f112]) ).
thf(f119,plain,
( ( ( f @ sK1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f114]) ).
thf(f121,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( $true
= ( irel @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f115]) ).
thf(f123,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f124,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f128,plain,
( ( ( f @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f119]) ).
thf(f129,plain,
( ( ( ( irel @ sK0 @ sK1 )
=> ( f @ sK1 ) )
= $false )
| ( ( f @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f130,plain,
( ( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) )
@ sK1 )
= $false )
| ( $true
= ( irel @ sK0 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f121]) ).
thf(f131,plain,
( ( ( ( irel @ sK0 @ sK1 )
=> ( f @ sK1 ) )
= $false )
| ( $true
= ( irel @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f133,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b4 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f134,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f139,plain,
( ( ( f @ sK1 )
= $false )
| ( ( f @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f141,plain,
( ( f @ sK1 )
= $false ),
inference(duplicate_literal_removal,[],[f139]) ).
thf(f143,plain,
( ( $true
= ( irel @ sK0 @ sK1 ) )
| ( $true
= ( irel @ sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f144,plain,
( $true
= ( irel @ sK0 @ sK1 ) ),
inference(duplicate_literal_removal,[],[f143]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f134]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f156]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
@ ( sK3 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f183]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f182]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f213,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a3 @ Y0 ) )
@ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f214,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X1 @ X3 )
=> ( a3 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f196]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f202]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) )
@ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X1 @ X3 )
=> ( a3 @ X3 ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f214]) ).
thf(f241,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) )
@ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f215]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f248,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f256,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f226]) ).
thf(f257,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f266,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f271,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X1 @ X3 )
=> ( a3 @ X3 ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f272,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( ( irel @ X1 @ X3 )
=> ( a3 @ X3 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f275,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK4 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f242]) ).
thf(f276,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f290,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) )
= $false )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f257]) ).
thf(f291,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f257]) ).
thf(f300,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) )
@ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f266]) ).
thf(f301,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f300]) ).
thf(f306,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( ( irel @ X1 @ X3 )
=> ( a3 @ X3 ) )
= $true )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f272]) ).
thf(f308,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f271]) ).
thf(f311,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f276]) ).
thf(f318,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f319,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f318]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f331,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f291]) ).
thf(f332,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) )
= $false )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f290]) ).
thf(f343,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( f @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f301]) ).
thf(f349,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f306]) ).
thf(f351,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f308]) ).
thf(f356,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( $true
= ( a4 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f357,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f311]) ).
thf(f364,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f319]) ).
thf(f374,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f377,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f331]) ).
thf(f381,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f332]) ).
thf(f394,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true )
| ( $true
= ( f @ X3 ) ) ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f402,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f349]) ).
thf(f405,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( a4 @ Y0 ) )
@ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f351]) ).
thf(f406,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ( $true
= ( a3 @ X3 ) )
| ( ( ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) )
=> ( a4 @ ( sK8 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f405]) ).
thf(f411,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f357]) ).
thf(f413,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f356]) ).
thf(f420,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f431,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f374]) ).
thf(f432,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X1 @ X3 )
=> ( a1 @ X3 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f431]) ).
thf(f436,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( a2 @ X3 )
= $true )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f377]) ).
thf(f442,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f381]) ).
thf(f458,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( $true
= ( f @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) )
@ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f394]) ).
thf(f459,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( f @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( f @ X4 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f458]) ).
thf(f465,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f402]) ).
thf(f467,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) )
=> ( a4 @ ( sK8 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f406]) ).
thf(f477,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f411]) ).
thf(f481,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f413]) ).
thf(f490,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK7 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f420]) ).
thf(f491,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK7 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f490]) ).
thf(f505,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f432]) ).
thf(f509,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f436]) ).
thf(f518,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( a2 @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f442]) ).
thf(f534,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
= $false )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( f @ X3 ) )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( f @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f459]) ).
thf(f543,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f465]) ).
thf(f544,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f543]) ).
thf(f547,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) )
=> ( a4 @ ( sK8 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| ( $true
= ( a3 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f467]) ).
thf(f557,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f477]) ).
thf(f564,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f481]) ).
thf(f565,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
=> ( b0 @ ( sK9 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f564]) ).
thf(f576,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f491]) ).
thf(f577,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f491]) ).
thf(f592,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
@ ( sK6 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f505]) ).
thf(f593,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f592]) ).
thf(f598,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( a2 @ X3 )
= $true )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f509]) ).
thf(f609,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f518]) ).
thf(f611,definition,
( spl11_1
<=> ! [X4: $i,X1: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( a3 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f612,plain,
( ! [X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( a3 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f611]) ).
thf(f614,definition,
( spl11_2
<=> ! [X2: $i,X3: $i] :
( ( $true
= ( f @ X3 ) )
| ( ( irel @ X2 @ ( sK2 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f615,plain,
( ! [X2: $i,X3: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( f @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X2 @ ( sK2 @ X2 ) )
= $true ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f614]) ).
thf(f622,definition,
( spl11_3
<=> ! [X2: $i,X3: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ ( sK2 @ X2 ) )
= $false )
| ( $true
= ( f @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f623,plain,
( ! [X2: $i,X3: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( f @ X3 ) )
| ( ( a0 @ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f622]) ).
thf(f638,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( f @ X4 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) )
@ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( f @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f534]) ).
thf(f639,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( f @ X3 ) )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( f @ X4 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a0 @ ( sK2 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f638]) ).
thf(f649,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( a3 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f544]) ).
thf(f654,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f547]) ).
thf(f655,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a3 @ X3 ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f547]) ).
thf(f664,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f557]) ).
thf(f665,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( ( irel @ X1 @ X4 )
=> ( a4 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f664]) ).
thf(f675,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
= $true )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
=> ( b0 @ ( sK9 @ X2 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f565]) ).
thf(f691,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f577]) ).
thf(f692,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f576]) ).
thf(f693,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( a0 @ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(or_proxy_clausification,[],[f576]) ).
thf(f708,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f593]) ).
thf(f709,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK6 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f708]) ).
thf(f714,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f598]) ).
thf(f727,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( a2 @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f609]) ).
thf(f735,definition,
( spl11_4
<=> ! [X4: $i,X1: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f736,plain,
( ! [X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f735]) ).
thf(f753,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( f @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ ( sK2 @ X2 ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( f @ X4 ) ) )
| ( ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a0 @ ( sK2 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f639]) ).
thf(f754,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a0 @ ( sK2 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( f @ X4 ) ) )
| ( ( irel @ X2 @ ( sK2 @ X2 ) )
= $true )
| ( $true
= ( f @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f639]) ).
thf(f760,definition,
( spl11_5
<=> ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ X2 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f761,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f760]) ).
thf(f767,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a3 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f649]) ).
thf(f774,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f654]) ).
thf(f775,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f655]) ).
thf(f787,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X1 @ X4 )
=> ( a4 @ X4 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f665]) ).
thf(f795,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
=> ( b0 @ ( sK9 @ X2 ) ) )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f675]) ).
thf(f815,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK7 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f691]) ).
thf(f816,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ ( sK7 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f815]) ).
thf(f817,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( a0 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f692]) ).
thf(f818,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f817]) ).
thf(f819,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f693]) ).
thf(f836,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f709]) ).
thf(f837,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) ) ),
inference(imp_proxy_clausification,[],[f709]) ).
thf(f843,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
@ ( sK5 @ X2 ) )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f714]) ).
thf(f844,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
= $true )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f843]) ).
thf(f859,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a3 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f727]) ).
thf(f860,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
= $true )
| ( ( ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) )
=> ( a3 @ ( sK10 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f859]) ).
thf(f876,definition,
( spl11_6
<=> ! [X1: $i,X3: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK6 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f877,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK6 @ X1 ) ) ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f876]) ).
thf(f886,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( f @ X4 )
= $true )
| ( $true
= ( f @ X3 ) )
| ( ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a0 @ ( sK2 @ X1 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f753]) ).
thf(f888,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( irel @ X1 @ X4 )
=> ( f @ X4 ) ) )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( irel @ X2 @ ( sK2 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( f @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f754]) ).
thf(f904,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
@ ( sK3 @ X2 ) )
= $false )
| ( ( a3 @ X4 )
= $true )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f767]) ).
thf(f905,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a3 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f904]) ).
thf(f912,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f774]) ).
thf(f913,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a3 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f775]) ).
thf(f914,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( $true
= ( a3 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f913]) ).
thf(f924,definition,
( spl11_7
<=> ! [X4: $i,X2: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK7 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f925,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK7 @ X2 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f924]) ).
thf(f932,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f787]) ).
thf(f942,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
=> ( b0 @ ( sK9 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a4 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f795]) ).
thf(f943,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
=> ( b0 @ ( sK9 @ X2 ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ X4 )
=> ( a4 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f942]) ).
thf(f969,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( irel @ X2 @ ( sK7 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f816]) ).
thf(f970,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f818]) ).
thf(f971,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( a0 @ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f819]) ).
thf(f972,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ ( sK7 @ X1 ) @ X4 )
=> ( b0 @ X4 ) ) )
| ( ( a0 @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f971]) ).
thf(f992,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f836]) ).
thf(f993,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
@ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f837]) ).
thf(f994,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f993]) ).
thf(f1000,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f844]) ).
thf(f1001,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1000]) ).
thf(f1017,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) )
=> ( a3 @ ( sK10 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f860]) ).
thf(f1018,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) )
=> ( a3 @ ( sK10 @ X1 ) ) )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1017]) ).
thf(f1020,definition,
( spl11_8
<=> ! [X4: $i,X1: $i] :
( ( ( a3 @ X4 )
= $true )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f1021,plain,
( ! [X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a3 @ X4 )
= $true ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f1020]) ).
thf(f1024,definition,
( spl11_9
<=> ! [X4: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( a3 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f1025,plain,
( ! [X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a3 @ X4 )
= $true )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f1024]) ).
thf(f1048,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( f @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( f @ X3 ) )
| ( ( a0 @ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f886]) ).
thf(f1051,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X2 @ ( sK2 @ X2 ) )
= $true )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( f @ X4 )
= $true )
| ( $true
= ( f @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f888]) ).
thf(f1071,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK3 @ X1 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a3 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ ( sK3 @ X2 ) )
= $true )
| ( $true
= ( a3 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f905]) ).
thf(f1079,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
@ ( sK3 @ X2 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a3 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f912]) ).
thf(f1080,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a3 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1079]) ).
thf(f1081,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f914]) ).
thf(f1097,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK4 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f932]) ).
thf(f1098,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a4 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1097]) ).
thf(f1110,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X1 @ X4 )
=> ( a4 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
=> ( b0 @ ( sK9 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f943]) ).
thf(f1139,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK7 @ X2 ) ) )
| ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f969]) ).
thf(f1140,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK7 @ X2 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1139]) ).
thf(f1141,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK7 @ X2 ) )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f970]) ).
thf(f1142,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) )
| ( ( ( irel @ X2 @ ( sK7 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1141]) ).
thf(f1143,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( ( irel @ ( sK7 @ X1 ) @ X4 )
=> ( b0 @ X4 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) )
@ X5 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f972]) ).
thf(f1144,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ( irel @ X1 @ X5 )
=> ( a0 @ X5 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ( irel @ ( sK7 @ X1 ) @ X4 )
=> ( b0 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f1143]) ).
thf(f1167,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( ( a1 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f992]) ).
thf(f1170,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK6 @ X1 ) ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f994]) ).
thf(f1180,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ X2 @ ( sK5 @ X2 ) )
= $true )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1001]) ).
thf(f1199,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1018]) ).
thf(f1200,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( a2 @ X3 )
= $true )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1018]) ).
thf(f1207,definition,
( spl11_11
<=> ! [X4: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( a2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f1208,plain,
( ! [X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f1207]) ).
thf(f1211,definition,
( spl11_12
<=> ! [X4: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f1212,plain,
( ! [X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( irel @ X1 @ X4 )
= $false ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f1211]) ).
thf(f1234,plain,
( spl11_3
| spl11_3 ),
inference(avatar_split_clause,[],[f1048,f622,f622]) ).
thf(f1236,plain,
( spl11_2
| spl11_2 ),
inference(avatar_split_clause,[],[f1051,f614,f614]) ).
thf(f1244,definition,
( spl11_13
<=> ! [X4: $i,X2: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f1245,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a4 @ X4 ) ) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f1244]) ).
thf(f1248,definition,
( spl11_14
<=> ! [X4: $i,X2: $i] :
( ( $true
= ( a4 @ X4 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f1249,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f1248]) ).
thf(f1265,plain,
( spl11_1
| spl11_1 ),
inference(avatar_split_clause,[],[f1071,f611,f611]) ).
thf(f1273,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1080]) ).
thf(f1275,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( $true
= ( a3 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
@ ( sK3 @ X2 ) )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1081]) ).
thf(f1276,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a3 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1275]) ).
thf(f1294,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( $true
= ( a4 @ X3 ) )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK4 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1098]) ).
thf(f1309,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
=> ( b0 @ ( sK9 @ X2 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1110]) ).
thf(f1348,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK7 @ X2 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK7 @ X1 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1140]) ).
thf(f1349,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK7 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK13 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X2 @ ( sK7 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( a0 @ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f1142]) ).
thf(f1350,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) )
=> ( a1 @ ( sK13 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK7 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1349]) ).
thf(f1351,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ( irel @ ( sK7 @ X1 ) @ X4 )
=> ( b0 @ X4 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1144]) ).
thf(f1384,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
@ ( sK6 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1167]) ).
thf(f1385,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1384]) ).
thf(f1386,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK6 @ X1 ) ) )
| ( ( a1 @ X4 )
= $true )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK6 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1170]) ).
thf(f1399,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ ( sK5 @ X2 ) )
= $true )
| ( ( a2 @ X4 )
= $true )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1180]) ).
thf(f1422,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( a2 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1199]) ).
thf(f1423,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a2 @ X3 )
= $true )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f1200]) ).
thf(f1432,definition,
( spl11_16
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( a2 @ ( sK12 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f1433,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ ( sK12 @ X1 ) )
= $false ) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f1432]) ).
thf(f1436,definition,
( spl11_17
<=> ! [X1: $i,X3: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK6 @ X1 ) @ ( sK12 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
thf(f1437,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK6 @ X1 ) @ ( sK12 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a1 @ X3 ) ) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f1436]) ).
thf(f1485,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1273]) ).
thf(f1487,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1276]) ).
thf(f1498,definition,
( spl11_19
<=> ! [X4: $i,X2: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( a1 @ ( sK13 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
thf(f1499,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a1 @ ( sK13 @ X2 ) )
= $false )
| ( ( a0 @ X4 )
= $true ) )
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f1498]) ).
thf(f1502,definition,
( spl11_20
<=> ! [X2: $i,X4: $i] :
( ( $true
= ( irel @ ( sK7 @ X2 ) @ ( sK13 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
thf(f1503,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( irel @ ( sK7 @ X2 ) @ ( sK13 @ X2 ) ) )
| ( ( a0 @ X4 )
= $true ) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f1502]) ).
thf(f1517,plain,
( spl11_5
| spl11_5 ),
inference(avatar_split_clause,[],[f1294,f760,f760]) ).
thf(f1529,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1309]) ).
thf(f1530,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1309]) ).
thf(f1577,plain,
( spl11_7
| spl11_7 ),
inference(avatar_split_clause,[],[f1348,f924,f924]) ).
thf(f1578,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK7 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) )
=> ( a1 @ ( sK13 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1350]) ).
thf(f1579,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( a0 @ X3 )
= $true )
| ( ( b0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( irel @ X1 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f1351]) ).
thf(f1621,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK6 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK12 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1385]) ).
thf(f1622,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( irel @ ( sK6 @ X2 ) @ ( sK12 @ X2 ) )
=> ( a2 @ ( sK12 @ X2 ) ) ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f1621]) ).
thf(f1623,plain,
( spl11_6
| spl11_6 ),
inference(avatar_split_clause,[],[f1386,f876,f876]) ).
thf(f1643,plain,
( spl11_4
| spl11_4 ),
inference(avatar_split_clause,[],[f1399,f735,f735]) ).
thf(f1668,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f1422]) ).
thf(f1669,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1423]) ).
thf(f1720,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) )
@ ( sK8 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1485]) ).
thf(f1721,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( $true
= ( a3 @ X3 ) )
| ( ( ( irel @ ( sK3 @ X2 ) @ ( sK8 @ X2 ) )
=> ( a4 @ ( sK8 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1720]) ).
thf(f1722,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) ) )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( a3 @ X4 )
= $true )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1487]) ).
thf(f1737,definition,
( spl11_22
<=> ! [X2: $i,X5: $i,X4: $i] :
( ( ( irel @ ( sK7 @ X2 ) @ X5 )
= $false )
| ( ( b0 @ X5 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_22])],[avatar_definition]) ).
thf(f1738,plain,
( ! [X2: $i,X4: $i,X5: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK7 @ X2 ) @ X5 )
= $false )
| ( ( b0 @ X5 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true ) )
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f1737]) ).
thf(f1766,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK4 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( $true
= ( a4 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f1530]) ).
thf(f1767,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f1766]) ).
thf(f1768,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK4 @ X1 ) )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1529]) ).
thf(f1769,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1768]) ).
thf(f1815,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( ( a0 @ X4 )
= $true )
| ( ( ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) )
=> ( a1 @ ( sK13 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1578]) ).
thf(f1817,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f1579]) ).
thf(f1877,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( a1 @ X4 )
= $true )
| ( $false
= ( ( irel @ ( sK6 @ X2 ) @ ( sK12 @ X2 ) )
=> ( a2 @ ( sK12 @ X2 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1622]) ).
thf(f1932,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a2 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
@ ( sK5 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( a2 @ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f1668]) ).
thf(f1933,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1932]) ).
thf(f1934,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( a2 @ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
@ ( sK5 @ X2 ) )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1669]) ).
thf(f1935,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f1934]) ).
thf(f1970,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) )
@ X4 )
= $true )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( ( irel @ ( sK3 @ X2 ) @ ( sK8 @ X2 ) )
=> ( a4 @ ( sK8 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a3 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1721]) ).
thf(f1971,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK3 @ X2 ) @ ( sK8 @ X2 ) )
=> ( a4 @ ( sK8 @ X2 ) ) )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( $true
= ( a3 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f1970]) ).
thf(f1972,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( a3 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f1722]) ).
thf(f2018,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1767]) ).
thf(f2020,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( $true
= ( a4 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f1769]) ).
thf(f2069,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) )
=> ( a1 @ ( sK13 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(or_proxy_clausification,[],[f1815]) ).
thf(f2073,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( ( a0 @ X3 )
= $true )
| ( ( b0 @ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK7 @ X2 ) )
= $false )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1817]) ).
thf(f2074,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X1 @ X5 ) )
| ( ( ( irel @ X2 @ ( sK7 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( ( a0 @ X3 )
= $true )
| ( ( b0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f2073]) ).
thf(f2145,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ ( sK12 @ X2 ) )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( a1 @ X4 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1877]) ).
thf(f2146,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( $true
= ( irel @ ( sK6 @ X2 ) @ ( sK12 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1877]) ).
thf(f2214,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a2 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) )
= $false )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1933]) ).
thf(f2216,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1935]) ).
thf(f2234,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( ( a4 @ ( sK8 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a4 @ ( sK8 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1971]) ).
thf(f2237,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( a3 @ X4 )
= $true )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( a4 @ Y0 ) )
@ ( sK8 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1972]) ).
thf(f2238,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a3 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a3 @ X3 ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ ( sK3 @ X2 ) @ ( sK8 @ X2 ) )
=> ( a4 @ ( sK8 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f2237]) ).
thf(f2284,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(or_proxy_clausification,[],[f2018]) ).
thf(f2286,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a4 @ X4 ) )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f2020]) ).
thf(f2342,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK13 @ X2 ) )
= $false )
| ( ( ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) )
=> ( a1 @ ( sK13 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f2069]) ).
thf(f2343,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) )
=> ( a1 @ ( sK13 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( ( irel @ ( sK7 @ X2 ) @ ( sK13 @ X2 ) )
=> ( a1 @ ( sK13 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f2342]) ).
thf(f2346,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( b0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2074]) ).
thf(f2434,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ ( sK12 @ X2 ) )
= $false )
| ( ( a1 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f2145]) ).
thf(f2436,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( irel @ ( sK6 @ X2 ) @ ( sK12 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f2146]) ).
thf(f2509,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f2214]) ).
thf(f2513,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f2216]) ).
thf(f2527,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a4 @ ( sK8 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a3 @ X4 )
= $true )
| ( $true
= ( a3 @ X3 ) )
| ( ( a4 @ ( sK8 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2234]) ).
thf(f2531,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ ( sK3 @ X2 ) @ ( sK8 @ X2 ) )
= $true )
| ( $true
= ( a3 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a3 @ X4 )
= $true )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK8 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2238]) ).
thf(f2570,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ ( sK9 @ X1 ) )
= $false )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f2284]) ).
thf(f2571,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ ( sK4 @ X1 ) @ ( sK9 @ X1 ) )
=> ( b0 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( $true
= ( a4 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f2570]) ).
thf(f2573,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a4 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ ( sK9 @ X1 ) )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f2286]) ).
thf(f2574,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ ( sK4 @ X1 ) @ ( sK9 @ X1 ) )
=> ( b0 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f2573]) ).
thf(f2613,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ ( sK7 @ X2 ) @ ( sK13 @ X2 ) )
=> ( a1 @ ( sK13 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a1 @ ( sK13 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f2343]) ).
thf(f2614,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ( irel @ ( sK7 @ X2 ) @ ( sK13 @ X2 ) )
=> ( a1 @ ( sK13 @ X2 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f2343]) ).
thf(f2617,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( ( b0 @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f2346]) ).
thf(f2709,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK12 @ X1 ) )
= $false )
| ( ( a2 @ ( sK12 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f2434]) ).
thf(f2710,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ ( sK6 @ X1 ) @ ( sK12 @ X1 ) )
=> ( a2 @ ( sK12 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( a2 @ ( sK12 @ X2 ) )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f2709]) ).
thf(f2712,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK6 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK12 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( irel @ ( sK6 @ X2 ) @ ( sK12 @ X2 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f2436]) ).
thf(f2713,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a1 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK6 @ X2 ) @ ( sK12 @ X2 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ ( sK6 @ X1 ) @ ( sK12 @ X1 ) )
=> ( a2 @ ( sK12 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f2712]) ).
thf(f2778,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) )
@ ( sK10 @ X2 ) ) )
| ( ( a2 @ X3 )
= $true )
| ( ( a2 @ X4 )
= $true )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f2509]) ).
thf(f2779,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK5 @ X2 ) @ ( sK10 @ X2 ) )
=> ( a3 @ ( sK10 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f2778]) ).
thf(f2781,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) )
@ ( sK10 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f2513]) ).
thf(f2782,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a2 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( ( irel @ ( sK5 @ X2 ) @ ( sK10 @ X2 ) )
=> ( a3 @ ( sK10 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f2781]) ).
thf(f2792,plain,
( spl11_9
| spl11_9 ),
inference(avatar_split_clause,[],[f2527,f1024,f1024]) ).
thf(f2795,plain,
( spl11_8
| spl11_8 ),
inference(avatar_split_clause,[],[f2531,f1020,f1020]) ).
thf(f2824,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X4 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ ( sK4 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( ( irel @ ( sK4 @ X1 ) @ ( sK9 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f2571]) ).
thf(f2827,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( a4 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( b0 @ ( sK9 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a4 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f2574]) ).
thf(f2850,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a1 @ ( sK13 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a1 @ ( sK13 @ X2 ) )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2613]) ).
thf(f2853,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK7 @ X1 ) @ ( sK13 @ X1 ) ) )
| ( $true
= ( irel @ ( sK7 @ X2 ) @ ( sK13 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f2614]) ).
thf(f2854,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( b0 @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f2617]) ).
thf(f2956,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( a2 @ ( sK12 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ ( sK12 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f2710]) ).
thf(f2961,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a1 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK6 @ X2 ) @ ( sK12 @ X2 ) ) )
| ( $true
= ( irel @ ( sK6 @ X1 ) @ ( sK12 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2713]) ).
thf(f3014,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a3 @ ( sK10 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( a3 @ ( sK10 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f2779]) ).
thf(f3019,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a2 @ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X2 ) @ ( sK10 @ X2 ) ) )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK10 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f2782]) ).
thf(f3043,plain,
( spl11_14
| spl11_14 ),
inference(avatar_split_clause,[],[f2824,f1248,f1248]) ).
thf(f3046,plain,
( spl11_13
| spl11_13 ),
inference(avatar_split_clause,[],[f2827,f1244,f1244]) ).
thf(f3059,plain,
( spl11_19
| spl11_19 ),
inference(avatar_split_clause,[],[f2850,f1498,f1498]) ).
thf(f3062,plain,
( spl11_20
| spl11_20 ),
inference(avatar_split_clause,[],[f2853,f1502,f1502]) ).
thf(f3063,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ ( sK7 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ X6 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ X4 )
= $true )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( a0 @ X5 ) ) ),
inference(pi_proxy_clausification,[],[f2854]) ).
thf(f3064,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( $true
= ( ( irel @ ( sK7 @ X2 ) @ X6 )
=> ( b0 @ X6 ) ) )
| ( ( a0 @ X3 )
= $true )
| ( ( b0 @ X4 )
= $true )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f3063]) ).
thf(f3158,plain,
( spl11_16
| spl11_16 ),
inference(avatar_split_clause,[],[f2956,f1432,f1432]) ).
thf(f3161,plain,
( spl11_17
| spl11_17 ),
inference(avatar_split_clause,[],[f2961,f1436,f1436]) ).
thf(f3201,plain,
( spl11_11
| spl11_11 ),
inference(avatar_split_clause,[],[f3014,f1207,f1207]) ).
thf(f3204,plain,
( spl11_12
| spl11_12 ),
inference(avatar_split_clause,[],[f3019,f1211,f1211]) ).
thf(f3227,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( b0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ ( sK7 @ X1 ) @ X4 )
= $false )
| ( $true
= ( b0 @ X6 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK7 @ X2 ) @ X6 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X3 )
= $true )
| ( $true
= ( a0 @ X5 ) )
| ( $false
= ( irel @ X1 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f3064]) ).
thf(f3341,plain,
( spl11_22
| spl11_22 ),
inference(avatar_split_clause,[],[f3227,f1737,f1737]) ).
thf(f3488,definition,
( spl11_26
<=> ( ( a0 @ ( sK2 @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_26])],[avatar_definition]) ).
thf(f3490,plain,
( ( ( a0 @ ( sK2 @ sK0 ) )
= $false )
| ~ spl11_26 ),
inference(avatar_component_clause,[],[f3488]) ).
thf(f3745,plain,
( ! [X0: $i] :
( ( $true
= ( f @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true = $false ) )
| ~ spl11_2 ),
inference(superposition,[],[f95,f615]) ).
thf(f3746,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( f @ X0 ) )
| ( ( a0 @ ( sK2 @ sK0 ) )
= $false ) )
| ~ spl11_3 ),
inference(superposition,[],[f95,f623]) ).
thf(f3754,plain,
( ! [X0: $i] :
( ( ( a0 @ X0 )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a1 @ ( sK13 @ sK0 ) )
= $false )
| ( $true = $false ) )
| ~ spl11_19 ),
inference(superposition,[],[f95,f1499]) ).
thf(f3782,plain,
( ! [X0: $i] :
( ( ( a0 @ X0 )
= $true )
| ( ( a1 @ ( sK13 @ sK0 ) )
= $false )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl11_19 ),
inference(trivial_inequality_removal,[],[f3754]) ).
thf(f3783,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( f @ X0 ) )
| ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f3745]) ).
thf(f3784,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( f @ X0 ) )
| ( ( a0 @ ( sK2 @ sK0 ) )
= $false ) )
| ~ spl11_3 ),
inference(trivial_inequality_removal,[],[f3746]) ).
thf(f3805,definition,
( spl11_51
<=> ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_51])],[avatar_definition]) ).
thf(f3807,plain,
( ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl11_51 ),
inference(avatar_component_clause,[],[f3805]) ).
thf(f3809,definition,
( spl11_52
<=> ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( f @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_52])],[avatar_definition]) ).
thf(f3810,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( f @ X0 ) ) )
| ~ spl11_52 ),
inference(avatar_component_clause,[],[f3809]) ).
thf(f3834,plain,
( spl11_52
| spl11_51
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f3783,f614,f3805,f3809]) ).
thf(f3835,plain,
( spl11_52
| spl11_26
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f3784,f622,f3488,f3809]) ).
thf(f4165,plain,
( ( $true = $false )
| ( ( f @ sK1 )
= $true )
| ~ spl11_52 ),
inference(superposition,[],[f144,f3810]) ).
thf(f4169,plain,
( ( ( f @ sK1 )
= $true )
| ~ spl11_52 ),
inference(trivial_inequality_removal,[],[f4165]) ).
thf(f4174,plain,
( ( $true = $false )
| ~ spl11_52 ),
inference(forward_demodulation,[],[f4169,f141]) ).
thf(f4175,plain,
( $false
| ~ spl11_52 ),
inference(trivial_inequality_removal,[],[f4174]) ).
thf(f4176,plain,
~ spl11_52,
inference(avatar_contradiction_clause,[],[f4175]) ).
thf(f5086,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( irel @ sK0 @ ( sK7 @ sK0 ) )
= $true )
| ( ( a0 @ X0 )
= $true )
| ( $true = $false ) )
| ~ spl11_7 ),
inference(superposition,[],[f95,f925]) ).
thf(f5100,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( irel @ sK0 @ ( sK7 @ sK0 ) )
= $true )
| ( ( a0 @ X0 )
= $true ) )
| ~ spl11_7 ),
inference(trivial_inequality_removal,[],[f5086]) ).
thf(f5116,definition,
( spl11_96
<=> ( ( irel @ sK0 @ ( sK7 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_96])],[avatar_definition]) ).
thf(f5118,plain,
( ( ( irel @ sK0 @ ( sK7 @ sK0 ) )
= $true )
| ~ spl11_96 ),
inference(avatar_component_clause,[],[f5116]) ).
thf(f5120,definition,
( spl11_97
<=> ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a0 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_97])],[avatar_definition]) ).
thf(f5121,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a0 @ X0 )
= $true ) )
| ~ spl11_97 ),
inference(avatar_component_clause,[],[f5120]) ).
thf(f5123,plain,
( spl11_96
| spl11_97
| ~ spl11_7 ),
inference(avatar_split_clause,[],[f5100,f924,f5120,f5116]) ).
thf(f5133,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true )
| ( ( a3 @ ( sK10 @ ( sK7 @ sK0 ) ) )
= $false )
| ( $true = $false ) )
| ~ spl11_11
| ~ spl11_96 ),
inference(superposition,[],[f5118,f1208]) ).
thf(f5134,plain,
( ! [X0: $i] :
( ( ( b0 @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $false )
| ( $true
= ( a4 @ X0 ) )
| ( $true = $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_13
| ~ spl11_96 ),
inference(superposition,[],[f5118,f1245]) ).
thf(f5156,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a3 @ X0 ) )
| ( $true = $false )
| ( ( a4 @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $false ) )
| ~ spl11_9
| ~ spl11_96 ),
inference(superposition,[],[f1025,f5118]) ).
thf(f5184,plain,
( ! [X0: $i] :
( ( ( a2 @ X0 )
= $true )
| ( ( a3 @ ( sK10 @ ( sK7 @ sK0 ) ) )
= $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_11
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5133]) ).
thf(f5205,plain,
( ! [X0: $i] :
( ( ( a4 @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a3 @ X0 ) ) )
| ~ spl11_9
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5156]) ).
thf(f5222,definition,
( spl11_98
<=> ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_98])],[avatar_definition]) ).
thf(f5223,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true ) )
| ~ spl11_98 ),
inference(avatar_component_clause,[],[f5222]) ).
thf(f5225,definition,
( spl11_99
<=> ( ( a2 @ ( sK12 @ ( sK7 @ sK0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_99])],[avatar_definition]) ).
thf(f5227,plain,
( ( ( a2 @ ( sK12 @ ( sK7 @ sK0 ) ) )
= $false )
| ~ spl11_99 ),
inference(avatar_component_clause,[],[f5225]) ).
thf(f5230,definition,
( spl11_100
<=> ( ( irel @ ( sK7 @ sK0 ) @ ( sK5 @ ( sK7 @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_100])],[avatar_definition]) ).
thf(f5232,plain,
( ( ( irel @ ( sK7 @ sK0 ) @ ( sK5 @ ( sK7 @ sK0 ) ) )
= $true )
| ~ spl11_100 ),
inference(avatar_component_clause,[],[f5230]) ).
thf(f5234,definition,
( spl11_101
<=> ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_101])],[avatar_definition]) ).
thf(f5235,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl11_101 ),
inference(avatar_component_clause,[],[f5234]) ).
thf(f5255,definition,
( spl11_106
<=> ( ( irel @ ( sK7 @ sK0 ) @ ( sK3 @ ( sK7 @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_106])],[avatar_definition]) ).
thf(f5257,plain,
( ( ( irel @ ( sK7 @ sK0 ) @ ( sK3 @ ( sK7 @ sK0 ) ) )
= $true )
| ~ spl11_106 ),
inference(avatar_component_clause,[],[f5255]) ).
thf(f5259,definition,
( spl11_107
<=> ! [X0: $i] :
( ( $true
= ( a3 @ X0 ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_107])],[avatar_definition]) ).
thf(f5260,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a3 @ X0 ) ) )
| ~ spl11_107 ),
inference(avatar_component_clause,[],[f5259]) ).
thf(f5264,definition,
( spl11_108
<=> ( ( a3 @ ( sK10 @ ( sK7 @ sK0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_108])],[avatar_definition]) ).
thf(f5266,plain,
( ( ( a3 @ ( sK10 @ ( sK7 @ sK0 ) ) )
= $false )
| ~ spl11_108 ),
inference(avatar_component_clause,[],[f5264]) ).
thf(f5282,definition,
( spl11_111
<=> ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK6 @ ( sK7 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_111])],[avatar_definition]) ).
thf(f5284,plain,
( ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK6 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_111 ),
inference(avatar_component_clause,[],[f5282]) ).
thf(f5288,definition,
( spl11_112
<=> ( ( a4 @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_112])],[avatar_definition]) ).
thf(f5290,plain,
( ( ( a4 @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $false )
| ~ spl11_112 ),
inference(avatar_component_clause,[],[f5288]) ).
thf(f5339,plain,
( ( $true
= ( a0 @ ( sK2 @ sK0 ) ) )
| ( $true = $false )
| ~ spl11_51
| ~ spl11_97 ),
inference(superposition,[],[f5121,f3807]) ).
thf(f5351,plain,
( ( $true
= ( a0 @ ( sK2 @ sK0 ) ) )
| ~ spl11_51
| ~ spl11_97 ),
inference(trivial_inequality_removal,[],[f5339]) ).
thf(f5358,plain,
( ( $true = $false )
| ~ spl11_26
| ~ spl11_51
| ~ spl11_97 ),
inference(forward_demodulation,[],[f5351,f3490]) ).
thf(f5359,plain,
( $false
| ~ spl11_26
| ~ spl11_51
| ~ spl11_97 ),
inference(trivial_inequality_removal,[],[f5358]) ).
thf(f5360,plain,
( ~ spl11_26
| ~ spl11_51
| ~ spl11_97 ),
inference(avatar_contradiction_clause,[],[f5359]) ).
thf(f5377,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a4 @ X0 ) )
| ( ( b0 @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $false ) )
| ~ spl11_13
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5134]) ).
thf(f5387,definition,
( spl11_113
<=> ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a4 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_113])],[avatar_definition]) ).
thf(f5388,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a4 @ X0 ) ) )
| ~ spl11_113 ),
inference(avatar_component_clause,[],[f5387]) ).
thf(f5390,definition,
( spl11_114
<=> ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK4 @ ( sK7 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_114])],[avatar_definition]) ).
thf(f5392,plain,
( ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK4 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_114 ),
inference(avatar_component_clause,[],[f5390]) ).
thf(f5401,plain,
( spl11_107
| spl11_112
| ~ spl11_9
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5205,f5116,f1024,f5288,f5259]) ).
thf(f5403,definition,
( spl11_115
<=> ( ( b0 @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_115])],[avatar_definition]) ).
thf(f5405,plain,
( ( ( b0 @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $false )
| ~ spl11_115 ),
inference(avatar_component_clause,[],[f5403]) ).
thf(f5417,plain,
( spl11_113
| spl11_115
| ~ spl11_13
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5377,f5116,f1244,f5403,f5387]) ).
thf(f5421,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ ( sK5 @ ( sK7 @ sK0 ) ) )
= $true )
| ( ( a2 @ X0 )
= $true )
| ( $true = $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_4
| ~ spl11_96 ),
inference(superposition,[],[f5118,f736]) ).
thf(f5428,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true )
| ( ( a2 @ ( sK12 @ ( sK7 @ sK0 ) ) )
= $false ) )
| ~ spl11_16
| ~ spl11_96 ),
inference(superposition,[],[f5118,f1433]) ).
thf(f5442,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true = $false )
| ( ( irel @ ( sK7 @ sK0 ) @ ( sK3 @ ( sK7 @ sK0 ) ) )
= $true )
| ( $true
= ( a3 @ X0 ) ) )
| ~ spl11_1
| ~ spl11_96 ),
inference(superposition,[],[f612,f5118]) ).
thf(f5446,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK4 @ ( sK7 @ sK0 ) ) ) )
| ( $true
= ( a4 @ X0 ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_5
| ~ spl11_96 ),
inference(superposition,[],[f761,f5118]) ).
thf(f5447,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true )
| ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK6 @ ( sK7 @ sK0 ) ) ) )
| ( $true = $false ) )
| ~ spl11_6
| ~ spl11_96 ),
inference(superposition,[],[f877,f5118]) ).
thf(f5466,plain,
( ! [X0: $i] :
( ( $true
= ( a3 @ X0 ) )
| ( ( irel @ ( sK7 @ sK0 ) @ ( sK3 @ ( sK7 @ sK0 ) ) )
= $true )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_1
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5442]) ).
thf(f5477,plain,
( ! [X0: $i] :
( ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK6 @ ( sK7 @ sK0 ) ) ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true ) )
| ~ spl11_6
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5447]) ).
thf(f5494,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true )
| ( ( a2 @ ( sK12 @ ( sK7 @ sK0 ) ) )
= $false ) )
| ~ spl11_16
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5428]) ).
thf(f5497,plain,
( ! [X0: $i] :
( ( $true
= ( irel @ ( sK7 @ sK0 ) @ ( sK4 @ ( sK7 @ sK0 ) ) ) )
| ( $true
= ( a4 @ X0 ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_5
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5446]) ).
thf(f5511,plain,
( ! [X0: $i] :
( ( ( a2 @ X0 )
= $true )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( irel @ ( sK7 @ sK0 ) @ ( sK5 @ ( sK7 @ sK0 ) ) )
= $true ) )
| ~ spl11_4
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f5421]) ).
thf(f5587,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false )
| ( ( a2 @ X0 )
= $true )
| ( ( irel @ X1 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl11_101 ),
inference(superposition,[],[f5235,f107]) ).
thf(f5595,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false )
| ( ( a2 @ X0 )
= $true )
| ( ( irel @ X1 @ X0 )
= $false ) )
| ~ spl11_101 ),
inference(trivial_inequality_removal,[],[f5587]) ).
thf(f5623,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false )
| ( ( irel @ X1 @ X0 )
= $false )
| ( $true
= ( a3 @ X0 ) ) )
| ~ spl11_107 ),
inference(superposition,[],[f107,f5260]) ).
thf(f5627,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false )
| ( ( irel @ X1 @ X0 )
= $false )
| ( $true
= ( a3 @ X0 ) ) )
| ~ spl11_107 ),
inference(trivial_inequality_removal,[],[f5623]) ).
thf(f5630,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( a4 @ X0 ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false )
| ( ( irel @ X1 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl11_113 ),
inference(superposition,[],[f5388,f107]) ).
thf(f5634,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false )
| ( ( irel @ X1 @ X0 )
= $false )
| ( $true
= ( a4 @ X0 ) ) )
| ~ spl11_113 ),
inference(trivial_inequality_removal,[],[f5630]) ).
thf(f6313,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( irel @ ( sK3 @ ( sK7 @ sK0 ) ) @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $true )
| ( $true
= ( a3 @ X0 ) ) )
| ~ spl11_8
| ~ spl11_96 ),
inference(superposition,[],[f1021,f5118]) ).
thf(f6333,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a3 @ X0 ) )
| ( ( irel @ ( sK3 @ ( sK7 @ sK0 ) ) @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $true ) )
| ~ spl11_8
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f6313]) ).
thf(f6337,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( irel @ ( sK5 @ ( sK7 @ sK0 ) ) @ ( sK10 @ ( sK7 @ sK0 ) ) ) )
| ( ( a2 @ X0 )
= $true )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_12
| ~ spl11_96 ),
inference(superposition,[],[f1212,f5118]) ).
thf(f6355,plain,
( ! [X0: $i] :
( ( $true
= ( irel @ ( sK5 @ ( sK7 @ sK0 ) ) @ ( sK10 @ ( sK7 @ sK0 ) ) ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl11_12
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f6337]) ).
thf(f6367,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( irel @ ( sK4 @ ( sK7 @ sK0 ) ) @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $true )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a4 @ X0 ) ) )
| ~ spl11_14
| ~ spl11_96 ),
inference(superposition,[],[f5118,f1249]) ).
thf(f6372,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK4 @ ( sK7 @ sK0 ) ) @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $true )
| ( $true
= ( a4 @ X0 ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_14
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f6367]) ).
thf(f6385,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( irel @ ( sK6 @ ( sK7 @ sK0 ) ) @ ( sK12 @ ( sK7 @ sK0 ) ) ) )
| ( ( a1 @ X0 )
= $true ) )
| ~ spl11_17
| ~ spl11_96 ),
inference(superposition,[],[f1437,f5118]) ).
thf(f6398,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true )
| ( $true
= ( irel @ ( sK6 @ ( sK7 @ sK0 ) ) @ ( sK12 @ ( sK7 @ sK0 ) ) ) ) )
| ~ spl11_17
| ~ spl11_96 ),
inference(trivial_inequality_removal,[],[f6385]) ).
thf(f6412,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ ( sK13 @ sK0 ) )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true = $false )
| ( ( a0 @ X0 )
= $true ) )
| ~ spl11_20 ),
inference(superposition,[],[f95,f1503]) ).
thf(f6429,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ ( sK13 @ sK0 ) )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a0 @ X0 )
= $true ) )
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f6412]) ).
thf(f6431,definition,
( spl11_116
<=> ( ( irel @ ( sK7 @ sK0 ) @ ( sK13 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_116])],[avatar_definition]) ).
thf(f6433,plain,
( ( ( irel @ ( sK7 @ sK0 ) @ ( sK13 @ sK0 ) )
= $true )
| ~ spl11_116 ),
inference(avatar_component_clause,[],[f6431]) ).
thf(f6447,plain,
( spl11_116
| spl11_97
| ~ spl11_20 ),
inference(avatar_split_clause,[],[f6429,f1502,f5120,f6431]) ).
thf(f6448,plain,
( ( ( a1 @ ( sK13 @ sK0 ) )
= $true )
| ( $true = $false )
| ~ spl11_98
| ~ spl11_116 ),
inference(superposition,[],[f6433,f5223]) ).
thf(f6515,plain,
( ( ( a1 @ ( sK13 @ sK0 ) )
= $true )
| ~ spl11_98
| ~ spl11_116 ),
inference(trivial_inequality_removal,[],[f6448]) ).
thf(f6527,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a0 @ X0 )
= $true )
| ( $true = $false ) )
| ~ spl11_19
| ~ spl11_98
| ~ spl11_116 ),
inference(forward_demodulation,[],[f3782,f6515]) ).
thf(f6528,plain,
( ! [X0: $i] :
( ( ( a0 @ X0 )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl11_19
| ~ spl11_98
| ~ spl11_116 ),
inference(trivial_inequality_removal,[],[f6527]) ).
thf(f6531,plain,
( spl11_97
| ~ spl11_19
| ~ spl11_98
| ~ spl11_116 ),
inference(avatar_split_clause,[],[f6528,f6431,f5222,f1498,f5120]) ).
thf(f6534,plain,
( spl11_98
| spl11_99
| ~ spl11_16
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5494,f5116,f1432,f5225,f5222]) ).
thf(f6536,definition,
( spl11_119
<=> ( $true
= ( irel @ ( sK6 @ ( sK7 @ sK0 ) ) @ ( sK12 @ ( sK7 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_119])],[avatar_definition]) ).
thf(f6538,plain,
( ( $true
= ( irel @ ( sK6 @ ( sK7 @ sK0 ) ) @ ( sK12 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_119 ),
inference(avatar_component_clause,[],[f6536]) ).
thf(f6545,plain,
( spl11_98
| spl11_111
| ~ spl11_6
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5477,f5116,f876,f5282,f5222]) ).
thf(f6546,plain,
( spl11_98
| spl11_119
| ~ spl11_17
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f6398,f5116,f1436,f6536,f5222]) ).
thf(f10574,plain,
( ! [X0: $i] :
( ( ( a2 @ X0 )
= $true )
| ( ( irel @ ( sK6 @ ( sK7 @ sK0 ) ) @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl11_101
| ~ spl11_111 ),
inference(superposition,[],[f5595,f5284]) ).
thf(f10582,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK6 @ ( sK7 @ sK0 ) ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl11_101
| ~ spl11_111 ),
inference(trivial_inequality_removal,[],[f10574]) ).
thf(f10607,plain,
( ( $true
= ( a2 @ ( sK12 @ ( sK7 @ sK0 ) ) ) )
| ( $true = $false )
| ~ spl11_101
| ~ spl11_111
| ~ spl11_119 ),
inference(superposition,[],[f6538,f10582]) ).
thf(f10613,plain,
( ( $true
= ( a2 @ ( sK12 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_101
| ~ spl11_111
| ~ spl11_119 ),
inference(trivial_inequality_removal,[],[f10607]) ).
thf(f10618,plain,
( ( $true = $false )
| ~ spl11_99
| ~ spl11_101
| ~ spl11_111
| ~ spl11_119 ),
inference(forward_demodulation,[],[f10613,f5227]) ).
thf(f10619,plain,
( $false
| ~ spl11_99
| ~ spl11_101
| ~ spl11_111
| ~ spl11_119 ),
inference(trivial_inequality_removal,[],[f10618]) ).
thf(f10620,plain,
( ~ spl11_99
| ~ spl11_101
| ~ spl11_111
| ~ spl11_119 ),
inference(avatar_contradiction_clause,[],[f10619]) ).
thf(f10622,definition,
( spl11_256
<=> ( $true
= ( irel @ ( sK5 @ ( sK7 @ sK0 ) ) @ ( sK10 @ ( sK7 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_256])],[avatar_definition]) ).
thf(f10624,plain,
( ( $true
= ( irel @ ( sK5 @ ( sK7 @ sK0 ) ) @ ( sK10 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_256 ),
inference(avatar_component_clause,[],[f10622]) ).
thf(f10627,plain,
( spl11_108
| spl11_101
| ~ spl11_11
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5184,f5116,f1207,f5234,f5264]) ).
thf(f10632,plain,
( spl11_256
| spl11_101
| ~ spl11_12
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f6355,f5116,f1211,f5234,f10622]) ).
thf(f10633,plain,
( spl11_100
| spl11_101
| ~ spl11_4
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5511,f5116,f735,f5234,f5230]) ).
thf(f10765,plain,
( ! [X0: $i] :
( ( $true
= ( a3 @ X0 ) )
| ( ( irel @ ( sK5 @ ( sK7 @ sK0 ) ) @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl11_100
| ~ spl11_107 ),
inference(superposition,[],[f5232,f5627]) ).
thf(f10771,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ ( sK7 @ sK0 ) ) @ X0 )
= $false )
| ( $true
= ( a3 @ X0 ) ) )
| ~ spl11_100
| ~ spl11_107 ),
inference(trivial_inequality_removal,[],[f10765]) ).
thf(f10806,plain,
( ( $true = $false )
| ( $true
= ( a3 @ ( sK10 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_100
| ~ spl11_107
| ~ spl11_256 ),
inference(superposition,[],[f10771,f10624]) ).
thf(f10814,plain,
( ( $true
= ( a3 @ ( sK10 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_100
| ~ spl11_107
| ~ spl11_256 ),
inference(trivial_inequality_removal,[],[f10806]) ).
thf(f10821,plain,
( ( $true = $false )
| ~ spl11_100
| ~ spl11_107
| ~ spl11_108
| ~ spl11_256 ),
inference(forward_demodulation,[],[f10814,f5266]) ).
thf(f10822,plain,
( $false
| ~ spl11_100
| ~ spl11_107
| ~ spl11_108
| ~ spl11_256 ),
inference(trivial_inequality_removal,[],[f10821]) ).
thf(f10823,plain,
( ~ spl11_100
| ~ spl11_107
| ~ spl11_108
| ~ spl11_256 ),
inference(avatar_contradiction_clause,[],[f10822]) ).
thf(f10828,plain,
( spl11_107
| spl11_106
| ~ spl11_1
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5466,f5116,f611,f5255,f5259]) ).
thf(f10831,definition,
( spl11_259
<=> ( ( irel @ ( sK3 @ ( sK7 @ sK0 ) ) @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_259])],[avatar_definition]) ).
thf(f10833,plain,
( ( ( irel @ ( sK3 @ ( sK7 @ sK0 ) ) @ ( sK8 @ ( sK7 @ sK0 ) ) )
= $true )
| ~ spl11_259 ),
inference(avatar_component_clause,[],[f10831]) ).
thf(f10835,plain,
( spl11_259
| spl11_107
| ~ spl11_8
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f6333,f5116,f1020,f5259,f10831]) ).
thf(f10921,plain,
( ! [X0: $i] :
( ( $true
= ( a4 @ X0 ) )
| ( ( irel @ ( sK3 @ ( sK7 @ sK0 ) ) @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl11_106
| ~ spl11_113 ),
inference(superposition,[],[f5257,f5634]) ).
thf(f10926,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK3 @ ( sK7 @ sK0 ) ) @ X0 )
= $false )
| ( $true
= ( a4 @ X0 ) ) )
| ~ spl11_106
| ~ spl11_113 ),
inference(trivial_inequality_removal,[],[f10921]) ).
thf(f10969,plain,
( ( $true
= ( a4 @ ( sK8 @ ( sK7 @ sK0 ) ) ) )
| ( $true = $false )
| ~ spl11_106
| ~ spl11_113
| ~ spl11_259 ),
inference(superposition,[],[f10833,f10926]) ).
thf(f10975,plain,
( ( $true
= ( a4 @ ( sK8 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_106
| ~ spl11_113
| ~ spl11_259 ),
inference(trivial_inequality_removal,[],[f10969]) ).
thf(f10980,plain,
( ( $true = $false )
| ~ spl11_106
| ~ spl11_112
| ~ spl11_113
| ~ spl11_259 ),
inference(forward_demodulation,[],[f10975,f5290]) ).
thf(f10981,plain,
( $false
| ~ spl11_106
| ~ spl11_112
| ~ spl11_113
| ~ spl11_259 ),
inference(trivial_inequality_removal,[],[f10980]) ).
thf(f10982,plain,
( ~ spl11_106
| ~ spl11_112
| ~ spl11_113
| ~ spl11_259 ),
inference(avatar_contradiction_clause,[],[f10981]) ).
thf(f10987,plain,
( spl11_114
| spl11_113
| ~ spl11_5
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f5497,f5116,f760,f5387,f5390]) ).
thf(f10989,definition,
( spl11_261
<=> ( ( irel @ ( sK4 @ ( sK7 @ sK0 ) ) @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_261])],[avatar_definition]) ).
thf(f10991,plain,
( ( ( irel @ ( sK4 @ ( sK7 @ sK0 ) ) @ ( sK9 @ ( sK7 @ sK0 ) ) )
= $true )
| ~ spl11_261 ),
inference(avatar_component_clause,[],[f10989]) ).
thf(f10993,plain,
( spl11_261
| spl11_113
| ~ spl11_14
| ~ spl11_96 ),
inference(avatar_split_clause,[],[f6372,f5116,f1248,f5387,f10989]) ).
thf(f12546,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true = $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a0 @ X1 ) )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl11_22 ),
inference(superposition,[],[f95,f1738]) ).
thf(f12564,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a0 @ X1 ) )
| ( $true
= ( b0 @ X0 ) )
| ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false ) )
| ~ spl11_22 ),
inference(trivial_inequality_removal,[],[f12546]) ).
thf(f12581,definition,
( spl11_329
<=> ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_329])],[avatar_definition]) ).
thf(f12582,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl11_329 ),
inference(avatar_component_clause,[],[f12581]) ).
thf(f12584,plain,
( spl11_329
| spl11_97
| ~ spl11_22 ),
inference(avatar_split_clause,[],[f12564,f1737,f5120,f12581]) ).
thf(f12592,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( b0 @ X0 ) )
| ( $true = $false )
| ( ( irel @ X1 @ X0 )
= $false )
| ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false ) )
| ~ spl11_329 ),
inference(superposition,[],[f12582,f107]) ).
thf(f12611,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK7 @ sK0 ) @ X1 )
= $false )
| ( ( irel @ X1 @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl11_329 ),
inference(trivial_inequality_removal,[],[f12592]) ).
thf(f14107,plain,
( ! [X0: $i] :
( ( $true
= ( b0 @ X0 ) )
| ( $true = $false )
| ( ( irel @ ( sK4 @ ( sK7 @ sK0 ) ) @ X0 )
= $false ) )
| ~ spl11_114
| ~ spl11_329 ),
inference(superposition,[],[f5392,f12611]) ).
thf(f14121,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK4 @ ( sK7 @ sK0 ) ) @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl11_114
| ~ spl11_329 ),
inference(trivial_inequality_removal,[],[f14107]) ).
thf(f14185,plain,
( ( $true
= ( b0 @ ( sK9 @ ( sK7 @ sK0 ) ) ) )
| ( $true = $false )
| ~ spl11_114
| ~ spl11_261
| ~ spl11_329 ),
inference(superposition,[],[f10991,f14121]) ).
thf(f14190,plain,
( ( $true
= ( b0 @ ( sK9 @ ( sK7 @ sK0 ) ) ) )
| ~ spl11_114
| ~ spl11_261
| ~ spl11_329 ),
inference(trivial_inequality_removal,[],[f14185]) ).
thf(f14196,plain,
( ( $true = $false )
| ~ spl11_114
| ~ spl11_115
| ~ spl11_261
| ~ spl11_329 ),
inference(forward_demodulation,[],[f14190,f5405]) ).
thf(f14197,plain,
( $false
| ~ spl11_114
| ~ spl11_115
| ~ spl11_261
| ~ spl11_329 ),
inference(trivial_inequality_removal,[],[f14196]) ).
thf(f14198,plain,
( ~ spl11_114
| ~ spl11_115
| ~ spl11_261
| ~ spl11_329 ),
inference(avatar_contradiction_clause,[],[f14197]) ).
cnf(s28,plain,
( spl11_3
| spl11_3 ),
inference(sat_conversion,[],[f1234]) ).
cnf(s29,plain,
spl11_3,
inference(rat,[],[s28]) ).
cnf(s31,plain,
( spl11_2
| spl11_2 ),
inference(sat_conversion,[],[f1236]) ).
cnf(s32,plain,
spl11_2,
inference(rat,[],[s31]) ).
cnf(s38,plain,
( spl11_1
| spl11_1 ),
inference(sat_conversion,[],[f1265]) ).
cnf(s39,plain,
spl11_1,
inference(rat,[],[s38]) ).
cnf(s55,plain,
( spl11_5
| spl11_5 ),
inference(sat_conversion,[],[f1517]) ).
cnf(s56,plain,
spl11_5,
inference(rat,[],[s55]) ).
cnf(s63,plain,
( spl11_7
| spl11_7 ),
inference(sat_conversion,[],[f1577]) ).
cnf(s64,plain,
spl11_7,
inference(rat,[],[s63]) ).
cnf(s65,plain,
( spl11_6
| spl11_6 ),
inference(sat_conversion,[],[f1623]) ).
cnf(s66,plain,
spl11_6,
inference(rat,[],[s65]) ).
cnf(s68,plain,
( spl11_4
| spl11_4 ),
inference(sat_conversion,[],[f1643]) ).
cnf(s69,plain,
spl11_4,
inference(rat,[],[s68]) ).
cnf(s251,plain,
( spl11_9
| spl11_9 ),
inference(sat_conversion,[],[f2792]) ).
cnf(s252,plain,
spl11_9,
inference(rat,[],[s251]) ).
cnf(s254,plain,
( spl11_8
| spl11_8 ),
inference(sat_conversion,[],[f2795]) ).
cnf(s255,plain,
spl11_8,
inference(rat,[],[s254]) ).
cnf(s322,plain,
( spl11_14
| spl11_14 ),
inference(sat_conversion,[],[f3043]) ).
cnf(s323,plain,
spl11_14,
inference(rat,[],[s322]) ).
cnf(s325,plain,
( spl11_13
| spl11_13 ),
inference(sat_conversion,[],[f3046]) ).
cnf(s326,plain,
spl11_13,
inference(rat,[],[s325]) ).
cnf(s328,plain,
( spl11_19
| spl11_19 ),
inference(sat_conversion,[],[f3059]) ).
cnf(s329,plain,
spl11_19,
inference(rat,[],[s328]) ).
cnf(s332,plain,
( spl11_20
| spl11_20 ),
inference(sat_conversion,[],[f3062]) ).
cnf(s333,plain,
spl11_20,
inference(rat,[],[s332]) ).
cnf(s362,plain,
( spl11_16
| spl11_16 ),
inference(sat_conversion,[],[f3158]) ).
cnf(s363,plain,
spl11_16,
inference(rat,[],[s362]) ).
cnf(s365,plain,
( spl11_17
| spl11_17 ),
inference(sat_conversion,[],[f3161]) ).
cnf(s366,plain,
spl11_17,
inference(rat,[],[s365]) ).
cnf(s377,plain,
( spl11_11
| spl11_11 ),
inference(sat_conversion,[],[f3201]) ).
cnf(s378,plain,
spl11_11,
inference(rat,[],[s377]) ).
cnf(s380,plain,
( spl11_12
| spl11_12 ),
inference(sat_conversion,[],[f3204]) ).
cnf(s381,plain,
spl11_12,
inference(rat,[],[s380]) ).
cnf(s439,plain,
( spl11_22
| spl11_22 ),
inference(sat_conversion,[],[f3341]) ).
cnf(s440,plain,
spl11_22,
inference(rat,[],[s439]) ).
cnf(s538,plain,
( ~ spl11_2
| spl11_51
| spl11_52 ),
inference(sat_conversion,[],[f3834]) ).
cnf(s539,plain,
( ~ spl11_3
| spl11_26
| spl11_52 ),
inference(sat_conversion,[],[f3835]) ).
cnf(s597,plain,
~ spl11_52,
inference(sat_conversion,[],[f4176]) ).
cnf(s632,plain,
( ~ spl11_7
| spl11_96
| spl11_97 ),
inference(sat_conversion,[],[f5123]) ).
cnf(s661,plain,
( ~ spl11_26
| ~ spl11_51
| ~ spl11_97 ),
inference(sat_conversion,[],[f5360]) ).
cnf(s675,plain,
( ~ spl11_9
| ~ spl11_96
| spl11_107
| spl11_112 ),
inference(sat_conversion,[],[f5401]) ).
cnf(s687,plain,
( ~ spl11_13
| ~ spl11_96
| spl11_113
| spl11_115 ),
inference(sat_conversion,[],[f5417]) ).
cnf(s695,plain,
( ~ spl11_20
| spl11_97
| spl11_116 ),
inference(sat_conversion,[],[f6447]) ).
cnf(s698,plain,
( ~ spl11_19
| spl11_97
| ~ spl11_98
| ~ spl11_116 ),
inference(sat_conversion,[],[f6531]) ).
cnf(s702,plain,
( ~ spl11_16
| ~ spl11_96
| spl11_98
| spl11_99 ),
inference(sat_conversion,[],[f6534]) ).
cnf(s705,plain,
( ~ spl11_6
| ~ spl11_96
| spl11_98
| spl11_111 ),
inference(sat_conversion,[],[f6545]) ).
cnf(s706,plain,
( ~ spl11_17
| ~ spl11_96
| spl11_98
| spl11_119 ),
inference(sat_conversion,[],[f6546]) ).
cnf(s986,plain,
( ~ spl11_99
| ~ spl11_101
| ~ spl11_111
| ~ spl11_119 ),
inference(sat_conversion,[],[f10620]) ).
cnf(s989,plain,
( ~ spl11_11
| ~ spl11_96
| spl11_101
| spl11_108 ),
inference(sat_conversion,[],[f10627]) ).
cnf(s991,plain,
( ~ spl11_12
| ~ spl11_96
| spl11_101
| spl11_256 ),
inference(sat_conversion,[],[f10632]) ).
cnf(s992,plain,
( ~ spl11_4
| ~ spl11_96
| spl11_100
| spl11_101 ),
inference(sat_conversion,[],[f10633]) ).
cnf(s995,plain,
( ~ spl11_100
| ~ spl11_107
| ~ spl11_108
| ~ spl11_256 ),
inference(sat_conversion,[],[f10823]) ).
cnf(s997,plain,
( ~ spl11_1
| ~ spl11_96
| spl11_106
| spl11_107 ),
inference(sat_conversion,[],[f10828]) ).
cnf(s1000,plain,
( ~ spl11_8
| ~ spl11_96
| spl11_107
| spl11_259 ),
inference(sat_conversion,[],[f10835]) ).
cnf(s1002,plain,
( ~ spl11_106
| ~ spl11_112
| ~ spl11_113
| ~ spl11_259 ),
inference(sat_conversion,[],[f10982]) ).
cnf(s1004,plain,
( ~ spl11_5
| ~ spl11_96
| spl11_113
| spl11_114 ),
inference(sat_conversion,[],[f10987]) ).
cnf(s1006,plain,
( ~ spl11_14
| ~ spl11_96
| spl11_113
| spl11_261 ),
inference(sat_conversion,[],[f10993]) ).
cnf(s1096,plain,
( ~ spl11_22
| spl11_97
| spl11_329 ),
inference(sat_conversion,[],[f12584]) ).
cnf(s1119,plain,
( ~ spl11_114
| ~ spl11_115
| ~ spl11_261
| ~ spl11_329 ),
inference(sat_conversion,[],[f14198]) ).
cnf(s1120,plain,
( ~ spl11_3
| spl11_26 ),
inference(rat,[],[s539,s597]) ).
cnf(s1121,plain,
( ~ spl11_2
| spl11_51 ),
inference(rat,[],[s538,s597]) ).
cnf(s1128,plain,
spl11_51,
inference(rat,[],[s1121,s32]) ).
cnf(s1130,plain,
spl11_26,
inference(rat,[],[s1120,s29]) ).
cnf(s1132,plain,
~ spl11_97,
inference(rat,[],[s661,s1128,s1130]) ).
cnf(s1135,plain,
spl11_329,
inference(rat,[],[s1096,s440,s1132]) ).
cnf(s1136,plain,
spl11_116,
inference(rat,[],[s695,s333,s1132]) ).
cnf(s1138,plain,
spl11_96,
inference(rat,[],[s632,s64,s1132]) ).
cnf(s1147,plain,
~ spl11_98,
inference(rat,[],[s698,s1132,s329,s1136]) ).
cnf(s1152,plain,
spl11_119,
inference(rat,[],[s706,s1138,s366,s1147]) ).
cnf(s1153,plain,
spl11_99,
inference(rat,[],[s702,s1138,s363,s1147]) ).
cnf(s1154,plain,
spl11_111,
inference(rat,[],[s705,s1138,s66,s1147]) ).
cnf(s1167,plain,
~ spl11_101,
inference(rat,[],[s986,s1152,s1154,s1153]) ).
cnf(s1173,plain,
spl11_256,
inference(rat,[],[s991,s1138,s381,s1167]) ).
cnf(s1174,plain,
spl11_108,
inference(rat,[],[s989,s1138,s378,s1167]) ).
cnf(s1175,plain,
spl11_100,
inference(rat,[],[s992,s1138,s69,s1167]) ).
cnf(s1190,plain,
~ spl11_107,
inference(rat,[],[s995,s1173,s1174,s1175]) ).
cnf(s1202,plain,
spl11_259,
inference(rat,[],[s1000,s1138,s255,s1190]) ).
cnf(s1203,plain,
spl11_112,
inference(rat,[],[s675,s1138,s252,s1190]) ).
cnf(s1204,plain,
spl11_106,
inference(rat,[],[s997,s1138,s39,s1190]) ).
cnf(s1224,plain,
~ spl11_113,
inference(rat,[],[s1002,s1202,s1203,s1204]) ).
cnf(s1241,plain,
spl11_115,
inference(rat,[],[s687,s1138,s326,s1224]) ).
cnf(s1242,plain,
spl11_261,
inference(rat,[],[s1006,s1138,s323,s1224]) ).
cnf(s1243,plain,
spl11_114,
inference(rat,[],[s1004,s1138,s56,s1224]) ).
cnf(s1265,plain,
$false,
inference(rat,[],[s1119,s1135,s1242,s1241,s1243]) ).
thf(f14199,plain,
$false,
inference(avatar_sat_refutation,[],[s1265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO069^4.004 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 % Computer : n019.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Tue Sep 29 16:29:48 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running higher-order theorem proving
% 0.26/0.34 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.20/0.53 % (1005596)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.20/0.53 % (1005601)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2280251500:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.20/0.53 % (1005607)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.20/0.53 % (1005607)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.20/0.53 % (1005605)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3675530769:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.20/0.53 % (1005603)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3783590834:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.20/0.53 % (1005602)lrs+10_16_si=on:nwc=1.5:random_seed=4057284148:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.20/0.53 % (1005604)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2127239561:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 1.20/0.53 % (1005607)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2045278418:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.20/0.53 % (1005606)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1799998102:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.20/0.53 % (1005603)Instruction limit reached!
% 1.20/0.53 % (1005603)------------------------------
% 1.20/0.53 % (1005603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (1005603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (1005603)CaDiCaL version: 2.1.3
% 1.20/0.53 % (1005603)Termination reason: Instruction limit
% 1.20/0.53 % (1005603)Termination phase: Property scanning
% 1.20/0.53 % (1005603)Time elapsed: 0.003 s
% 1.20/0.53 % (1005603)Peak memory usage: 10 MB
% 1.20/0.53 % (1005603)Instructions burned: 6 (million)
% 1.20/0.53 % (1005602)Instruction limit reached!
% 1.20/0.53 % (1005602)------------------------------
% 1.20/0.53 % (1005602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (1005602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (1005602)CaDiCaL version: 2.1.3
% 1.20/0.53 % (1005602)Termination reason: Instruction limit
% 1.20/0.53 % (1005602)Termination phase: Saturation
% 1.20/0.53 % (1005602)Time elapsed: 0.014 s
% 1.20/0.53 % (1005602)Peak memory usage: 11 MB
% 1.20/0.53 % (1005602)Instructions burned: 18 (million)
% 1.20/0.53 % (1005605)Instruction limit reached!
% 1.20/0.53 % (1005605)------------------------------
% 1.20/0.53 % (1005605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (1005605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (1005601)Instruction limit reached!
% 1.20/0.53 % (1005601)------------------------------
% 1.20/0.53 % (1005601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.53 % (1005605)CaDiCaL version: 2.1.3
% 1.20/0.53 % (1005605)Termination reason: Instruction limit
% 1.20/0.53 % (1005605)Termination phase: Saturation
% 1.20/0.53 % (1005605)Time elapsed: 0.023 s
% 1.20/0.53 % (1005605)Peak memory usage: 11 MB
% 1.20/0.53 % (1005605)Instructions burned: 25 (million)
% 1.20/0.53 % (1005601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.53 % (1005601)CaDiCaL version: 2.1.3
% 1.20/0.53 % (1005601)Termination reason: Instruction limit
% 1.20/0.53 % (1005601)Termination phase: Saturation
% 1.20/0.53 % (1005601)Time elapsed: 0.036 s
% 1.20/0.53 % (1005601)Peak memory usage: 12 MB
% 1.20/0.53 % (1005601)Instructions burned: 89 (million)
% 1.20/0.53 % (1005615)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2511546586:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.20/0.53 % (1005618)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2514260622:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.20/0.59 % (1005615)Instruction limit reached!
% 1.20/0.59 % (1005615)------------------------------
% 1.20/0.59 % (1005615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.59 % (1005615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.59 % (1005615)CaDiCaL version: 2.1.3
% 1.20/0.59 % (1005615)Termination reason: Instruction limit
% 1.20/0.59 % (1005615)Termination phase: shuffling
% 1.20/0.59 % (1005615)Time elapsed: 0.002 s
% 1.20/0.59 % (1005615)Peak memory usage: 9 MB
% 1.20/0.59 % (1005615)Instructions burned: 2 (million)
% 1.20/0.59 % (1005618)Instruction limit reached!
% 1.20/0.59 % (1005618)------------------------------
% 1.20/0.59 % (1005618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.59 % (1005618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.59 % (1005618)CaDiCaL version: 2.1.3
% 1.20/0.59 % (1005616)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1206257580:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.20/0.59 % (1005618)Termination reason: Instruction limit
% 1.20/0.59 % (1005618)Termination phase: Saturation
% 1.20/0.59 % (1005618)Time elapsed: 0.005 s
% 1.20/0.59 % (1005618)Peak memory usage: 11 MB
% 1.20/0.59 % (1005618)Instructions burned: 13 (million)
% 1.20/0.59 % (1005617)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.20/0.59 % (1005616)Instruction limit reached!
% 1.20/0.59 % (1005616)------------------------------
% 1.20/0.59 % (1005616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.59 % (1005616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.59 % (1005616)CaDiCaL version: 2.1.3
% 1.20/0.59 % (1005616)Termination reason: Instruction limit
% 1.20/0.59 % (1005616)Termination phase: Property scanning
% 1.20/0.59 % (1005616)Time elapsed: 0.004 s
% 1.20/0.59 % (1005616)Peak memory usage: 10 MB
% 1.20/0.59 % (1005616)Instructions burned: 5 (million)
% 1.20/0.59 % (1005617)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3422764060:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.20/0.59 % (1005606)Instruction limit reached!
% 1.20/0.59 % (1005606)------------------------------
% 1.20/0.59 % (1005606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.59 % (1005606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.59 % (1005606)CaDiCaL version: 2.1.3
% 1.20/0.59 % (1005606)Termination reason: Instruction limit
% 1.20/0.59 % (1005606)Termination phase: Saturation
% 1.20/0.59 % (1005606)Time elapsed: 0.059 s
% 1.20/0.59 % (1005606)Peak memory usage: 12 MB
% 1.20/0.59 % (1005606)Instructions burned: 76 (million)
% 1.20/0.59 % (1005617)Instruction limit reached!
% 1.20/0.59 % (1005617)------------------------------
% 1.20/0.59 % (1005617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.20/0.59 % (1005617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.20/0.59 % (1005617)CaDiCaL version: 2.1.3
% 1.20/0.59 % (1005617)Termination reason: Instruction limit
% 1.20/0.59 % (1005617)Termination phase: Property scanning
% 1.20/0.59 % (1005617)Time elapsed: 0.006 s
% 1.20/0.59 % (1005617)Peak memory usage: 10 MB
% 1.20/0.59 % (1005617)Instructions burned: 8 (million)
% 1.20/0.59 % (1005623)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1792203238:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.20/0.59 % (1005621)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.20/0.59 % (1005621)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.20/0.59 % (1005621)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2452134979:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.20/0.59 % (1005624)lrs+10_1_si=on:cs=on:random_seed=1257904643:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.20/0.59 % (1005626)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.88/0.64 % (1005624)Instruction limit reached!
% 1.88/0.64 % (1005624)------------------------------
% 1.88/0.64 % (1005624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.64 % (1005624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.64 % (1005624)CaDiCaL version: 2.1.3
% 1.88/0.64 % (1005624)Termination reason: Instruction limit
% 1.88/0.64 % (1005624)Termination phase: Property scanning
% 1.88/0.64 % (1005624)Time elapsed: 0.007 s
% 1.88/0.64 % (1005624)Peak memory usage: 10 MB
% 1.88/0.64 % (1005624)Instructions burned: 8 (million)
% 1.88/0.64 % (1005626)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3691057085:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.88/0.64 % (1005628)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2529170673:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.88/0.64 % (1005626)Instruction limit reached!
% 1.88/0.64 % (1005626)------------------------------
% 1.88/0.64 % (1005626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.64 % (1005626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.64 % (1005626)CaDiCaL version: 2.1.3
% 1.88/0.64 % (1005626)Termination reason: Instruction limit
% 1.88/0.64 % (1005626)Termination phase: Property scanning
% 1.88/0.64 % (1005626)Time elapsed: 0.003 s
% 1.88/0.64 % (1005626)Peak memory usage: 10 MB
% 1.88/0.64 % (1005626)Instructions burned: 4 (million)
% 1.88/0.64 % (1005623)Instruction limit reached!
% 1.88/0.64 % (1005623)------------------------------
% 1.88/0.64 % (1005623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.64 % (1005623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.64 % (1005623)CaDiCaL version: 2.1.3
% 1.88/0.64 % (1005623)Termination reason: Instruction limit
% 1.88/0.64 % (1005623)Termination phase: Saturation
% 1.88/0.64 % (1005623)Time elapsed: 0.036 s
% 1.88/0.64 % (1005623)Peak memory usage: 13 MB
% 1.88/0.64 % (1005623)Instructions burned: 88 (million)
% 1.88/0.64 % (1005621)Instruction limit reached!
% 1.88/0.64 % (1005621)------------------------------
% 1.88/0.64 % (1005621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.64 % (1005621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.64 % (1005621)CaDiCaL version: 2.1.3
% 1.88/0.64 % (1005621)Termination reason: Instruction limit
% 1.88/0.64 % (1005621)Termination phase: Saturation
% 1.88/0.64 % (1005621)Time elapsed: 0.022 s
% 1.88/0.64 % (1005621)Peak memory usage: 11 MB
% 1.88/0.64 % (1005621)Instructions burned: 28 (million)
% 1.88/0.64 % (1005628)Refutation not found, incomplete strategy
% 1.88/0.64 % (1005628)------------------------------
% 1.88/0.64 % (1005628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.64 % (1005628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.64 % (1005628)CaDiCaL version: 2.1.3
% 1.88/0.64 % (1005628)Termination reason: Refutation not found, incomplete strategy
% 1.88/0.64 % (1005628)Time elapsed: 0.008 s
% 1.88/0.64 % (1005628)Peak memory usage: 12 MB
% 1.88/0.64 % (1005628)Instructions burned: 8 (million)
% 1.88/0.64 % (1005628)------------------------------
% 1.88/0.64 % (1005628)------------------------------
% 1.88/0.64 % (1005636)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4058265982:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.88/0.64 % (1005631)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2743630156:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.88/0.64 % (1005607)Instruction limit reached!
% 1.88/0.64 % (1005607)------------------------------
% 1.88/0.64 % (1005607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.64 % (1005607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.64 % (1005607)CaDiCaL version: 2.1.3
% 1.88/0.64 % (1005607)Termination reason: Instruction limit
% 1.88/0.64 % (1005607)Termination phase: Saturation
% 1.88/0.64 % (1005607)Time elapsed: 0.125 s
% 1.88/0.64 % (1005607)Peak memory usage: 13 MB
% 1.88/0.64 % (1005607)Instructions burned: 158 (million)
% 1.88/0.64 % (1005634)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3470038089:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.10/0.69 % (1005631)Refutation not found, incomplete strategy
% 2.10/0.69 % (1005631)------------------------------
% 2.10/0.69 % (1005631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.69 % (1005631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.69 % (1005631)CaDiCaL version: 2.1.3
% 2.10/0.69 % (1005631)Termination reason: Refutation not found, incomplete strategy
% 2.10/0.69 % (1005631)Time elapsed: 0.010 s
% 2.10/0.69 % (1005631)Peak memory usage: 12 MB
% 2.10/0.69 % (1005631)Instructions burned: 12 (million)
% 2.10/0.69 % (1005635)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2562324348:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.10/0.69 % (1005631)------------------------------
% 2.10/0.69 % (1005631)------------------------------
% 2.10/0.69 % (1005637)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1232249874:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.10/0.69 % (1005635)Instruction limit reached!
% 2.10/0.69 % (1005635)------------------------------
% 2.10/0.69 % (1005635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.69 % (1005635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.69 % (1005635)CaDiCaL version: 2.1.3
% 2.10/0.69 % (1005635)Termination reason: Instruction limit
% 2.10/0.69 % (1005635)Termination phase: Saturation
% 2.10/0.69 % (1005635)Time elapsed: 0.012 s
% 2.10/0.69 % (1005635)Peak memory usage: 11 MB
% 2.10/0.69 % (1005635)Instructions burned: 14 (million)
% 2.10/0.69 % (1005634)Instruction limit reached!
% 2.10/0.69 % (1005634)------------------------------
% 2.10/0.69 % (1005634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.69 % (1005634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.69 % (1005634)CaDiCaL version: 2.1.3
% 2.10/0.69 % (1005634)Termination reason: Instruction limit
% 2.10/0.69 % (1005634)Termination phase: Saturation
% 2.10/0.69 % (1005634)Time elapsed: 0.025 s
% 2.10/0.69 % (1005634)Peak memory usage: 12 MB
% 2.10/0.69 % (1005634)Instructions burned: 25 (million)
% 2.10/0.69 % (1005637)Instruction limit reached!
% 2.10/0.69 % (1005637)------------------------------
% 2.10/0.69 % (1005637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.69 % (1005637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.69 % (1005637)CaDiCaL version: 2.1.3
% 2.10/0.69 % (1005637)Termination reason: Instruction limit
% 2.10/0.69 % (1005637)Termination phase: Saturation
% 2.10/0.69 % (1005637)Time elapsed: 0.012 s
% 2.10/0.69 % (1005637)Peak memory usage: 11 MB
% 2.10/0.69 % (1005637)Instructions burned: 15 (million)
% 2.10/0.69 % (1005640)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=751350025:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.10/0.69 % (1005640)Instruction limit reached!
% 2.10/0.69 % (1005640)------------------------------
% 2.10/0.69 % (1005640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.69 % (1005640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.69 % (1005640)CaDiCaL version: 2.1.3
% 2.10/0.69 % (1005640)Termination reason: Instruction limit
% 2.10/0.69 % (1005640)Termination phase: Property scanning
% 2.10/0.69 % (1005640)Time elapsed: 0.003 s
% 2.10/0.69 % (1005640)Peak memory usage: 10 MB
% 2.10/0.69 % (1005640)Instructions burned: 4 (million)
% 2.10/0.69 % (1005643)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=173986161:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.10/0.69 % (1005645)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1660472034:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.10/0.69 % (1005647)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.10/0.69 % (1005647)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.41/0.74 % (1005643)Instruction limit reached!
% 2.41/0.74 % (1005643)------------------------------
% 2.41/0.74 % (1005643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.74 % (1005643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.74 % (1005643)CaDiCaL version: 2.1.3
% 2.41/0.74 % (1005643)Termination reason: Instruction limit
% 2.41/0.74 % (1005643)Termination phase: Saturation
% 2.41/0.74 % (1005643)Time elapsed: 0.020 s
% 2.41/0.74 % (1005643)Peak memory usage: 11 MB
% 2.41/0.74 % (1005643)Instructions burned: 26 (million)
% 2.41/0.74 % (1005646)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=600808203:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.41/0.74 % (1005649)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.41/0.74 % (1005647)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2385306846:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.41/0.74 % (1005649)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3575027559:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.41/0.74 % (1005645)Instruction limit reached!
% 2.41/0.74 % (1005645)------------------------------
% 2.41/0.74 % (1005645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.74 % (1005645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.74 % (1005645)CaDiCaL version: 2.1.3
% 2.41/0.74 % (1005645)Termination reason: Instruction limit
% 2.41/0.74 % (1005645)Termination phase: Saturation
% 2.41/0.74 % (1005645)Time elapsed: 0.019 s
% 2.41/0.74 % (1005645)Peak memory usage: 11 MB
% 2.41/0.74 % (1005645)Instructions burned: 24 (million)
% 2.41/0.74 % (1005649)Instruction limit reached!
% 2.41/0.74 % (1005649)------------------------------
% 2.41/0.74 % (1005649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.74 % (1005649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.74 % (1005649)CaDiCaL version: 2.1.3
% 2.41/0.74 % (1005649)Termination reason: Instruction limit
% 2.41/0.74 % (1005649)Termination phase: Property scanning
% 2.41/0.74 % (1005649)Time elapsed: 0.006 s
% 2.41/0.74 % (1005649)Peak memory usage: 10 MB
% 2.41/0.74 % (1005649)Instructions burned: 8 (million)
% 2.41/0.74 % (1005647)Instruction limit reached!
% 2.41/0.74 % (1005647)------------------------------
% 2.41/0.74 % (1005647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.74 % (1005647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.74 % (1005647)CaDiCaL version: 2.1.3
% 2.41/0.74 % (1005647)Termination reason: Instruction limit
% 2.41/0.74 % (1005647)Termination phase: Saturation
% 2.41/0.74 % (1005647)Time elapsed: 0.012 s
% 2.41/0.74 % (1005647)Peak memory usage: 11 MB
% 2.41/0.74 % (1005647)Instructions burned: 14 (million)
% 2.41/0.74 % (1005653)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=993198149:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.41/0.74 % (1005656)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2655021032:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.41/0.74 % (1005657)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=221607666:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.41/0.74 % (1005658)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1065510287:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.41/0.74 % (1005656)Instruction limit reached!
% 2.41/0.74 % (1005656)------------------------------
% 2.41/0.74 % (1005656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.74 % (1005656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.74 % (1005656)CaDiCaL version: 2.1.3
% 2.41/0.74 % (1005656)Termination reason: Instruction limit
% 2.41/0.74 % (1005656)Termination phase: Property scanning
% 2.41/0.74 % (1005656)Time elapsed: 0.006 s
% 2.41/0.74 % (1005656)Peak memory usage: 10 MB
% 2.92/0.82 % (1005656)Instructions burned: 9 (million)
% 2.92/0.82 % (1005646)Instruction limit reached!
% 2.92/0.82 % (1005646)------------------------------
% 2.92/0.82 % (1005646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.92/0.82 % (1005646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/0.82 % (1005646)CaDiCaL version: 2.1.3
% 2.92/0.82 % (1005646)Termination reason: Instruction limit
% 2.92/0.82 % (1005646)Termination phase: Saturation
% 2.92/0.82 % (1005646)Time elapsed: 0.057 s
% 2.92/0.82 % (1005646)Peak memory usage: 12 MB
% 2.92/0.82 % (1005646)Instructions burned: 60 (million)
% 2.92/0.82 % (1005653)Instruction limit reached!
% 2.92/0.82 % (1005653)------------------------------
% 2.92/0.82 % (1005653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.92/0.82 % (1005653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/0.82 % (1005653)CaDiCaL version: 2.1.3
% 2.92/0.82 % (1005653)Termination reason: Instruction limit
% 2.92/0.82 % (1005653)Termination phase: Saturation
% 2.92/0.82 % (1005653)Time elapsed: 0.028 s
% 2.92/0.82 % (1005653)Peak memory usage: 12 MB
% 2.92/0.82 % (1005653)Instructions burned: 31 (million)
% 2.92/0.82 % (1005657)Instruction limit reached!
% 2.92/0.82 % (1005657)------------------------------
% 2.92/0.82 % (1005657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.92/0.82 % (1005657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/0.82 % (1005657)CaDiCaL version: 2.1.3
% 2.92/0.82 % (1005657)Termination reason: Instruction limit
% 2.92/0.82 % (1005657)Termination phase: Saturation
% 2.92/0.82 % (1005657)Time elapsed: 0.018 s
% 2.92/0.82 % (1005657)Peak memory usage: 11 MB
% 2.92/0.82 % (1005657)Instructions burned: 24 (million)
% 2.92/0.82 % (1005658)Instruction limit reached!
% 2.92/0.82 % (1005658)------------------------------
% 2.92/0.82 % (1005658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.92/0.82 % (1005658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/0.82 % (1005658)CaDiCaL version: 2.1.3
% 2.92/0.82 % (1005658)Termination reason: Instruction limit
% 2.92/0.82 % (1005658)Termination phase: Saturation
% 2.92/0.82 % (1005658)Time elapsed: 0.018 s
% 2.92/0.82 % (1005658)Peak memory usage: 12 MB
% 2.92/0.82 % (1005658)Instructions burned: 20 (million)
% 2.92/0.82 % (1005636)Instruction limit reached!
% 2.92/0.82 % (1005636)------------------------------
% 2.92/0.82 % (1005636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.92/0.82 % (1005636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/0.82 % (1005636)CaDiCaL version: 2.1.3
% 2.92/0.82 % (1005636)Termination reason: Instruction limit
% 2.92/0.82 % (1005636)Termination phase: Saturation
% 2.92/0.82 % (1005636)Time elapsed: 0.144 s
% 2.92/0.82 % (1005636)Peak memory usage: 15 MB
% 2.92/0.82 % (1005636)Instructions burned: 329 (million)
% 2.92/0.82 % (1005663)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3195289297:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.92/0.82 % (1005667)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.92/0.82 % (1005664)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1183854287:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.92/0.82 % (1005668)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3219499943:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.92/0.82 % (1005665)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2385134584:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.92/0.82 % (1005666)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1920252850:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.92/0.82 % (1005668)Refutation not found, incomplete strategy
% 2.92/0.82 % (1005668)------------------------------
% 2.92/0.82 % (1005668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.92/0.82 % (1005668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/0.82 % (1005668)CaDiCaL version: 2.1.3
% 2.92/0.82 % (1005668)Termination reason: Refutation not found, incomplete strategy
% 2.92/0.82 % (1005668)Time elapsed: 0.004 s
% 2.92/0.82 % (1005668)Peak memory usage: 12 MB
% 3.36/0.91 % (1005668)Instructions burned: 8 (million)
% 3.36/0.91 % (1005667)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2693561036:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 3.36/0.91 % (1005668)------------------------------
% 3.36/0.91 % (1005668)------------------------------
% 3.36/0.91 % (1005667)Instruction limit reached!
% 3.36/0.91 % (1005667)------------------------------
% 3.36/0.91 % (1005667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.91 % (1005667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.91 % (1005667)CaDiCaL version: 2.1.3
% 3.36/0.91 % (1005667)Termination reason: Instruction limit
% 3.36/0.91 % (1005667)Termination phase: Property scanning
% 3.36/0.91 % (1005667)Time elapsed: 0.006 s
% 3.36/0.91 % (1005667)Peak memory usage: 10 MB
% 3.36/0.91 % (1005667)Instructions burned: 8 (million)
% 3.36/0.91 % (1005665)Refutation not found, incomplete strategy
% 3.36/0.91 % (1005665)------------------------------
% 3.36/0.91 % (1005665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.91 % (1005665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.91 % (1005665)CaDiCaL version: 2.1.3
% 3.36/0.91 % (1005665)Termination reason: Refutation not found, incomplete strategy
% 3.36/0.91 % (1005665)Time elapsed: 0.012 s
% 3.36/0.91 % (1005665)Peak memory usage: 12 MB
% 3.36/0.91 % (1005665)Instructions burned: 14 (million)
% 3.36/0.91 % (1005665)------------------------------
% 3.36/0.91 % (1005665)------------------------------
% 3.36/0.91 % (1005675)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3646160385:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 3.36/0.91 % (1005666)Instruction limit reached!
% 3.36/0.91 % (1005666)------------------------------
% 3.36/0.91 % (1005666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.91 % (1005666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.91 % (1005666)CaDiCaL version: 2.1.3
% 3.36/0.91 % (1005666)Termination reason: Instruction limit
% 3.36/0.91 % (1005666)Termination phase: Saturation
% 3.36/0.91 % (1005666)Time elapsed: 0.031 s
% 3.36/0.91 % (1005666)Peak memory usage: 11 MB
% 3.36/0.91 % (1005666)Instructions burned: 42 (million)
% 3.36/0.91 % (1005675)Refutation not found, incomplete strategy
% 3.36/0.91 % (1005675)------------------------------
% 3.36/0.91 % (1005675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.91 % (1005675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.91 % (1005675)CaDiCaL version: 2.1.3
% 3.36/0.91 % (1005675)Termination reason: Refutation not found, incomplete strategy
% 3.36/0.91 % (1005675)Time elapsed: 0.012 s
% 3.36/0.91 % (1005675)Peak memory usage: 12 MB
% 3.36/0.91 % (1005675)Instructions burned: 29 (million)
% 3.36/0.91 % (1005675)------------------------------
% 3.36/0.91 % (1005675)------------------------------
% 3.36/0.91 % (1005676)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.36/0.91 % (1005676)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3566752738:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 3.36/0.91 % (1005677)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1759106903:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.36/0.91 % (1005676)Instruction limit reached!
% 3.36/0.91 % (1005676)------------------------------
% 3.36/0.91 % (1005676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.91 % (1005676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.91 % (1005676)CaDiCaL version: 2.1.3
% 3.36/0.91 % (1005676)Termination reason: Instruction limit
% 3.36/0.91 % (1005676)Termination phase: Function definition elimination
% 3.36/0.91 % (1005676)Time elapsed: 0.005 s
% 3.36/0.91 % (1005676)Peak memory usage: 10 MB
% 3.36/0.91 % (1005676)Instructions burned: 6 (million)
% 3.36/0.91 % (1005680)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=342544829:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.36/0.99 % (1005677)Instruction limit reached!
% 3.36/0.99 % (1005677)------------------------------
% 3.36/0.99 % (1005677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.99 % (1005677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.99 % (1005677)CaDiCaL version: 2.1.3
% 3.36/0.99 % (1005677)Termination reason: Instruction limit
% 3.36/0.99 % (1005677)Termination phase: Saturation
% 3.36/0.99 % (1005677)Time elapsed: 0.017 s
% 3.36/0.99 % (1005677)Peak memory usage: 11 MB
% 3.36/0.99 % (1005677)Instructions burned: 23 (million)
% 3.36/0.99 % (1005679)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3772819133:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 3.36/0.99 % (1005683)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=471099407:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.36/0.99 % (1005679)Instruction limit reached!
% 3.36/0.99 % (1005679)------------------------------
% 3.36/0.99 % (1005679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.99 % (1005679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.99 % (1005679)CaDiCaL version: 2.1.3
% 3.36/0.99 % (1005679)Termination reason: Instruction limit
% 3.36/0.99 % (1005679)Termination phase: Saturation
% 3.36/0.99 % (1005679)Time elapsed: 0.015 s
% 3.36/0.99 % (1005679)Peak memory usage: 12 MB
% 3.36/0.99 % (1005679)Instructions burned: 19 (million)
% 3.36/0.99 % (1005604)Instruction limit reached!
% 3.36/0.99 % (1005604)------------------------------
% 3.36/0.99 % (1005604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.99 % (1005604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.99 % (1005604)CaDiCaL version: 2.1.3
% 3.36/0.99 % (1005604)Termination reason: Instruction limit
% 3.36/0.99 % (1005604)Termination phase: Saturation
% 3.36/0.99 % (1005604)Time elapsed: 0.372 s
% 3.36/0.99 % (1005604)Peak memory usage: 13 MB
% 3.36/0.99 % (1005604)Instructions burned: 635 (million)
% 3.36/0.99 % (1005685)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=184388145:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.36/0.99 % (1005664)Instruction limit reached!
% 3.36/0.99 % (1005664)------------------------------
% 3.36/0.99 % (1005664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.99 % (1005664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.99 % (1005664)CaDiCaL version: 2.1.3
% 3.36/0.99 % (1005664)Termination reason: Instruction limit
% 3.36/0.99 % (1005664)Termination phase: Saturation
% 3.36/0.99 % (1005664)Time elapsed: 0.111 s
% 3.36/0.99 % (1005664)Peak memory usage: 13 MB
% 3.36/0.99 % (1005664)Instructions burned: 144 (million)
% 3.36/0.99 % (1005688)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3906941173:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 3.36/0.99 % (1005689)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=821902730:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 3.36/0.99 % (1005688)Refutation not found, incomplete strategy
% 3.36/0.99 % (1005688)------------------------------
% 3.36/0.99 % (1005688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.99 % (1005688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.99 % (1005688)CaDiCaL version: 2.1.3
% 3.36/0.99 % (1005688)Termination reason: Refutation not found, incomplete strategy
% 3.36/0.99 % (1005688)Time elapsed: 0.010 s
% 3.36/0.99 % (1005688)Peak memory usage: 12 MB
% 3.36/0.99 % (1005688)Instructions burned: 10 (million)
% 3.36/0.99 % (1005688)------------------------------
% 3.36/0.99 % (1005688)------------------------------
% 3.36/0.99 % (1005685)Instruction limit reached!
% 3.36/0.99 % (1005685)------------------------------
% 3.36/0.99 % (1005685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.99 % (1005685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.09 % (1005685)CaDiCaL version: 2.1.3
% 5.13/1.09 % (1005685)Termination reason: Instruction limit
% 5.13/1.09 % (1005685)Termination phase: Saturation
% 5.13/1.09 % (1005685)Time elapsed: 0.034 s
% 5.13/1.09 % (1005685)Peak memory usage: 11 MB
% 5.13/1.09 % (1005685)Instructions burned: 45 (million)
% 5.13/1.09 % (1005689)Instruction limit reached!
% 5.13/1.09 % (1005689)------------------------------
% 5.13/1.09 % (1005689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.13/1.09 % (1005689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.09 % (1005689)CaDiCaL version: 2.1.3
% 5.13/1.09 % (1005689)Termination reason: Instruction limit
% 5.13/1.09 % (1005689)Termination phase: Saturation
% 5.13/1.09 % (1005689)Time elapsed: 0.016 s
% 5.13/1.09 % (1005689)Peak memory usage: 11 MB
% 5.13/1.09 % (1005689)Instructions burned: 22 (million)
% 5.13/1.09 % (1005691)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 5.13/1.09 % (1005691)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2632208018:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 5.13/1.09 % (1005694)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2351290310:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 5.13/1.09 % (1005695)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1955829865:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 5.13/1.09 % (1005696)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1479078188:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.13/1.09 % (1005694)Instruction limit reached!
% 5.13/1.09 % (1005694)------------------------------
% 5.13/1.09 % (1005694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.13/1.09 % (1005694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.09 % (1005694)CaDiCaL version: 2.1.3
% 5.13/1.09 % (1005694)Termination reason: Instruction limit
% 5.13/1.09 % (1005694)Termination phase: Saturation
% 5.13/1.09 % (1005694)Time elapsed: 0.013 s
% 5.13/1.09 % (1005694)Peak memory usage: 12 MB
% 5.13/1.09 % (1005694)Instructions burned: 14 (million)
% 5.13/1.09 % (1005680)Instruction limit reached!
% 5.13/1.09 % (1005680)------------------------------
% 5.13/1.09 % (1005680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.13/1.09 % (1005680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.09 % (1005680)CaDiCaL version: 2.1.3
% 5.13/1.09 % (1005680)Termination reason: Instruction limit
% 5.13/1.09 % (1005680)Termination phase: Saturation
% 5.13/1.09 % (1005680)Time elapsed: 0.140 s
% 5.13/1.09 % (1005680)Peak memory usage: 15 MB
% 5.13/1.09 % (1005680)Instructions burned: 317 (million)
% 5.13/1.09 % (1005701)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2540232551:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/31Mi)
% 5.13/1.09 % (1005696)Instruction limit reached!
% 5.13/1.09 % (1005696)------------------------------
% 5.13/1.09 % (1005696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.13/1.09 % (1005696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.09 % (1005696)CaDiCaL version: 2.1.3
% 5.13/1.09 % (1005696)Termination reason: Instruction limit
% 5.13/1.09 % (1005696)Termination phase: Saturation
% 5.13/1.09 % (1005696)Time elapsed: 0.038 s
% 5.13/1.09 % (1005696)Peak memory usage: 12 MB
% 5.13/1.09 % (1005696)Instructions burned: 51 (million)
% 5.13/1.09 % (1005695)Instruction limit reached!
% 5.13/1.09 % (1005695)------------------------------
% 5.13/1.09 % (1005695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.13/1.09 % (1005695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.09 % (1005695)CaDiCaL version: 2.1.3
% 5.13/1.09 % (1005695)Termination reason: Instruction limit
% 5.13/1.09 % (1005695)Termination phase: Saturation
% 5.13/1.09 % (1005695)Time elapsed: 0.050 s
% 5.13/1.09 % (1005695)Peak memory usage: 12 MB
% 5.13/1.09 % (1005695)Instructions burned: 67 (million)
% 5.13/1.09 % (1005702)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3387937312:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2994 on theBenchmark for (2994ds/137Mi)
% 5.85/1.26 % (1005701)Instruction limit reached!
% 5.85/1.26 % (1005701)------------------------------
% 5.85/1.26 % (1005701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.85/1.26 % (1005701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.26 % (1005701)CaDiCaL version: 2.1.3
% 5.85/1.26 % (1005701)Termination reason: Instruction limit
% 5.85/1.26 % (1005701)Termination phase: Saturation
% 5.85/1.26 % (1005701)Time elapsed: 0.023 s
% 5.85/1.26 % (1005701)Peak memory usage: 11 MB
% 5.85/1.26 % (1005701)Instructions burned: 31 (million)
% 5.85/1.26 % (1005704)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1180619610:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 5.85/1.26 % (1005705)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=4113283115:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2994 on theBenchmark for (2994ds/67Mi)
% 5.85/1.26 % (1005691)Instruction limit reached!
% 5.85/1.26 % (1005691)------------------------------
% 5.85/1.26 % (1005691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.85/1.26 % (1005691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.26 % (1005691)CaDiCaL version: 2.1.3
% 5.85/1.26 % (1005691)Termination reason: Instruction limit
% 5.85/1.26 % (1005691)Termination phase: Saturation
% 5.85/1.26 % (1005691)Time elapsed: 0.111 s
% 5.85/1.26 % (1005691)Peak memory usage: 12 MB
% 5.85/1.26 % (1005691)Instructions burned: 202 (million)
% 5.85/1.26 % (1005707)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.85/1.26 % (1005707)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3588773175:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 5.85/1.26 % (1005704)Instruction limit reached!
% 5.85/1.26 % (1005704)------------------------------
% 5.85/1.26 % (1005704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.85/1.26 % (1005704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.26 % (1005704)CaDiCaL version: 2.1.3
% 5.85/1.26 % (1005704)Termination reason: Instruction limit
% 5.85/1.26 % (1005704)Termination phase: Saturation
% 5.85/1.26 % (1005704)Time elapsed: 0.026 s
% 5.85/1.26 % (1005704)Peak memory usage: 12 MB
% 5.85/1.26 % (1005704)Instructions burned: 35 (million)
% 5.85/1.26 % (1005710)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3152560163:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 5.85/1.26 % (1005710)Refutation not found, incomplete strategy
% 5.85/1.26 % (1005710)------------------------------
% 5.85/1.26 % (1005710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.85/1.26 % (1005710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.26 % (1005710)CaDiCaL version: 2.1.3
% 5.85/1.26 % (1005710)Termination reason: Refutation not found, incomplete strategy
% 5.85/1.26 % (1005710)Time elapsed: 0.008 s
% 5.85/1.26 % (1005710)Peak memory usage: 12 MB
% 5.85/1.26 % (1005710)Instructions burned: 20 (million)
% 5.85/1.26 % (1005710)------------------------------
% 5.85/1.26 % (1005710)------------------------------
% 5.85/1.26 % (1005705)Instruction limit reached!
% 5.85/1.26 % (1005705)------------------------------
% 5.85/1.26 % (1005705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.85/1.26 % (1005714)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=402740657:i=427:sd=1:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/427Mi)
% 5.85/1.26 % (1005705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.26 % (1005705)CaDiCaL version: 2.1.3
% 5.85/1.26 % (1005705)Termination reason: Instruction limit
% 5.85/1.26 % (1005705)Termination phase: Saturation
% 5.85/1.26 % (1005705)Time elapsed: 0.052 s
% 5.85/1.26 % (1005705)Peak memory usage: 12 MB
% 5.85/1.26 % (1005705)Instructions burned: 67 (million)
% 5.85/1.26 % (1005712)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2317489339:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 5.85/1.26 % (1005714)Refutation not found, incomplete strategy
% 5.85/1.26 % (1005714)------------------------------
% 5.85/1.26 % (1005714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1005714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1005714)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1005714)Termination reason: Refutation not found, incomplete strategy
% 6.88/1.49 % (1005714)Time elapsed: 0.004 s
% 6.88/1.49 % (1005714)Peak memory usage: 12 MB
% 6.88/1.49 % (1005714)Instructions burned: 8 (million)
% 6.88/1.49 % (1005714)------------------------------
% 6.88/1.49 % (1005714)------------------------------
% 6.88/1.49 % (1005718)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1604471751:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/515Mi)
% 6.88/1.49 % (1005718)Refutation not found, incomplete strategy
% 6.88/1.49 % (1005718)------------------------------
% 6.88/1.49 % (1005718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1005718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1005718)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1005718)Termination reason: Refutation not found, incomplete strategy
% 6.88/1.49 % (1005718)Time elapsed: 0.015 s
% 6.88/1.49 % (1005718)Peak memory usage: 13 MB
% 6.88/1.49 % (1005718)Instructions burned: 35 (million)
% 6.88/1.49 % (1005718)------------------------------
% 6.88/1.49 % (1005718)------------------------------
% 6.88/1.49 % (1005702)Instruction limit reached!
% 6.88/1.49 % (1005702)------------------------------
% 6.88/1.49 % (1005702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1005702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1005702)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1005702)Termination reason: Instruction limit
% 6.88/1.49 % (1005702)Termination phase: Saturation
% 6.88/1.49 % (1005702)Time elapsed: 0.119 s
% 6.88/1.49 % (1005702)Peak memory usage: 13 MB
% 6.88/1.49 % (1005702)Instructions burned: 137 (million)
% 6.88/1.49 % (1005720)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=577858946:st=1.5:i=130:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/130Mi)
% 6.88/1.49 % (1005717)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1800035270:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/874Mi)
% 6.88/1.49 % (1005712)Instruction limit reached!
% 6.88/1.49 % (1005712)------------------------------
% 6.88/1.49 % (1005712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1005712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1005712)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1005712)Termination reason: Instruction limit
% 6.88/1.49 % (1005712)Termination phase: Saturation
% 6.88/1.49 % (1005712)Time elapsed: 0.069 s
% 6.88/1.49 % (1005712)Peak memory usage: 11 MB
% 6.88/1.49 % (1005712)Instructions burned: 97 (million)
% 6.88/1.49 % (1005720)Refutation not found, incomplete strategy
% 6.88/1.49 % (1005720)------------------------------
% 6.88/1.49 % (1005720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1005720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1005720)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1005720)Termination reason: Refutation not found, incomplete strategy
% 6.88/1.49 % (1005720)Time elapsed: 0.017 s
% 6.88/1.49 % (1005720)Peak memory usage: 12 MB
% 6.88/1.49 % (1005720)Instructions burned: 43 (million)
% 6.88/1.49 % (1005721)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=321485075:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 6.88/1.49 % (1005720)------------------------------
% 6.88/1.49 % (1005720)------------------------------
% 6.88/1.49 % (1005707)Instruction limit reached!
% 6.88/1.49 % (1005707)------------------------------
% 6.88/1.49 % (1005707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1005707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1005707)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1005707)Termination reason: Instruction limit
% 6.88/1.49 % (1005707)Termination phase: Saturation
% 6.88/1.49 % (1005707)Time elapsed: 0.133 s
% 6.88/1.49 % (1005707)Peak memory usage: 12 MB
% 6.88/1.49 % (1005707)Instructions burned: 180 (million)
% 6.88/1.49 % (1005726)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1827434173:i=450:rtra=on:ixr=off:ntd=on_2992 on theBenchmark for (2992ds/450Mi)
% 6.88/1.49 % (1005724)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1588647580:s2a=on:i=571:nm=16:rtra=on_2992 on theBenchmark for (2992ds/571Mi)
% 7.87/1.64 % (1005721)Instruction limit reached!
% 7.87/1.64 % (1005721)------------------------------
% 7.87/1.64 % (1005721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.87/1.64 % (1005721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.64 % (1005721)CaDiCaL version: 2.1.3
% 7.87/1.64 % (1005721)Termination reason: Instruction limit
% 7.87/1.64 % (1005721)Termination phase: Saturation
% 7.87/1.64 % (1005721)Time elapsed: 0.034 s
% 7.87/1.64 % (1005721)Peak memory usage: 12 MB
% 7.87/1.64 % (1005721)Instructions burned: 44 (million)
% 7.87/1.64 % (1005724)Refutation not found, incomplete strategy
% 7.87/1.64 % (1005724)------------------------------
% 7.87/1.64 % (1005724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.87/1.64 % (1005724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.64 % (1005724)CaDiCaL version: 2.1.3
% 7.87/1.64 % (1005724)Termination reason: Refutation not found, incomplete strategy
% 7.87/1.64 % (1005724)Time elapsed: 0.011 s
% 7.87/1.64 % (1005724)Peak memory usage: 12 MB
% 7.87/1.64 % (1005724)Instructions burned: 11 (million)
% 7.87/1.64 % (1005724)------------------------------
% 7.87/1.64 % (1005724)------------------------------
% 7.87/1.64 % (1005728)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=4257468079:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/95Mi)
% 7.87/1.64 % (1005730)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=1097270914:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 7.87/1.64 % (1005731)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=467744088:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2992 on theBenchmark for (2992ds/105Mi)
% 7.87/1.64 % (1005730)Instruction limit reached!
% 7.87/1.64 % (1005730)------------------------------
% 7.87/1.64 % (1005730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.87/1.64 % (1005730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.64 % (1005730)CaDiCaL version: 2.1.3
% 7.87/1.64 % (1005730)Termination reason: Instruction limit
% 7.87/1.64 % (1005730)Termination phase: Saturation
% 7.87/1.64 % (1005730)Time elapsed: 0.056 s
% 7.87/1.64 % (1005730)Peak memory usage: 12 MB
% 7.87/1.64 % (1005730)Instructions burned: 65 (million)
% 7.87/1.64 % (1005728)Instruction limit reached!
% 7.87/1.64 % (1005728)------------------------------
% 7.87/1.64 % (1005728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.87/1.64 % (1005728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.64 % (1005728)CaDiCaL version: 2.1.3
% 7.87/1.64 % (1005728)Termination reason: Instruction limit
% 7.87/1.64 % (1005728)Termination phase: Saturation
% 7.87/1.64 % (1005728)Time elapsed: 0.075 s
% 7.87/1.64 % (1005728)Peak memory usage: 13 MB
% 7.87/1.64 % (1005728)Instructions burned: 96 (million)
% 7.87/1.64 % (1005731)Instruction limit reached!
% 7.87/1.64 % (1005731)------------------------------
% 7.87/1.64 % (1005731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.87/1.64 % (1005731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.87/1.64 % (1005731)CaDiCaL version: 2.1.3
% 7.87/1.64 % (1005731)Termination reason: Instruction limit
% 7.87/1.64 % (1005731)Termination phase: Saturation
% 7.87/1.64 % (1005731)Time elapsed: 0.086 s
% 7.87/1.64 % (1005731)Peak memory usage: 13 MB
% 7.87/1.64 % (1005731)Instructions burned: 105 (million)
% 7.87/1.64 % (1005735)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=917382234:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 7.87/1.64 % (1005736)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3914309564:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 7.87/1.64 % (1005738)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2312850129:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 9.23/1.81 % (1005726)Instruction limit reached!
% 9.23/1.81 % (1005726)------------------------------
% 9.23/1.81 % (1005726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.23/1.81 % (1005726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.23/1.81 % (1005726)CaDiCaL version: 2.1.3
% 9.23/1.81 % (1005726)Termination reason: Instruction limit
% 9.23/1.81 % (1005726)Termination phase: Saturation
% 9.23/1.81 % (1005726)Time elapsed: 0.181 s
% 9.23/1.81 % (1005726)Peak memory usage: 16 MB
% 9.23/1.81 % (1005726)Instructions burned: 450 (million)
% 9.23/1.81 % (1005741)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1606979813:cond=on:i=34:hud=10:nm=10:rtra=on_2990 on theBenchmark for (2990ds/34Mi)
% 9.23/1.81 % (1005741)Instruction limit reached!
% 9.23/1.81 % (1005741)------------------------------
% 9.23/1.81 % (1005741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.23/1.81 % (1005741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.23/1.81 % (1005741)CaDiCaL version: 2.1.3
% 9.23/1.81 % (1005741)Termination reason: Instruction limit
% 9.23/1.81 % (1005741)Termination phase: Saturation
% 9.23/1.81 % (1005741)Time elapsed: 0.014 s
% 9.23/1.81 % (1005741)Peak memory usage: 12 MB
% 9.23/1.81 % (1005741)Instructions burned: 35 (million)
% 9.23/1.81 % (1005743)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2116795075:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/91Mi)
% 9.23/1.81 % (1005743)Instruction limit reached!
% 9.23/1.81 % (1005743)------------------------------
% 9.23/1.81 % (1005743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.23/1.81 % (1005743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.23/1.81 % (1005743)CaDiCaL version: 2.1.3
% 9.23/1.81 % (1005743)Termination reason: Instruction limit
% 9.23/1.81 % (1005743)Termination phase: Saturation
% 9.23/1.81 % (1005743)Time elapsed: 0.042 s
% 9.23/1.81 % (1005743)Peak memory usage: 13 MB
% 9.23/1.81 % (1005743)Instructions burned: 91 (million)
% 9.23/1.81 % (1005745)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2971588846:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2989 on theBenchmark for (2989ds/66Mi)
% 9.23/1.81 % (1005745)Refutation not found, incomplete strategy
% 9.23/1.81 % (1005745)------------------------------
% 9.23/1.81 % (1005745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.23/1.81 % (1005745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.23/1.81 % (1005745)CaDiCaL version: 2.1.3
% 9.23/1.81 % (1005745)Termination reason: Refutation not found, incomplete strategy
% 9.23/1.81 % (1005745)Time elapsed: 0.011 s
% 9.23/1.81 % (1005745)Peak memory usage: 12 MB
% 9.23/1.81 % (1005745)Instructions burned: 8 (million)
% 9.23/1.81 % (1005745)------------------------------
% 9.23/1.81 % (1005745)------------------------------
% 9.23/1.81 % (1005683)Instruction limit reached!
% 9.23/1.81 % (1005683)------------------------------
% 9.23/1.81 % (1005683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.23/1.81 % (1005683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.23/1.81 % (1005683)CaDiCaL version: 2.1.3
% 9.23/1.81 % (1005683)Termination reason: Instruction limit
% 9.23/1.81 % (1005683)Termination phase: Saturation
% 9.23/1.81 % (1005683)Time elapsed: 0.686 s
% 9.23/1.81 % (1005683)Peak memory usage: 14 MB
% 9.23/1.81 % (1005683)Instructions burned: 854 (million)
% 9.23/1.81 % (1005747)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1880989085:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2989 on theBenchmark for (2989ds/22Mi)
% 9.23/1.81 % (1005747)Instruction limit reached!
% 9.23/1.81 % (1005747)------------------------------
% 9.23/1.81 % (1005747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.23/1.81 % (1005747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.23/1.81 % (1005747)CaDiCaL version: 2.1.3
% 9.23/1.81 % (1005747)Termination reason: Instruction limit
% 9.23/1.81 % (1005747)Termination phase: Saturation
% 9.23/1.81 % (1005747)Time elapsed: 0.019 s
% 9.23/1.81 % (1005747)Peak memory usage: 11 MB
% 9.23/1.81 % (1005747)Instructions burned: 23 (million)
% 9.23/1.81 % (1005749)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=3106130617:i=338:bd=all:ins=4:rtra=on_2989 on theBenchmark for (2989ds/338Mi)
% 9.72/1.92 % (1005750)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2790287632:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2988 on theBenchmark for (2988ds/28Mi)
% 9.72/1.92 % (1005750)Instruction limit reached!
% 9.72/1.92 % (1005750)------------------------------
% 9.72/1.92 % (1005750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.72/1.92 % (1005750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.72/1.92 % (1005750)CaDiCaL version: 2.1.3
% 9.72/1.92 % (1005750)Termination reason: Instruction limit
% 9.72/1.92 % (1005750)Termination phase: Saturation
% 9.72/1.92 % (1005750)Time elapsed: 0.023 s
% 9.72/1.92 % (1005750)Peak memory usage: 11 MB
% 9.72/1.92 % (1005750)Instructions burned: 28 (million)
% 9.72/1.92 % (1005736)Instruction limit reached!
% 9.72/1.92 % (1005736)------------------------------
% 9.72/1.92 % (1005736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.72/1.92 % (1005736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.72/1.92 % (1005736)CaDiCaL version: 2.1.3
% 9.72/1.92 % (1005736)Termination reason: Instruction limit
% 9.72/1.92 % (1005736)Termination phase: Saturation
% 9.72/1.92 % (1005736)Time elapsed: 0.322 s
% 9.72/1.92 % (1005736)Peak memory usage: 13 MB
% 9.72/1.92 % (1005736)Instructions burned: 376 (million)
% 9.72/1.92 % (1005753)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 9.72/1.92 % (1005753)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=401322824:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2988 on theBenchmark for (2988ds/137Mi)
% 9.72/1.92 % (1005754)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=4025400380:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2988 on theBenchmark for (2988ds/340Mi)
% 9.72/1.92 % (1005663)Instruction limit reached!
% 9.72/1.92 % (1005663)------------------------------
% 9.72/1.92 % (1005663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.72/1.92 % (1005663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.72/1.92 % (1005663)CaDiCaL version: 2.1.3
% 9.72/1.92 % (1005663)Termination reason: Instruction limit
% 9.72/1.92 % (1005663)Termination phase: Saturation
% 9.72/1.92 % (1005663)Time elapsed: 0.915 s
% 9.72/1.92 % (1005663)Peak memory usage: 13 MB
% 9.72/1.92 % (1005663)Instructions burned: 1241 (million)
% 9.72/1.92 % (1005753)Instruction limit reached!
% 9.72/1.92 % (1005753)------------------------------
% 9.72/1.92 % (1005753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.72/1.92 % (1005753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.72/1.92 % (1005753)CaDiCaL version: 2.1.3
% 9.72/1.92 % (1005753)Termination reason: Instruction limit
% 9.72/1.92 % (1005753)Termination phase: Saturation
% 9.72/1.92 % (1005753)Time elapsed: 0.054 s
% 9.72/1.92 % (1005753)Peak memory usage: 12 MB
% 9.72/1.92 % (1005753)Instructions burned: 137 (million)
% 9.72/1.92 % (1005757)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=1373240425:i=227:sd=1:bd=all:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/227Mi)
% 9.72/1.92 % (1005758)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 9.72/1.92 % (1005758)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=841275376:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/373Mi)
% 9.72/1.92 % (1005757)Refutation not found, incomplete strategy
% 9.72/1.92 % (1005757)------------------------------
% 9.72/1.92 % (1005757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.72/1.92 % (1005757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.72/1.92 % (1005757)CaDiCaL version: 2.1.3
% 9.72/1.92 % (1005757)Termination reason: Refutation not found, incomplete strategy
% 9.72/1.92 % (1005757)Time elapsed: 0.009 s
% 9.72/1.92 % (1005757)Peak memory usage: 12 MB
% 9.72/1.92 % (1005757)Instructions burned: 8 (million)
% 9.72/1.92 % (1005757)------------------------------
% 9.72/1.92 % (1005757)------------------------------
% 13.01/2.22 % (1005761)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2802571559:i=116:ep=RSTC:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/116Mi)
% 13.01/2.22 % (1005738)Instruction limit reached!
% 13.01/2.22 % (1005738)------------------------------
% 13.01/2.22 % (1005738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.01/2.22 % (1005738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.01/2.22 % (1005738)CaDiCaL version: 2.1.3
% 13.01/2.22 % (1005738)Termination reason: Instruction limit
% 13.01/2.22 % (1005738)Termination phase: Saturation
% 13.01/2.22 % (1005738)Time elapsed: 0.415 s
% 13.01/2.22 % (1005738)Peak memory usage: 15 MB
% 13.01/2.22 % (1005738)Instructions burned: 496 (million)
% 13.01/2.22 % (1005763)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=4287181345:i=575:rtra=on_2986 on theBenchmark for (2986ds/575Mi)
% 13.01/2.22 % (1005717)Instruction limit reached!
% 13.01/2.22 % (1005717)------------------------------
% 13.01/2.22 % (1005717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.01/2.22 % (1005717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.01/2.22 % (1005717)CaDiCaL version: 2.1.3
% 13.01/2.22 % (1005717)Termination reason: Instruction limit
% 13.01/2.22 % (1005717)Termination phase: Saturation
% 13.01/2.22 % (1005717)Time elapsed: 0.699 s
% 13.01/2.22 % (1005717)Peak memory usage: 17 MB
% 13.01/2.22 % (1005717)Instructions burned: 874 (million)
% 13.01/2.22 % (1005758)Instruction limit reached!
% 13.01/2.22 % (1005758)------------------------------
% 13.01/2.22 % (1005758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.01/2.22 % (1005758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.01/2.22 % (1005758)CaDiCaL version: 2.1.3
% 13.01/2.22 % (1005758)Termination reason: Instruction limit
% 13.01/2.22 % (1005758)Termination phase: Saturation
% 13.01/2.22 % (1005758)Time elapsed: 0.138 s
% 13.01/2.22 % (1005758)Peak memory usage: 13 MB
% 13.01/2.22 % (1005758)Instructions burned: 374 (million)
% 13.01/2.22 % (1005761)Instruction limit reached!
% 13.01/2.22 % (1005761)------------------------------
% 13.01/2.22 % (1005761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.01/2.22 % (1005761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.01/2.22 % (1005761)CaDiCaL version: 2.1.3
% 13.01/2.22 % (1005761)Termination reason: Instruction limit
% 13.01/2.22 % (1005761)Termination phase: Saturation
% 13.01/2.22 % (1005761)Time elapsed: 0.096 s
% 13.01/2.22 % (1005761)Peak memory usage: 13 MB
% 13.01/2.22 % (1005761)Instructions burned: 116 (million)
% 13.01/2.22 % (1005749)Instruction limit reached!
% 13.01/2.22 % (1005749)------------------------------
% 13.01/2.22 % (1005749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.01/2.22 % (1005749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.01/2.22 % (1005749)CaDiCaL version: 2.1.3
% 13.01/2.22 % (1005749)Termination reason: Instruction limit
% 13.01/2.22 % (1005749)Termination phase: Saturation
% 13.01/2.22 % (1005749)Time elapsed: 0.293 s
% 13.01/2.22 % (1005749)Peak memory usage: 16 MB
% 13.01/2.22 % (1005749)Instructions burned: 339 (million)
% 13.01/2.22 % (1005766)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=77564272:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2985 on theBenchmark for (2985ds/9840Mi)
% 13.01/2.22 % (1005765)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2735462821:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2986 on theBenchmark for (2986ds/270Mi)
% 13.01/2.22 % (1005767)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=1145059167:i=421:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/421Mi)
% 13.01/2.22 % (1005768)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 13.01/2.22 % (1005767)Refutation not found, incomplete strategy
% 13.01/2.22 % (1005767)------------------------------
% 13.01/2.22 % (1005767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.01/2.22 % (1005767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.64/2.74 % (1005767)CaDiCaL version: 2.1.3
% 15.64/2.74 % (1005767)Termination reason: Refutation not found, incomplete strategy
% 15.64/2.74 % (1005767)Time elapsed: 0.007 s
% 15.64/2.74 % (1005767)Peak memory usage: 12 MB
% 15.64/2.74 % (1005767)Instructions burned: 8 (million)
% 15.64/2.74 % (1005767)------------------------------
% 15.64/2.74 % (1005767)------------------------------
% 15.64/2.74 % (1005768)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3449796635:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/270Mi)
% 15.64/2.74 % (1005754)Instruction limit reached!
% 15.64/2.74 % (1005754)------------------------------
% 15.64/2.74 % (1005754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.64/2.74 % (1005754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.64/2.74 % (1005754)CaDiCaL version: 2.1.3
% 15.64/2.74 % (1005754)Termination reason: Instruction limit
% 15.64/2.74 % (1005754)Termination phase: Saturation
% 15.64/2.74 % (1005754)Time elapsed: 0.243 s
% 15.64/2.74 % (1005754)Peak memory usage: 13 MB
% 15.64/2.74 % (1005754)Instructions burned: 340 (million)
% 15.64/2.74 % (1005768)Refutation not found, incomplete strategy
% 15.64/2.74 % (1005768)------------------------------
% 15.64/2.74 % (1005768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.64/2.74 % (1005768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.64/2.74 % (1005768)CaDiCaL version: 2.1.3
% 15.64/2.74 % (1005768)Termination reason: Refutation not found, incomplete strategy
% 15.64/2.74 % (1005768)Time elapsed: 0.029 s
% 15.64/2.74 % (1005768)Peak memory usage: 12 MB
% 15.64/2.74 % (1005768)Instructions burned: 38 (million)
% 15.64/2.74 % (1005768)------------------------------
% 15.64/2.74 % (1005768)------------------------------
% 15.64/2.74 % (1005772)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2837886579:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/31Mi)
% 15.64/2.74 % (1005774)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 15.64/2.74 % (1005774)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 15.64/2.74 % (1005774)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2869588437:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2985 on theBenchmark for (2985ds/1440Mi)
% 15.64/2.74 % (1005772)Instruction limit reached!
% 15.64/2.74 % (1005772)------------------------------
% 15.64/2.74 % (1005772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.64/2.74 % (1005772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.64/2.74 % (1005772)CaDiCaL version: 2.1.3
% 15.64/2.74 % (1005772)Termination reason: Instruction limit
% 15.64/2.74 % (1005772)Termination phase: Saturation
% 15.64/2.74 % (1005772)Time elapsed: 0.022 s
% 15.64/2.74 % (1005772)Peak memory usage: 11 MB
% 15.64/2.74 % (1005772)Instructions burned: 31 (million)
% 15.64/2.74 % (1005776)dis+10_2_sil=128000:si=on:random_seed=2673609797:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2985 on theBenchmark for (2985ds/339Mi)
% 15.64/2.74 % (1005776)Refutation not found, incomplete strategy
% 15.64/2.74 % (1005776)------------------------------
% 15.64/2.74 % (1005776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.64/2.74 % (1005776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.64/2.74 % (1005776)CaDiCaL version: 2.1.3
% 15.64/2.74 % (1005776)Termination reason: Refutation not found, incomplete strategy
% 15.64/2.74 % (1005776)Time elapsed: 0.007 s
% 15.64/2.74 % (1005776)Peak memory usage: 12 MB
% 15.64/2.74 % (1005776)Instructions burned: 8 (million)
% 15.64/2.74 % (1005776)------------------------------
% 15.64/2.74 % (1005776)------------------------------
% 15.64/2.74 % (1005778)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1311967473:i=111:add=on:fgj=on:rtra=on:fdi=1024_2984 on theBenchmark for (2984ds/111Mi)
% 15.64/2.74 % (1005780)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=495568782:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2984 on theBenchmark for (2984ds/122Mi)
% 17.23/3.01 % (1005780)Refutation not found, incomplete strategy
% 17.23/3.01 % (1005780)------------------------------
% 17.23/3.01 % (1005780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.23/3.01 % (1005780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.23/3.01 % (1005780)CaDiCaL version: 2.1.3
% 17.23/3.01 % (1005780)Termination reason: Refutation not found, incomplete strategy
% 17.23/3.01 % (1005780)Time elapsed: 0.023 s
% 17.23/3.01 % (1005780)Peak memory usage: 12 MB
% 17.23/3.01 % (1005780)Instructions burned: 29 (million)
% 17.23/3.01 % (1005780)------------------------------
% 17.23/3.01 % (1005780)------------------------------
% 17.23/3.01 % (1005783)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=151022728:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/136Mi)
% 17.23/3.01 % (1005778)Instruction limit reached!
% 17.23/3.01 % (1005778)------------------------------
% 17.23/3.01 % (1005778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.23/3.01 % (1005778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.23/3.01 % (1005778)CaDiCaL version: 2.1.3
% 17.23/3.01 % (1005778)Termination reason: Instruction limit
% 17.23/3.01 % (1005778)Termination phase: Saturation
% 17.23/3.01 % (1005778)Time elapsed: 0.086 s
% 17.23/3.01 % (1005778)Peak memory usage: 13 MB
% 17.23/3.01 % (1005778)Instructions burned: 111 (million)
% 17.23/3.01 % (1005765)Instruction limit reached!
% 17.23/3.01 % (1005765)------------------------------
% 17.23/3.01 % (1005765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.23/3.01 % (1005765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.23/3.01 % (1005765)CaDiCaL version: 2.1.3
% 17.23/3.01 % (1005765)Termination reason: Instruction limit
% 17.23/3.01 % (1005765)Termination phase: Saturation
% 17.23/3.01 % (1005765)Time elapsed: 0.205 s
% 17.23/3.01 % (1005765)Peak memory usage: 12 MB
% 17.23/3.01 % (1005765)Instructions burned: 270 (million)
% 17.23/3.01 % (1005785)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2317713096:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2983 on theBenchmark for (2983ds/232Mi)
% 17.23/3.01 % (1005786)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=3359976197:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2983 on theBenchmark for (2983ds/1254Mi)
% 17.23/3.01 % (1005783)Instruction limit reached!
% 17.23/3.01 % (1005783)------------------------------
% 17.23/3.01 % (1005783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.23/3.01 % (1005783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.23/3.01 % (1005783)CaDiCaL version: 2.1.3
% 17.23/3.01 % (1005783)Termination reason: Instruction limit
% 17.23/3.01 % (1005783)Termination phase: Saturation
% 17.23/3.01 % (1005783)Time elapsed: 0.105 s
% 17.23/3.01 % (1005783)Peak memory usage: 13 MB
% 17.23/3.01 % (1005783)Instructions burned: 136 (million)
% 17.23/3.01 % (1005789)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 17.23/3.01 % (1005789)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=1221294556:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2982 on theBenchmark for (2982ds/281Mi)
% 17.23/3.01 % (1005763)Instruction limit reached!
% 17.23/3.01 % (1005763)------------------------------
% 17.23/3.01 % (1005763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.23/3.01 % (1005763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.23/3.01 % (1005763)CaDiCaL version: 2.1.3
% 17.23/3.01 % (1005763)Termination reason: Instruction limit
% 17.23/3.01 % (1005763)Termination phase: Saturation
% 17.23/3.01 % (1005763)Time elapsed: 0.476 s
% 17.23/3.01 % (1005763)Peak memory usage: 15 MB
% 17.23/3.01 % (1005763)Instructions burned: 575 (million)
% 17.23/3.01 % (1005785)Instruction limit reached!
% 17.23/3.01 % (1005785)------------------------------
% 17.23/3.01 % (1005785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.23/3.01 % (1005785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.23/3.01 % (1005785)CaDiCaL version: 2.1.3
% 19.77/3.17 % (1005785)Termination reason: Instruction limit
% 19.77/3.17 % (1005785)Termination phase: Saturation
% 19.77/3.17 % (1005785)Time elapsed: 0.195 s
% 19.77/3.17 % (1005785)Peak memory usage: 13 MB
% 19.77/3.17 % (1005785)Instructions burned: 232 (million)
% 19.77/3.17 % (1005791)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1677690927:i=619:add=on:rtra=on_2981 on theBenchmark for (2981ds/619Mi)
% 19.77/3.17 % (1005792)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3336864020:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/865Mi)
% 19.77/3.17 % (1005789)Instruction limit reached!
% 19.77/3.17 % (1005789)------------------------------
% 19.77/3.17 % (1005789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.77/3.17 % (1005789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.77/3.17 % (1005789)CaDiCaL version: 2.1.3
% 19.77/3.17 % (1005789)Termination reason: Instruction limit
% 19.77/3.17 % (1005789)Termination phase: Saturation
% 19.77/3.17 % (1005789)Time elapsed: 0.211 s
% 19.77/3.17 % (1005789)Peak memory usage: 12 MB
% 19.77/3.17 % (1005789)Instructions burned: 282 (million)
% 19.77/3.17 % (1005795)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1544147473:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2980 on theBenchmark for (2980ds/212Mi)
% 19.77/3.17 % (1005795)Instruction limit reached!
% 19.77/3.17 % (1005795)------------------------------
% 19.77/3.17 % (1005795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.77/3.17 % (1005795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.77/3.17 % (1005795)CaDiCaL version: 2.1.3
% 19.77/3.17 % (1005795)Termination reason: Instruction limit
% 19.77/3.17 % (1005795)Termination phase: Saturation
% 19.77/3.17 % (1005795)Time elapsed: 0.164 s
% 19.77/3.17 % (1005795)Peak memory usage: 14 MB
% 19.77/3.17 % (1005795)Instructions burned: 212 (million)
% 19.77/3.17 % (1005797)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=2523565494:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2978 on theBenchmark for (2978ds/130Mi)
% 19.77/3.17 % (1005797)Refutation not found, incomplete strategy
% 19.77/3.17 % (1005797)------------------------------
% 19.77/3.17 % (1005797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.77/3.17 % (1005797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.77/3.17 % (1005797)CaDiCaL version: 2.1.3
% 19.77/3.17 % (1005797)Termination reason: Refutation not found, incomplete strategy
% 19.77/3.17 % (1005797)Time elapsed: 0.013 s
% 19.77/3.17 % (1005797)Peak memory usage: 12 MB
% 19.77/3.17 % (1005797)Instructions burned: 13 (million)
% 19.77/3.17 % (1005797)------------------------------
% 19.77/3.17 % (1005797)------------------------------
% 19.77/3.17 % (1005799)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2969148587:st=1.5:i=346:rtra=on:ss=axioms_2977 on theBenchmark for (2977ds/346Mi)
% 19.77/3.17 % (1005799)Refutation not found, incomplete strategy
% 19.77/3.17 % (1005799)------------------------------
% 19.77/3.17 % (1005799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.77/3.17 % (1005799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.77/3.17 % (1005799)CaDiCaL version: 2.1.3
% 19.77/3.17 % (1005799)Termination reason: Refutation not found, incomplete strategy
% 19.77/3.17 % (1005799)Time elapsed: 0.033 s
% 19.77/3.17 % (1005799)Peak memory usage: 12 MB
% 19.77/3.17 % (1005799)Instructions burned: 43 (million)
% 19.77/3.17 % (1005799)------------------------------
% 19.77/3.17 % (1005799)------------------------------
% 19.77/3.17 % (1005801)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=3227798888:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2977 on theBenchmark for (2977ds/152Mi)
% 19.77/3.17 % (1005791)Instruction limit reached!
% 19.77/3.17 % (1005791)------------------------------
% 19.77/3.17 % (1005791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.77/3.17 % (1005791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.77/3.17 % (1005791)CaDiCaL version: 2.1.3
% 19.77/3.17 % (1005791)Termination reason: Instruction limit
% 19.77/3.17 % (1005791)Termination phase: Saturation
% 19.77/3.17 % (1005791)Time elapsed: 0.488 s
% 19.77/3.17 % (1005791)Peak memory usage: 14 MB
% 19.77/3.17 % (1005791)Instructions burned: 619 (million)
% 19.77/3.17 % (1005803)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1857245357:i=75:ep=R:rtra=on:ntd=on_2976 on theBenchmark for (2976ds/75Mi)
% 21.97/3.66 % (1005801)Instruction limit reached!
% 21.97/3.66 % (1005801)------------------------------
% 21.97/3.66 % (1005801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.97/3.66 % (1005801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.97/3.66 % (1005801)CaDiCaL version: 2.1.3
% 21.97/3.66 % (1005801)Termination reason: Instruction limit
% 21.97/3.66 % (1005801)Termination phase: Saturation
% 21.97/3.66 % (1005801)Time elapsed: 0.117 s
% 21.97/3.66 % (1005801)Peak memory usage: 13 MB
% 21.97/3.66 % (1005801)Instructions burned: 153 (million)
% 21.97/3.66 % (1005803)Instruction limit reached!
% 21.97/3.66 % (1005803)------------------------------
% 21.97/3.66 % (1005803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.97/3.66 % (1005803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.97/3.66 % (1005803)CaDiCaL version: 2.1.3
% 21.97/3.66 % (1005803)Termination reason: Instruction limit
% 21.97/3.66 % (1005803)Termination phase: Saturation
% 21.97/3.66 % (1005803)Time elapsed: 0.060 s
% 21.97/3.66 % (1005803)Peak memory usage: 12 MB
% 21.97/3.66 % (1005803)Instructions burned: 75 (million)
% 21.97/3.66 % (1005805)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=2182055139:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2975 on theBenchmark for (2975ds/387Mi)
% 21.97/3.66 % (1005806)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3068783851:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2975 on theBenchmark for (2975ds/148Mi)
% 21.97/3.66 % (1005786)Instruction limit reached!
% 21.97/3.66 % (1005786)------------------------------
% 21.97/3.66 % (1005786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.97/3.66 % (1005786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.97/3.66 % (1005786)CaDiCaL version: 2.1.3
% 21.97/3.66 % (1005786)Termination reason: Instruction limit
% 21.97/3.66 % (1005786)Termination phase: Saturation
% 21.97/3.66 % (1005786)Time elapsed: 0.914 s
% 21.97/3.66 % (1005786)Peak memory usage: 16 MB
% 21.97/3.66 % (1005786)Instructions burned: 1254 (million)
% 21.97/3.66 % (1005806)Instruction limit reached!
% 21.97/3.66 % (1005806)------------------------------
% 21.97/3.66 % (1005806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.97/3.66 % (1005806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.97/3.66 % (1005806)CaDiCaL version: 2.1.3
% 21.97/3.66 % (1005806)Termination reason: Instruction limit
% 21.97/3.66 % (1005806)Termination phase: Saturation
% 21.97/3.66 % (1005806)Time elapsed: 0.117 s
% 21.97/3.66 % (1005806)Peak memory usage: 12 MB
% 21.97/3.66 % (1005806)Instructions burned: 148 (million)
% 21.97/3.66 % (1005792)Instruction limit reached!
% 21.97/3.66 % (1005792)------------------------------
% 21.97/3.66 % (1005792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.97/3.66 % (1005792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.97/3.66 % (1005792)CaDiCaL version: 2.1.3
% 21.97/3.66 % (1005792)Termination reason: Instruction limit
% 21.97/3.66 % (1005792)Termination phase: Saturation
% 21.97/3.66 % (1005792)Time elapsed: 0.722 s
% 21.97/3.66 % (1005792)Peak memory usage: 18 MB
% 21.97/3.66 % (1005792)Instructions burned: 865 (million)
% 21.97/3.66 % (1005774)Instruction limit reached!
% 21.97/3.66 % (1005774)------------------------------
% 21.97/3.66 % (1005774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.97/3.66 % (1005774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.97/3.66 % (1005774)CaDiCaL version: 2.1.3
% 21.97/3.66 % (1005774)Termination reason: Instruction limit
% 21.97/3.66 % (1005774)Termination phase: Saturation
% 21.97/3.66 % (1005809)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=383826964:i=161:piset=and:rtra=on:ntd=on_2974 on theBenchmark for (2974ds/161Mi)
% 21.97/3.66 % (1005774)Time elapsed: 1.115 s
% 21.97/3.66 % (1005774)Peak memory usage: 29 MB
% 21.97/3.66 % (1005774)Instructions burned: 1440 (million)
% 21.97/3.66 % (1005810)lrs+10_1_sil=128000:si=on:random_seed=525840352:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2974 on theBenchmark for (2974ds/888Mi)
% 21.97/3.66 % (1005812)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=1227831867:i=136:add=on:ins=4:rtra=on:sup=off_2973 on theBenchmark for (2973ds/136Mi)
% 23.52/4.00 % (1005813)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2059576194:i=88:s2at=3:nm=2:rtra=on:rawr=on_2973 on theBenchmark for (2973ds/88Mi)
% 23.52/4.00 % (1005812)Refutation not found, incomplete strategy
% 23.52/4.00 % (1005812)------------------------------
% 23.52/4.00 % (1005812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.52/4.00 % (1005812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.52/4.00 % (1005812)CaDiCaL version: 2.1.3
% 23.52/4.00 % (1005812)Termination reason: Refutation not found, incomplete strategy
% 23.52/4.00 % (1005812)Time elapsed: 0.027 s
% 23.52/4.00 % (1005812)Peak memory usage: 12 MB
% 23.52/4.00 % (1005812)Instructions burned: 34 (million)
% 23.52/4.00 % (1005812)------------------------------
% 23.52/4.00 % (1005812)------------------------------
% 23.52/4.00 % (1005817)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=4106147543:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2973 on theBenchmark for (2973ds/93Mi)
% 23.52/4.00 % (1005813)Instruction limit reached!
% 23.52/4.00 % (1005813)------------------------------
% 23.52/4.00 % (1005813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.52/4.00 % (1005813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.52/4.00 % (1005813)CaDiCaL version: 2.1.3
% 23.52/4.00 % (1005813)Termination reason: Instruction limit
% 23.52/4.00 % (1005813)Termination phase: Saturation
% 23.52/4.00 % (1005813)Time elapsed: 0.068 s
% 23.52/4.00 % (1005813)Peak memory usage: 12 MB
% 23.52/4.00 % (1005813)Instructions burned: 88 (million)
% 23.52/4.00 % (1005805)Instruction limit reached!
% 23.52/4.00 % (1005805)------------------------------
% 23.52/4.00 % (1005805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.52/4.00 % (1005805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.52/4.00 % (1005805)CaDiCaL version: 2.1.3
% 23.52/4.00 % (1005805)Termination reason: Instruction limit
% 23.52/4.00 % (1005805)Termination phase: Saturation
% 23.52/4.00 % (1005805)Time elapsed: 0.265 s
% 23.52/4.00 % (1005805)Peak memory usage: 13 MB
% 23.52/4.00 % (1005805)Instructions burned: 387 (million)
% 23.52/4.00 % (1005809)Instruction limit reached!
% 23.52/4.00 % (1005809)------------------------------
% 23.52/4.00 % (1005809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.52/4.00 % (1005809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.52/4.00 % (1005809)CaDiCaL version: 2.1.3
% 23.52/4.00 % (1005809)Termination reason: Instruction limit
% 23.52/4.00 % (1005809)Termination phase: Saturation
% 23.52/4.00 % (1005809)Time elapsed: 0.128 s
% 23.52/4.00 % (1005809)Peak memory usage: 14 MB
% 23.52/4.00 % (1005809)Instructions burned: 161 (million)
% 23.52/4.00 % (1005819)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3439495897:i=2186:rtra=on:ixr=off_2972 on theBenchmark for (2972ds/2186Mi)
% 23.52/4.00 % (1005820)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=982972206:s2a=on:i=240:rtra=on:ntd=on_2972 on theBenchmark for (2972ds/240Mi)
% 23.52/4.00 % (1005821)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2469417690:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2972 on theBenchmark for (2972ds/805Mi)
% 23.52/4.00 % (1005817)Instruction limit reached!
% 23.52/4.00 % (1005817)------------------------------
% 23.52/4.00 % (1005817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.52/4.00 % (1005817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.52/4.00 % (1005817)CaDiCaL version: 2.1.3
% 23.52/4.00 % (1005817)Termination reason: Instruction limit
% 23.52/4.00 % (1005817)Termination phase: Saturation
% 23.52/4.00 % (1005817)Time elapsed: 0.069 s
% 23.52/4.00 % (1005817)Peak memory usage: 12 MB
% 23.52/4.00 % (1005817)Instructions burned: 94 (million)
% 23.52/4.00 % (1005825)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 23.52/4.00 % (1005825)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=2040339114:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2972 on theBenchmark for (2972ds/391Mi)
% 27.29/4.26 % (1005825)Refutation not found, incomplete strategy
% 27.29/4.26 % (1005825)------------------------------
% 27.29/4.26 % (1005825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.29/4.26 % (1005825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.29/4.26 % (1005825)CaDiCaL version: 2.1.3
% 27.29/4.26 % (1005825)Termination reason: Refutation not found, incomplete strategy
% 27.29/4.26 % (1005825)Time elapsed: 0.030 s
% 27.29/4.26 % (1005825)Peak memory usage: 12 MB
% 27.29/4.26 % (1005825)Instructions burned: 38 (million)
% 27.29/4.26 % (1005825)------------------------------
% 27.29/4.26 % (1005825)------------------------------
% 27.29/4.26 % (1005827)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=2582928650:i=355:av=off:fsr=off:rtra=on:ixr=off_2971 on theBenchmark for (2971ds/355Mi)
% 27.29/4.26 % (1005820)Instruction limit reached!
% 27.29/4.26 % (1005820)------------------------------
% 27.29/4.26 % (1005820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.29/4.26 % (1005820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.29/4.26 % (1005820)CaDiCaL version: 2.1.3
% 27.29/4.26 % (1005820)Termination reason: Instruction limit
% 27.29/4.26 % (1005820)Termination phase: Saturation
% 27.29/4.26 % (1005820)Time elapsed: 0.191 s
% 27.29/4.26 % (1005820)Peak memory usage: 15 MB
% 27.29/4.26 % (1005820)Instructions burned: 240 (million)
% 27.29/4.26 % (1005829)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=4179340461:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2970 on theBenchmark for (2970ds/314Mi)
% 27.29/4.26 % (1005829)Refutation not found, incomplete strategy
% 27.29/4.26 % (1005829)------------------------------
% 27.29/4.26 % (1005829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.29/4.26 % (1005829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.29/4.26 % (1005829)CaDiCaL version: 2.1.3
% 27.29/4.26 % (1005829)Termination reason: Refutation not found, incomplete strategy
% 27.29/4.26 % (1005829)Time elapsed: 0.008 s
% 27.29/4.26 % (1005829)Peak memory usage: 12 MB
% 27.29/4.26 % (1005829)Instructions burned: 9 (million)
% 27.29/4.26 % (1005829)------------------------------
% 27.29/4.26 % (1005829)------------------------------
% 27.29/4.26 % (1005831)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=3227975285:s2a=on:i=251:fsr=off:rtra=on_2969 on theBenchmark for (2969ds/251Mi)
% 27.29/4.26 % (1005827)Instruction limit reached!
% 27.29/4.26 % (1005827)------------------------------
% 27.29/4.26 % (1005827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.29/4.26 % (1005827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.29/4.26 % (1005827)CaDiCaL version: 2.1.3
% 27.29/4.26 % (1005827)Termination reason: Instruction limit
% 27.29/4.26 % (1005827)Termination phase: Saturation
% 27.29/4.26 % (1005827)Time elapsed: 0.275 s
% 27.29/4.26 % (1005827)Peak memory usage: 13 MB
% 27.29/4.26 % (1005827)Instructions burned: 355 (million)
% 27.29/4.26 % (1005833)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=4247629534:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2968 on theBenchmark for (2968ds/2470Mi)
% 27.29/4.26 % (1005831)Instruction limit reached!
% 27.29/4.26 % (1005831)------------------------------
% 27.29/4.26 % (1005831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.29/4.26 % (1005831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.29/4.26 % (1005831)CaDiCaL version: 2.1.3
% 27.29/4.26 % (1005831)Termination reason: Instruction limit
% 27.29/4.26 % (1005831)Termination phase: Saturation
% 27.29/4.26 % (1005831)Time elapsed: 0.187 s
% 27.29/4.26 % (1005831)Peak memory usage: 12 MB
% 27.29/4.26 % (1005831)Instructions burned: 252 (million)
% 27.29/4.26 % (1005835)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=2361589188:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2967 on theBenchmark for (2967ds/673Mi)
% 27.29/4.26 % (1005810)Instruction limit reached!
% 27.29/4.26 % (1005810)------------------------------
% 27.29/4.26 % (1005810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.29/4.26 % (1005810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.61/4.61 % (1005810)CaDiCaL version: 2.1.3
% 29.61/4.61 % (1005810)Termination reason: Instruction limit
% 29.61/4.61 % (1005810)Termination phase: Saturation
% 29.61/4.61 % (1005810)Time elapsed: 0.675 s
% 29.61/4.61 % (1005810)Peak memory usage: 15 MB
% 29.61/4.61 % (1005810)Instructions burned: 888 (million)
% 29.61/4.61 % (1005837)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3392564398:i=116:ep=RSTC:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/116Mi)
% 29.61/4.61 % (1005821)Instruction limit reached!
% 29.61/4.61 % (1005821)------------------------------
% 29.61/4.61 % (1005821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.61/4.61 % (1005821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.61/4.61 % (1005821)CaDiCaL version: 2.1.3
% 29.61/4.61 % (1005821)Termination reason: Instruction limit
% 29.61/4.61 % (1005821)Termination phase: Saturation
% 29.61/4.61 % (1005821)Time elapsed: 0.625 s
% 29.61/4.61 % (1005821)Peak memory usage: 20 MB
% 29.61/4.61 % (1005821)Instructions burned: 805 (million)
% 29.61/4.61 % (1005837)Instruction limit reached!
% 29.61/4.61 % (1005837)------------------------------
% 29.61/4.61 % (1005837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.61/4.61 % (1005837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.61/4.61 % (1005837)CaDiCaL version: 2.1.3
% 29.61/4.61 % (1005837)Termination reason: Instruction limit
% 29.61/4.61 % (1005837)Termination phase: Saturation
% 29.61/4.61 % (1005837)Time elapsed: 0.092 s
% 29.61/4.61 % (1005837)Peak memory usage: 13 MB
% 29.61/4.61 % (1005837)Instructions burned: 116 (million)
% 29.61/4.61 % (1005839)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1339160449:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2965 on theBenchmark for (2965ds/270Mi)
% 29.61/4.61 % (1005840)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=835609727:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2965 on theBenchmark for (2965ds/30Mi)
% 29.61/4.61 % (1005840)Instruction limit reached!
% 29.61/4.61 % (1005840)------------------------------
% 29.61/4.61 % (1005840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.61/4.61 % (1005840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.61/4.61 % (1005840)CaDiCaL version: 2.1.3
% 29.61/4.61 % (1005840)Termination reason: Instruction limit
% 29.61/4.61 % (1005840)Termination phase: Saturation
% 29.61/4.61 % (1005840)Time elapsed: 0.027 s
% 29.61/4.61 % (1005840)Peak memory usage: 12 MB
% 29.61/4.61 % (1005840)Instructions burned: 31 (million)
% 29.61/4.61 % (1005843)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 29.61/4.61 % (1005843)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=2842998735:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2965 on theBenchmark for (2965ds/39Mi)
% 29.61/4.61 % (1005843)Instruction limit reached!
% 29.61/4.61 % (1005843)------------------------------
% 29.61/4.61 % (1005843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.61/4.61 % (1005843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.61/4.61 % (1005843)CaDiCaL version: 2.1.3
% 29.61/4.61 % (1005843)Termination reason: Instruction limit
% 29.61/4.61 % (1005843)Termination phase: Saturation
% 29.61/4.61 % (1005843)Time elapsed: 0.030 s
% 29.61/4.61 % (1005843)Peak memory usage: 12 MB
% 29.61/4.61 % (1005843)Instructions burned: 39 (million)
% 29.61/4.61 % (1005845)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3330104136:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2964 on theBenchmark for (2964ds/365Mi)
% 29.61/4.61 % (1005839)Instruction limit reached!
% 29.61/4.61 % (1005839)------------------------------
% 29.61/4.61 % (1005839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.61/4.61 % (1005839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.61/4.61 % (1005839)CaDiCaL version: 2.1.3
% 29.61/4.61 % (1005839)Termination reason: Instruction limit
% 29.61/4.61 % (1005839)Termination phase: Saturation
% 29.61/4.61 % (1005839)Time elapsed: 0.205 s
% 29.61/4.61 % (1005839)Peak memory usage: 13 MB
% 29.61/4.61 % (1005839)Instructions burned: 272 (million)
% 31.03/4.90 % (1005847)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1098258033:i=158:av=off:rtra=on_2963 on theBenchmark for (2963ds/158Mi)
% 31.03/4.90 % (1005835)Instruction limit reached!
% 31.03/4.90 % (1005835)------------------------------
% 31.03/4.90 % (1005835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.90 % (1005835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.90 % (1005835)CaDiCaL version: 2.1.3
% 31.03/4.90 % (1005835)Termination reason: Instruction limit
% 31.03/4.90 % (1005835)Termination phase: Saturation
% 31.03/4.90 % (1005835)Time elapsed: 0.544 s
% 31.03/4.90 % (1005835)Peak memory usage: 16 MB
% 31.03/4.90 % (1005835)Instructions burned: 674 (million)
% 31.03/4.90 % (1005847)Instruction limit reached!
% 31.03/4.90 % (1005847)------------------------------
% 31.03/4.90 % (1005847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.90 % (1005847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.90 % (1005847)CaDiCaL version: 2.1.3
% 31.03/4.90 % (1005847)Termination reason: Instruction limit
% 31.03/4.90 % (1005847)Termination phase: Saturation
% 31.03/4.90 % (1005847)Time elapsed: 0.140 s
% 31.03/4.90 % (1005847)Peak memory usage: 12 MB
% 31.03/4.90 % (1005847)Instructions burned: 158 (million)
% 31.03/4.90 % (1005849)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 31.03/4.90 % (1005849)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3080325329:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2961 on theBenchmark for (2961ds/252Mi)
% 31.03/4.90 % (1005850)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2823441701:i=213:rtra=on:ss=axioms_2961 on theBenchmark for (2961ds/213Mi)
% 31.03/4.90 % (1005850)Refutation not found, incomplete strategy
% 31.03/4.90 % (1005850)------------------------------
% 31.03/4.90 % (1005850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.90 % (1005850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.90 % (1005850)CaDiCaL version: 2.1.3
% 31.03/4.90 % (1005850)Termination reason: Refutation not found, incomplete strategy
% 31.03/4.90 % (1005850)Time elapsed: 0.008 s
% 31.03/4.90 % (1005850)Peak memory usage: 12 MB
% 31.03/4.90 % (1005850)Instructions burned: 9 (million)
% 31.03/4.90 % (1005850)------------------------------
% 31.03/4.90 % (1005850)------------------------------
% 31.03/4.90 % (1005849)Refutation not found, incomplete strategy
% 31.03/4.90 % (1005849)------------------------------
% 31.03/4.90 % (1005849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.90 % (1005849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.90 % (1005849)CaDiCaL version: 2.1.3
% 31.03/4.90 % (1005849)Termination reason: Refutation not found, incomplete strategy
% 31.03/4.90 % (1005849)Time elapsed: 0.028 s
% 31.03/4.90 % (1005849)Peak memory usage: 12 MB
% 31.03/4.90 % (1005849)Instructions burned: 38 (million)
% 31.03/4.90 % (1005849)------------------------------
% 31.03/4.90 % (1005849)------------------------------
% 31.03/4.90 % (1005845)Instruction limit reached!
% 31.03/4.90 % (1005845)------------------------------
% 31.03/4.90 % (1005845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.90 % (1005845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.90 % (1005845)CaDiCaL version: 2.1.3
% 31.03/4.90 % (1005845)Termination reason: Instruction limit
% 31.03/4.90 % (1005845)Termination phase: Saturation
% 31.03/4.90 % (1005845)Time elapsed: 0.281 s
% 31.03/4.90 % (1005845)Peak memory usage: 15 MB
% 31.03/4.90 % (1005845)Instructions burned: 365 (million)
% 31.03/4.90 % (1005853)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=2159926526:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2961 on theBenchmark for (2961ds/160Mi)
% 31.03/4.90 % (1005855)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 31.03/4.90 % (1005854)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=3190448826:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2961 on theBenchmark for (2961ds/763Mi)
% 31.03/4.99 % (1005855)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1066991456:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2961 on theBenchmark for (2961ds/237Mi)
% 31.03/4.99 % (1005854)Refutation not found, incomplete strategy
% 31.03/4.99 % (1005854)------------------------------
% 31.03/4.99 % (1005854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.99 % (1005854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.99 % (1005854)CaDiCaL version: 2.1.3
% 31.03/4.99 % (1005854)Termination reason: Refutation not found, incomplete strategy
% 31.03/4.99 % (1005854)Time elapsed: 0.026 s
% 31.03/4.99 % (1005854)Peak memory usage: 12 MB
% 31.03/4.99 % (1005854)Instructions burned: 34 (million)
% 31.03/4.99 % (1005853)Refutation not found, incomplete strategy
% 31.03/4.99 % (1005853)------------------------------
% 31.03/4.99 % (1005853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.99 % (1005853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.99 % (1005853)CaDiCaL version: 2.1.3
% 31.03/4.99 % (1005853)Termination reason: Refutation not found, incomplete strategy
% 31.03/4.99 % (1005853)Time elapsed: 0.030 s
% 31.03/4.99 % (1005853)Peak memory usage: 12 MB
% 31.03/4.99 % (1005853)Instructions burned: 40 (million)
% 31.03/4.99 % (1005854)------------------------------
% 31.03/4.99 % (1005854)------------------------------
% 31.03/4.99 % (1005853)------------------------------
% 31.03/4.99 % (1005853)------------------------------
% 31.03/4.99 % (1005859)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=3411850951:s2a=on:i=386:rtra=on:ntd=on_2960 on theBenchmark for (2960ds/386Mi)
% 31.03/4.99 % (1005860)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=3542895872:i=300:piset=and:nm=32:rtra=on_2960 on theBenchmark for (2960ds/300Mi)
% 31.03/4.99 % (1005855)Instruction limit reached!
% 31.03/4.99 % (1005855)------------------------------
% 31.03/4.99 % (1005855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.99 % (1005855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.99 % (1005855)CaDiCaL version: 2.1.3
% 31.03/4.99 % (1005855)Termination reason: Instruction limit
% 31.03/4.99 % (1005855)Termination phase: Saturation
% 31.03/4.99 % (1005855)Time elapsed: 0.187 s
% 31.03/4.99 % (1005855)Peak memory usage: 14 MB
% 31.03/4.99 % (1005855)Instructions burned: 238 (million)
% 31.03/4.99 % (1005863)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=217303952:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2959 on theBenchmark for (2959ds/567Mi)
% 31.03/4.99 % (1005766)Instruction limit reached!
% 31.03/4.99 % (1005766)------------------------------
% 31.03/4.99 % (1005766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.99 % (1005766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.99 % (1005766)CaDiCaL version: 2.1.3
% 31.03/4.99 % (1005766)Termination reason: Instruction limit
% 31.03/4.99 % (1005766)Termination phase: Saturation
% 31.03/4.99 % (1005766)Time elapsed: 2.723 s
% 31.03/4.99 % (1005766)Peak memory usage: 13 MB
% 31.03/4.99 % (1005766)Instructions burned: 9843 (million)
% 31.03/4.99 % (1005865)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=2238871490:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2958 on theBenchmark for (2958ds/379Mi)
% 31.03/4.99 % (1005860)Instruction limit reached!
% 31.03/4.99 % (1005860)------------------------------
% 31.03/4.99 % (1005860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.03/4.99 % (1005860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.03/4.99 % (1005860)CaDiCaL version: 2.1.3
% 31.03/4.99 % (1005860)Termination reason: Instruction limit
% 31.03/4.99 % (1005860)Termination phase: Saturation
% 31.03/4.99 % (1005860)Time elapsed: 0.237 s
% 31.03/4.99 % (1005860)Peak memory usage: 14 MB
% 31.03/4.99 % (1005860)Instructions burned: 300 (million)
% 31.03/4.99 % (1005867)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=3254390692:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2957 on theBenchmark for (2957ds/429Mi)
% 31.03/4.99 % (1005859)Instruction limit reached!
% 31.03/4.99 % (1005859)------------------------------
% 31.03/4.99 % (1005859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.34/5.29 % (1005859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.34/5.29 % (1005859)CaDiCaL version: 2.1.3
% 34.34/5.29 % (1005859)Termination reason: Instruction limit
% 34.34/5.29 % (1005859)Termination phase: Saturation
% 34.34/5.29 % (1005859)Time elapsed: 0.288 s
% 34.34/5.29 % (1005859)Peak memory usage: 13 MB
% 34.34/5.29 % (1005859)Instructions burned: 386 (million)
% 34.34/5.29 % (1005869)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=3814089675:i=478:bd=all:rtra=on_2957 on theBenchmark for (2957ds/478Mi)
% 34.34/5.29 % (1005865)Instruction limit reached!
% 34.34/5.29 % (1005865)------------------------------
% 34.34/5.29 % (1005865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.34/5.29 % (1005865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.34/5.29 % (1005865)CaDiCaL version: 2.1.3
% 34.34/5.29 % (1005865)Termination reason: Instruction limit
% 34.34/5.29 % (1005865)Termination phase: Saturation
% 34.34/5.29 % (1005865)Time elapsed: 0.165 s
% 34.34/5.29 % (1005865)Peak memory usage: 15 MB
% 34.34/5.29 % (1005865)Instructions burned: 381 (million)
% 34.34/5.29 % (1005871)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=357052595:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2956 on theBenchmark for (2956ds/445Mi)
% 34.34/5.29 % (1005819)Instruction limit reached!
% 34.34/5.29 % (1005819)------------------------------
% 34.34/5.29 % (1005819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.34/5.29 % (1005819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.34/5.29 % (1005819)CaDiCaL version: 2.1.3
% 34.34/5.29 % (1005819)Termination reason: Instruction limit
% 34.34/5.29 % (1005819)Termination phase: Saturation
% 34.34/5.29 % (1005819)Time elapsed: 1.610 s
% 34.34/5.29 % (1005819)Peak memory usage: 14 MB
% 34.34/5.29 % (1005819)Instructions burned: 2187 (million)
% 34.34/5.29 % (1005873)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=1030474912:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2956 on theBenchmark for (2956ds/71Mi)
% 34.34/5.29 % (1005873)Instruction limit reached!
% 34.34/5.29 % (1005873)------------------------------
% 34.34/5.29 % (1005873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.34/5.29 % (1005873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.34/5.29 % (1005873)CaDiCaL version: 2.1.3
% 34.34/5.29 % (1005873)Termination reason: Instruction limit
% 34.34/5.29 % (1005873)Termination phase: Saturation
% 34.34/5.29 % (1005873)Time elapsed: 0.055 s
% 34.34/5.29 % (1005873)Peak memory usage: 12 MB
% 34.34/5.29 % (1005873)Instructions burned: 71 (million)
% 34.34/5.29 % (1005875)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=616729498:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2955 on theBenchmark for (2955ds/302Mi)
% 34.34/5.29 % (1005875)Refutation not found, incomplete strategy
% 34.34/5.29 % (1005875)------------------------------
% 34.34/5.29 % (1005875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.34/5.29 % (1005875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.34/5.29 % (1005875)CaDiCaL version: 2.1.3
% 34.34/5.29 % (1005875)Termination reason: Refutation not found, incomplete strategy
% 34.34/5.29 % (1005875)Time elapsed: 0.008 s
% 34.34/5.29 % (1005875)Peak memory usage: 12 MB
% 34.34/5.29 % (1005875)Instructions burned: 8 (million)
% 34.34/5.29 % (1005875)------------------------------
% 34.34/5.29 % (1005875)------------------------------
% 34.34/5.29 % (1005871)Instruction limit reached!
% 34.34/5.29 % (1005871)------------------------------
% 34.34/5.29 % (1005871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.34/5.29 % (1005871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.34/5.29 % (1005871)CaDiCaL version: 2.1.3
% 34.34/5.29 % (1005871)Termination reason: Instruction limit
% 34.34/5.29 % (1005871)Termination phase: Saturation
% 34.34/5.29 % (1005871)Time elapsed: 0.182 s
% 34.34/5.29 % (1005871)Peak memory usage: 15 MB
% 34.34/5.29 % (1005871)Instructions burned: 445 (million)
% 34.34/5.29 % (1005863)Instruction limit reached!
% 34.34/5.29 % (1005863)------------------------------
% 34.34/5.29 % (1005863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.34/5.29 % (1005863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.34/5.29 % (1005863)CaDiCaL version: 2.1.3
% 34.34/5.29 % (1005863)Termination reason: Instruction limit
% 34.34/5.29 % (1005863)Termination phase: Saturation
% 35.39/5.48 % (1005863)Time elapsed: 0.420 s
% 35.39/5.48 % (1005863)Peak memory usage: 13 MB
% 35.39/5.48 % (1005863)Instructions burned: 567 (million)
% 35.39/5.48 % (1005877)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=2294141093:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2954 on theBenchmark for (2954ds/4980Mi)
% 35.39/5.48 % (1005878)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 35.39/5.48 % (1005878)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 35.39/5.48 % (1005877)Refutation not found, incomplete strategy
% 35.39/5.48 % (1005877)------------------------------
% 35.39/5.48 % (1005877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.39/5.48 % (1005877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.39/5.48 % (1005877)CaDiCaL version: 2.1.3
% 35.39/5.48 % (1005877)Termination reason: Refutation not found, incomplete strategy
% 35.39/5.48 % (1005877)Time elapsed: 0.012 s
% 35.39/5.48 % (1005877)Peak memory usage: 12 MB
% 35.39/5.48 % (1005877)Instructions burned: 13 (million)
% 35.39/5.48 % (1005877)------------------------------
% 35.39/5.48 % (1005877)------------------------------
% 35.39/5.48 % (1005878)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4169290088:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2954 on theBenchmark for (2954ds/100Mi)
% 35.39/5.48 % (1005879)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2272545246:i=76:piset=equals:rtra=on:ntd=on_2954 on theBenchmark for (2954ds/76Mi)
% 35.39/5.48 % (1005867)Instruction limit reached!
% 35.39/5.48 % (1005867)------------------------------
% 35.39/5.48 % (1005867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.39/5.48 % (1005867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.39/5.48 % (1005867)CaDiCaL version: 2.1.3
% 35.39/5.48 % (1005867)Termination reason: Instruction limit
% 35.39/5.48 % (1005867)Termination phase: Saturation
% 35.39/5.48 % (1005867)Time elapsed: 0.346 s
% 35.39/5.48 % (1005867)Peak memory usage: 15 MB
% 35.39/5.48 % (1005867)Instructions burned: 429 (million)
% 35.39/5.48 % (1005882)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=2635394308:i=289:rtra=on_2954 on theBenchmark for (2954ds/289Mi)
% 35.39/5.48 % (1005878)Instruction limit reached!
% 35.39/5.48 % (1005878)------------------------------
% 35.39/5.48 % (1005878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.39/5.48 % (1005878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.39/5.48 % (1005878)CaDiCaL version: 2.1.3
% 35.39/5.48 % (1005878)Termination reason: Instruction limit
% 35.39/5.48 % (1005878)Termination phase: Saturation
% 35.39/5.48 % (1005878)Time elapsed: 0.038 s
% 35.39/5.48 % (1005878)Peak memory usage: 12 MB
% 35.39/5.48 % (1005878)Instructions burned: 100 (million)
% 35.39/5.48 % (1005884)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=1948109762:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2954 on theBenchmark for (2954ds/493Mi)
% 35.39/5.48 % (1005886)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1571780144:cond=on:i=34:hud=10:nm=10:rtra=on_2953 on theBenchmark for (2953ds/34Mi)
% 35.39/5.48 % (1005882)Refutation not found, incomplete strategy
% 35.39/5.48 % (1005882)------------------------------
% 35.39/5.48 % (1005882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.39/5.48 % (1005882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.39/5.48 % (1005882)CaDiCaL version: 2.1.3
% 35.39/5.48 % (1005882)Termination reason: Refutation not found, incomplete strategy
% 35.39/5.48 % (1005882)Time elapsed: 0.029 s
% 35.39/5.48 % (1005882)Peak memory usage: 12 MB
% 35.39/5.48 % (1005882)Instructions burned: 37 (million)
% 35.39/5.48 % (1005882)------------------------------
% 35.39/5.48 % (1005882)------------------------------
% 35.39/5.48 % (1005886)Instruction limit reached!
% 35.39/5.48 % (1005886)------------------------------
% 35.39/5.48 % (1005886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.93/5.75 % (1005886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.93/5.75 % (1005886)CaDiCaL version: 2.1.3
% 36.93/5.75 % (1005886)Termination reason: Instruction limit
% 36.93/5.75 % (1005886)Termination phase: Saturation
% 36.93/5.75 % (1005886)Time elapsed: 0.013 s
% 36.93/5.75 % (1005886)Peak memory usage: 12 MB
% 36.93/5.75 % (1005886)Instructions burned: 35 (million)
% 36.93/5.75 % (1005879)Instruction limit reached!
% 36.93/5.75 % (1005879)------------------------------
% 36.93/5.75 % (1005879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.93/5.75 % (1005879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.93/5.75 % (1005879)CaDiCaL version: 2.1.3
% 36.93/5.75 % (1005879)Termination reason: Instruction limit
% 36.93/5.75 % (1005879)Termination phase: Saturation
% 36.93/5.75 % (1005879)Time elapsed: 0.058 s
% 36.93/5.75 % (1005879)Peak memory usage: 13 MB
% 36.93/5.75 % (1005879)Instructions burned: 76 (million)
% 36.93/5.75 % (1005890)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=1753223782:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2953 on theBenchmark for (2953ds/670Mi)
% 36.93/5.75 % (1005889)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 36.93/5.75 % (1005889)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=4088271549:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2953 on theBenchmark for (2953ds/372Mi)
% 36.93/5.75 % (1005891)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1473488156:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2953 on theBenchmark for (2953ds/647Mi)
% 36.93/5.75 % (1005869)Instruction limit reached!
% 36.93/5.75 % (1005869)------------------------------
% 36.93/5.75 % (1005869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.93/5.75 % (1005869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.93/5.75 % (1005869)CaDiCaL version: 2.1.3
% 36.93/5.75 % (1005869)Termination reason: Instruction limit
% 36.93/5.75 % (1005869)Termination phase: Saturation
% 36.93/5.75 % (1005869)Time elapsed: 0.395 s
% 36.93/5.75 % (1005869)Peak memory usage: 15 MB
% 36.93/5.75 % (1005869)Instructions burned: 479 (million)
% 36.93/5.75 % (1005895)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=1513408559:i=857:add=off:kws=frequency:rtra=on:ntd=on_2953 on theBenchmark for (2953ds/857Mi)
% 36.93/5.75 % (1005895)Refutation not found, incomplete strategy
% 36.93/5.75 % (1005895)------------------------------
% 36.93/5.75 % (1005895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.93/5.75 % (1005895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.93/5.75 % (1005895)CaDiCaL version: 2.1.3
% 36.93/5.75 % (1005895)Termination reason: Refutation not found, incomplete strategy
% 36.93/5.75 % (1005895)Time elapsed: 0.029 s
% 36.93/5.75 % (1005895)Peak memory usage: 12 MB
% 36.93/5.75 % (1005895)Instructions burned: 38 (million)
% 36.93/5.75 % (1005895)------------------------------
% 36.93/5.75 % (1005895)------------------------------
% 36.93/5.75 % (1005897)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=2745816886:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2952 on theBenchmark for (2952ds/693Mi)
% 36.93/5.75 % (1005890)Instruction limit reached!
% 36.93/5.75 % (1005890)------------------------------
% 36.93/5.75 % (1005890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.93/5.75 % (1005890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.93/5.75 % (1005890)CaDiCaL version: 2.1.3
% 36.93/5.75 % (1005890)Termination reason: Instruction limit
% 36.93/5.75 % (1005890)Termination phase: Saturation
% 36.93/5.75 % (1005890)Time elapsed: 0.270 s
% 36.93/5.75 % (1005890)Peak memory usage: 19 MB
% 36.93/5.75 % (1005890)Instructions burned: 671 (million)
% 36.93/5.75 % (1005884)Instruction limit reached!
% 36.93/5.75 % (1005884)------------------------------
% 36.93/5.75 % (1005884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.93/5.75 % (1005884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.96/5.99 % (1005884)CaDiCaL version: 2.1.3
% 37.96/5.99 % (1005884)Termination reason: Instruction limit
% 37.96/5.99 % (1005884)Termination phase: Saturation
% 37.96/5.99 % (1005884)Time elapsed: 0.322 s
% 37.96/5.99 % (1005884)Peak memory usage: 12 MB
% 37.96/5.99 % (1005884)Instructions burned: 494 (million)
% 37.96/5.99 % (1005899)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=1718463564:i=285:hud=10:bd=all:rtra=on:ss=axioms_2950 on theBenchmark for (2950ds/285Mi)
% 37.96/5.99 % (1005889)Instruction limit reached!
% 37.96/5.99 % (1005889)------------------------------
% 37.96/5.99 % (1005889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.96/5.99 % (1005899)Refutation not found, incomplete strategy
% 37.96/5.99 % (1005899)------------------------------
% 37.96/5.99 % (1005899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.96/5.99 % (1005899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.96/5.99 % (1005889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.96/5.99 % (1005899)CaDiCaL version: 2.1.3
% 37.96/5.99 % (1005899)Termination reason: Refutation not found, incomplete strategy
% 37.96/5.99 % (1005899)Time elapsed: 0.006 s
% 37.96/5.99 % (1005899)Peak memory usage: 12 MB
% 37.96/5.99 % (1005889)CaDiCaL version: 2.1.3
% 37.96/5.99 % (1005899)Instructions burned: 11 (million)
% 37.96/5.99 % (1005889)Termination reason: Instruction limit
% 37.96/5.99 % (1005889)Termination phase: Saturation
% 37.96/5.99 % (1005889)Time elapsed: 0.289 s
% 37.96/5.99 % (1005889)Peak memory usage: 12 MB
% 37.96/5.99 % (1005889)Instructions burned: 373 (million)
% 37.96/5.99 % (1005899)------------------------------
% 37.96/5.99 % (1005899)------------------------------
% 37.96/5.99 % (1005900)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 37.96/5.99 % (1005902)dis+10_1_si=on:random_seed=3339822558:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2950 on theBenchmark for (2950ds/407Mi)
% 37.96/5.99 % (1005900)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=576367865:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2950 on theBenchmark for (2950ds/52Mi)
% 37.96/5.99 % (1005903)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1049552077:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2950 on theBenchmark for (2950ds/2240Mi)
% 37.96/5.99 % (1005900)Instruction limit reached!
% 37.96/5.99 % (1005900)------------------------------
% 37.96/5.99 % (1005900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.96/5.99 % (1005900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.96/5.99 % (1005900)CaDiCaL version: 2.1.3
% 37.96/5.99 % (1005900)Termination reason: Instruction limit
% 37.96/5.99 % (1005900)Termination phase: Saturation
% 37.96/5.99 % (1005900)Time elapsed: 0.038 s
% 37.96/5.99 % (1005900)Peak memory usage: 12 MB
% 37.96/5.99 % (1005900)Instructions burned: 52 (million)
% 37.96/5.99 % (1005907)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=197362403:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2949 on theBenchmark for (2949ds/336Mi)
% 37.96/5.99 % (1005907)Refutation not found, incomplete strategy
% 37.96/5.99 % (1005907)------------------------------
% 37.96/5.99 % (1005907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.96/5.99 % (1005907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.96/5.99 % (1005907)CaDiCaL version: 2.1.3
% 37.96/5.99 % (1005907)Termination reason: Refutation not found, incomplete strategy
% 37.96/5.99 % (1005907)Time elapsed: 0.011 s
% 37.96/5.99 % (1005907)Peak memory usage: 12 MB
% 37.96/5.99 % (1005907)Instructions burned: 12 (million)
% 37.96/5.99 % (1005907)------------------------------
% 37.96/5.99 % (1005907)------------------------------
% 37.96/5.99 % (1005909)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=912662678:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2949 on theBenchmark for (2949ds/1142Mi)
% 37.96/5.99 % (1005909)Refutation not found, incomplete strategy
% 37.96/5.99 % (1005909)------------------------------
% 37.96/5.99 % (1005909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.96/5.99 % (1005909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.47/6.29 % (1005909)CaDiCaL version: 2.1.3
% 41.47/6.29 % (1005909)Termination reason: Refutation not found, incomplete strategy
% 41.47/6.29 % (1005909)Time elapsed: 0.037 s
% 41.47/6.29 % (1005909)Peak memory usage: 13 MB
% 41.47/6.29 % (1005909)Instructions burned: 38 (million)
% 41.47/6.29 % (1005909)------------------------------
% 41.47/6.29 % (1005909)------------------------------
% 41.47/6.29 % (1005902)Instruction limit reached!
% 41.47/6.29 % (1005902)------------------------------
% 41.47/6.29 % (1005902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.47/6.29 % (1005902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.47/6.29 % (1005902)CaDiCaL version: 2.1.3
% 41.47/6.29 % (1005902)Termination reason: Instruction limit
% 41.47/6.29 % (1005902)Termination phase: Saturation
% 41.47/6.29 % (1005902)Time elapsed: 0.164 s
% 41.47/6.29 % (1005902)Peak memory usage: 14 MB
% 41.47/6.29 % (1005902)Instructions burned: 408 (million)
% 41.47/6.29 % (1005912)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=3252676911:i=766:bd=all:rtra=on_2948 on theBenchmark for (2948ds/766Mi)
% 41.47/6.30 % (1005911)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=1763150942:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2948 on theBenchmark for (2948ds/376Mi)
% 41.47/6.30 % (1005891)Instruction limit reached!
% 41.47/6.30 % (1005891)------------------------------
% 41.47/6.30 % (1005891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.47/6.30 % (1005891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.47/6.30 % (1005891)CaDiCaL version: 2.1.3
% 41.47/6.30 % (1005891)Termination reason: Instruction limit
% 41.47/6.30 % (1005891)Termination phase: Saturation
% 41.47/6.30 % (1005891)Time elapsed: 0.524 s
% 41.47/6.30 % (1005891)Peak memory usage: 14 MB
% 41.47/6.30 % (1005891)Instructions burned: 648 (million)
% 41.47/6.30 % (1005833)Instruction limit reached!
% 41.47/6.30 % (1005833)------------------------------
% 41.47/6.30 % (1005833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.47/6.30 % (1005833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.47/6.30 % (1005833)CaDiCaL version: 2.1.3
% 41.47/6.30 % (1005833)Termination reason: Instruction limit
% 41.47/6.30 % (1005833)Termination phase: Saturation
% 41.47/6.30 % (1005833)Time elapsed: 2.012 s
% 41.47/6.30 % (1005833)Peak memory usage: 18 MB
% 41.47/6.30 % (1005833)Instructions burned: 2471 (million)
% 41.47/6.30 % (1005915)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 41.47/6.30 % (1005915)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=3969332264:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2948 on theBenchmark for (2948ds/959Mi)
% 41.47/6.30 % (1005916)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=3623496001:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2947 on theBenchmark for (2947ds/6359Mi)
% 41.47/6.30 % (1005897)Instruction limit reached!
% 41.47/6.30 % (1005897)------------------------------
% 41.47/6.30 % (1005897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.47/6.30 % (1005897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.47/6.30 % (1005897)CaDiCaL version: 2.1.3
% 41.47/6.30 % (1005897)Termination reason: Instruction limit
% 41.47/6.30 % (1005897)Termination phase: Saturation
% 41.47/6.30 % (1005897)Time elapsed: 0.551 s
% 41.47/6.30 % (1005897)Peak memory usage: 14 MB
% 41.47/6.30 % (1005897)Instructions burned: 694 (million)
% 41.47/6.30 % (1005919)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3930842224:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2946 on theBenchmark for (2946ds/35Mi)
% 41.47/6.30 % (1005919)Instruction limit reached!
% 41.47/6.30 % (1005919)------------------------------
% 41.47/6.30 % (1005919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.47/6.30 % (1005919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.47/6.30 % (1005919)CaDiCaL version: 2.1.3
% 41.47/6.30 % (1005919)Termination reason: Instruction limit
% 41.47/6.30 % (1005919)Termination phase: Saturation
% 41.47/6.30 % (1005919)Time elapsed: 0.026 s
% 41.47/6.30 % (1005919)Peak memory usage: 11 MB
% 41.47/6.30 % (1005919)Instructions burned: 36 (million)
% 42.52/6.44 % (1005921)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=1180572545:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2946 on theBenchmark for (2946ds/53Mi)
% 42.52/6.44 % (1005921)Instruction limit reached!
% 42.52/6.44 % (1005921)------------------------------
% 42.52/6.44 % (1005921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.44 % (1005921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.44 % (1005921)CaDiCaL version: 2.1.3
% 42.52/6.44 % (1005921)Termination reason: Instruction limit
% 42.52/6.44 % (1005921)Termination phase: Saturation
% 42.52/6.44 % (1005921)Time elapsed: 0.041 s
% 42.52/6.44 % (1005921)Peak memory usage: 13 MB
% 42.52/6.44 % (1005921)Instructions burned: 54 (million)
% 42.52/6.44 % (1005911)Instruction limit reached!
% 42.52/6.44 % (1005911)------------------------------
% 42.52/6.44 % (1005911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.44 % (1005911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.44 % (1005911)CaDiCaL version: 2.1.3
% 42.52/6.44 % (1005911)Termination reason: Instruction limit
% 42.52/6.44 % (1005911)Termination phase: Saturation
% 42.52/6.44 % (1005911)Time elapsed: 0.320 s
% 42.52/6.44 % (1005911)Peak memory usage: 15 MB
% 42.52/6.44 % (1005911)Instructions burned: 376 (million)
% 42.52/6.44 % (1005912)Instruction limit reached!
% 42.52/6.44 % (1005912)------------------------------
% 42.52/6.44 % (1005912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.44 % (1005912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.44 % (1005912)CaDiCaL version: 2.1.3
% 42.52/6.44 % (1005912)Termination reason: Instruction limit
% 42.52/6.44 % (1005912)Termination phase: Saturation
% 42.52/6.44 % (1005912)Time elapsed: 0.334 s
% 42.52/6.44 % (1005912)Peak memory usage: 17 MB
% 42.52/6.44 % (1005912)Instructions burned: 768 (million)
% 42.52/6.44 % (1005927)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 42.52/6.44 % (1005927)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3329206916:i=306:bd=all:rtra=on_2945 on theBenchmark for (2945ds/306Mi)
% 42.52/6.44 % (1005735)Instruction limit reached!
% 42.52/6.44 % (1005735)------------------------------
% 42.52/6.44 % (1005735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.44 % (1005735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.44 % (1005735)CaDiCaL version: 2.1.3
% 42.52/6.44 % (1005735)Termination reason: Instruction limit
% 42.52/6.44 % (1005735)Termination phase: Saturation
% 42.52/6.44 % (1005735)Time elapsed: 4.634 s
% 42.52/6.44 % (1005735)Peak memory usage: 40 MB
% 42.52/6.44 % (1005735)Instructions burned: 5755 (million)
% 42.52/6.44 % (1005925)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=793010744:s2a=on:i=876:s2at=6:nm=2:rtra=on_2945 on theBenchmark for (2945ds/876Mi)
% 42.52/6.44 % (1005926)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2770875555:i=57:ep=R:rtra=on:ntd=on_2945 on theBenchmark for (2945ds/57Mi)
% 42.52/6.44 % (1005930)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=498100983:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2944 on theBenchmark for (2944ds/262Mi)
% 42.52/6.44 % (1005926)Instruction limit reached!
% 42.52/6.44 % (1005926)------------------------------
% 42.52/6.44 % (1005926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.44 % (1005926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.44 % (1005926)CaDiCaL version: 2.1.3
% 42.52/6.44 % (1005926)Termination reason: Instruction limit
% 42.52/6.44 % (1005926)Termination phase: Saturation
% 42.52/6.44 % (1005926)Time elapsed: 0.044 s
% 42.52/6.44 % (1005926)Peak memory usage: 12 MB
% 42.52/6.44 % (1005926)Instructions burned: 57 (million)
% 42.52/6.44 % (1005933)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 42.52/6.44 % (1005933)ott+1002_16_sil=128000:si=on:random_seed=976632786:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2944 on theBenchmark for (2944ds/409Mi)
% 42.52/6.44 % (1005927)Instruction limit reached!
% 42.52/6.44 % (1005927)------------------------------
% 42.52/6.44 % (1005927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.87/6.63 % (1005927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.87/6.63 % (1005927)CaDiCaL version: 2.1.3
% 43.87/6.63 % (1005927)Termination reason: Instruction limit
% 43.87/6.63 % (1005927)Termination phase: Saturation
% 43.87/6.63 % (1005927)Time elapsed: 0.128 s
% 43.87/6.63 % (1005927)Peak memory usage: 15 MB
% 43.87/6.63 % (1005927)Instructions burned: 308 (million)
% 43.87/6.63 % (1005935)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=2027078220:s2a=on:i=381:rtra=on_2943 on theBenchmark for (2943ds/381Mi)
% 43.87/6.63 % (1005930)Instruction limit reached!
% 43.87/6.63 % (1005930)------------------------------
% 43.87/6.63 % (1005930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.87/6.63 % (1005930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.87/6.63 % (1005930)CaDiCaL version: 2.1.3
% 43.87/6.63 % (1005930)Termination reason: Instruction limit
% 43.87/6.63 % (1005930)Termination phase: Saturation
% 43.87/6.63 % (1005930)Time elapsed: 0.194 s
% 43.87/6.63 % (1005930)Peak memory usage: 12 MB
% 43.87/6.63 % (1005930)Instructions burned: 262 (million)
% 43.87/6.63 % (1005937)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3210012328:cond=on:i=324:rtra=on:ntd=on_2942 on theBenchmark for (2942ds/324Mi)
% 43.87/6.63 % (1005935)Instruction limit reached!
% 43.87/6.63 % (1005935)------------------------------
% 43.87/6.63 % (1005935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.87/6.63 % (1005935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.87/6.63 % (1005935)CaDiCaL version: 2.1.3
% 43.87/6.63 % (1005935)Termination reason: Instruction limit
% 43.87/6.63 % (1005935)Termination phase: Saturation
% 43.87/6.63 % (1005935)Time elapsed: 0.162 s
% 43.87/6.63 % (1005935)Peak memory usage: 15 MB
% 43.87/6.63 % (1005935)Instructions burned: 382 (million)
% 43.87/6.63 % (1005939)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=1563941077:i=240:kws=inv_precedence:rtra=on_2941 on theBenchmark for (2941ds/240Mi)
% 43.87/6.63 % (1005939)Refutation not found, incomplete strategy
% 43.87/6.63 % (1005939)------------------------------
% 43.87/6.63 % (1005939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.87/6.63 % (1005939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.87/6.63 % (1005939)CaDiCaL version: 2.1.3
% 43.87/6.63 % (1005939)Termination reason: Refutation not found, incomplete strategy
% 43.87/6.63 % (1005939)Time elapsed: 0.006 s
% 43.87/6.63 % (1005939)Peak memory usage: 12 MB
% 43.87/6.63 % (1005939)Instructions burned: 13 (million)
% 43.87/6.63 % (1005939)------------------------------
% 43.87/6.63 % (1005939)------------------------------
% 43.87/6.63 % (1005941)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 43.87/6.63 % (1005941)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3789354829:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2941 on theBenchmark for (2941ds/124Mi)
% 43.87/6.63 % (1005941)Instruction limit reached!
% 43.87/6.63 % (1005941)------------------------------
% 43.87/6.63 % (1005941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.87/6.63 % (1005941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.87/6.63 % (1005941)CaDiCaL version: 2.1.3
% 43.87/6.63 % (1005941)Termination reason: Instruction limit
% 43.87/6.63 % (1005941)Termination phase: Saturation
% 43.87/6.63 % (1005941)Time elapsed: 0.049 s
% 43.87/6.63 % (1005941)Peak memory usage: 12 MB
% 43.87/6.63 % (1005941)Instructions burned: 126 (million)
% 43.87/6.63 % (1005933)Instruction limit reached!
% 43.87/6.63 % (1005933)------------------------------
% 43.87/6.63 % (1005933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.87/6.63 % (1005933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.87/6.63 % (1005933)CaDiCaL version: 2.1.3
% 43.87/6.63 % (1005933)Termination reason: Instruction limit
% 43.87/6.63 % (1005933)Termination phase: Saturation
% 43.87/6.63 % (1005933)Time elapsed: 0.330 s
% 43.87/6.63 % (1005933)Peak memory usage: 15 MB
% 43.87/6.63 % (1005933)Instructions burned: 410 (million)
% 43.87/6.63 % (1005943)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=3060143808:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2940 on theBenchmark for (2940ds/223Mi)
% 43.87/6.63 % (1005943)Refutation not found, incomplete strategy
% 48.43/7.19 % (1005943)------------------------------
% 48.43/7.19 % (1005943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.43/7.19 % (1005943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.43/7.19 % (1005943)CaDiCaL version: 2.1.3
% 48.43/7.19 % (1005943)Termination reason: Refutation not found, incomplete strategy
% 48.43/7.19 % (1005943)Time elapsed: 0.013 s
% 48.43/7.19 % (1005943)Peak memory usage: 12 MB
% 48.43/7.19 % (1005943)Instructions burned: 33 (million)
% 48.43/7.19 % (1005943)------------------------------
% 48.43/7.19 % (1005943)------------------------------
% 48.43/7.19 % (1005946)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=515178502:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2940 on theBenchmark for (2940ds/464Mi)
% 48.43/7.19 % (1005945)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1904374905:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2940 on theBenchmark for (2940ds/282Mi)
% 48.43/7.19 % (1005946)Refutation not found, incomplete strategy
% 48.43/7.19 % (1005946)------------------------------
% 48.43/7.19 % (1005946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.43/7.19 % (1005946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.43/7.19 % (1005946)CaDiCaL version: 2.1.3
% 48.43/7.19 % (1005946)Termination reason: Refutation not found, incomplete strategy
% 48.43/7.19 % (1005946)Time elapsed: 0.006 s
% 48.43/7.19 % (1005946)Peak memory usage: 12 MB
% 48.43/7.19 % (1005946)Instructions burned: 13 (million)
% 48.43/7.19 % (1005946)------------------------------
% 48.43/7.19 % (1005946)------------------------------
% 48.43/7.19 % (1005949)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3569737808:i=88:s2at=3:nm=2:rtra=on:rawr=on_2940 on theBenchmark for (2940ds/88Mi)
% 48.43/7.19 % (1005915)Instruction limit reached!
% 48.43/7.19 % (1005915)------------------------------
% 48.43/7.19 % (1005915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.43/7.19 % (1005915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.43/7.19 % (1005915)CaDiCaL version: 2.1.3
% 48.43/7.19 % (1005915)Termination reason: Instruction limit
% 48.43/7.19 % (1005915)Termination phase: Saturation
% 48.43/7.19 % (1005915)Time elapsed: 0.780 s
% 48.43/7.19 % (1005915)Peak memory usage: 17 MB
% 48.43/7.19 % (1005915)Instructions burned: 960 (million)
% 48.43/7.19 % (1005949)Instruction limit reached!
% 48.43/7.19 % (1005949)------------------------------
% 48.43/7.19 % (1005949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.43/7.19 % (1005949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.43/7.19 % (1005949)CaDiCaL version: 2.1.3
% 48.43/7.19 % (1005949)Termination reason: Instruction limit
% 48.43/7.19 % (1005949)Termination phase: Saturation
% 48.43/7.19 % (1005949)Time elapsed: 0.034 s
% 48.43/7.19 % (1005949)Peak memory usage: 12 MB
% 48.43/7.19 % (1005949)Instructions burned: 89 (million)
% 48.43/7.19 % (1005952)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 48.43/7.19 % (1005952)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2128073831:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2939 on theBenchmark for (2939ds/4386Mi)
% 48.43/7.19 % (1005951)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2717822398:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2939 on theBenchmark for (2939ds/280Mi)
% 48.43/7.19 % (1005937)Instruction limit reached!
% 48.43/7.19 % (1005937)------------------------------
% 48.43/7.19 % (1005937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.43/7.19 % (1005937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.43/7.19 % (1005937)CaDiCaL version: 2.1.3
% 48.43/7.19 % (1005937)Termination reason: Instruction limit
% 48.43/7.19 % (1005937)Termination phase: Saturation
% 48.43/7.19 % (1005937)Time elapsed: 0.275 s
% 48.43/7.19 % (1005937)Peak memory usage: 13 MB
% 48.43/7.19 % (1005937)Instructions burned: 324 (million)
% 48.43/7.19 % (1005955)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 48.43/7.19 % (1005955)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 48.43/7.19 % (1005955)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=3403107261:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2939 on theBenchmark for (2939ds/483Mi)
% 51.08/7.72 % (1005955)Refutation not found, incomplete strategy
% 51.08/7.72 % (1005955)------------------------------
% 51.08/7.72 % (1005955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.08/7.72 % (1005955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.08/7.72 % (1005955)CaDiCaL version: 2.1.3
% 51.08/7.72 % (1005955)Termination reason: Refutation not found, incomplete strategy
% 51.08/7.72 % (1005955)Time elapsed: 0.028 s
% 51.08/7.72 % (1005955)Peak memory usage: 13 MB
% 51.08/7.72 % (1005955)Instructions burned: 35 (million)
% 51.08/7.72 % (1005955)------------------------------
% 51.08/7.72 % (1005955)------------------------------
% 51.08/7.72 % (1005957)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=50553255:i=73:rtra=on_2938 on theBenchmark for (2938ds/73Mi)
% 51.08/7.72 % (1005945)Instruction limit reached!
% 51.08/7.72 % (1005945)------------------------------
% 51.08/7.72 % (1005945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.08/7.72 % (1005945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.08/7.72 % (1005945)CaDiCaL version: 2.1.3
% 51.08/7.72 % (1005945)Termination reason: Instruction limit
% 51.08/7.72 % (1005945)Termination phase: Saturation
% 51.08/7.72 % (1005945)Time elapsed: 0.239 s
% 51.08/7.72 % (1005945)Peak memory usage: 13 MB
% 51.08/7.72 % (1005945)Instructions burned: 282 (million)
% 51.08/7.72 % (1005957)Instruction limit reached!
% 51.08/7.72 % (1005957)------------------------------
% 51.08/7.72 % (1005957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.08/7.72 % (1005957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.08/7.72 % (1005957)CaDiCaL version: 2.1.3
% 51.08/7.72 % (1005957)Termination reason: Instruction limit
% 51.08/7.72 % (1005957)Termination phase: Saturation
% 51.08/7.72 % (1005957)Time elapsed: 0.058 s
% 51.08/7.72 % (1005957)Peak memory usage: 12 MB
% 51.08/7.72 % (1005957)Instructions burned: 73 (million)
% 51.08/7.72 % (1005925)Instruction limit reached!
% 51.08/7.72 % (1005925)------------------------------
% 51.08/7.72 % (1005925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.08/7.72 % (1005925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.08/7.72 % (1005925)CaDiCaL version: 2.1.3
% 51.08/7.72 % (1005925)Termination reason: Instruction limit
% 51.08/7.72 % (1005925)Termination phase: Saturation
% 51.08/7.72 % (1005925)Time elapsed: 0.722 s
% 51.08/7.72 % (1005925)Peak memory usage: 14 MB
% 51.08/7.72 % (1005925)Instructions burned: 876 (million)
% 51.08/7.72 % (1005959)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=448865167:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2938 on theBenchmark for (2938ds/176Mi)
% 51.08/7.72 % (1005960)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 51.08/7.72 % (1005960)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=347503532:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2937 on theBenchmark for (2937ds/39Mi)
% 51.08/7.72 % (1005951)Instruction limit reached!
% 51.08/7.72 % (1005951)------------------------------
% 51.08/7.72 % (1005951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.08/7.72 % (1005951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.08/7.72 % (1005951)CaDiCaL version: 2.1.3
% 51.08/7.72 % (1005951)Termination reason: Instruction limit
% 51.08/7.72 % (1005951)Termination phase: Saturation
% 51.08/7.72 % (1005951)Time elapsed: 0.216 s
% 51.08/7.72 % (1005951)Peak memory usage: 12 MB
% 51.08/7.72 % (1005951)Instructions burned: 280 (million)
% 51.08/7.72 % (1005960)Instruction limit reached!
% 51.08/7.72 % (1005960)------------------------------
% 51.08/7.72 % (1005960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.08/7.72 % (1005960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.08/7.72 % (1005960)CaDiCaL version: 2.1.3
% 51.08/7.72 % (1005960)Termination reason: Instruction limit
% 51.08/7.72 % (1005960)Termination phase: Saturation
% 51.08/7.72 % (1005960)Time elapsed: 0.030 s
% 51.08/7.72 % (1005960)Peak memory usage: 12 MB
% 52.83/8.02 % (1005960)Instructions burned: 39 (million)
% 52.83/8.02 % (1005961)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1069245480:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2937 on theBenchmark for (2937ds/708Mi)
% 52.83/8.02 % (1005964)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 52.83/8.02 % (1005964)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=4268728377:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2937 on theBenchmark for (2937ds/252Mi)
% 52.83/8.02 % (1005965)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=20409860:i=823:fsr=off:rtra=on_2937 on theBenchmark for (2937ds/823Mi)
% 52.83/8.02 % (1005964)Refutation not found, incomplete strategy
% 52.83/8.02 % (1005964)------------------------------
% 52.83/8.02 % (1005964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.83/8.02 % (1005964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.83/8.02 % (1005964)CaDiCaL version: 2.1.3
% 52.83/8.02 % (1005964)Termination reason: Refutation not found, incomplete strategy
% 52.83/8.02 % (1005964)Time elapsed: 0.029 s
% 52.83/8.02 % (1005964)Peak memory usage: 12 MB
% 52.83/8.02 % (1005964)Instructions burned: 38 (million)
% 52.83/8.02 % (1005964)------------------------------
% 52.83/8.02 % (1005964)------------------------------
% 52.83/8.02 % (1005959)Instruction limit reached!
% 52.83/8.02 % (1005959)------------------------------
% 52.83/8.02 % (1005959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.83/8.02 % (1005959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.83/8.02 % (1005959)CaDiCaL version: 2.1.3
% 52.83/8.02 % (1005959)Termination reason: Instruction limit
% 52.83/8.02 % (1005959)Termination phase: Saturation
% 52.83/8.02 % (1005959)Time elapsed: 0.133 s
% 52.83/8.02 % (1005959)Peak memory usage: 12 MB
% 52.83/8.02 % (1005959)Instructions burned: 176 (million)
% 52.83/8.02 % (1005969)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 52.83/8.02 % (1005969)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=2327957533:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2936 on theBenchmark for (2936ds/16202Mi)
% 52.83/8.02 % (1005970)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=1045978592:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2936 on theBenchmark for (2936ds/300Mi)
% 52.83/8.02 % (1005970)Instruction limit reached!
% 52.83/8.02 % (1005970)------------------------------
% 52.83/8.02 % (1005970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.83/8.02 % (1005970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.83/8.02 % (1005970)CaDiCaL version: 2.1.3
% 52.83/8.02 % (1005970)Termination reason: Instruction limit
% 52.83/8.02 % (1005970)Termination phase: Saturation
% 52.83/8.02 % (1005970)Time elapsed: 0.226 s
% 52.83/8.02 % (1005970)Peak memory usage: 13 MB
% 52.83/8.02 % (1005970)Instructions burned: 301 (million)
% 52.83/8.02 % (1005973)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 52.83/8.02 % (1005973)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 52.83/8.02 % (1005973)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=2183974561:i=177:add=on:bd=preordered:rtra=on:rawr=on_2933 on theBenchmark for (2933ds/177Mi)
% 52.83/8.02 % (1005961)Instruction limit reached!
% 52.83/8.02 % (1005961)------------------------------
% 52.83/8.02 % (1005961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 52.83/8.02 % (1005961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.83/8.02 % (1005961)CaDiCaL version: 2.1.3
% 52.83/8.02 % (1005961)Termination reason: Instruction limit
% 52.83/8.02 % (1005961)Termination phase: Saturation
% 52.83/8.02 % (1005961)Time elapsed: 0.552 s
% 52.83/8.02 % (1005961)Peak memory usage: 19 MB
% 52.83/8.02 % (1005961)Instructions burned: 708 (million)
% 52.83/8.02 % (1005973)Instruction limit reached!
% 52.83/8.02 % (1005973)------------------------------
% 52.83/8.02 % (1005973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 57.76/8.63 % (1005973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 57.76/8.63 % (1005973)CaDiCaL version: 2.1.3
% 57.76/8.63 % (1005973)Termination reason: Instruction limit
% 57.76/8.63 % (1005973)Termination phase: Saturation
% 57.76/8.63 % (1005973)Time elapsed: 0.151 s
% 57.76/8.63 % (1005973)Peak memory usage: 14 MB
% 57.76/8.63 % (1005973)Instructions burned: 178 (million)
% 57.76/8.63 % (1005975)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=588345904:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2931 on theBenchmark for (2931ds/715Mi)
% 57.76/8.63 % (1005976)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 57.76/8.63 % (1005976)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 57.76/8.63 % (1005903)Instruction limit reached!
% 57.76/8.63 % (1005903)------------------------------
% 57.76/8.63 % (1005903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 57.76/8.63 % (1005903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 57.76/8.63 % (1005903)CaDiCaL version: 2.1.3
% 57.76/8.63 % (1005903)Termination reason: Instruction limit
% 57.76/8.63 % (1005903)Termination phase: Saturation
% 57.76/8.63 % (1005903)Time elapsed: 1.884 s
% 57.76/8.63 % (1005903)Peak memory usage: 29 MB
% 57.76/8.63 % (1005903)Instructions burned: 2240 (million)
% 57.76/8.63 % (1005976)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=1497458146:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2931 on theBenchmark for (2931ds/230Mi)
% 57.76/8.63 % (1005976)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 57.76/8.63 % (1005979)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=1073040911:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2931 on theBenchmark for (2931ds/606Mi)
% 57.76/8.63 % (1005965)Instruction limit reached!
% 57.76/8.63 % (1005965)------------------------------
% 57.76/8.63 % (1005965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 57.76/8.63 % (1005965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 57.76/8.63 % (1005965)CaDiCaL version: 2.1.3
% 57.76/8.63 % (1005965)Termination reason: Instruction limit
% 57.76/8.63 % (1005965)Termination phase: Saturation
% 57.76/8.63 % (1005965)Time elapsed: 0.652 s
% 57.76/8.63 % (1005965)Peak memory usage: 14 MB
% 57.76/8.63 % (1005965)Instructions burned: 824 (million)
% 57.76/8.63 % (1005981)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 57.76/8.63 % (1005981)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=2472445464:lrd=on:i=841:nm=0:rtra=on_2930 on theBenchmark for (2930ds/841Mi)
% 57.76/8.63 % (1005976)Instruction limit reached!
% 57.76/8.63 % (1005976)------------------------------
% 57.76/8.63 % (1005976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 57.76/8.63 % (1005976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 57.76/8.63 % (1005976)CaDiCaL version: 2.1.3
% 57.76/8.63 % (1005976)Termination reason: Instruction limit
% 57.76/8.63 % (1005976)Termination phase: Saturation
% 57.76/8.63 % (1005976)Time elapsed: 0.180 s
% 57.76/8.63 % (1005976)Peak memory usage: 13 MB
% 57.76/8.63 % (1005976)Instructions burned: 231 (million)
% 57.76/8.63 % (1005983)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1750413779:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2929 on theBenchmark for (2929ds/445Mi)
% 57.76/8.63 % (1005975)Instruction limit reached!
% 57.76/8.63 % (1005975)------------------------------
% 57.76/8.63 % (1005975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 57.76/8.63 % (1005975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 57.76/8.63 % (1005975)CaDiCaL version: 2.1.3
% 57.76/8.63 % (1005975)Termination reason: Instruction limit
% 57.76/8.63 % (1005975)Termination phase: Saturation
% 57.76/8.63 % (1005975)Time elapsed: 0.470 s
% 57.76/8.63 % (1005975)Peak memory usage: 12 MB
% 57.76/8.63 % (1005975)Instructions burned: 716 (million)
% 57.76/8.63 % (1005985)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3119232167:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2926 on theBenchmark for (2926ds/71Mi)
% 58.19/8.79 % (1005979)Instruction limit reached!
% 58.19/8.79 % (1005979)------------------------------
% 58.19/8.79 % (1005979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.19/8.79 % (1005979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.19/8.79 % (1005979)CaDiCaL version: 2.1.3
% 58.19/8.79 % (1005979)Termination reason: Instruction limit
% 58.19/8.79 % (1005979)Termination phase: Saturation
% 58.19/8.79 % (1005979)Time elapsed: 0.483 s
% 58.19/8.79 % (1005979)Peak memory usage: 15 MB
% 58.19/8.79 % (1005979)Instructions burned: 606 (million)
% 58.19/8.79 % (1005985)Instruction limit reached!
% 58.19/8.79 % (1005985)------------------------------
% 58.19/8.79 % (1005985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.19/8.79 % (1005985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.19/8.79 % (1005985)CaDiCaL version: 2.1.3
% 58.19/8.79 % (1005985)Termination reason: Instruction limit
% 58.19/8.79 % (1005985)Termination phase: Saturation
% 58.19/8.79 % (1005985)Time elapsed: 0.055 s
% 58.19/8.79 % (1005985)Peak memory usage: 12 MB
% 58.19/8.79 % (1005985)Instructions burned: 71 (million)
% 58.19/8.79 % (1005987)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 58.19/8.79 % (1005987)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 58.19/8.79 % (1005987)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4225055888:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2926 on theBenchmark for (2926ds/100Mi)
% 58.19/8.79 % (1005983)Instruction limit reached!
% 58.19/8.79 % (1005983)------------------------------
% 58.19/8.79 % (1005983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.19/8.79 % (1005983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.19/8.79 % (1005983)CaDiCaL version: 2.1.3
% 58.19/8.79 % (1005983)Termination reason: Instruction limit
% 58.19/8.79 % (1005983)Termination phase: Saturation
% 58.19/8.79 % (1005983)Time elapsed: 0.346 s
% 58.19/8.79 % (1005983)Peak memory usage: 15 MB
% 58.19/8.79 % (1005983)Instructions burned: 445 (million)
% 58.19/8.79 % (1005988)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 58.19/8.79 % (1005988)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=3564174206:i=1352:add=on:aac=none:rtra=on_2925 on theBenchmark for (2925ds/1352Mi)
% 58.19/8.79 % (1005990)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=1849660897:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2925 on theBenchmark for (2925ds/646Mi)
% 58.19/8.79 % (1005987)Instruction limit reached!
% 58.19/8.79 % (1005987)------------------------------
% 58.19/8.79 % (1005987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.19/8.79 % (1005987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.19/8.79 % (1005987)CaDiCaL version: 2.1.3
% 58.19/8.79 % (1005987)Termination reason: Instruction limit
% 58.19/8.79 % (1005987)Termination phase: Saturation
% 58.19/8.79 % (1005987)Time elapsed: 0.075 s
% 58.19/8.79 % (1005987)Peak memory usage: 12 MB
% 58.19/8.79 % (1005987)Instructions burned: 101 (million)
% 58.19/8.79 % (1005993)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=2215594985:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2924 on theBenchmark for (2924ds/1924Mi)
% 58.19/8.79 % (1005981)Instruction limit reached!
% 58.19/8.79 % (1005981)------------------------------
% 58.19/8.79 % (1005981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.19/8.79 % (1005981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.19/8.79 % (1005981)CaDiCaL version: 2.1.3
% 58.19/8.79 % (1005981)Termination reason: Instruction limit
% 58.19/8.79 % (1005981)Termination phase: Saturation
% 58.19/8.79 % (1005981)Time elapsed: 0.653 s
% 58.19/8.79 % (1005981)Peak memory usage: 21 MB
% 58.19/8.79 % (1005981)Instructions burned: 842 (million)
% 60.42/8.99 % (1005952)Instruction limit reached!
% 60.42/8.99 % (1005952)------------------------------
% 60.42/8.99 % (1005952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 60.42/8.99 % (1005952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 60.42/8.99 % (1005952)CaDiCaL version: 2.1.3
% 60.42/8.99 % (1005952)Termination reason: Instruction limit
% 60.42/8.99 % (1005952)Termination phase: Saturation
% 60.42/8.99 % (1005952)Time elapsed: 1.644 s
% 60.42/8.99 % (1005952)Peak memory usage: 15 MB
% 60.42/8.99 % (1005952)Instructions burned: 4386 (million)
% 60.42/8.99 % (1005995)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=2326331834:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2923 on theBenchmark for (2923ds/984Mi)
% 60.42/8.99 % (1005996)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=2827188139:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2923 on theBenchmark for (2923ds/592Mi)
% 60.42/8.99 % (1005996)Instruction limit reached!
% 60.42/8.99 % (1005996)------------------------------
% 60.42/8.99 % (1005996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 60.42/8.99 % (1005996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 60.42/8.99 % (1005996)CaDiCaL version: 2.1.3
% 60.42/8.99 % (1005996)Termination reason: Instruction limit
% 60.42/8.99 % (1005996)Termination phase: Saturation
% 60.42/8.99 % (1005996)Time elapsed: 0.246 s
% 60.42/8.99 % (1005996)Peak memory usage: 13 MB
% 60.42/8.99 % (1005996)Instructions burned: 595 (million)
% 60.42/8.99 % (1005999)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=3978908612:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2920 on theBenchmark for (2920ds/872Mi)
% 60.42/8.99 % (1005999)Refutation not found, incomplete strategy
% 60.42/8.99 % (1005999)------------------------------
% 60.42/8.99 % (1005999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 60.42/8.99 % (1005999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 60.42/8.99 % (1005999)CaDiCaL version: 2.1.3
% 60.42/8.99 % (1005999)Termination reason: Refutation not found, incomplete strategy
% 60.42/8.99 % (1005999)Time elapsed: 0.007 s
% 60.42/8.99 % (1005999)Peak memory usage: 12 MB
% 60.42/8.99 % (1005999)Instructions burned: 20 (million)
% 60.42/8.99 % (1005999)------------------------------
% 60.42/8.99 % (1005999)------------------------------
% 60.42/8.99 % (1006001)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 60.42/8.99 % (1006001)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2975005083:i=999:add=on:rtra=on_2920 on theBenchmark for (2920ds/999Mi)
% 60.42/8.99 % (1005990)Instruction limit reached!
% 60.42/8.99 % (1005990)------------------------------
% 60.42/8.99 % (1005990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 60.42/8.99 % (1005990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 60.42/8.99 % (1005990)CaDiCaL version: 2.1.3
% 60.42/8.99 % (1005990)Termination reason: Instruction limit
% 60.42/8.99 % (1005990)Termination phase: Saturation
% 60.42/8.99 % (1005990)Time elapsed: 0.538 s
% 60.42/8.99 % (1005990)Peak memory usage: 17 MB
% 60.42/8.99 % (1005990)Instructions burned: 646 (million)
% 60.42/8.99 % (1006003)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 60.42/8.99 % (1006003)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=1673719678:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2919 on theBenchmark for (2919ds/244Mi)
% 60.42/8.99 % (1006003)Instruction limit reached!
% 60.42/8.99 % (1006003)------------------------------
% 60.42/8.99 % (1006003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 60.42/8.99 % (1006003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 60.42/8.99 % (1006003)CaDiCaL version: 2.1.3
% 60.42/8.99 % (1006003)Termination reason: Instruction limit
% 60.42/8.99 % (1006003)Termination phase: Saturation
% 60.42/8.99 % (1006003)Time elapsed: 0.189 s
% 60.42/8.99 % (1006003)Peak memory usage: 12 MB
% 60.42/8.99 % (1006003)Instructions burned: 244 (million)
% 60.42/8.99 % (1006005)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=930556936:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2917 on theBenchmark for (2917ds/113Mi)
% 64.36/9.50 % (1006005)Instruction limit reached!
% 64.36/9.50 % (1006005)------------------------------
% 64.36/9.50 % (1006005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.36/9.50 % (1006005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.36/9.50 % (1006005)CaDiCaL version: 2.1.3
% 64.36/9.50 % (1006005)Termination reason: Instruction limit
% 64.36/9.50 % (1006005)Termination phase: Saturation
% 64.36/9.50 % (1006005)Time elapsed: 0.088 s
% 64.36/9.50 % (1006005)Peak memory usage: 13 MB
% 64.36/9.50 % (1006005)Instructions burned: 113 (million)
% 64.36/9.50 % (1006001)Instruction limit reached!
% 64.36/9.50 % (1006001)------------------------------
% 64.36/9.50 % (1006001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.36/9.50 % (1006001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.36/9.50 % (1006001)CaDiCaL version: 2.1.3
% 64.36/9.50 % (1006001)Termination reason: Instruction limit
% 64.36/9.50 % (1006001)Termination phase: Saturation
% 64.36/9.50 % (1006001)Time elapsed: 0.379 s
% 64.36/9.50 % (1006001)Peak memory usage: 15 MB
% 64.36/9.50 % (1006001)Instructions burned: 1001 (million)
% 64.36/9.50 % (1006008)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4007224448:st=2:i=5026:sd=1:rtra=on:ss=axioms_2916 on theBenchmark for (2916ds/5026Mi)
% 64.36/9.50 % (1006008)Refutation not found, incomplete strategy
% 64.36/9.50 % (1006008)------------------------------
% 64.36/9.50 % (1006008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.36/9.50 % (1006008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.36/9.50 % (1006008)CaDiCaL version: 2.1.3
% 64.36/9.50 % (1006008)Termination reason: Refutation not found, incomplete strategy
% 64.36/9.50 % (1006008)Time elapsed: 0.005 s
% 64.36/9.50 % (1006008)Peak memory usage: 12 MB
% 64.36/9.50 % (1006008)Instructions burned: 12 (million)
% 64.36/9.50 % (1006008)------------------------------
% 64.36/9.50 % (1006008)------------------------------
% 64.36/9.50 % (1006007)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3953678955:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2916 on theBenchmark for (2916ds/7795Mi)
% 64.36/9.50 % (1006007)Refutation not found, incomplete strategy
% 64.36/9.50 % (1006007)------------------------------
% 64.36/9.50 % (1006007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.36/9.50 % (1006007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.36/9.50 % (1006007)CaDiCaL version: 2.1.3
% 64.36/9.50 % (1006007)Termination reason: Refutation not found, incomplete strategy
% 64.36/9.50 % (1006007)Time elapsed: 0.007 s
% 64.36/9.50 % (1006007)Peak memory usage: 12 MB
% 64.36/9.50 % (1006007)Instructions burned: 8 (million)
% 64.36/9.50 % (1006007)------------------------------
% 64.36/9.50 % (1006007)------------------------------
% 64.36/9.50 % (1006010)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 64.36/9.50 % (1006010)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=1633902625:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2916 on theBenchmark for (2916ds/763Mi)
% 64.36/9.50 % (1006010)Refutation not found, incomplete strategy
% 64.36/9.50 % (1006010)------------------------------
% 64.36/9.50 % (1006010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.36/9.50 % (1006010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.36/9.50 % (1006010)CaDiCaL version: 2.1.3
% 64.36/9.50 % (1006010)Termination reason: Refutation not found, incomplete strategy
% 64.36/9.50 % (1006010)Time elapsed: 0.004 s
% 64.36/9.50 % (1006010)Peak memory usage: 12 MB
% 64.36/9.50 % (1006010)Instructions burned: 9 (million)
% 64.36/9.50 % (1006010)------------------------------
% 64.36/9.50 % (1006010)------------------------------
% 64.36/9.50 % (1006014)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 64.36/9.50 % (1006014)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=3243928804:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2915 on theBenchmark for (2915ds/52Mi)
% 64.36/9.50 % (1006012)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3480963339:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2915 on theBenchmark for (2915ds/1144Mi)
% 69.44/10.21 % (1005988)Instruction limit reached!
% 69.44/10.21 % (1005988)------------------------------
% 69.44/10.21 % (1005988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 69.44/10.21 % (1005988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 69.44/10.21 % (1005988)CaDiCaL version: 2.1.3
% 69.44/10.21 % (1005988)Termination reason: Instruction limit
% 69.44/10.21 % (1005988)Termination phase: Saturation
% 69.44/10.21 % (1005988)Time elapsed: 0.986 s
% 69.44/10.21 % (1005988)Peak memory usage: 15 MB
% 69.44/10.21 % (1005988)Instructions burned: 1354 (million)
% 69.44/10.21 % (1006014)Instruction limit reached!
% 69.44/10.21 % (1006014)------------------------------
% 69.44/10.21 % (1006014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 69.44/10.21 % (1006014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 69.44/10.21 % (1006014)CaDiCaL version: 2.1.3
% 69.44/10.21 % (1006014)Termination reason: Instruction limit
% 69.44/10.21 % (1006014)Termination phase: Saturation
% 69.44/10.21 % (1006014)Time elapsed: 0.019 s
% 69.44/10.21 % (1006014)Peak memory usage: 11 MB
% 69.44/10.21 % (1006014)Instructions burned: 53 (million)
% 69.44/10.21 % (1006018)dis-1004_128_to=kbo:sil=128000:tgt=full:si=on:fdtod=off:sp=const_frequency:spb=goal:uwa=off:slsqc=3:slsq=on:random_seed=283266129:i=439:add=on:slsql=off:rtra=on:ntd=on_2915 on theBenchmark for (2915ds/439Mi)
% 69.44/10.21 % (1006017)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=3305675010:i=1724:fsr=off:rtra=on:fe=abstraction_2915 on theBenchmark for (2915ds/1724Mi)
% 69.44/10.21 % (1005995)Instruction limit reached!
% 69.44/10.21 % (1005995)------------------------------
% 69.44/10.21 % (1005995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 69.44/10.21 % (1005995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 69.44/10.21 % (1005995)CaDiCaL version: 2.1.3
% 69.44/10.21 % (1005995)Termination reason: Instruction limit
% 69.44/10.21 % (1005995)Termination phase: Saturation
% 69.44/10.21 % (1005995)Time elapsed: 0.806 s
% 69.44/10.21 % (1005995)Peak memory usage: 17 MB
% 69.44/10.21 % (1005995)Instructions burned: 984 (million)
% 69.44/10.21 % (1006022)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=266098173:i=6395:sd=1:rtra=on:ss=axioms_2914 on theBenchmark for (2914ds/6395Mi)
% 69.44/10.21 % (1006022)Refutation not found, incomplete strategy
% 69.44/10.21 % (1006022)------------------------------
% 69.44/10.21 % (1006022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 69.44/10.21 % (1006022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 69.44/10.21 % (1006022)CaDiCaL version: 2.1.3
% 69.44/10.21 % (1006022)Termination reason: Refutation not found, incomplete strategy
% 69.44/10.21 % (1006022)Time elapsed: 0.008 s
% 69.44/10.21 % (1006022)Peak memory usage: 12 MB
% 69.44/10.21 % (1006022)Instructions burned: 8 (million)
% 69.44/10.21 % (1006022)------------------------------
% 69.44/10.21 % (1006022)------------------------------
% 69.44/10.21 % (1006024)WARNING Broken Constraint: if ho_split_queue_lambda_weight(5) has been set then ho_split_queue(off) is equal to on
% 69.44/10.21 % (1006024)ott+2_16:1_sil=128000:si=on:hsqlw=5:sos=on:urr=on:bce=on:uwa=off:random_seed=2682349011:i=6762:add=off:bd=all:rtra=on:ss=axioms:ntd=on_2914 on theBenchmark for (2914ds/6762Mi)
% 69.44/10.21 % (1006024)Refutation not found, incomplete strategy
% 69.44/10.21 % (1006024)------------------------------
% 69.44/10.21 % (1006024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 69.44/10.21 % (1006024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 69.44/10.21 % (1006024)CaDiCaL version: 2.1.3
% 69.44/10.21 % (1006024)Termination reason: Refutation not found, incomplete strategy
% 69.44/10.21 % (1006024)Time elapsed: 0.008 s
% 69.44/10.21 % (1006024)Peak memory usage: 12 MB
% 69.44/10.21 % (1006024)Instructions burned: 8 (million)
% 69.44/10.21 % (1006024)------------------------------
% 69.44/10.21 % (1006024)------------------------------
% 69.44/10.21 % (1006026)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 69.44/10.21 % (1006018)Instruction limit reached!
% 69.44/10.21 % (1006018)------------------------------
% 69.44/10.21 % (1006018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 69.44/10.21 % (1006018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.60/10.86 % (1006018)CaDiCaL version: 2.1.3
% 72.60/10.86 % (1006018)Termination reason: Instruction limit
% 72.60/10.86 % (1006018)Termination phase: Saturation
% 72.60/10.86 % (1006018)Time elapsed: 0.164 s
% 72.60/10.86 % (1006018)Peak memory usage: 16 MB
% 72.60/10.86 % (1006018)Instructions burned: 440 (million)
% 72.60/10.86 % (1006026)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=3241338838:s2a=on:i=376:add=on:rtra=on:fe=axiom:fdi=1024_2914 on theBenchmark for (2914ds/376Mi)
% 72.60/10.86 % (1006028)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=303920415:i=965:bd=all:ins=4:rtra=on_2913 on theBenchmark for (2913ds/965Mi)
% 72.60/10.86 % (1005993)Instruction limit reached!
% 72.60/10.86 % (1005993)------------------------------
% 72.60/10.86 % (1005993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.60/10.86 % (1005993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.60/10.86 % (1005993)CaDiCaL version: 2.1.3
% 72.60/10.86 % (1005993)Termination reason: Instruction limit
% 72.60/10.86 % (1005993)Termination phase: Saturation
% 72.60/10.86 % (1005993)Time elapsed: 1.162 s
% 72.60/10.86 % (1005993)Peak memory usage: 16 MB
% 72.60/10.86 % (1005993)Instructions burned: 1926 (million)
% 72.60/10.86 % (1006030)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2143098943:i=5013:sd=1:rtra=on:ss=axioms:sgt=64_2912 on theBenchmark for (2912ds/5013Mi)
% 72.60/10.86 % (1006026)Instruction limit reached!
% 72.60/10.86 % (1006026)------------------------------
% 72.60/10.86 % (1006026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.60/10.86 % (1006026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.60/10.86 % (1006026)CaDiCaL version: 2.1.3
% 72.60/10.86 % (1006026)Termination reason: Instruction limit
% 72.60/10.86 % (1006026)Termination phase: Saturation
% 72.60/10.86 % (1006026)Time elapsed: 0.288 s
% 72.60/10.86 % (1006026)Peak memory usage: 12 MB
% 72.60/10.86 % (1006026)Instructions burned: 377 (million)
% 72.60/10.86 % (1006032)dis+2_1_tgt=full:si=on:uwa=one_side_interpreted:random_seed=698867168:i=1583:kws=inv_frequency:bd=preordered:nm=0:rtra=on_2910 on theBenchmark for (2910ds/1583Mi)
% 72.60/10.86 % (1006028)Instruction limit reached!
% 72.60/10.86 % (1006028)------------------------------
% 72.60/10.86 % (1006028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.60/10.86 % (1006028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.60/10.86 % (1006028)CaDiCaL version: 2.1.3
% 72.60/10.86 % (1006028)Termination reason: Instruction limit
% 72.60/10.86 % (1006028)Termination phase: Saturation
% 72.60/10.86 % (1006028)Time elapsed: 0.452 s
% 72.60/10.86 % (1006028)Peak memory usage: 21 MB
% 72.60/10.86 % (1006028)Instructions burned: 967 (million)
% 72.60/10.86 % (1006034)WARNING Broken Constraint: if sine_level_split_queue_ratios(1,32) has been set then sine_level_split_queue(off) is equal to on
% 72.60/10.86 % (1006034)WARNING Broken Constraint: if ho_split_queue_cutoffs(2) has been set then ho_split_queue(off) is equal to on
% 72.60/10.86 % (1006034)WARNING Broken Constraint: if sine_to_age_generality_threshold(16) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 72.60/10.86 % (1006034)WARNING Broken Constraint: if ho_split_queue_ratios(4,1) has been set then ho_split_queue(off) is equal to on
% 72.60/10.86 % (1006034)ott+1002_1_slsqr=1,32:sil=128000:fde=none:e2e=on:hsqc=2:si=on:sp=const_min:sos=on:uwa=interpreted_only:s2agt=16:chr=on:random_seed=42115437:hsqr=4,1:avsq=on:cond=on:i=1774:add=on:avsqr=1,16:kws=arity_squared:nm=120:rtra=on:fe=abstraction:ss=axioms_2908 on theBenchmark for (2908ds/1774Mi)
% 72.60/10.86 % (1006034)Refutation not found, incomplete strategy
% 72.60/10.86 % (1006034)------------------------------
% 72.60/10.86 % (1006034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.60/10.86 % (1006034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.60/10.86 % (1006034)CaDiCaL version: 2.1.3
% 72.60/10.86 % (1006034)Termination reason: Refutation not found, incomplete strategy
% 72.60/10.86 % (1006034)Time elapsed: 0.004 s
% 72.60/10.86 % (1006034)Peak memory usage: 12 MB
% 72.60/10.86 % (1006034)Instructions burned: 9 (million)
% 72.60/10.86 % (1006034)------------------------------
% 72.60/10.86 % (1006034)------------------------------
% 72.60/10.86 % (1006036)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2945628008:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2908 on theBenchmark for (2908ds/515Mi)
% 78.83/11.52 % (1006036)Instruction limit reached!
% 78.83/11.52 % (1006036)------------------------------
% 78.83/11.52 % (1006036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.83/11.52 % (1006036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.83/11.52 % (1006036)CaDiCaL version: 2.1.3
% 78.83/11.52 % (1006036)Termination reason: Instruction limit
% 78.83/11.52 % (1006036)Termination phase: Saturation
% 78.83/11.52 % (1006036)Time elapsed: 0.163 s
% 78.83/11.52 % (1006036)Peak memory usage: 13 MB
% 78.83/11.52 % (1006036)Instructions burned: 516 (million)
% 78.83/11.52 % (1006038)WARNING Broken Constraint: if sine_to_age_generality_threshold(60) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 78.83/11.52 % (1006038)lrs-30_5:1_sil=128000:drc=off:sas=cadical:si=on:lma=off:cbe=off:uwa=one_side_interpreted:s2agt=60:lwlo=on:random_seed=3327707405:avsq=on:i=1297:add=on:avsqr=1,8:rtra=on:fsd=on_2906 on theBenchmark for (2906ds/1297Mi)
% 78.83/11.52 % (1006012)Instruction limit reached!
% 78.83/11.52 % (1006012)------------------------------
% 78.83/11.52 % (1006012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.83/11.52 % (1006012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.83/11.52 % (1006012)CaDiCaL version: 2.1.3
% 78.83/11.52 % (1006012)Termination reason: Instruction limit
% 78.83/11.52 % (1006012)Termination phase: Saturation
% 78.83/11.52 % (1006012)Time elapsed: 0.897 s
% 78.83/11.52 % (1006012)Peak memory usage: 15 MB
% 78.83/11.52 % (1006012)Instructions burned: 1144 (million)
% 78.83/11.52 % (1006040)dis+1002_1_to=lpo:drc=ordering:fde=none:bsd=on:si=on:ser=on:sp=const_min:cbe=off:uwa=off:flr=on:random_seed=1894396132:s2a=on:i=611:rtra=on:gsp=on_2906 on theBenchmark for (2906ds/611Mi)
% 78.83/11.52 % (1006040)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 78.83/11.52 % (1006017)Instruction limit reached!
% 78.83/11.52 % (1006017)------------------------------
% 78.83/11.52 % (1006017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.83/11.52 % (1006017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.83/11.52 % (1006017)CaDiCaL version: 2.1.3
% 78.83/11.52 % (1006017)Termination reason: Instruction limit
% 78.83/11.52 % (1006017)Termination phase: Saturation
% 78.83/11.52 % (1006017)Time elapsed: 1.295 s
% 78.83/11.52 % (1006017)Peak memory usage: 17 MB
% 78.83/11.52 % (1006017)Instructions burned: 1724 (million)
% 78.83/11.52 % (1006042)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 78.83/11.52 % (1006042)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=2384394673:i=72:bd=all:rtra=on_2902 on theBenchmark for (2902ds/72Mi)
% 78.83/11.52 % (1006038)Instruction limit reached!
% 78.83/11.52 % (1006038)------------------------------
% 78.83/11.52 % (1006038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.83/11.52 % (1006038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.83/11.52 % (1006038)CaDiCaL version: 2.1.3
% 78.83/11.52 % (1006038)Termination reason: Instruction limit
% 78.83/11.52 % (1006038)Termination phase: Saturation
% 78.83/11.52 % (1006038)Time elapsed: 0.507 s
% 78.83/11.52 % (1006038)Peak memory usage: 17 MB
% 78.83/11.52 % (1006038)Instructions burned: 1298 (million)
% 78.83/11.52 % (1006040)Instruction limit reached!
% 78.83/11.52 % (1006040)------------------------------
% 78.83/11.52 % (1006040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.83/11.52 % (1006040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.83/11.52 % (1006040)CaDiCaL version: 2.1.3
% 78.83/11.52 % (1006040)Termination reason: Instruction limit
% 78.83/11.52 % (1006040)Termination phase: Saturation
% 78.83/11.52 % (1006040)Time elapsed: 0.474 s
% 78.83/11.52 % (1006040)Peak memory usage: 14 MB
% 78.83/11.52 % (1006040)Instructions burned: 611 (million)
% 78.83/11.52 % (1006044)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2434297967:hsq=on:hsqr=16,1:s2a=on:i=6580:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2901 on theBenchmark for (2901ds/6580Mi)
% 88.31/13.04 % (1006042)Instruction limit reached!
% 88.31/13.04 % (1006042)------------------------------
% 88.31/13.04 % (1006042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.31/13.04 % (1006042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.31/13.04 % (1006042)CaDiCaL version: 2.1.3
% 88.31/13.04 % (1006042)Termination reason: Instruction limit
% 88.31/13.04 % (1006042)Termination phase: Saturation
% 88.31/13.04 % (1006042)Time elapsed: 0.056 s
% 88.31/13.04 % (1006042)Peak memory usage: 12 MB
% 88.31/13.04 % (1006042)Instructions burned: 73 (million)
% 88.31/13.04 % (1006045)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=1579831125:i=6209:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2901 on theBenchmark for (2901ds/6209Mi)
% 88.31/13.04 % (1006047)lrs+1002_14_sil=128000:e2e=on:si=on:urr=on:nwc=1.2:random_seed=3347334929:cond=fast:i=1003:bd=all:fsr=off:rtra=on:sup=off_2901 on theBenchmark for (2901ds/1003Mi)
% 88.31/13.04 % (1006047)Refutation not found, incomplete strategy
% 88.31/13.04 % (1006047)------------------------------
% 88.31/13.04 % (1006047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.31/13.04 % (1006047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.31/13.04 % (1006047)CaDiCaL version: 2.1.3
% 88.31/13.04 % (1006047)Termination reason: Refutation not found, incomplete strategy
% 88.31/13.04 % (1006047)Time elapsed: 0.221 s
% 88.31/13.04 % (1006047)Peak memory usage: 14 MB
% 88.31/13.04 % (1006047)Instructions burned: 273 (million)
% 88.31/13.04 % (1006047)------------------------------
% 88.31/13.04 % (1006047)------------------------------
% 88.31/13.04 % (1006050)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 88.31/13.04 % (1006050)ott+1002_16_sil=128000:si=on:random_seed=2977522088:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2898 on theBenchmark for (2898ds/409Mi)
% 88.31/13.04 % (1006032)Instruction limit reached!
% 88.31/13.04 % (1006032)------------------------------
% 88.31/13.04 % (1006032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.31/13.04 % (1006032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.31/13.04 % (1006032)CaDiCaL version: 2.1.3
% 88.31/13.04 % (1006032)Termination reason: Instruction limit
% 88.31/13.04 % (1006032)Termination phase: Saturation
% 88.31/13.04 % (1006032)Time elapsed: 1.220 s
% 88.31/13.04 % (1006032)Peak memory usage: 31 MB
% 88.31/13.04 % (1006032)Instructions burned: 1584 (million)
% 88.31/13.04 % (1006052)ott+10_1024_sil=128000:tgt=ground:cnfonf=lazy_pi_sigma_gen:si=on:sp=const_frequency:sos=on:lma=off:bsr=on:uwa=one_side_interpreted:nwc=20:random_seed=3740180217:cond=on:i=403:kws=precedence:erml=3:bs=unit_only:bd=all:rtra=on:ss=axioms:er=known:ntd=on_2898 on theBenchmark for (2898ds/403Mi)
% 88.31/13.04 % (1006052)Refutation not found, incomplete strategy
% 88.31/13.04 % (1006052)------------------------------
% 88.31/13.04 % (1006052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.31/13.04 % (1006052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.31/13.04 % (1006052)CaDiCaL version: 2.1.3
% 88.31/13.04 % (1006052)Termination reason: Refutation not found, incomplete strategy
% 88.31/13.04 % (1006052)Time elapsed: 0.011 s
% 88.31/13.04 % (1006052)Peak memory usage: 12 MB
% 88.31/13.04 % (1006052)Instructions burned: 10 (million)
% 88.31/13.04 % (1006052)------------------------------
% 88.31/13.04 % (1006052)------------------------------
% 88.31/13.04 % (1006054)lrs+10_1_sil=128000:fde=none:cnfonf=lazy_pi_sigma_gen:si=on:random_seed=2655417433:st=2:i=6843:sd=2:bd=all:rtra=on:sup=off:ss=axioms_2897 on theBenchmark for (2897ds/6843Mi)
% 88.31/13.04 % (1006054)Refutation not found, incomplete strategy
% 88.31/13.04 % (1006054)------------------------------
% 88.31/13.04 % (1006054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 88.31/13.04 % (1006054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 88.31/13.04 % (1006054)CaDiCaL version: 2.1.3
% 88.31/13.04 % (1006054)Termination reason: Refutation not found, incomplete strategy
% 88.31/13.04 % (1006054)Time elapsed: 0.023 s
% 88.31/13.04 % (1006054)Peak memory usage: 12 MB
% 88.31/13.04 % (1006054)Instructions burned: 23 (million)
% 88.31/13.04 % (1006054)------------------------------
% 88.31/13.04 % (1006054)------------------------------
% 88.31/13.04 % (1006056)lrs+10_2:1_si=on:random_seed=284160324:s2a=on:i=506:rtra=on:fe=abstraction_2897 on theBenchmark for (2897ds/506Mi)
% 88.31/13.04 % (1006050)Instruction limit reached!
% 88.31/13.04 % (1006050)------------------------------
% 92.65/13.54 % (1006050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006050)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006050)Termination reason: Instruction limit
% 92.65/13.54 % (1006050)Termination phase: Saturation
% 92.65/13.54 % (1006050)Time elapsed: 0.344 s
% 92.65/13.54 % (1006050)Peak memory usage: 15 MB
% 92.65/13.54 % (1006050)Instructions burned: 410 (million)
% 92.65/13.54 % (1006058)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3332505099:uwa_fpi=on:i=888:doe=on:bd=preordered:rtra=on:fsd=on_2894 on theBenchmark for (2894ds/888Mi)
% 92.65/13.54 % (1005916)Instruction limit reached!
% 92.65/13.54 % (1005916)------------------------------
% 92.65/13.54 % (1005916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1005916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1005916)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1005916)Termination reason: Instruction limit
% 92.65/13.54 % (1005916)Termination phase: Saturation
% 92.65/13.54 % (1005916)Time elapsed: 5.328 s
% 92.65/13.54 % (1005916)Peak memory usage: 54 MB
% 92.65/13.54 % (1005916)Instructions burned: 6359 (million)
% 92.65/13.54 % (1006060)WARNING Broken Constraint: if positive_literal_split_queue_ratios(32,1) has been set then positive_literal_split_queue(off) is equal to on
% 92.65/13.54 % (1006060)ott+1002_3:2_to=kbo:sil=128000:cnfonf=lazy_gen:si=on:sp=reverse_frequency:lma=off:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=1.5:random_seed=3708524405:cond=fast:i=416:fgj=on:bd=preordered:rtra=on_2894 on theBenchmark for (2894ds/416Mi)
% 92.65/13.54 % (1006056)Instruction limit reached!
% 92.65/13.54 % (1006056)------------------------------
% 92.65/13.54 % (1006056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006056)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006056)Termination reason: Instruction limit
% 92.65/13.54 % (1006056)Termination phase: Saturation
% 92.65/13.54 % (1006056)Time elapsed: 0.405 s
% 92.65/13.54 % (1006056)Peak memory usage: 15 MB
% 92.65/13.54 % (1006056)Instructions burned: 506 (million)
% 92.65/13.54 % (1006062)dis+10_3:2_sfv=off:to=kbo:plsq=on:fde=unused:e2e=on:si=on:sp=reverse_frequency:acc=on:uwa=off:fd=preordered:slsqc=1:pe=on:slsq=on:random_seed=393245981:hsq=on:hsqr=16,1:avsq=on:s2a=on:i=13534:hsql=off:nm=16:nicw=on:ins=20:rtra=on:ss=axioms:ntd=on_2892 on theBenchmark for (2892ds/13534Mi)
% 92.65/13.54 % (1006060)Instruction limit reached!
% 92.65/13.54 % (1006060)------------------------------
% 92.65/13.54 % (1006060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006060)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006060)Termination reason: Instruction limit
% 92.65/13.54 % (1006060)Termination phase: Saturation
% 92.65/13.54 % (1006060)Time elapsed: 0.330 s
% 92.65/13.54 % (1006060)Peak memory usage: 14 MB
% 92.65/13.54 % (1006060)Instructions burned: 417 (million)
% 92.65/13.54 % (1006064)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(10) has been set then forward_subsumption_demodulation(off) is equal to on
% 92.65/13.54 % (1006064)dis+1002_3_tgt=ground:cnfonf=lazy_simp:si=on:sp=unary_first:cbe=off:uwa=ground:updr=off:random_seed=2943313828:i=206:fgj=on:hud=10:nm=30:rtra=on:fsdmm=10_2890 on theBenchmark for (2890ds/206Mi)
% 92.65/13.54 % (1006064)Instruction limit reached!
% 92.65/13.54 % (1006064)------------------------------
% 92.65/13.54 % (1006064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006064)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006064)Termination reason: Instruction limit
% 92.65/13.54 % (1006064)Termination phase: Saturation
% 92.65/13.54 % (1006064)Time elapsed: 0.153 s
% 92.65/13.54 % (1006064)Peak memory usage: 12 MB
% 92.65/13.54 % (1006064)Instructions burned: 207 (million)
% 92.65/13.54 % (1006066)dis+1010_1_sfv=off:slsqr=2,1:to=kbo:plsq=on:cnfonf=lazy_simp:si=on:cbe=off:uwa=hol:nwc=2:s2agt=16:slsq=on:random_seed=475624019:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2295:avsqr=1,16:aac=none:hud=3:rtra=on_2888 on theBenchmark for (2888ds/2295Mi)
% 92.65/13.54 % (1006058)Instruction limit reached!
% 92.65/13.54 % (1006058)------------------------------
% 92.65/13.54 % (1006058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006058)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006058)Termination reason: Instruction limit
% 92.65/13.54 % (1006058)Termination phase: Saturation
% 92.65/13.54 % (1006058)Time elapsed: 0.697 s
% 92.65/13.54 % (1006058)Peak memory usage: 13 MB
% 92.65/13.54 % (1006058)Instructions burned: 888 (million)
% 92.65/13.54 % (1006068)ott+1010_1_to=lpo:sil=128000:fde=none:si=on:sp=unary_first:uwa=off:nwc=1:random_seed=1866508376:i=637:piset=not:ep=RST:bd=all:av=off:rtra=on_2887 on theBenchmark for (2887ds/637Mi)
% 92.65/13.54 % (1006030)Instruction limit reached!
% 92.65/13.54 % (1006030)------------------------------
% 92.65/13.54 % (1006030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006030)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006030)Termination reason: Instruction limit
% 92.65/13.54 % (1006030)Termination phase: Saturation
% 92.65/13.54 % (1006030)Time elapsed: 3.061 s
% 92.65/13.54 % (1006030)Peak memory usage: 16 MB
% 92.65/13.54 % (1006030)Instructions burned: 5015 (million)
% 92.65/13.54 % (1006068)Instruction limit reached!
% 92.65/13.54 % (1006068)------------------------------
% 92.65/13.54 % (1006068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006068)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006068)Termination reason: Instruction limit
% 92.65/13.54 % (1006068)Termination phase: Saturation
% 92.65/13.54 % (1006068)Time elapsed: 0.547 s
% 92.65/13.54 % (1006068)Peak memory usage: 16 MB
% 92.65/13.54 % (1006068)Instructions burned: 637 (million)
% 92.65/13.54 % (1006070)dis+1002_15:31_sil=128000:cnfonf=lazy_not_gen:si=on:cbe=off:uwa=off:random_seed=534362994:hsq=on:i=667:rtra=on:ixr=off_2881 on theBenchmark for (2881ds/667Mi)
% 92.65/13.54 % (1006071)lrs-1004_16_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:lma=off:uwa=off:random_seed=39973842:i=1801:bd=preordered:nm=32:rtra=on:fdi=1024_2881 on theBenchmark for (2881ds/1801Mi)
% 92.65/13.54 % (1006070)Instruction limit reached!
% 92.65/13.54 % (1006070)------------------------------
% 92.65/13.54 % (1006070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006070)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006070)Termination reason: Instruction limit
% 92.65/13.54 % (1006070)Termination phase: Saturation
% 92.65/13.54 % (1006070)Time elapsed: 0.531 s
% 92.65/13.54 % (1006070)Peak memory usage: 14 MB
% 92.65/13.54 % (1006070)Instructions burned: 667 (million)
% 92.65/13.54 % (1006074)lrs+1002_1024_anc=all_dependent:sil=128000:drc=off:cnfonf=lazy_not_be_gen:si=on:cbe=off:cs=on:random_seed=303874903:i=555:aac=none:rtra=on:fe=abstraction:ntd=on_2876 on theBenchmark for (2876ds/555Mi)
% 92.65/13.54 % (1006044)Instruction limit reached!
% 92.65/13.54 % (1006044)------------------------------
% 92.65/13.54 % (1006044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006044)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006044)Termination reason: Instruction limit
% 92.65/13.54 % (1006044)Termination phase: Saturation
% 92.65/13.54 % (1006044)Time elapsed: 2.770 s
% 92.65/13.54 % (1006044)Peak memory usage: 43 MB
% 92.65/13.54 % (1006044)Instructions burned: 6580 (million)
% 92.65/13.54 % (1006076)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3563280502:i=88:s2at=3:nm=2:rtra=on:rawr=on_2873 on theBenchmark for (2873ds/88Mi)
% 92.65/13.54 % (1006076)Instruction limit reached!
% 92.65/13.54 % (1006076)------------------------------
% 92.65/13.54 % (1006076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006076)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006076)Termination reason: Instruction limit
% 92.65/13.54 % (1006076)Termination phase: Saturation
% 92.65/13.54 % (1006076)Time elapsed: 0.034 s
% 92.65/13.54 % (1006076)Peak memory usage: 12 MB
% 92.65/13.54 % (1006076)Instructions burned: 89 (million)
% 92.65/13.54 % (1006078)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2269366760:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2873 on theBenchmark for (2873ds/280Mi)
% 92.65/13.54 % (1006074)Instruction limit reached!
% 92.65/13.54 % (1006074)------------------------------
% 92.65/13.54 % (1006074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006074)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006074)Termination reason: Instruction limit
% 92.65/13.54 % (1006074)Termination phase: Saturation
% 92.65/13.54 % (1006074)Time elapsed: 0.390 s
% 92.65/13.54 % (1006074)Peak memory usage: 11 MB
% 92.65/13.54 % (1006074)Instructions burned: 556 (million)
% 92.65/13.54 % (1006078)Instruction limit reached!
% 92.65/13.54 % (1006078)------------------------------
% 92.65/13.54 % (1006078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006078)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006078)Termination reason: Instruction limit
% 92.65/13.54 % (1006078)Termination phase: Saturation
% 92.65/13.54 % (1006078)Time elapsed: 0.109 s
% 92.65/13.54 % (1006078)Peak memory usage: 12 MB
% 92.65/13.54 % (1006078)Instructions burned: 280 (million)
% 92.65/13.54 % (1006081)WARNING Broken Constraint: if avatar_split_queue_ratios(1,2) has been set then avatar_split_queue(off) is equal to on
% 92.65/13.54 % (1006080)dis+10_5:4_e2e=on:si=on:urr=on:uwa=interpreted_only:nwc=3:random_seed=1115723338:s2a=on:i=3166:bd=preordered:rtra=on_2872 on theBenchmark for (2872ds/3166Mi)
% 92.65/13.54 % (1006081)lrs+1010_128_to=kbo:plsq=on:plsqc=4:cnfonf=lazy_pi_sigma_gen:bsd=on:si=on:sp=occurrence:sos=on:plsql=on:random_seed=2602313503:i=4201:add=off:avsqr=1,2:bsdmm=10:fsr=off:rtra=on:fe=axiom_2871 on theBenchmark for (2871ds/4201Mi)
% 92.65/13.54 % (1006066)Instruction limit reached!
% 92.65/13.54 % (1006066)------------------------------
% 92.65/13.54 % (1006066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.54 % (1006066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.54 % (1006066)CaDiCaL version: 2.1.3
% 92.65/13.54 % (1006066)Termination reason: Instruction limit
% 92.65/13.54 % (1006066)Termination phase: Saturation
% 92.65/13.54 % (1006066)Time elapsed: 1.820 s
% 92.65/13.54 % (1006066)Peak memory usage: 20 MB
% 92.65/13.54 % (1006066)Instructions burned: 2295 (million)
% 92.65/13.54 % (1006084)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2480728118:i=2352:rtra=on:ixr=off_2870 on theBenchmark for (2870ds/2352Mi)
% 92.65/13.54 % (1006071) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1005596-1006071"...
% 92.65/13.54 % (1006071)...printing done.
% 92.65/13.54 % (1006071)Refutation found. Thanks to Tanya!
% 92.65/13.54 % SZS status Theorem for theBenchmark
% 92.65/13.54 % SZS output start Proof for theBenchmark
% See solution above
% 92.65/13.56 % (1006071)------------------------------
% 92.65/13.56 % (1006071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 92.65/13.56 % (1006071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 92.65/13.56 % (1006071)CaDiCaL version: 2.1.3
% 92.65/13.56 % (1006071)Termination reason: Refutation
% 92.65/13.56 % (1006071)Time elapsed: 1.322 s
% 92.65/13.56 % (1006071)Peak memory usage: 18 MB
% 92.65/13.56 % (1006071)Instructions burned: 1558 (million)
% 92.65/13.56 % (1005596)Success in time 13.184 s
% 92.65/13.56 % Vampire exiting
%------------------------------------------------------------------------------