%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO069^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 87.79s 12.89s
% Output : Refutation 89.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 40
% Syntax : Number of formulae : 448 ( 92 unt; 0 typ; 28 def)
% Number of atoms : 9506 (1549 equ; 0 cnn)
% Maximal formula atoms : 72 ( 21 avg)
% Number of connectives : 15941 ( 857 ~;2046 |; 204 &;9985 @)
% ( 28 <=>;1464 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 264 ( 264 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 77 usr; 33 con; 0-6 aty)
% (1357 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 2506 ( 0 sgn 748 !; 0 ?;2506 :)
% 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,
b0: $i > $o ).
thf(func_def_25,type,
b1: $i > $o ).
thf(func_def_26,type,
b2: $i > $o ).
thf(func_def_27,type,
f: $i > $o ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_29,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
sK2: $i > $i ).
thf(func_def_43,type,
sK3: $i > $i ).
thf(func_def_44,type,
sK4: $i > $i ).
thf(func_def_45,type,
sK5: $i > $i ).
thf(func_def_46,type,
sK6: $i > $i ).
thf(func_def_47,type,
sK7: $i > $i ).
thf(func_def_49,type,
sK9: $i > $i ).
thf(func_def_50,type,
sF10:
!>[X0: $tType] : ( $i > ( $i > X0 ) > X0 ) ).
thf(func_def_51,type,
sF11:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X0 > X1 > X2 ) ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X0 @ X1 ) )
=> ( irel @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',trans_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) )
= iand ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) @ ( iatom @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) @ ( iatom @ f ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f24,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f25,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f27,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f28,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) @ ( iatom @ f ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f30,plain,
( $true
= ( ~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) @ ( iatom @ f ) ) ) ) ) ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[],[f5]) ).
thf(f32,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f33,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f35,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f36,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X0 @ X1 ) )
=> ( irel @ X0 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f38,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y2 @ Y1 )
& ( irel @ Y1 @ Y0 ) )
=> ( irel @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f37]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f45,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f46,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f51,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f52,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f55,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f60,plain,
( $true
= ( ~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ b0 ) ) @ ( iatom @ a2 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) @ ( iatom @ f ) ) ) ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f61,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y2 @ Y1 )
& ( irel @ Y1 @ Y0 ) )
=> ( irel @ Y2 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f62,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f63,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f64,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f66,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f70,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f72,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f74,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f75,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f78,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f52]) ).
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,[],[f59,f64,f63]) ).
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,[],[f72,f74]) ).
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,[],[f75,f81,f70,f70]) ).
thf(f90,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ 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
@ b2 )
@ ( ^ [Y0: $i > $o] : Y0
@ b0 ) )
@ ( ^ [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
@ 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 > $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] : 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
@ 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
@ b2 )
@ ( ^ [Y0: $i > $o] : Y0
@ b0 ) )
@ ( ^ [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] : Y0
@ a0 )
@ ( ^ [Y0: $i > $o] : Y0
@ f ) ) ) ) )
@ ( ^ [Y0: $i > $o] : Y0
@ f ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f60,f62,f84,f86,f84,f86,f66,f66,f84,f86,f86,f66,f66,f66,f84,f86,f86,f66,f66,f66,f86,f86,f66,f66,f66,f66,f86,f84,f86,f86,f66,f66,f66,f84,f86,f86,f66,f66,f66,f84,f86,f86,f66,f66,f66,f86,f66,f66,f66]) ).
thf(f91,plain,
( $true
= ( ~ ( !! @ $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 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ 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
@ ^ [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 )
=> ( 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 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ 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 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( irel @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f93,plain,
! [X1: $i] :
( ( irel @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,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 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ 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
@ ^ [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 )
=> ( 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 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ 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(f95,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y2 @ Y1 )
& ( irel @ Y1 @ Y0 ) )
=> ( irel @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f96,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y0 @ X1 ) )
=> ( irel @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( ( ^ [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 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ 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
@ ^ [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 )
=> ( 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 )
=> ( b2 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ 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 )
= $false ),
inference(sigma_proxy_clausification,[],[f94]) ).
thf(f98,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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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
@ ^ [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 )
=> ( 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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y0 @ X1 ) )
=> ( irel @ Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f100,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( irel @ Y0 @ X2 )
& ( irel @ X2 @ X1 ) )
=> ( irel @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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
@ ^ [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 )
=> ( 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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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(and_proxy_clausification,[],[f98]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( irel @ Y0 @ X2 )
& ( irel @ X2 @ X1 ) )
=> ( irel @ Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f100]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X3 @ X2 )
& ( irel @ X2 @ X1 ) )
=> ( irel @ X3 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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 )
=> ( f @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f101]) ).
thf(f105,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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 ) ) ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f101]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X3 @ X2 )
& ( irel @ X2 @ X1 ) )
= $false )
| ( $true
= ( irel @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f103]) ).
thf(f108,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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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 ) ) ) ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f105]) ).
thf(f109,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f104]) ).
thf(f111,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) ) )
= $false ),
inference(duplicate_literal_removal,[],[f109]) ).
thf(f112,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X3 @ X1 ) )
| ( ( irel @ X3 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f113,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f108]) ).
thf(f116,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( f @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f111]) ).
thf(f117,plain,
( ( ( irel @ sK0 @ sK1 )
=> ( f @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
( ( $true
= ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f113]) ).
thf(f123,plain,
( ( f @ sK1 )
= $false ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f124,plain,
( $true
= ( irel @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f117]) ).
thf(f125,plain,
! [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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ 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 ) ) ) ) ) )
@ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f126,plain,
! [X1: $i] :
( ( ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f131,plain,
! [X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f136,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $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 )
=> ( b2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) ) ) ) )
@ X2 )
= $true )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f131]) ).
thf(f137,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
= $true )
| ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f137]) ).
thf(f140,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 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $true )
| ( ( 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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f141,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f139]) ).
thf(f142,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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f143,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 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ 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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( f @ Y0 ) )
@ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f145,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ sK0 @ X2 )
=> ( ( ~ ( !! @ $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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( f @ X3 ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( 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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f147,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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f148,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 ) ) ) ) )
| ( ( 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f149,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X3 )
=> ( f @ X3 ) ) )
| ( ( ~ ( !! @ $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 )
=> ( 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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f150,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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f151,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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ 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 ) ) ) ) ) ) ) )
| ( ( 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f154,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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( ( 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 ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f147]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( f @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f149]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f158,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 ) ) ) ) ) ) ) )
| ( ( 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 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) )
@ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f159,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 )
=> ( 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 )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f161,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 @ 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 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f164,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ 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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( f @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ X3 )
=> ( a2 @ X3 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f167,plain,
! [X2: $i,X3: $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 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
| ( ( irel @ sK0 @ 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 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ 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 ) ) ) )
= $true )
| ( ( 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 ) ) ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( f @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) )
@ ( sK2 @ 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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f176,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 )
=> ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a0 @ ( sK2 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( f @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f178,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 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f179,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 ) ) ) ) ) ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
| ( ( 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 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f182,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) )
@ X3 )
= $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 ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
| ( ( 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 @ 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 ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( a0 @ ( sK2 @ 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f191,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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK3 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK3 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) ) )
| ( ( 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X3: $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 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
| ( ( 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 )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f197,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( 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 @ 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 ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( f @ 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ 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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( 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 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f209,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 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
| ( ( !! @ $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 @ X1 )
= $false )
| ( ( 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 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f213,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 ) ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $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 @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f220,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 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f203]) ).
thf(f222,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $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 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( f @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f204]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( 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 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f208]) ).
thf(f230,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f209]) ).
thf(f232,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) )
@ X4 )
= $true )
| ( ( 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
= ( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f210]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
| ( ( ( irel @ X1 @ X4 )
=> ( a1 @ X4 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( !! @ $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 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f236,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK5 @ X2 ) ) )
| ( ( ~ ( !! @ $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 ) ),
inference(sigma_proxy_clausification,[],[f213]) ).
thf(f237,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 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f245,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f220]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f222]) ).
thf(f256,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f259,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f230]) ).
thf(f261,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X1 @ X4 )
=> ( a1 @ X4 ) )
= $true )
| ( ( !! @ $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 )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f265,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) ) )
= $true )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $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 @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f274,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( f @ X3 )
= $true ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f277,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( f @ X3 )
= $true )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f286,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ ( sK3 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ ( sK6 @ X1 ) )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f256]) ).
thf(f287,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) )
=> ( b0 @ ( sK6 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f286]) ).
thf(f290,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $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 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f259]) ).
thf(f293,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( 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 )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f261]) ).
thf(f298,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ 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 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a0 @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f265]) ).
thf(f299,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ X1 @ X4 )
=> ( a0 @ X4 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f307,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( f @ X3 )
= $true )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f310,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( f @ X3 )
= $true ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f322,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $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 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f287]) ).
thf(f323,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f287]) ).
thf(f326,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f290]) ).
thf(f327,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f332,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
@ ( sK4 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( !! @ $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 @ X1 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f293]) ).
thf(f333,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ( irel @ X1 @ ( sK4 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f332]) ).
thf(f337,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK5 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( $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 )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f299]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( f @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f307]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( f @ X4 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( f @ X3 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f346]) ).
thf(f352,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) )
@ ( sK2 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( f @ X3 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f310]) ).
thf(f353,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( f @ X3 )
= $true )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f368,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f322]) ).
thf(f370,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $true
= ( a2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f323]) ).
thf(f374,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( ( a2 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f327]) ).
thf(f378,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $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
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f333]) ).
thf(f379,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ ( sK4 @ X1 ) )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f333]) ).
thf(f384,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a0 @ X3 ) )
| ( $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 )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f337]) ).
thf(f385,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( irel @ X2 @ ( sK5 @ X2 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f337]) ).
thf(f397,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( f @ X4 ) )
| ( ( f @ X3 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f347]) ).
thf(f400,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( f @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) )
@ X4 )
= $true )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f353]) ).
thf(f401,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( f @ X4 ) ) )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f400]) ).
thf(f417,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f368]) ).
thf(f418,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f422,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 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f374]) ).
thf(f425,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X1 @ ( sK4 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
@ ( sK4 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f379]) ).
thf(f426,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ ( sK4 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f425]) ).
thf(f427,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $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
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(or_proxy_clausification,[],[f378]) ).
thf(f434,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f384]) ).
thf(f435,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( $true
= ( irel @ X2 @ ( sK5 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f385]) ).
thf(f448,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( f @ X3 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) )
@ ( sK2 @ X2 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( f @ X4 ) )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f397]) ).
thf(f449,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X2 @ ( sK2 @ X2 ) )
=> ( a0 @ ( sK2 @ X2 ) ) )
= $false )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( f @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( f @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f448]) ).
thf(f455,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( f @ X4 ) ) )
| ( ( f @ X3 )
= $true )
| ( $true
= ( irel @ X2 @ ( sK2 @ X2 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f401]) ).
thf(f461,definition,
( spl8_1
<=> ! [X2: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f462,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f461]) ).
thf(f464,definition,
( spl8_2
<=> ! [X1: $i,X3: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ X3 )
= $true )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f465,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( f @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f464]) ).
thf(f468,definition,
( spl8_3
<=> ! [X1: $i,X3: $i] :
( ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( f @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f469,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( f @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f468]) ).
thf(f480,definition,
( spl8_4
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f481,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f480]) ).
thf(f488,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f417]) ).
thf(f489,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 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f418]) ).
thf(f495,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a2 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( a2 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK3 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f422]) ).
thf(f496,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a2 @ X4 )
= $true )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f495]) ).
thf(f502,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ ( sK4 @ X1 ) )
= $true )
| ( $true
= ( irel @ X2 @ ( sK4 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f426]) ).
thf(f504,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK4 @ X1 ) @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK7 @ X1 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( 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 )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f427]) ).
thf(f505,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X4 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
=> ( a2 @ ( sK7 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f504]) ).
thf(f514,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( $true
= ( a0 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f434]) ).
thf(f515,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f434]) ).
thf(f516,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK5 @ X2 ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( ( a0 @ X4 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f435]) ).
thf(f517,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK5 @ X2 ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true ) ),
inference(beta-eta_normalization,[],[f516]) ).
thf(f535,definition,
( spl8_5
<=> ! [X4: $i,X2: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( $true
= ( irel @ X2 @ ( sK5 @ X2 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f536,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ X2 @ ( sK5 @ X2 ) ) )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f535]) ).
thf(f540,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( f @ X3 )
= $true )
| ( $true
= ( f @ X4 ) )
| ( ( a0 @ ( sK2 @ X1 ) )
= $false )
| ( ( a0 @ ( sK2 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f449]) ).
thf(f547,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ X2 @ ( sK2 @ X2 ) ) )
| ( $true
= ( f @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( f @ X3 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f455]) ).
thf(f572,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f488]) ).
thf(f573,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $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 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f572]) ).
thf(f574,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK3 @ X2 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f489]) ).
thf(f575,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f574]) ).
thf(f582,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ ( sK3 @ X1 ) )
= $true )
| ( ( irel @ X2 @ ( sK3 @ X2 ) )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f496]) ).
thf(f590,plain,
( spl8_1
| spl8_1 ),
inference(avatar_split_clause,[],[f502,f461,f461]) ).
thf(f593,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
@ ( sK4 @ X2 ) )
= $false )
| ( ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
=> ( a2 @ ( sK7 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f505]) ).
thf(f594,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
=> ( a2 @ ( sK7 @ X1 ) ) )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f593]) ).
thf(f605,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f514]) ).
thf(f606,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f605]) ).
thf(f607,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a0 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f515]) ).
thf(f608,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f607]) ).
thf(f610,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( $true
= ( irel @ X2 @ ( sK5 @ X2 ) ) )
| ( $true
= ( irel @ X1 @ ( sK5 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f517]) ).
thf(f632,plain,
( spl8_2
| spl8_2 ),
inference(avatar_split_clause,[],[f540,f464,f464]) ).
thf(f641,plain,
( spl8_3
| spl8_3 ),
inference(avatar_split_clause,[],[f547,f468,f468]) ).
thf(f666,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f573]) ).
thf(f667,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) )
@ X4 )
= $true )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f575]) ).
thf(f668,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f667]) ).
thf(f673,plain,
( spl8_4
| spl8_4 ),
inference(avatar_split_clause,[],[f582,f480,f480]) ).
thf(f686,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( $false
= ( a2 @ ( sK7 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f594]) ).
thf(f687,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( ( irel @ X2 @ ( sK4 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f594]) ).
thf(f704,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f606]) ).
thf(f706,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
= $true )
| ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f608]) ).
thf(f709,plain,
( spl8_5
| spl8_5 ),
inference(avatar_split_clause,[],[f610,f535,f535]) ).
thf(f748,definition,
( spl8_6
<=> ! [X2: $i,X4: $i] :
( ( $true
= ( irel @ ( sK4 @ X2 ) @ ( sK7 @ X2 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f749,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK4 @ X2 ) @ ( sK7 @ X2 ) ) )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f748]) ).
thf(f752,definition,
( spl8_7
<=> ! [X4: $i,X2: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( a2 @ ( sK7 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f753,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a2 @ ( sK7 @ X2 ) )
= $false ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f752]) ).
thf(f761,definition,
( spl8_8
<=> ! [X1: $i,X3: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f762,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( $true
= ( a2 @ X3 ) ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f761]) ).
thf(f765,definition,
( spl8_9
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f766,plain,
( ! [X3: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f765]) ).
thf(f783,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) )
@ ( sK3 @ X2 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f666]) ).
thf(f784,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( ( irel @ X2 @ ( sK3 @ X2 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f783]) ).
thf(f785,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f668]) ).
thf(f804,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f687]) ).
thf(f806,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $false
= ( a2 @ ( sK7 @ X1 ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f686]) ).
thf(f829,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(or_proxy_clausification,[],[f704]) ).
thf(f831,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ X5 ) )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(pi_proxy_clausification,[],[f706]) ).
thf(f832,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( irel @ ( sK5 @ X2 ) @ X5 )
=> ( b0 @ X5 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(beta-eta_normalization,[],[f831]) ).
thf(f866,definition,
( spl8_10
<=> ! [X4: $i,X2: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X2 ) @ ( sK9 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f867,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X2 ) @ ( sK9 @ X2 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f866]) ).
thf(f870,definition,
( spl8_11
<=> ! [X2: $i,X4: $i] :
( ( ( a1 @ ( sK9 @ X2 ) )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
thf(f871,plain,
( ! [X2: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( a1 @ ( sK9 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f870]) ).
thf(f914,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f784]) ).
thf(f917,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f785]) ).
thf(f939,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f804]) ).
thf(f942,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( $false
= ( a2 @ ( sK7 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
= $false )
| ( $true
= ( a1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f806]) ).
thf(f972,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK5 @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( a0 @ X3 ) ) ),
inference(sigma_proxy_clausification,[],[f829]) ).
thf(f973,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( a0 @ X4 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( ( irel @ ( sK5 @ X2 ) @ ( sK9 @ X2 ) )
=> ( a1 @ ( sK9 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f972]) ).
thf(f974,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( irel @ X1 @ ( sK5 @ X1 ) )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( b0 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f832]) ).
thf(f1010,definition,
( spl8_14
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( $true
= ( b0 @ X5 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
thf(f1011,plain,
( ! [X2: $i,X4: $i,X5: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( b0 @ X5 ) )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false ) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f1010]) ).
thf(f1043,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f914]) ).
thf(f1047,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( a2 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f917]) ).
thf(f1064,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK7 @ X2 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
= $true )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f939]) ).
thf(f1065,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK7 @ X2 ) )
=> ( a2 @ ( sK7 @ X2 ) ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
= $true )
| ( $true
= ( a1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f1064]) ).
thf(f1067,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK4 @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) )
@ ( sK7 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( a2 @ ( sK7 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f942]) ).
thf(f1068,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( a2 @ ( sK7 @ X1 ) ) )
| ( ( ( irel @ ( sK4 @ X2 ) @ ( sK7 @ X2 ) )
=> ( a2 @ ( sK7 @ X2 ) ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f1067]) ).
thf(f1095,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $true
= ( a0 @ X3 ) )
| ( $false
= ( ( irel @ ( sK5 @ X2 ) @ ( sK9 @ X2 ) )
=> ( a1 @ ( sK9 @ X2 ) ) ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f973]) ).
thf(f1096,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( $false
= ( ( irel @ ( sK5 @ X2 ) @ ( sK9 @ X2 ) )
=> ( a1 @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( ( irel @ ( sK5 @ X1 ) @ ( sK9 @ X1 ) )
=> ( a1 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X4 )
= $true ) ),
inference(beta-eta_normalization,[],[f1095]) ).
thf(f1097,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false )
| ( $true
= ( b0 @ X5 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f974]) ).
thf(f1163,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( $true
= ( a2 @ X3 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ ( sK6 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1043]) ).
thf(f1164,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( ( irel @ ( sK3 @ X2 ) @ ( sK6 @ X2 ) )
=> ( b0 @ ( sK6 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1163]) ).
thf(f1165,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK3 @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ ( sK6 @ X2 ) )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1047]) ).
thf(f1166,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( a2 @ X3 ) )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( ( irel @ ( sK3 @ X2 ) @ ( sK6 @ X2 ) )
=> ( b0 @ ( sK6 @ X2 ) ) ) )
| ( ( irel @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f1165]) ).
thf(f1180,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( $true
= ( a1 @ X4 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK4 @ X2 ) @ ( sK7 @ X2 ) ) )
| ( ( irel @ ( sK4 @ X1 ) @ ( sK7 @ X1 ) )
= $true )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1065]) ).
thf(f1183,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a2 @ ( sK7 @ X2 ) )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $false
= ( a2 @ ( sK7 @ X1 ) ) )
| ( $true
= ( a1 @ X4 ) )
| ( $true
= ( a1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f1068]) ).
thf(f1207,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK5 @ X1 ) @ ( sK9 @ X1 ) )
=> ( a1 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( a1 @ ( sK9 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1096]) ).
thf(f1208,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK5 @ X2 ) @ ( sK9 @ X2 ) ) )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( ( irel @ ( sK5 @ X1 ) @ ( sK9 @ X1 ) )
=> ( a1 @ ( sK9 @ X1 ) ) )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1096]) ).
thf(f1210,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( a0 @ X4 )
= $true )
| ( $true
= ( b0 @ X5 ) )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false ) ),
inference(or_proxy_clausification,[],[f1097]) ).
thf(f1263,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( $false
= ( b0 @ ( sK6 @ X2 ) ) )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( b0 @ ( sK6 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1164]) ).
thf(f1266,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( irel @ ( sK3 @ X1 ) @ ( sK6 @ X1 ) ) )
| ( ( a2 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a2 @ X3 ) )
| ( $true
= ( irel @ ( sK3 @ X2 ) @ ( sK6 @ X2 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1166]) ).
thf(f1277,plain,
( spl8_6
| spl8_6 ),
inference(avatar_split_clause,[],[f1180,f748,f748]) ).
thf(f1281,plain,
( spl8_7
| spl8_7 ),
inference(avatar_split_clause,[],[f1183,f752,f752]) ).
thf(f1308,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X1 ) @ ( sK9 @ X1 ) ) )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( irel @ ( sK5 @ X2 ) @ ( sK9 @ X2 ) ) )
| ( ( a0 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1208]) ).
thf(f1309,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $false
= ( a1 @ ( sK9 @ X1 ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( a1 @ ( sK9 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1207]) ).
thf(f1311,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( b0 @ X5 ) )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f1210]) ).
thf(f1345,plain,
( spl8_8
| spl8_8 ),
inference(avatar_split_clause,[],[f1263,f761,f761]) ).
thf(f1347,plain,
( spl8_9
| spl8_9 ),
inference(avatar_split_clause,[],[f1266,f765,f765]) ).
thf(f1376,plain,
( spl8_10
| spl8_10 ),
inference(avatar_split_clause,[],[f1308,f866,f866]) ).
thf(f1378,plain,
( spl8_11
| spl8_11 ),
inference(avatar_split_clause,[],[f1309,f870,f870]) ).
thf(f1380,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( $true
= ( b0 @ X5 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ ( sK5 @ X1 ) @ Y0 )
=> ( b0 @ Y0 ) )
@ X6 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1311]) ).
thf(f1381,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false )
| ( $true
= ( b0 @ X5 ) )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ X2 @ X3 )
= $false )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( $true
= ( ( irel @ ( sK5 @ X1 ) @ X6 )
=> ( b0 @ X6 ) ) ) ),
inference(beta-eta_normalization,[],[f1380]) ).
thf(f1421,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X4 )
= $false )
| ( ( irel @ ( sK5 @ X1 ) @ X6 )
= $false )
| ( ( b0 @ X6 )
= $true )
| ( $true
= ( a0 @ X3 ) )
| ( ( irel @ X2 @ X3 )
= $false )
| ( ( irel @ ( sK5 @ X2 ) @ X5 )
= $false )
| ( ( irel @ sK0 @ X2 )
= $false )
| ( ( a0 @ X4 )
= $true )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( b0 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f1381]) ).
thf(f1446,plain,
( spl8_14
| spl8_14 ),
inference(avatar_split_clause,[],[f1421,f1010,f1010]) ).
thf(f1481,definition,
( spl8_18
<=> ( ( a0 @ ( sK2 @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_18])],[avatar_definition]) ).
thf(f1483,plain,
( ( ( a0 @ ( sK2 @ sK0 ) )
= $false )
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f1481]) ).
thf(f1559,definition,
( spl8_30
<=> ( ( a1 @ ( sK9 @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_30])],[avatar_definition]) ).
thf(f1561,plain,
( ( ( a1 @ ( sK9 @ sK0 ) )
= $false )
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f1559]) ).
thf(f1711,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a0 @ ( sK2 @ sK0 ) )
= $false )
| ( $true
= ( f @ X0 ) ) )
| ~ spl8_2 ),
inference(superposition,[],[f93,f465]) ).
thf(f1712,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( f @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) ) )
| ~ spl8_3 ),
inference(superposition,[],[f93,f469]) ).
thf(f1714,plain,
( ! [X0: $i] :
( ( $true
= ( a0 @ X0 ) )
| ( $true = $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( irel @ sK0 @ ( sK5 @ sK0 ) ) ) )
| ~ spl8_5 ),
inference(superposition,[],[f93,f536]) ).
thf(f1719,plain,
( ! [X0: $i] :
( ( $true
= ( a0 @ X0 ) )
| ( $true = $false )
| ( ( irel @ ( sK5 @ sK0 ) @ ( sK9 @ sK0 ) )
= $true )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl8_10 ),
inference(superposition,[],[f93,f867]) ).
thf(f1720,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( a0 @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a1 @ ( sK9 @ sK0 ) )
= $false ) )
| ~ spl8_11 ),
inference(superposition,[],[f93,f871]) ).
thf(f1741,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( b0 @ X0 ) )
| ( $true
= ( a0 @ X1 ) )
| ( $true = $false )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false ) )
| ~ spl8_14 ),
inference(superposition,[],[f1011,f93]) ).
thf(f1760,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) )
| ( $true
= ( f @ X0 ) ) )
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f1712]) ).
thf(f1763,plain,
( ! [X0: $i] :
( ( ( a0 @ ( sK2 @ sK0 ) )
= $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( f @ X0 ) ) )
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f1711]) ).
thf(f1769,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( ( a1 @ ( sK9 @ sK0 ) )
= $false )
| ( $true
= ( a0 @ X0 ) ) )
| ~ spl8_11 ),
inference(trivial_inequality_removal,[],[f1720]) ).
thf(f1771,plain,
( ! [X0: $i] :
( ( $true
= ( a0 @ X0 ) )
| ( $true
= ( irel @ sK0 @ ( sK5 @ sK0 ) ) )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f1714]) ).
thf(f1780,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ ( sK9 @ sK0 ) )
= $true )
| ( $true
= ( a0 @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f1719]) ).
thf(f1781,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( a0 @ X1 ) )
| ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl8_14 ),
inference(trivial_inequality_removal,[],[f1741]) ).
thf(f1790,definition,
( spl8_38
<=> ! [X0: $i] :
( ( $true
= ( f @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_38])],[avatar_definition]) ).
thf(f1791,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( f @ X0 ) ) )
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f1790]) ).
thf(f1807,definition,
( spl8_42
<=> ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_42])],[avatar_definition]) ).
thf(f1809,plain,
( ( $true
= ( irel @ sK0 @ ( sK2 @ sK0 ) ) )
| ~ spl8_42 ),
inference(avatar_component_clause,[],[f1807]) ).
thf(f1813,definition,
( spl8_43
<=> ( $true
= ( irel @ sK0 @ ( sK5 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_43])],[avatar_definition]) ).
thf(f1815,plain,
( ( $true
= ( irel @ sK0 @ ( sK5 @ sK0 ) ) )
| ~ spl8_43 ),
inference(avatar_component_clause,[],[f1813]) ).
thf(f1817,definition,
( spl8_44
<=> ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( a0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_44])],[avatar_definition]) ).
thf(f1818,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( a0 @ X0 ) ) )
| ~ spl8_44 ),
inference(avatar_component_clause,[],[f1817]) ).
thf(f1820,plain,
( spl8_38
| spl8_42
| ~ spl8_3 ),
inference(avatar_split_clause,[],[f1760,f468,f1807,f1790]) ).
thf(f1822,definition,
( spl8_45
<=> ( ( irel @ ( sK5 @ sK0 ) @ ( sK9 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_45])],[avatar_definition]) ).
thf(f1824,plain,
( ( ( irel @ ( sK5 @ sK0 ) @ ( sK9 @ sK0 ) )
= $true )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f1822]) ).
thf(f1827,definition,
( spl8_46
<=> ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_46])],[avatar_definition]) ).
thf(f1828,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl8_46 ),
inference(avatar_component_clause,[],[f1827]) ).
thf(f1830,plain,
( spl8_38
| spl8_18
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f1763,f464,f1481,f1790]) ).
thf(f1836,plain,
( spl8_30
| spl8_44
| ~ spl8_11 ),
inference(avatar_split_clause,[],[f1769,f870,f1817,f1559]) ).
thf(f1838,plain,
( spl8_44
| spl8_43
| ~ spl8_5 ),
inference(avatar_split_clause,[],[f1771,f535,f1813,f1817]) ).
thf(f1851,plain,
( spl8_44
| spl8_45
| ~ spl8_10 ),
inference(avatar_split_clause,[],[f1780,f866,f1822,f1817]) ).
thf(f1852,plain,
( spl8_44
| spl8_46
| ~ spl8_14 ),
inference(avatar_split_clause,[],[f1781,f1010,f1827,f1817]) ).
thf(f1964,plain,
( ( $true
= ( f @ sK1 ) )
| ( $true = $false )
| ~ spl8_38 ),
inference(superposition,[],[f1791,f124]) ).
thf(f1973,plain,
( ( $true
= ( f @ sK1 ) )
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f1964]) ).
thf(f1979,plain,
( ( $true = $false )
| ~ spl8_38 ),
inference(forward_demodulation,[],[f1973,f123]) ).
thf(f1980,plain,
( $false
| ~ spl8_38 ),
inference(trivial_inequality_removal,[],[f1979]) ).
thf(f1981,plain,
~ spl8_38,
inference(avatar_contradiction_clause,[],[f1980]) ).
thf(f2158,plain,
( ( $true = $false )
| ( $true
= ( a0 @ ( sK2 @ sK0 ) ) )
| ~ spl8_42
| ~ spl8_44 ),
inference(superposition,[],[f1809,f1818]) ).
thf(f2167,plain,
( ( $true
= ( a0 @ ( sK2 @ sK0 ) ) )
| ~ spl8_42
| ~ spl8_44 ),
inference(trivial_inequality_removal,[],[f2158]) ).
thf(f2172,plain,
( ( $true = $false )
| ~ spl8_18
| ~ spl8_42
| ~ spl8_44 ),
inference(forward_demodulation,[],[f2167,f1483]) ).
thf(f2173,plain,
( $false
| ~ spl8_18
| ~ spl8_42
| ~ spl8_44 ),
inference(trivial_inequality_removal,[],[f2172]) ).
thf(f2174,plain,
( ~ spl8_18
| ~ spl8_42
| ~ spl8_44 ),
inference(avatar_contradiction_clause,[],[f2173]) ).
thf(f2177,plain,
( ! [X0: $i] :
( ( ( a1 @ X0 )
= $true )
| ( $true = $false )
| ( ( irel @ ( sK5 @ sK0 ) @ ( sK4 @ ( sK5 @ sK0 ) ) )
= $true )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false ) )
| ~ spl8_1
| ~ spl8_43 ),
inference(superposition,[],[f1815,f462]) ).
thf(f2183,plain,
( ! [X0: $i] :
( ( ( a2 @ ( sK7 @ ( sK5 @ sK0 ) ) )
= $false )
| ( $true = $false )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true ) )
| ~ spl8_7
| ~ spl8_43 ),
inference(superposition,[],[f1815,f753]) ).
thf(f2184,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true )
| ( ( b0 @ ( sK6 @ ( sK5 @ sK0 ) ) )
= $false ) )
| ~ spl8_8
| ~ spl8_43 ),
inference(superposition,[],[f1815,f762]) ).
thf(f2185,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( irel @ ( sK3 @ ( sK5 @ sK0 ) ) @ ( sK6 @ ( sK5 @ sK0 ) ) ) )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl8_9
| ~ spl8_43 ),
inference(superposition,[],[f1815,f766]) ).
thf(f2195,plain,
( ! [X0: $i] :
( ( ( a2 @ X0 )
= $true )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( $true = $false )
| ( ( irel @ ( sK5 @ sK0 ) @ ( sK3 @ ( sK5 @ sK0 ) ) )
= $true ) )
| ~ spl8_4
| ~ spl8_43 ),
inference(superposition,[],[f481,f1815]) ).
thf(f2197,plain,
( ! [X0: $i] :
( ( $true
= ( irel @ ( sK4 @ ( sK5 @ sK0 ) ) @ ( sK7 @ ( sK5 @ sK0 ) ) ) )
| ( ( a1 @ X0 )
= $true )
| ( $true = $false )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false ) )
| ~ spl8_6
| ~ spl8_43 ),
inference(superposition,[],[f749,f1815]) ).
thf(f2215,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ ( sK4 @ ( sK5 @ sK0 ) ) )
= $true )
| ( ( a1 @ X0 )
= $true )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false ) )
| ~ spl8_1
| ~ spl8_43 ),
inference(trivial_inequality_removal,[],[f2177]) ).
thf(f2221,plain,
( ! [X0: $i] :
( ( ( a2 @ ( sK7 @ ( sK5 @ sK0 ) ) )
= $false )
| ( ( a1 @ X0 )
= $true )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false ) )
| ~ spl8_7
| ~ spl8_43 ),
inference(trivial_inequality_removal,[],[f2183]) ).
thf(f2226,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true )
| ( $true
= ( irel @ ( sK3 @ ( sK5 @ sK0 ) ) @ ( sK6 @ ( sK5 @ sK0 ) ) ) ) )
| ~ spl8_9
| ~ spl8_43 ),
inference(trivial_inequality_removal,[],[f2185]) ).
thf(f2228,plain,
( ! [X0: $i] :
( ( ( b0 @ ( sK6 @ ( sK5 @ sK0 ) ) )
= $false )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl8_8
| ~ spl8_43 ),
inference(trivial_inequality_removal,[],[f2184]) ).
thf(f2230,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( $true
= ( irel @ ( sK4 @ ( sK5 @ sK0 ) ) @ ( sK7 @ ( sK5 @ sK0 ) ) ) )
| ( ( a1 @ X0 )
= $true ) )
| ~ spl8_6
| ~ spl8_43 ),
inference(trivial_inequality_removal,[],[f2197]) ).
thf(f2234,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( irel @ ( sK5 @ sK0 ) @ ( sK3 @ ( sK5 @ sK0 ) ) )
= $true )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl8_4
| ~ spl8_43 ),
inference(trivial_inequality_removal,[],[f2195]) ).
thf(f2238,definition,
( spl8_68
<=> ( ( irel @ ( sK5 @ sK0 ) @ ( sK3 @ ( sK5 @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_68])],[avatar_definition]) ).
thf(f2240,plain,
( ( ( irel @ ( sK5 @ sK0 ) @ ( sK3 @ ( sK5 @ sK0 ) ) )
= $true )
| ~ spl8_68 ),
inference(avatar_component_clause,[],[f2238]) ).
thf(f2242,definition,
( spl8_69
<=> ! [X0: $i] :
( ( ( a2 @ X0 )
= $true )
| ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl8_69])],[avatar_definition]) ).
thf(f2243,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl8_69 ),
inference(avatar_component_clause,[],[f2242]) ).
thf(f2262,definition,
( spl8_74
<=> ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl8_74])],[avatar_definition]) ).
thf(f2263,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X0 )
= $false )
| ( ( a1 @ X0 )
= $true ) )
| ~ spl8_74 ),
inference(avatar_component_clause,[],[f2262]) ).
thf(f2265,definition,
( spl8_75
<=> ( ( a2 @ ( sK7 @ ( sK5 @ sK0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_75])],[avatar_definition]) ).
thf(f2267,plain,
( ( ( a2 @ ( sK7 @ ( sK5 @ sK0 ) ) )
= $false )
| ~ spl8_75 ),
inference(avatar_component_clause,[],[f2265]) ).
thf(f2278,definition,
( spl8_78
<=> ( ( irel @ ( sK5 @ sK0 ) @ ( sK4 @ ( sK5 @ sK0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_78])],[avatar_definition]) ).
thf(f2280,plain,
( ( ( irel @ ( sK5 @ sK0 ) @ ( sK4 @ ( sK5 @ sK0 ) ) )
= $true )
| ~ spl8_78 ),
inference(avatar_component_clause,[],[f2278]) ).
thf(f2282,plain,
( spl8_78
| spl8_74
| ~ spl8_1
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f2215,f1813,f461,f2262,f2278]) ).
thf(f2294,definition,
( spl8_81
<=> ( ( b0 @ ( sK6 @ ( sK5 @ sK0 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl8_81])],[avatar_definition]) ).
thf(f2296,plain,
( ( ( b0 @ ( sK6 @ ( sK5 @ sK0 ) ) )
= $false )
| ~ spl8_81 ),
inference(avatar_component_clause,[],[f2294]) ).
thf(f2299,definition,
( spl8_82
<=> ( $true
= ( irel @ ( sK3 @ ( sK5 @ sK0 ) ) @ ( sK6 @ ( sK5 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_82])],[avatar_definition]) ).
thf(f2301,plain,
( ( $true
= ( irel @ ( sK3 @ ( sK5 @ sK0 ) ) @ ( sK6 @ ( sK5 @ sK0 ) ) ) )
| ~ spl8_82 ),
inference(avatar_component_clause,[],[f2299]) ).
thf(f2307,plain,
( spl8_75
| spl8_74
| ~ spl8_7
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f2221,f1813,f752,f2262,f2265]) ).
thf(f2315,definition,
( spl8_85
<=> ( $true
= ( irel @ ( sK4 @ ( sK5 @ sK0 ) ) @ ( sK7 @ ( sK5 @ sK0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_85])],[avatar_definition]) ).
thf(f2317,plain,
( ( $true
= ( irel @ ( sK4 @ ( sK5 @ sK0 ) ) @ ( sK7 @ ( sK5 @ sK0 ) ) ) )
| ~ spl8_85 ),
inference(avatar_component_clause,[],[f2315]) ).
thf(f2319,plain,
( spl8_82
| spl8_69
| ~ spl8_9
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f2226,f1813,f765,f2242,f2299]) ).
thf(f2321,plain,
( spl8_69
| spl8_81
| ~ spl8_8
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f2228,f1813,f761,f2294,f2242]) ).
thf(f2323,plain,
( spl8_74
| spl8_85
| ~ spl8_6
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f2230,f1813,f748,f2315,f2262]) ).
thf(f2327,plain,
( spl8_69
| spl8_68
| ~ spl8_4
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f2234,f1813,f480,f2238,f2242]) ).
thf(f2394,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X1 )
= $false )
| ( $true = $false )
| ( ( irel @ X1 @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl8_46 ),
inference(superposition,[],[f1828,f112]) ).
thf(f2400,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X1 )
= $false )
| ( $true
= ( b0 @ X0 ) )
| ( ( irel @ X1 @ X0 )
= $false ) )
| ~ spl8_46 ),
inference(trivial_inequality_removal,[],[f2394]) ).
thf(f2426,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( a2 @ X0 )
= $true )
| ( ( irel @ X1 @ X0 )
= $false )
| ( ( irel @ ( sK5 @ sK0 ) @ X1 )
= $false ) )
| ~ spl8_69 ),
inference(superposition,[],[f112,f2243]) ).
thf(f2429,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ ( sK5 @ sK0 ) @ X1 )
= $false )
| ( ( a2 @ X0 )
= $true )
| ( ( irel @ X1 @ X0 )
= $false ) )
| ~ spl8_69 ),
inference(trivial_inequality_removal,[],[f2426]) ).
thf(f2454,plain,
( ( $true = $false )
| ( ( a1 @ ( sK9 @ sK0 ) )
= $true )
| ~ spl8_45
| ~ spl8_74 ),
inference(superposition,[],[f2263,f1824]) ).
thf(f2465,plain,
( ( ( a1 @ ( sK9 @ sK0 ) )
= $true )
| ~ spl8_45
| ~ spl8_74 ),
inference(trivial_inequality_removal,[],[f2454]) ).
thf(f2469,plain,
( ( $true = $false )
| ~ spl8_30
| ~ spl8_45
| ~ spl8_74 ),
inference(forward_demodulation,[],[f2465,f1561]) ).
thf(f2470,plain,
( $false
| ~ spl8_30
| ~ spl8_45
| ~ spl8_74 ),
inference(trivial_inequality_removal,[],[f2469]) ).
thf(f2471,plain,
( ~ spl8_30
| ~ spl8_45
| ~ spl8_74 ),
inference(avatar_contradiction_clause,[],[f2470]) ).
thf(f3643,plain,
( ! [X0: $i] :
( ( ( a2 @ X0 )
= $true )
| ( ( irel @ ( sK4 @ ( sK5 @ sK0 ) ) @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl8_69
| ~ spl8_78 ),
inference(superposition,[],[f2429,f2280]) ).
thf(f3651,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK4 @ ( sK5 @ sK0 ) ) @ X0 )
= $false )
| ( ( a2 @ X0 )
= $true ) )
| ~ spl8_69
| ~ spl8_78 ),
inference(trivial_inequality_removal,[],[f3643]) ).
thf(f3672,plain,
( ( $true
= ( a2 @ ( sK7 @ ( sK5 @ sK0 ) ) ) )
| ( $true = $false )
| ~ spl8_69
| ~ spl8_78
| ~ spl8_85 ),
inference(superposition,[],[f3651,f2317]) ).
thf(f3683,plain,
( ( $true
= ( a2 @ ( sK7 @ ( sK5 @ sK0 ) ) ) )
| ~ spl8_69
| ~ spl8_78
| ~ spl8_85 ),
inference(trivial_inequality_removal,[],[f3672]) ).
thf(f3687,plain,
( ( $true = $false )
| ~ spl8_69
| ~ spl8_75
| ~ spl8_78
| ~ spl8_85 ),
inference(forward_demodulation,[],[f3683,f2267]) ).
thf(f3688,plain,
( $false
| ~ spl8_69
| ~ spl8_75
| ~ spl8_78
| ~ spl8_85 ),
inference(trivial_inequality_removal,[],[f3687]) ).
thf(f3689,plain,
( ~ spl8_69
| ~ spl8_75
| ~ spl8_78
| ~ spl8_85 ),
inference(avatar_contradiction_clause,[],[f3688]) ).
thf(f3692,plain,
( ! [X0: $i] :
( ( $true
= ( b0 @ X0 ) )
| ( ( irel @ ( sK3 @ ( sK5 @ sK0 ) ) @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl8_46
| ~ spl8_68 ),
inference(superposition,[],[f2240,f2400]) ).
thf(f3703,plain,
( ! [X0: $i] :
( ( ( irel @ ( sK3 @ ( sK5 @ sK0 ) ) @ X0 )
= $false )
| ( $true
= ( b0 @ X0 ) ) )
| ~ spl8_46
| ~ spl8_68 ),
inference(trivial_inequality_removal,[],[f3692]) ).
thf(f3730,plain,
( ( $true = $false )
| ( $true
= ( b0 @ ( sK6 @ ( sK5 @ sK0 ) ) ) )
| ~ spl8_46
| ~ spl8_68
| ~ spl8_82 ),
inference(superposition,[],[f3703,f2301]) ).
thf(f3735,plain,
( ( $true
= ( b0 @ ( sK6 @ ( sK5 @ sK0 ) ) ) )
| ~ spl8_46
| ~ spl8_68
| ~ spl8_82 ),
inference(trivial_inequality_removal,[],[f3730]) ).
thf(f3739,plain,
( ( $true = $false )
| ~ spl8_46
| ~ spl8_68
| ~ spl8_81
| ~ spl8_82 ),
inference(forward_demodulation,[],[f3735,f2296]) ).
thf(f3740,plain,
( $false
| ~ spl8_46
| ~ spl8_68
| ~ spl8_81
| ~ spl8_82 ),
inference(trivial_inequality_removal,[],[f3739]) ).
thf(f3741,plain,
( ~ spl8_46
| ~ spl8_68
| ~ spl8_81
| ~ spl8_82 ),
inference(avatar_contradiction_clause,[],[f3740]) ).
cnf(s7,plain,
( spl8_1
| spl8_1 ),
inference(sat_conversion,[],[f590]) ).
cnf(s8,plain,
spl8_1,
inference(rat,[],[s7]) ).
cnf(s10,plain,
( spl8_2
| spl8_2 ),
inference(sat_conversion,[],[f632]) ).
cnf(s11,plain,
spl8_2,
inference(rat,[],[s10]) ).
cnf(s16,plain,
( spl8_3
| spl8_3 ),
inference(sat_conversion,[],[f641]) ).
cnf(s17,plain,
spl8_3,
inference(rat,[],[s16]) ).
cnf(s18,plain,
( spl8_4
| spl8_4 ),
inference(sat_conversion,[],[f673]) ).
cnf(s19,plain,
spl8_4,
inference(rat,[],[s18]) ).
cnf(s23,plain,
( spl8_5
| spl8_5 ),
inference(sat_conversion,[],[f709]) ).
cnf(s24,plain,
spl8_5,
inference(rat,[],[s23]) ).
cnf(s125,plain,
( spl8_6
| spl8_6 ),
inference(sat_conversion,[],[f1277]) ).
cnf(s126,plain,
spl8_6,
inference(rat,[],[s125]) ).
cnf(s129,plain,
( spl8_7
| spl8_7 ),
inference(sat_conversion,[],[f1281]) ).
cnf(s130,plain,
spl8_7,
inference(rat,[],[s129]) ).
cnf(s148,plain,
( spl8_8
| spl8_8 ),
inference(sat_conversion,[],[f1345]) ).
cnf(s149,plain,
spl8_8,
inference(rat,[],[s148]) ).
cnf(s151,plain,
( spl8_9
| spl8_9 ),
inference(sat_conversion,[],[f1347]) ).
cnf(s152,plain,
spl8_9,
inference(rat,[],[s151]) ).
cnf(s166,plain,
( spl8_10
| spl8_10 ),
inference(sat_conversion,[],[f1376]) ).
cnf(s167,plain,
spl8_10,
inference(rat,[],[s166]) ).
cnf(s169,plain,
( spl8_11
| spl8_11 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s170,plain,
spl8_11,
inference(rat,[],[s169]) ).
cnf(s199,plain,
( spl8_14
| spl8_14 ),
inference(sat_conversion,[],[f1446]) ).
cnf(s200,plain,
spl8_14,
inference(rat,[],[s199]) ).
cnf(s239,plain,
( ~ spl8_3
| spl8_38
| spl8_42 ),
inference(sat_conversion,[],[f1820]) ).
cnf(s242,plain,
( ~ spl8_2
| spl8_18
| spl8_38 ),
inference(sat_conversion,[],[f1830]) ).
cnf(s246,plain,
( ~ spl8_11
| spl8_30
| spl8_44 ),
inference(sat_conversion,[],[f1836]) ).
cnf(s248,plain,
( ~ spl8_5
| spl8_43
| spl8_44 ),
inference(sat_conversion,[],[f1838]) ).
cnf(s255,plain,
( ~ spl8_10
| spl8_44
| spl8_45 ),
inference(sat_conversion,[],[f1851]) ).
cnf(s256,plain,
( ~ spl8_14
| spl8_44
| spl8_46 ),
inference(sat_conversion,[],[f1852]) ).
cnf(s264,plain,
~ spl8_38,
inference(sat_conversion,[],[f1981]) ).
cnf(s294,plain,
( ~ spl8_18
| ~ spl8_42
| ~ spl8_44 ),
inference(sat_conversion,[],[f2174]) ).
cnf(s302,plain,
( ~ spl8_1
| ~ spl8_43
| spl8_74
| spl8_78 ),
inference(sat_conversion,[],[f2282]) ).
cnf(s308,plain,
( ~ spl8_7
| ~ spl8_43
| spl8_74
| spl8_75 ),
inference(sat_conversion,[],[f2307]) ).
cnf(s312,plain,
( ~ spl8_9
| ~ spl8_43
| spl8_69
| spl8_82 ),
inference(sat_conversion,[],[f2319]) ).
cnf(s314,plain,
( ~ spl8_8
| ~ spl8_43
| spl8_69
| spl8_81 ),
inference(sat_conversion,[],[f2321]) ).
cnf(s316,plain,
( ~ spl8_6
| ~ spl8_43
| spl8_74
| spl8_85 ),
inference(sat_conversion,[],[f2323]) ).
cnf(s320,plain,
( ~ spl8_4
| ~ spl8_43
| spl8_68
| spl8_69 ),
inference(sat_conversion,[],[f2327]) ).
cnf(s326,plain,
( ~ spl8_30
| ~ spl8_45
| ~ spl8_74 ),
inference(sat_conversion,[],[f2471]) ).
cnf(s410,plain,
( ~ spl8_69
| ~ spl8_75
| ~ spl8_78
| ~ spl8_85 ),
inference(sat_conversion,[],[f3689]) ).
cnf(s412,plain,
( ~ spl8_46
| ~ spl8_68
| ~ spl8_81
| ~ spl8_82 ),
inference(sat_conversion,[],[f3741]) ).
cnf(s413,plain,
( ~ spl8_2
| spl8_18 ),
inference(rat,[],[s242,s264]) ).
cnf(s414,plain,
( ~ spl8_3
| spl8_42 ),
inference(rat,[],[s239,s264]) ).
cnf(s421,plain,
spl8_42,
inference(rat,[],[s414,s17]) ).
cnf(s423,plain,
spl8_18,
inference(rat,[],[s413,s11]) ).
cnf(s426,plain,
~ spl8_44,
inference(rat,[],[s294,s421,s423]) ).
cnf(s432,plain,
spl8_46,
inference(rat,[],[s256,s200,s426]) ).
cnf(s433,plain,
spl8_45,
inference(rat,[],[s255,s167,s426]) ).
cnf(s434,plain,
spl8_30,
inference(rat,[],[s246,s170,s426]) ).
cnf(s435,plain,
spl8_43,
inference(rat,[],[s248,s24,s426]) ).
cnf(s441,plain,
~ spl8_74,
inference(rat,[],[s326,s433,s434]) ).
cnf(s448,plain,
spl8_75,
inference(rat,[],[s308,s435,s130,s441]) ).
cnf(s449,plain,
spl8_85,
inference(rat,[],[s316,s435,s126,s441]) ).
cnf(s457,plain,
spl8_78,
inference(rat,[],[s302,s435,s441,s8]) ).
cnf(s461,plain,
~ spl8_69,
inference(rat,[],[s410,s449,s448,s457]) ).
cnf(s469,plain,
spl8_82,
inference(rat,[],[s312,s435,s152,s461]) ).
cnf(s470,plain,
spl8_81,
inference(rat,[],[s314,s435,s149,s461]) ).
cnf(s471,plain,
spl8_68,
inference(rat,[],[s320,s435,s19,s461]) ).
cnf(s479,plain,
$false,
inference(rat,[],[s412,s469,s432,s470,s471]) ).
thf(f3742,plain,
$false,
inference(avatar_sat_refutation,[],[s479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO069^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 % Computer : n017.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8046.5625MB
% 0.10/0.28 % OS : Linux 6.8.0-71-generic
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue Sep 29 16:24:53 UTC 2026
% 0.25/0.28 % CPUTime :
% 0.25/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.34 Running higher-order theorem proving
% 0.25/0.36 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/0.55 % (548796)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.07/0.55 % (548807)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.07/0.55 % (548807)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
% 1.07/0.55 % (548807)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=1211862759:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.07/0.55 % (548801)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2681342052:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.07/0.55 % (548802)lrs+10_16_si=on:nwc=1.5:random_seed=3880581307:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.07/0.55 % (548803)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3805998121:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.07/0.55 % (548804)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=3383654514: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)
% 1.07/0.55 % (548806)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4121311194:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.07/0.55 % (548805)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4206709475:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.07/0.55 % (548803)Instruction limit reached!
% 1.07/0.55 % (548803)------------------------------
% 1.07/0.55 % (548803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (548803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (548803)CaDiCaL version: 2.1.3
% 1.07/0.55 % (548803)Termination reason: Instruction limit
% 1.07/0.55 % (548803)Termination phase: Property scanning
% 1.07/0.55 % (548803)Time elapsed: 0.003 s
% 1.07/0.55 % (548803)Peak memory usage: 10 MB
% 1.07/0.55 % (548803)Instructions burned: 3 (million)
% 1.07/0.55 % (548802)Instruction limit reached!
% 1.07/0.55 % (548802)------------------------------
% 1.07/0.55 % (548802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (548802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (548802)CaDiCaL version: 2.1.3
% 1.07/0.55 % (548802)Termination reason: Instruction limit
% 1.07/0.55 % (548802)Termination phase: Saturation
% 1.07/0.55 % (548802)Time elapsed: 0.014 s
% 1.07/0.55 % (548802)Peak memory usage: 11 MB
% 1.07/0.55 % (548802)Instructions burned: 18 (million)
% 1.07/0.55 % (548805)Instruction limit reached!
% 1.07/0.55 % (548805)------------------------------
% 1.07/0.55 % (548805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (548805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (548805)CaDiCaL version: 2.1.3
% 1.07/0.55 % (548805)Termination reason: Instruction limit
% 1.07/0.55 % (548805)Termination phase: Saturation
% 1.07/0.55 % (548805)Time elapsed: 0.023 s
% 1.07/0.55 % (548805)Peak memory usage: 11 MB
% 1.07/0.55 % (548805)Instructions burned: 24 (million)
% 1.07/0.55 % (548815)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=457316312:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.07/0.55 % (548815)Instruction limit reached!
% 1.07/0.55 % (548815)------------------------------
% 1.07/0.55 % (548815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.55 % (548815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.55 % (548815)CaDiCaL version: 2.1.3
% 1.07/0.55 % (548815)Termination reason: Instruction limit
% 1.07/0.55 % (548815)Termination phase: Property scanning
% 1.07/0.55 % (548815)Time elapsed: 0.002 s
% 1.07/0.55 % (548815)Peak memory usage: 10 MB
% 1.07/0.55 % (548815)Instructions burned: 2 (million)
% 1.07/0.55 % (548807)Instruction limit reached!
% 1.07/0.55 % (548807)------------------------------
% 1.07/0.55 % (548807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.59 % (548807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.59 % (548807)CaDiCaL version: 2.1.3
% 1.07/0.59 % (548807)Termination reason: Instruction limit
% 1.07/0.59 % (548807)Termination phase: Saturation
% 1.07/0.59 % (548807)Time elapsed: 0.066 s
% 1.07/0.59 % (548807)Peak memory usage: 13 MB
% 1.07/0.59 % (548807)Instructions burned: 160 (million)
% 1.07/0.59 % (548817)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.07/0.59 % (548816)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2596454773:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.07/0.59 % (548806)Instruction limit reached!
% 1.07/0.59 % (548806)------------------------------
% 1.07/0.59 % (548806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.59 % (548806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.59 % (548806)CaDiCaL version: 2.1.3
% 1.07/0.59 % (548806)Termination reason: Instruction limit
% 1.07/0.59 % (548806)Termination phase: Saturation
% 1.07/0.59 % (548806)Time elapsed: 0.060 s
% 1.07/0.59 % (548806)Peak memory usage: 12 MB
% 1.07/0.59 % (548806)Instructions burned: 75 (million)
% 1.07/0.59 % (548817)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2762463293:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.07/0.59 % (548816)Instruction limit reached!
% 1.07/0.59 % (548816)------------------------------
% 1.07/0.59 % (548816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.59 % (548816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.59 % (548816)CaDiCaL version: 2.1.3
% 1.07/0.59 % (548816)Termination reason: Instruction limit
% 1.07/0.59 % (548816)Termination phase: Property scanning
% 1.07/0.59 % (548816)Time elapsed: 0.005 s
% 1.07/0.59 % (548816)Peak memory usage: 10 MB
% 1.07/0.59 % (548816)Instructions burned: 6 (million)
% 1.07/0.59 % (548820)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
% 1.07/0.59 % (548817)Instruction limit reached!
% 1.07/0.59 % (548817)------------------------------
% 1.07/0.59 % (548817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.59 % (548820)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.07/0.59 % (548817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.59 % (548817)CaDiCaL version: 2.1.3
% 1.07/0.59 % (548817)Termination reason: Instruction limit
% 1.07/0.59 % (548817)Termination phase: Property scanning
% 1.07/0.59 % (548817)Time elapsed: 0.007 s
% 1.07/0.59 % (548817)Peak memory usage: 10 MB
% 1.07/0.59 % (548817)Instructions burned: 8 (million)
% 1.07/0.59 % (548801)Instruction limit reached!
% 1.07/0.59 % (548801)------------------------------
% 1.07/0.59 % (548801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.59 % (548801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.59 % (548801)CaDiCaL version: 2.1.3
% 1.07/0.59 % (548801)Termination reason: Instruction limit
% 1.07/0.59 % (548801)Termination phase: Saturation
% 1.07/0.59 % (548801)Time elapsed: 0.069 s
% 1.07/0.59 % (548801)Peak memory usage: 12 MB
% 1.07/0.59 % (548801)Instructions burned: 87 (million)
% 1.07/0.59 % (548820)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3136428020:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.07/0.59 % (548819)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=25640580:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.07/0.59 % (548819)Instruction limit reached!
% 1.07/0.59 % (548819)------------------------------
% 1.07/0.59 % (548819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.59 % (548819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.59 % (548819)CaDiCaL version: 2.1.3
% 1.07/0.59 % (548819)Termination reason: Instruction limit
% 1.07/0.59 % (548819)Termination phase: Saturation
% 1.07/0.59 % (548819)Time elapsed: 0.010 s
% 1.07/0.59 % (548819)Peak memory usage: 11 MB
% 1.85/0.65 % (548819)Instructions burned: 13 (million)
% 1.85/0.65 % (548820)Instruction limit reached!
% 1.85/0.65 % (548820)------------------------------
% 1.85/0.65 % (548820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.65 % (548820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.65 % (548820)CaDiCaL version: 2.1.3
% 1.85/0.65 % (548820)Termination reason: Instruction limit
% 1.85/0.65 % (548820)Termination phase: Saturation
% 1.85/0.65 % (548820)Time elapsed: 0.012 s
% 1.85/0.65 % (548820)Peak memory usage: 12 MB
% 1.85/0.65 % (548820)Instructions burned: 29 (million)
% 1.85/0.65 % (548825)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.85/0.65 % (548829)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1020294886:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.85/0.65 % (548825)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=1566345564:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.85/0.65 % (548826)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1843322500:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.85/0.65 % (548825)Instruction limit reached!
% 1.85/0.65 % (548825)------------------------------
% 1.85/0.65 % (548825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.65 % (548825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.65 % (548825)CaDiCaL version: 2.1.3
% 1.85/0.65 % (548825)Termination reason: Instruction limit
% 1.85/0.65 % (548825)Termination phase: Naming
% 1.85/0.65 % (548825)Time elapsed: 0.002 s
% 1.85/0.65 % (548825)Peak memory usage: 10 MB
% 1.85/0.65 % (548825)Instructions burned: 2 (million)
% 1.85/0.65 % (548829)Refutation not found, incomplete strategy
% 1.85/0.65 % (548829)------------------------------
% 1.85/0.65 % (548829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.65 % (548829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.65 % (548829)CaDiCaL version: 2.1.3
% 1.85/0.65 % (548829)Termination reason: Refutation not found, incomplete strategy
% 1.85/0.65 % (548829)Time elapsed: 0.004 s
% 1.85/0.65 % (548829)Peak memory usage: 12 MB
% 1.85/0.65 % (548829)Instructions burned: 8 (million)
% 1.85/0.65 % (548829)------------------------------
% 1.85/0.65 % (548829)------------------------------
% 1.85/0.65 % (548826)Refutation not found, incomplete strategy
% 1.85/0.65 % (548826)------------------------------
% 1.85/0.65 % (548826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.65 % (548826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.65 % (548826)CaDiCaL version: 2.1.3
% 1.85/0.65 % (548826)Termination reason: Refutation not found, incomplete strategy
% 1.85/0.65 % (548826)Time elapsed: 0.005 s
% 1.85/0.65 % (548826)Peak memory usage: 12 MB
% 1.85/0.65 % (548826)Instructions burned: 6 (million)
% 1.85/0.65 % (548826)------------------------------
% 1.85/0.65 % (548826)------------------------------
% 1.85/0.65 % (548830)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=218931065:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.85/0.65 % (548823)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=1600909706:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.85/0.65 % (548836)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=925940058:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.85/0.65 % (548824)lrs+10_1_si=on:cs=on:random_seed=1238179693:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.85/0.65 % (548836)Instruction limit reached!
% 1.85/0.65 % (548836)------------------------------
% 1.85/0.65 % (548836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.65 % (548836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.65 % (548836)CaDiCaL version: 2.1.3
% 1.85/0.65 % (548836)Termination reason: Instruction limit
% 1.85/0.65 % (548836)Termination phase: Saturation
% 1.85/0.65 % (548836)Time elapsed: 0.006 s
% 2.26/0.73 % (548836)Peak memory usage: 11 MB
% 2.26/0.73 % (548836)Instructions burned: 15 (million)
% 2.26/0.73 % (548824)Instruction limit reached!
% 2.26/0.73 % (548824)------------------------------
% 2.26/0.73 % (548824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.73 % (548824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.73 % (548824)CaDiCaL version: 2.1.3
% 2.26/0.73 % (548824)Termination reason: Instruction limit
% 2.26/0.73 % (548824)Termination phase: Property scanning
% 2.26/0.73 % (548824)Time elapsed: 0.006 s
% 2.26/0.73 % (548824)Peak memory usage: 11 MB
% 2.26/0.73 % (548824)Instructions burned: 8 (million)
% 2.26/0.73 % (548834)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=26165936:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.26/0.73 % (548835)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2446367063:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.26/0.73 % (548830)Instruction limit reached!
% 2.26/0.73 % (548830)------------------------------
% 2.26/0.73 % (548830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.73 % (548830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.73 % (548830)CaDiCaL version: 2.1.3
% 2.26/0.73 % (548830)Termination reason: Instruction limit
% 2.26/0.73 % (548830)Termination phase: Saturation
% 2.26/0.73 % (548830)Time elapsed: 0.025 s
% 2.26/0.73 % (548830)Peak memory usage: 12 MB
% 2.26/0.73 % (548830)Instructions burned: 25 (million)
% 2.26/0.73 % (548834)Instruction limit reached!
% 2.26/0.73 % (548834)------------------------------
% 2.26/0.73 % (548834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.73 % (548834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.73 % (548834)CaDiCaL version: 2.1.3
% 2.26/0.73 % (548834)Termination reason: Instruction limit
% 2.26/0.73 % (548834)Termination phase: Saturation
% 2.26/0.73 % (548834)Time elapsed: 0.012 s
% 2.26/0.73 % (548834)Peak memory usage: 11 MB
% 2.26/0.73 % (548834)Instructions burned: 14 (million)
% 2.26/0.73 % (548841)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2693480164: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)
% 2.26/0.73 % (548841)Instruction limit reached!
% 2.26/0.73 % (548841)------------------------------
% 2.26/0.73 % (548841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.73 % (548841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.73 % (548841)CaDiCaL version: 2.1.3
% 2.26/0.73 % (548841)Termination reason: Instruction limit
% 2.26/0.73 % (548841)Termination phase: Property scanning
% 2.26/0.73 % (548841)Time elapsed: 0.004 s
% 2.26/0.73 % (548841)Peak memory usage: 11 MB
% 2.26/0.73 % (548841)Instructions burned: 9 (million)
% 2.26/0.73 % (548842)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1640172716:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.26/0.73 % (548848)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
% 2.26/0.73 % (548848)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.26/0.73 % (548845)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3750612018:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.26/0.73 % (548848)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=1224154376:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.26/0.73 % (548848)Instruction limit reached!
% 2.26/0.73 % (548848)------------------------------
% 2.26/0.73 % (548848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.73 % (548848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.73 % (548848)CaDiCaL version: 2.1.3
% 2.26/0.73 % (548848)Termination reason: Instruction limit
% 2.26/0.73 % (548848)Termination phase: Saturation
% 2.26/0.73 % (548848)Time elapsed: 0.006 s
% 2.26/0.73 % (548848)Peak memory usage: 11 MB
% 2.26/0.73 % (548848)Instructions burned: 15 (million)
% 2.26/0.80 % (548842)Instruction limit reached!
% 2.26/0.80 % (548842)------------------------------
% 2.26/0.80 % (548842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.80 % (548842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.80 % (548842)CaDiCaL version: 2.1.3
% 2.26/0.80 % (548842)Termination reason: Instruction limit
% 2.26/0.80 % (548842)Termination phase: Saturation
% 2.26/0.80 % (548842)Time elapsed: 0.021 s
% 2.26/0.80 % (548842)Peak memory usage: 12 MB
% 2.26/0.80 % (548842)Instructions burned: 26 (million)
% 2.26/0.80 % (548845)Instruction limit reached!
% 2.26/0.80 % (548845)------------------------------
% 2.26/0.80 % (548845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.80 % (548845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.80 % (548845)CaDiCaL version: 2.1.3
% 2.26/0.80 % (548845)Termination reason: Instruction limit
% 2.26/0.80 % (548845)Termination phase: Saturation
% 2.26/0.80 % (548845)Time elapsed: 0.018 s
% 2.26/0.80 % (548845)Peak memory usage: 11 MB
% 2.26/0.80 % (548845)Instructions burned: 23 (million)
% 2.26/0.80 % (548846)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3894596466:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.26/0.80 % (548823)Instruction limit reached!
% 2.26/0.80 % (548823)------------------------------
% 2.26/0.80 % (548823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.80 % (548823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.80 % (548823)CaDiCaL version: 2.1.3
% 2.26/0.80 % (548823)Termination reason: Instruction limit
% 2.26/0.80 % (548823)Termination phase: Saturation
% 2.26/0.80 % (548823)Time elapsed: 0.077 s
% 2.26/0.80 % (548823)Peak memory usage: 13 MB
% 2.26/0.80 % (548823)Instructions burned: 86 (million)
% 2.26/0.80 % (548852)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.26/0.80 % (548852)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=3687381402:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.26/0.80 % (548853)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=2578224617:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.26/0.80 % (548852)Instruction limit reached!
% 2.26/0.80 % (548852)------------------------------
% 2.26/0.80 % (548852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.80 % (548852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.80 % (548852)CaDiCaL version: 2.1.3
% 2.26/0.80 % (548852)Termination reason: Instruction limit
% 2.26/0.80 % (548852)Termination phase: Property scanning
% 2.26/0.80 % (548852)Time elapsed: 0.007 s
% 2.26/0.80 % (548852)Peak memory usage: 10 MB
% 2.26/0.80 % (548852)Instructions burned: 8 (million)
% 2.26/0.80 % (548853)Instruction limit reached!
% 2.26/0.80 % (548853)------------------------------
% 2.26/0.80 % (548853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.80 % (548853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.80 % (548853)CaDiCaL version: 2.1.3
% 2.26/0.80 % (548853)Termination reason: Instruction limit
% 2.26/0.80 % (548853)Termination phase: Saturation
% 2.26/0.80 % (548853)Time elapsed: 0.016 s
% 2.26/0.80 % (548853)Peak memory usage: 12 MB
% 2.26/0.80 % (548853)Instructions burned: 32 (million)
% 2.26/0.80 % (548855)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3296640666:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.26/0.80 % (548856)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1593684901:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.26/0.80 % (548855)Instruction limit reached!
% 2.26/0.80 % (548855)------------------------------
% 2.26/0.80 % (548855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.26/0.80 % (548855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.26/0.80 % (548855)CaDiCaL version: 2.1.3
% 2.26/0.80 % (548855)Termination reason: Instruction limit
% 2.26/0.80 % (548855)Termination phase: Property scanning
% 2.94/0.86 % (548855)Time elapsed: 0.007 s
% 2.94/0.86 % (548855)Peak memory usage: 10 MB
% 2.94/0.86 % (548855)Instructions burned: 8 (million)
% 2.94/0.86 % (548859)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=327024724:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.94/0.86 % (548846)Instruction limit reached!
% 2.94/0.86 % (548846)------------------------------
% 2.94/0.86 % (548846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.86 % (548846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.86 % (548846)CaDiCaL version: 2.1.3
% 2.94/0.86 % (548846)Termination reason: Instruction limit
% 2.94/0.86 % (548846)Termination phase: Saturation
% 2.94/0.86 % (548846)Time elapsed: 0.057 s
% 2.94/0.86 % (548846)Peak memory usage: 12 MB
% 2.94/0.86 % (548846)Instructions burned: 60 (million)
% 2.94/0.86 % (548856)Instruction limit reached!
% 2.94/0.86 % (548856)------------------------------
% 2.94/0.86 % (548856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.86 % (548856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.86 % (548856)CaDiCaL version: 2.1.3
% 2.94/0.86 % (548856)Termination reason: Instruction limit
% 2.94/0.86 % (548856)Termination phase: Saturation
% 2.94/0.86 % (548856)Time elapsed: 0.018 s
% 2.94/0.86 % (548856)Peak memory usage: 11 MB
% 2.94/0.86 % (548856)Instructions burned: 24 (million)
% 2.94/0.86 % (548860)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3799078056:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.94/0.86 % (548859)Instruction limit reached!
% 2.94/0.86 % (548859)------------------------------
% 2.94/0.86 % (548859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.86 % (548859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.86 % (548859)CaDiCaL version: 2.1.3
% 2.94/0.86 % (548859)Termination reason: Instruction limit
% 2.94/0.86 % (548859)Termination phase: Saturation
% 2.94/0.86 % (548859)Time elapsed: 0.019 s
% 2.94/0.86 % (548859)Peak memory usage: 12 MB
% 2.94/0.86 % (548859)Instructions burned: 20 (million)
% 2.94/0.86 % (548863)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=718856515:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.94/0.86 % (548865)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=689006865:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.94/0.86 % (548866)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1036813005:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.94/0.86 % (548868)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.94/0.86 % (548865)Refutation not found, incomplete strategy
% 2.94/0.86 % (548865)------------------------------
% 2.94/0.86 % (548865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.86 % (548865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.86 % (548865)CaDiCaL version: 2.1.3
% 2.94/0.86 % (548865)Termination reason: Refutation not found, incomplete strategy
% 2.94/0.86 % (548865)Time elapsed: 0.010 s
% 2.94/0.86 % (548865)Peak memory usage: 12 MB
% 2.94/0.86 % (548865)Instructions burned: 10 (million)
% 2.94/0.86 % (548865)------------------------------
% 2.94/0.86 % (548865)------------------------------
% 2.94/0.86 % (548868)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1688055738:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 2.94/0.86 % (548868)Instruction limit reached!
% 2.94/0.86 % (548868)------------------------------
% 2.94/0.86 % (548868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.94/0.86 % (548868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/0.86 % (548868)CaDiCaL version: 2.1.3
% 2.94/0.86 % (548868)Termination reason: Instruction limit
% 2.94/0.86 % (548868)Termination phase: Property scanning
% 2.94/0.86 % (548868)Time elapsed: 0.006 s
% 2.94/0.86 % (548868)Peak memory usage: 10 MB
% 2.94/0.86 % (548868)Instructions burned: 8 (million)
% 2.94/0.86 % (548866)Instruction limit reached!
% 2.94/0.86 % (548866)------------------------------
% 2.94/0.86 % (548866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/1.01 % (548866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.01 % (548866)CaDiCaL version: 2.1.3
% 3.24/1.01 % (548866)Termination reason: Instruction limit
% 3.24/1.01 % (548866)Termination phase: Saturation
% 3.24/1.01 % (548866)Time elapsed: 0.033 s
% 3.24/1.01 % (548866)Peak memory usage: 11 MB
% 3.24/1.01 % (548866)Instructions burned: 42 (million)
% 3.24/1.01 % (548872)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3681504074:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 3.24/1.01 % (548872)Refutation not found, incomplete strategy
% 3.24/1.01 % (548872)------------------------------
% 3.24/1.01 % (548872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/1.01 % (548872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.01 % (548872)CaDiCaL version: 2.1.3
% 3.24/1.01 % (548872)Termination reason: Refutation not found, incomplete strategy
% 3.24/1.01 % (548872)Time elapsed: 0.006 s
% 3.24/1.01 % (548872)Peak memory usage: 12 MB
% 3.24/1.01 % (548872)Instructions burned: 6 (million)
% 3.24/1.01 % (548872)------------------------------
% 3.24/1.01 % (548872)------------------------------
% 3.24/1.01 % (548874)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=2650394706: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)
% 3.24/1.01 % (548875)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.24/1.01 % (548875)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=21502244:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 3.24/1.01 % (548874)Refutation not found, incomplete strategy
% 3.24/1.01 % (548874)------------------------------
% 3.24/1.01 % (548874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/1.01 % (548874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.01 % (548874)CaDiCaL version: 2.1.3
% 3.24/1.01 % (548874)Termination reason: Refutation not found, incomplete strategy
% 3.24/1.01 % (548874)Time elapsed: 0.016 s
% 3.24/1.01 % (548874)Peak memory usage: 12 MB
% 3.24/1.01 % (548874)Instructions burned: 20 (million)
% 3.24/1.01 % (548874)------------------------------
% 3.24/1.01 % (548874)------------------------------
% 3.24/1.01 % (548875)Instruction limit reached!
% 3.24/1.01 % (548875)------------------------------
% 3.24/1.01 % (548875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/1.01 % (548875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.01 % (548875)CaDiCaL version: 2.1.3
% 3.24/1.01 % (548875)Termination reason: Instruction limit
% 3.24/1.01 % (548875)Termination phase: Property scanning
% 3.24/1.01 % (548875)Time elapsed: 0.005 s
% 3.24/1.01 % (548875)Peak memory usage: 10 MB
% 3.24/1.01 % (548875)Instructions burned: 6 (million)
% 3.24/1.01 % (548878)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3837765565:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 3.24/1.01 % (548804)Instruction limit reached!
% 3.24/1.01 % (548804)------------------------------
% 3.24/1.01 % (548804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/1.01 % (548804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.01 % (548804)CaDiCaL version: 2.1.3
% 3.24/1.01 % (548804)Termination reason: Instruction limit
% 3.24/1.01 % (548804)Termination phase: Saturation
% 3.24/1.01 % (548804)Time elapsed: 0.373 s
% 3.24/1.01 % (548804)Peak memory usage: 12 MB
% 3.24/1.01 % (548804)Instructions burned: 635 (million)
% 3.24/1.01 % (548863)Instruction limit reached!
% 3.24/1.01 % (548863)------------------------------
% 3.24/1.01 % (548863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.24/1.01 % (548863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.01 % (548863)CaDiCaL version: 2.1.3
% 3.24/1.01 % (548863)Termination reason: Instruction limit
% 3.24/1.01 % (548863)Termination phase: Saturation
% 3.24/1.01 % (548863)Time elapsed: 0.116 s
% 3.24/1.01 % (548863)Peak memory usage: 13 MB
% 3.24/1.01 % (548863)Instructions burned: 144 (million)
% 3.24/1.01 % (548878)Instruction limit reached!
% 3.24/1.01 % (548878)------------------------------
% 4.95/1.12 % (548878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.95/1.12 % (548878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.12 % (548878)CaDiCaL version: 2.1.3
% 4.95/1.12 % (548878)Termination reason: Instruction limit
% 4.95/1.12 % (548878)Termination phase: Saturation
% 4.95/1.12 % (548878)Time elapsed: 0.018 s
% 4.95/1.12 % (548878)Peak memory usage: 12 MB
% 4.95/1.12 % (548878)Instructions burned: 23 (million)
% 4.95/1.12 % (548880)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3180229855:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 4.95/1.12 % (548881)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=4253096548:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 4.95/1.12 % (548880)Instruction limit reached!
% 4.95/1.12 % (548880)------------------------------
% 4.95/1.12 % (548880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.95/1.12 % (548880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.12 % (548880)CaDiCaL version: 2.1.3
% 4.95/1.12 % (548880)Termination reason: Instruction limit
% 4.95/1.12 % (548880)Termination phase: Saturation
% 4.95/1.12 % (548880)Time elapsed: 0.015 s
% 4.95/1.12 % (548880)Peak memory usage: 12 MB
% 4.95/1.12 % (548880)Instructions burned: 20 (million)
% 4.95/1.12 % (548835)Instruction limit reached!
% 4.95/1.12 % (548835)------------------------------
% 4.95/1.12 % (548835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.95/1.12 % (548835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.12 % (548835)CaDiCaL version: 2.1.3
% 4.95/1.12 % (548835)Termination reason: Instruction limit
% 4.95/1.12 % (548835)Termination phase: Saturation
% 4.95/1.12 % (548835)Time elapsed: 0.268 s
% 4.95/1.12 % (548835)Peak memory usage: 14 MB
% 4.95/1.12 % (548835)Instructions burned: 327 (million)
% 4.95/1.12 % (548883)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=4215142551:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 4.95/1.12 % (548884)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=353191960:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 4.95/1.12 % (548887)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1066483818:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 4.95/1.12 % (548887)Refutation not found, incomplete strategy
% 4.95/1.12 % (548887)------------------------------
% 4.95/1.12 % (548887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.95/1.12 % (548887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.12 % (548887)CaDiCaL version: 2.1.3
% 4.95/1.12 % (548887)Termination reason: Refutation not found, incomplete strategy
% 4.95/1.12 % (548887)Time elapsed: 0.008 s
% 4.95/1.12 % (548887)Peak memory usage: 12 MB
% 4.95/1.12 % (548887)Instructions burned: 8 (million)
% 4.95/1.12 % (548887)------------------------------
% 4.95/1.12 % (548887)------------------------------
% 4.95/1.12 % (548890)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 4.95/1.12 % (548888)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=669715469: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)
% 4.95/1.12 % (548890)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2221233141:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 4.95/1.12 % (548884)Instruction limit reached!
% 4.95/1.12 % (548884)------------------------------
% 4.95/1.12 % (548884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.95/1.12 % (548884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.95/1.12 % (548884)CaDiCaL version: 2.1.3
% 4.95/1.12 % (548884)Termination reason: Instruction limit
% 4.95/1.12 % (548884)Termination phase: Saturation
% 5.77/1.21 % (548884)Time elapsed: 0.035 s
% 5.77/1.21 % (548884)Peak memory usage: 12 MB
% 5.77/1.21 % (548884)Instructions burned: 45 (million)
% 5.77/1.21 % (548888)Instruction limit reached!
% 5.77/1.21 % (548888)------------------------------
% 5.77/1.21 % (548888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.21 % (548888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.21 % (548888)CaDiCaL version: 2.1.3
% 5.77/1.21 % (548888)Termination reason: Instruction limit
% 5.77/1.21 % (548888)Termination phase: Saturation
% 5.77/1.21 % (548888)Time elapsed: 0.018 s
% 5.77/1.21 % (548888)Peak memory usage: 11 MB
% 5.77/1.21 % (548888)Instructions burned: 22 (million)
% 5.77/1.21 % (548893)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2028089719:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 5.77/1.21 % (548893)Instruction limit reached!
% 5.77/1.21 % (548893)------------------------------
% 5.77/1.21 % (548893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.21 % (548893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.21 % (548893)CaDiCaL version: 2.1.3
% 5.77/1.21 % (548893)Termination reason: Instruction limit
% 5.77/1.21 % (548893)Termination phase: Saturation
% 5.77/1.21 % (548893)Time elapsed: 0.013 s
% 5.77/1.21 % (548893)Peak memory usage: 12 MB
% 5.77/1.21 % (548893)Instructions burned: 13 (million)
% 5.77/1.21 % (548896)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=2884748304:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 5.77/1.21 % (548897)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1003760057:i=51:fsr=off:rtra=on_2994 on theBenchmark for (2994ds/51Mi)
% 5.77/1.21 % (548899)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=4286120359:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/31Mi)
% 5.77/1.21 % (548899)Instruction limit reached!
% 5.77/1.21 % (548899)------------------------------
% 5.77/1.21 % (548899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.21 % (548899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.21 % (548899)CaDiCaL version: 2.1.3
% 5.77/1.21 % (548899)Termination reason: Instruction limit
% 5.77/1.21 % (548899)Termination phase: Saturation
% 5.77/1.21 % (548899)Time elapsed: 0.025 s
% 5.77/1.21 % (548899)Peak memory usage: 12 MB
% 5.77/1.21 % (548899)Instructions burned: 32 (million)
% 5.77/1.21 % (548897)Instruction limit reached!
% 5.77/1.21 % (548897)------------------------------
% 5.77/1.21 % (548897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.21 % (548897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.21 % (548897)CaDiCaL version: 2.1.3
% 5.77/1.21 % (548897)Termination reason: Instruction limit
% 5.77/1.21 % (548897)Termination phase: Saturation
% 5.77/1.21 % (548897)Time elapsed: 0.044 s
% 5.77/1.21 % (548897)Peak memory usage: 12 MB
% 5.77/1.21 % (548897)Instructions burned: 52 (million)
% 5.77/1.21 % (548896)Instruction limit reached!
% 5.77/1.21 % (548896)------------------------------
% 5.77/1.21 % (548896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.77/1.21 % (548896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.21 % (548896)CaDiCaL version: 2.1.3
% 5.77/1.21 % (548896)Termination reason: Instruction limit
% 5.77/1.21 % (548896)Termination phase: Saturation
% 5.77/1.21 % (548896)Time elapsed: 0.051 s
% 5.77/1.21 % (548896)Peak memory usage: 12 MB
% 5.77/1.21 % (548896)Instructions burned: 66 (million)
% 5.77/1.21 % (548903)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3006140109:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2994 on theBenchmark for (2994ds/137Mi)
% 5.77/1.21 % (548905)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3241062094:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2994 on theBenchmark for (2994ds/67Mi)
% 5.77/1.21 % (548904)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=3722473887:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 5.77/1.21 % (548890)Instruction limit reached!
% 5.77/1.21 % (548890)------------------------------
% 5.77/1.21 % (548890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.19/1.37 % (548890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.19/1.37 % (548890)CaDiCaL version: 2.1.3
% 6.19/1.37 % (548890)Termination reason: Instruction limit
% 6.19/1.37 % (548890)Termination phase: Saturation
% 6.19/1.37 % (548890)Time elapsed: 0.157 s
% 6.19/1.37 % (548890)Peak memory usage: 12 MB
% 6.19/1.37 % (548890)Instructions burned: 201 (million)
% 6.19/1.37 % (548904)Instruction limit reached!
% 6.19/1.37 % (548904)------------------------------
% 6.19/1.37 % (548904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.19/1.37 % (548904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.19/1.37 % (548904)CaDiCaL version: 2.1.3
% 6.19/1.37 % (548904)Termination reason: Instruction limit
% 6.19/1.37 % (548904)Termination phase: Saturation
% 6.19/1.37 % (548904)Time elapsed: 0.036 s
% 6.19/1.37 % (548904)Peak memory usage: 12 MB
% 6.19/1.37 % (548904)Instructions burned: 34 (million)
% 6.19/1.37 % (548905)Instruction limit reached!
% 6.19/1.37 % (548905)------------------------------
% 6.19/1.37 % (548905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.19/1.37 % (548905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.19/1.37 % (548905)CaDiCaL version: 2.1.3
% 6.19/1.37 % (548905)Termination reason: Instruction limit
% 6.19/1.37 % (548905)Termination phase: Saturation
% 6.19/1.37 % (548905)Time elapsed: 0.054 s
% 6.19/1.37 % (548905)Peak memory usage: 12 MB
% 6.19/1.37 % (548905)Instructions burned: 68 (million)
% 6.19/1.37 % (548909)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 6.19/1.37 % (548909)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1459839918:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2993 on theBenchmark for (2993ds/180Mi)
% 6.19/1.37 % (548911)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3717597919:cond=on:i=96:bd=all:rtra=on_2993 on theBenchmark for (2993ds/96Mi)
% 6.19/1.37 % (548910)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1275002394:st=2:i=246:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/246Mi)
% 6.19/1.37 % (548881)Instruction limit reached!
% 6.19/1.37 % (548881)------------------------------
% 6.19/1.37 % (548881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.19/1.37 % (548881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.19/1.37 % (548881)CaDiCaL version: 2.1.3
% 6.19/1.37 % (548881)Termination reason: Instruction limit
% 6.19/1.37 % (548881)Termination phase: Saturation
% 6.19/1.37 % (548881)Time elapsed: 0.278 s
% 6.19/1.37 % (548881)Peak memory usage: 15 MB
% 6.19/1.37 % (548881)Instructions burned: 316 (million)
% 6.19/1.37 % (548910)Refutation not found, incomplete strategy
% 6.19/1.37 % (548910)------------------------------
% 6.19/1.37 % (548910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.19/1.37 % (548910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.19/1.37 % (548910)CaDiCaL version: 2.1.3
% 6.19/1.37 % (548910)Termination reason: Refutation not found, incomplete strategy
% 6.19/1.37 % (548910)Time elapsed: 0.014 s
% 6.19/1.37 % (548910)Peak memory usage: 12 MB
% 6.19/1.37 % (548910)Instructions burned: 14 (million)
% 6.19/1.37 % (548910)------------------------------
% 6.19/1.37 % (548910)------------------------------
% 6.19/1.37 % (548903)Instruction limit reached!
% 6.19/1.37 % (548903)------------------------------
% 6.19/1.37 % (548903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.19/1.37 % (548903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.19/1.37 % (548903)CaDiCaL version: 2.1.3
% 6.19/1.37 % (548903)Termination reason: Instruction limit
% 6.19/1.37 % (548903)Termination phase: Saturation
% 6.19/1.37 % (548903)Time elapsed: 0.121 s
% 6.19/1.37 % (548903)Peak memory usage: 13 MB
% 6.19/1.37 % (548903)Instructions burned: 138 (million)
% 6.19/1.37 % (548915)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=4201067236:i=427:sd=1:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/427Mi)
% 6.19/1.37 % (548915)Refutation not found, incomplete strategy
% 6.19/1.37 % (548915)------------------------------
% 6.19/1.37 % (548915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.19/1.37 % (548915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.24/1.61 % (548915)CaDiCaL version: 2.1.3
% 7.24/1.61 % (548915)Termination reason: Refutation not found, incomplete strategy
% 7.24/1.61 % (548915)Time elapsed: 0.006 s
% 7.24/1.61 % (548915)Peak memory usage: 12 MB
% 7.24/1.61 % (548915)Instructions burned: 6 (million)
% 7.24/1.61 % (548915)------------------------------
% 7.24/1.61 % (548915)------------------------------
% 7.24/1.61 % (548916)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1218557245:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/874Mi)
% 7.24/1.61 % (548917)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3104986979:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/515Mi)
% 7.24/1.61 % (548911)Instruction limit reached!
% 7.24/1.61 % (548911)------------------------------
% 7.24/1.61 % (548911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.24/1.61 % (548911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.24/1.61 % (548911)CaDiCaL version: 2.1.3
% 7.24/1.61 % (548911)Termination reason: Instruction limit
% 7.24/1.61 % (548911)Termination phase: Saturation
% 7.24/1.61 % (548911)Time elapsed: 0.078 s
% 7.24/1.61 % (548911)Peak memory usage: 12 MB
% 7.24/1.61 % (548911)Instructions burned: 96 (million)
% 7.24/1.61 % (548917)Refutation not found, incomplete strategy
% 7.24/1.61 % (548917)------------------------------
% 7.24/1.61 % (548917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.24/1.61 % (548917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.24/1.61 % (548917)CaDiCaL version: 2.1.3
% 7.24/1.61 % (548917)Termination reason: Refutation not found, incomplete strategy
% 7.24/1.61 % (548917)Time elapsed: 0.020 s
% 7.24/1.61 % (548917)Peak memory usage: 13 MB
% 7.24/1.61 % (548917)Instructions burned: 24 (million)
% 7.24/1.61 % (548917)------------------------------
% 7.24/1.61 % (548917)------------------------------
% 7.24/1.61 % (548919)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1728060672:st=1.5:i=130:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/130Mi)
% 7.24/1.61 % (548919)Refutation not found, incomplete strategy
% 7.24/1.61 % (548919)------------------------------
% 7.24/1.61 % (548919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.24/1.61 % (548919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.24/1.61 % (548919)CaDiCaL version: 2.1.3
% 7.24/1.61 % (548919)Termination reason: Refutation not found, incomplete strategy
% 7.24/1.61 % (548919)Time elapsed: 0.025 s
% 7.24/1.61 % (548919)Peak memory usage: 12 MB
% 7.24/1.61 % (548919)Instructions burned: 29 (million)
% 7.24/1.61 % (548922)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3768793306:i=44:ep=R:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/44Mi)
% 7.24/1.61 % (548919)------------------------------
% 7.24/1.61 % (548919)------------------------------
% 7.24/1.61 % (548909)Instruction limit reached!
% 7.24/1.61 % (548909)------------------------------
% 7.24/1.61 % (548909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.24/1.61 % (548909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.24/1.61 % (548909)CaDiCaL version: 2.1.3
% 7.24/1.61 % (548909)Termination reason: Instruction limit
% 7.24/1.61 % (548909)Termination phase: Saturation
% 7.24/1.61 % (548909)Time elapsed: 0.137 s
% 7.24/1.61 % (548909)Peak memory usage: 12 MB
% 7.24/1.61 % (548909)Instructions burned: 180 (million)
% 7.24/1.61 % (548923)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4171810659:s2a=on:i=571:nm=16:rtra=on_2992 on theBenchmark for (2992ds/571Mi)
% 7.24/1.61 % (548923)Refutation not found, incomplete strategy
% 7.24/1.61 % (548923)------------------------------
% 7.24/1.61 % (548923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.24/1.61 % (548923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.24/1.61 % (548923)CaDiCaL version: 2.1.3
% 7.24/1.61 % (548923)Termination reason: Refutation not found, incomplete strategy
% 7.24/1.61 % (548923)Time elapsed: 0.008 s
% 7.24/1.61 % (548923)Peak memory usage: 12 MB
% 7.24/1.61 % (548923)Instructions burned: 9 (million)
% 7.24/1.61 % (548923)------------------------------
% 7.24/1.61 % (548923)------------------------------
% 7.24/1.61 % (548927)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1403776532:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/95Mi)
% 8.33/1.82 % (548926)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=4221262942:i=450:rtra=on:ixr=off:ntd=on_2991 on theBenchmark for (2991ds/450Mi)
% 8.33/1.82 % (548922)Instruction limit reached!
% 8.33/1.82 % (548922)------------------------------
% 8.33/1.82 % (548922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.33/1.82 % (548922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.33/1.82 % (548922)CaDiCaL version: 2.1.3
% 8.33/1.82 % (548922)Termination reason: Instruction limit
% 8.33/1.82 % (548922)Termination phase: Saturation
% 8.33/1.82 % (548922)Time elapsed: 0.036 s
% 8.33/1.82 % (548922)Peak memory usage: 12 MB
% 8.33/1.82 % (548922)Instructions burned: 44 (million)
% 8.33/1.82 % (548860)Instruction limit reached!
% 8.33/1.82 % (548860)------------------------------
% 8.33/1.82 % (548860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.33/1.82 % (548860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.33/1.82 % (548860)CaDiCaL version: 2.1.3
% 8.33/1.82 % (548860)Termination reason: Instruction limit
% 8.33/1.82 % (548860)Termination phase: Saturation
% 8.33/1.82 % (548860)Time elapsed: 0.554 s
% 8.33/1.82 % (548860)Peak memory usage: 14 MB
% 8.33/1.82 % (548860)Instructions burned: 1242 (million)
% 8.33/1.82 % (548929)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=2145651987:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2991 on theBenchmark for (2991ds/65Mi)
% 8.33/1.82 % (548933)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=816267333: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)
% 8.33/1.82 % (548932)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=616658804: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_2991 on theBenchmark for (2991ds/105Mi)
% 8.33/1.82 % (548929)Instruction limit reached!
% 8.33/1.82 % (548929)------------------------------
% 8.33/1.82 % (548929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.33/1.82 % (548929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.33/1.82 % (548929)CaDiCaL version: 2.1.3
% 8.33/1.82 % (548929)Termination reason: Instruction limit
% 8.33/1.82 % (548929)Termination phase: Saturation
% 8.33/1.82 % (548929)Time elapsed: 0.055 s
% 8.33/1.82 % (548929)Peak memory usage: 13 MB
% 8.33/1.82 % (548929)Instructions burned: 65 (million)
% 8.33/1.82 % (548927)Instruction limit reached!
% 8.33/1.82 % (548927)------------------------------
% 8.33/1.82 % (548927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.33/1.82 % (548927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.33/1.82 % (548927)CaDiCaL version: 2.1.3
% 8.33/1.82 % (548927)Termination reason: Instruction limit
% 8.33/1.82 % (548927)Termination phase: Saturation
% 8.33/1.82 % (548927)Time elapsed: 0.077 s
% 8.33/1.82 % (548927)Peak memory usage: 12 MB
% 8.33/1.82 % (548927)Instructions burned: 95 (million)
% 8.33/1.82 % (548938)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1336585361:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/495Mi)
% 8.33/1.82 % (548937)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3295145334:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/375Mi)
% 8.33/1.82 % (548932)Instruction limit reached!
% 8.33/1.82 % (548932)------------------------------
% 8.33/1.82 % (548932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.33/1.82 % (548932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.33/1.82 % (548932)CaDiCaL version: 2.1.3
% 8.33/1.82 % (548932)Termination reason: Instruction limit
% 8.33/1.82 % (548932)Termination phase: Saturation
% 8.33/1.82 % (548932)Time elapsed: 0.087 s
% 8.33/1.82 % (548932)Peak memory usage: 12 MB
% 8.33/1.82 % (548932)Instructions burned: 106 (million)
% 8.33/1.82 % (548941)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=1109642902:cond=on:i=34:hud=10:nm=10:rtra=on_2990 on theBenchmark for (2990ds/34Mi)
% 9.21/1.96 % (548941)Instruction limit reached!
% 9.21/1.96 % (548941)------------------------------
% 9.21/1.96 % (548941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.21/1.96 % (548941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.21/1.96 % (548941)CaDiCaL version: 2.1.3
% 9.21/1.96 % (548941)Termination reason: Instruction limit
% 9.21/1.96 % (548941)Termination phase: Saturation
% 9.21/1.96 % (548941)Time elapsed: 0.030 s
% 9.21/1.96 % (548941)Peak memory usage: 12 MB
% 9.21/1.96 % (548941)Instructions burned: 37 (million)
% 9.21/1.96 % (548943)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=3597104523:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2989 on theBenchmark for (2989ds/91Mi)
% 9.21/1.96 % (548943)Instruction limit reached!
% 9.21/1.96 % (548943)------------------------------
% 9.21/1.96 % (548943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.21/1.96 % (548943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.21/1.96 % (548943)CaDiCaL version: 2.1.3
% 9.21/1.96 % (548943)Termination reason: Instruction limit
% 9.21/1.96 % (548943)Termination phase: Saturation
% 9.21/1.96 % (548943)Time elapsed: 0.082 s
% 9.21/1.96 % (548943)Peak memory usage: 13 MB
% 9.21/1.96 % (548943)Instructions burned: 92 (million)
% 9.21/1.96 % (548883)Instruction limit reached!
% 9.21/1.96 % (548883)------------------------------
% 9.21/1.96 % (548883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.21/1.96 % (548883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.21/1.96 % (548883)CaDiCaL version: 2.1.3
% 9.21/1.96 % (548883)Termination reason: Instruction limit
% 9.21/1.96 % (548883)Termination phase: Saturation
% 9.21/1.96 % (548883)Time elapsed: 0.701 s
% 9.21/1.96 % (548883)Peak memory usage: 14 MB
% 9.21/1.96 % (548883)Instructions burned: 854 (million)
% 9.21/1.96 % (548945)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3980347350:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2988 on theBenchmark for (2988ds/66Mi)
% 9.21/1.96 % (548946)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=125743122:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2988 on theBenchmark for (2988ds/22Mi)
% 9.21/1.96 % (548945)Refutation not found, incomplete strategy
% 9.21/1.96 % (548945)------------------------------
% 9.21/1.96 % (548945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.21/1.96 % (548945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.21/1.96 % (548945)CaDiCaL version: 2.1.3
% 9.21/1.96 % (548945)Termination reason: Refutation not found, incomplete strategy
% 9.21/1.96 % (548945)Time elapsed: 0.006 s
% 9.21/1.96 % (548945)Peak memory usage: 12 MB
% 9.21/1.96 % (548945)Instructions burned: 6 (million)
% 9.21/1.96 % (548945)------------------------------
% 9.21/1.96 % (548945)------------------------------
% 9.21/1.96 % (548946)Instruction limit reached!
% 9.21/1.96 % (548946)------------------------------
% 9.21/1.96 % (548946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.21/1.96 % (548946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.21/1.96 % (548946)CaDiCaL version: 2.1.3
% 9.21/1.96 % (548946)Termination reason: Instruction limit
% 9.21/1.96 % (548946)Termination phase: Saturation
% 9.21/1.96 % (548946)Time elapsed: 0.017 s
% 9.21/1.96 % (548946)Peak memory usage: 12 MB
% 9.21/1.96 % (548946)Instructions burned: 22 (million)
% 9.21/1.96 % (548926)Instruction limit reached!
% 9.21/1.96 % (548926)------------------------------
% 9.21/1.96 % (548926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.21/1.96 % (548926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.21/1.96 % (548926)CaDiCaL version: 2.1.3
% 9.21/1.96 % (548926)Termination reason: Instruction limit
% 9.21/1.96 % (548926)Termination phase: Saturation
% 9.21/1.96 % (548926)Time elapsed: 0.375 s
% 9.21/1.96 % (548926)Peak memory usage: 16 MB
% 9.21/1.96 % (548926)Instructions burned: 450 (million)
% 9.21/1.96 % (548949)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=784961367:i=338:bd=all:ins=4:rtra=on_2988 on theBenchmark for (2988ds/338Mi)
% 9.21/1.96 % (548950)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3237236050:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/28Mi)
% 11.89/2.11 % (548952)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 11.89/2.11 % (548950)Instruction limit reached!
% 11.89/2.11 % (548950)------------------------------
% 11.89/2.11 % (548950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.89/2.11 % (548950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.89/2.11 % (548950)CaDiCaL version: 2.1.3
% 11.89/2.11 % (548950)Termination reason: Instruction limit
% 11.89/2.11 % (548950)Termination phase: Saturation
% 11.89/2.11 % (548950)Time elapsed: 0.021 s
% 11.89/2.11 % (548950)Peak memory usage: 12 MB
% 11.89/2.11 % (548950)Instructions burned: 28 (million)
% 11.89/2.11 % (548952)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2173205347:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2987 on theBenchmark for (2987ds/137Mi)
% 11.89/2.11 % (548954)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=42546924:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2987 on theBenchmark for (2987ds/340Mi)
% 11.89/2.11 % (548937)Instruction limit reached!
% 11.89/2.11 % (548937)------------------------------
% 11.89/2.11 % (548937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.89/2.11 % (548937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.89/2.11 % (548937)CaDiCaL version: 2.1.3
% 11.89/2.11 % (548937)Termination reason: Instruction limit
% 11.89/2.11 % (548937)Termination phase: Saturation
% 11.89/2.11 % (548937)Time elapsed: 0.344 s
% 11.89/2.11 % (548937)Peak memory usage: 13 MB
% 11.89/2.11 % (548937)Instructions burned: 376 (million)
% 11.89/2.11 % (548957)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=2697742485:i=227:sd=1:bd=all:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/227Mi)
% 11.89/2.11 % (548957)Refutation not found, incomplete strategy
% 11.89/2.11 % (548957)------------------------------
% 11.89/2.11 % (548957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.89/2.11 % (548957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.89/2.11 % (548957)CaDiCaL version: 2.1.3
% 11.89/2.11 % (548957)Termination reason: Refutation not found, incomplete strategy
% 11.89/2.11 % (548957)Time elapsed: 0.006 s
% 11.89/2.11 % (548957)Peak memory usage: 12 MB
% 11.89/2.11 % (548957)Instructions burned: 6 (million)
% 11.89/2.11 % (548957)------------------------------
% 11.89/2.11 % (548957)------------------------------
% 11.89/2.11 % (548959)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 11.89/2.11 % (548959)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2640604270:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/373Mi)
% 11.89/2.11 % (548938)Instruction limit reached!
% 11.89/2.11 % (548938)------------------------------
% 11.89/2.11 % (548938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.89/2.11 % (548938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.89/2.11 % (548938)CaDiCaL version: 2.1.3
% 11.89/2.11 % (548938)Termination reason: Instruction limit
% 11.89/2.11 % (548938)Termination phase: Saturation
% 11.89/2.11 % (548938)Time elapsed: 0.422 s
% 11.89/2.11 % (548938)Peak memory usage: 14 MB
% 11.89/2.11 % (548938)Instructions burned: 495 (million)
% 11.89/2.11 % (548952)Instruction limit reached!
% 11.89/2.11 % (548952)------------------------------
% 11.89/2.11 % (548952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 11.89/2.11 % (548952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.89/2.11 % (548952)CaDiCaL version: 2.1.3
% 11.89/2.11 % (548952)Termination reason: Instruction limit
% 11.89/2.11 % (548952)Termination phase: Saturation
% 11.89/2.11 % (548952)Time elapsed: 0.117 s
% 11.89/2.11 % (548952)Peak memory usage: 12 MB
% 11.89/2.11 % (548952)Instructions burned: 137 (million)
% 11.89/2.11 % (548961)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3502810300:i=116:ep=RSTC:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/116Mi)
% 11.89/2.11 % (548962)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3521100778:i=575:rtra=on_2986 on theBenchmark for (2986ds/575Mi)
% 11.89/2.11 % (548916)Instruction limit reached!
% 13.85/2.42 % (548916)------------------------------
% 13.85/2.42 % (548916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.42 % (548916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.42 % (548916)CaDiCaL version: 2.1.3
% 13.85/2.42 % (548916)Termination reason: Instruction limit
% 13.85/2.42 % (548916)Termination phase: Saturation
% 13.85/2.42 % (548916)Time elapsed: 0.694 s
% 13.85/2.42 % (548916)Peak memory usage: 16 MB
% 13.85/2.42 % (548916)Instructions burned: 874 (million)
% 13.85/2.42 % (548965)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3012602530:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2985 on theBenchmark for (2985ds/270Mi)
% 13.85/2.42 % (548961)Instruction limit reached!
% 13.85/2.42 % (548961)------------------------------
% 13.85/2.42 % (548961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.42 % (548961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.42 % (548961)CaDiCaL version: 2.1.3
% 13.85/2.42 % (548961)Termination reason: Instruction limit
% 13.85/2.42 % (548961)Termination phase: Saturation
% 13.85/2.42 % (548961)Time elapsed: 0.098 s
% 13.85/2.42 % (548961)Peak memory usage: 13 MB
% 13.85/2.42 % (548961)Instructions burned: 117 (million)
% 13.85/2.42 % (548949)Instruction limit reached!
% 13.85/2.42 % (548949)------------------------------
% 13.85/2.42 % (548949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.42 % (548949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.42 % (548949)CaDiCaL version: 2.1.3
% 13.85/2.42 % (548949)Termination reason: Instruction limit
% 13.85/2.42 % (548949)Termination phase: Saturation
% 13.85/2.42 % (548949)Time elapsed: 0.313 s
% 13.85/2.42 % (548949)Peak memory usage: 16 MB
% 13.85/2.42 % (548949)Instructions burned: 339 (million)
% 13.85/2.42 % (548954)Instruction limit reached!
% 13.85/2.42 % (548954)------------------------------
% 13.85/2.42 % (548954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.42 % (548967)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=1457041481: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_2984 on theBenchmark for (2984ds/9840Mi)
% 13.85/2.42 % (548954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.42 % (548954)CaDiCaL version: 2.1.3
% 13.85/2.42 % (548954)Termination reason: Instruction limit
% 13.85/2.42 % (548954)Termination phase: Saturation
% 13.85/2.42 % (548954)Time elapsed: 0.251 s
% 13.85/2.42 % (548954)Peak memory usage: 13 MB
% 13.85/2.42 % (548954)Instructions burned: 340 (million)
% 13.85/2.42 % (548970)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
% 13.85/2.42 % (548968)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=3048445727:i=421:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/421Mi)
% 13.85/2.42 % (548970)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=2835674863:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/270Mi)
% 13.85/2.42 % (548968)Refutation not found, incomplete strategy
% 13.85/2.42 % (548968)------------------------------
% 13.85/2.42 % (548968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.42 % (548968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.42 % (548968)CaDiCaL version: 2.1.3
% 13.85/2.42 % (548968)Termination reason: Refutation not found, incomplete strategy
% 13.85/2.42 % (548968)Time elapsed: 0.007 s
% 13.85/2.42 % (548968)Peak memory usage: 12 MB
% 13.85/2.42 % (548968)Instructions burned: 6 (million)
% 13.85/2.42 % (548968)------------------------------
% 13.85/2.42 % (548968)------------------------------
% 13.85/2.42 % (548970)Refutation not found, incomplete strategy
% 13.85/2.42 % (548970)------------------------------
% 13.85/2.42 % (548970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.85/2.42 % (548970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.85/2.42 % (548970)CaDiCaL version: 2.1.3
% 13.85/2.42 % (548970)Termination reason: Refutation not found, incomplete strategy
% 15.47/2.78 % (548970)Time elapsed: 0.020 s
% 15.47/2.78 % (548970)Peak memory usage: 12 MB
% 15.47/2.78 % (548970)Instructions burned: 26 (million)
% 15.47/2.78 % (548970)------------------------------
% 15.47/2.78 % (548970)------------------------------
% 15.47/2.78 % (548973)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=976595598:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/31Mi)
% 15.47/2.78 % (548974)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 15.47/2.78 % (548974)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
% 15.47/2.78 % (548974)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=2777582397:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2984 on theBenchmark for (2984ds/1440Mi)
% 15.47/2.78 % (548973)Instruction limit reached!
% 15.47/2.78 % (548973)------------------------------
% 15.47/2.78 % (548973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.47/2.78 % (548973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.47/2.78 % (548973)CaDiCaL version: 2.1.3
% 15.47/2.78 % (548973)Termination reason: Instruction limit
% 15.47/2.78 % (548973)Termination phase: Saturation
% 15.47/2.78 % (548973)Time elapsed: 0.026 s
% 15.47/2.78 % (548973)Peak memory usage: 12 MB
% 15.47/2.78 % (548973)Instructions burned: 32 (million)
% 15.47/2.78 % (548959)Instruction limit reached!
% 15.47/2.78 % (548959)------------------------------
% 15.47/2.78 % (548959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.47/2.78 % (548959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.47/2.78 % (548959)CaDiCaL version: 2.1.3
% 15.47/2.78 % (548959)Termination reason: Instruction limit
% 15.47/2.78 % (548959)Termination phase: Saturation
% 15.47/2.78 % (548959)Time elapsed: 0.274 s
% 15.47/2.78 % (548959)Peak memory usage: 13 MB
% 15.47/2.78 % (548959)Instructions burned: 374 (million)
% 15.47/2.78 % (548977)dis+10_2_sil=128000:si=on:random_seed=3266979803:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2983 on theBenchmark for (2983ds/339Mi)
% 15.47/2.78 % (548978)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2108862031:i=111:add=on:fgj=on:rtra=on:fdi=1024_2983 on theBenchmark for (2983ds/111Mi)
% 15.47/2.78 % (548977)Refutation not found, incomplete strategy
% 15.47/2.78 % (548977)------------------------------
% 15.47/2.78 % (548977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.47/2.78 % (548977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.47/2.78 % (548977)CaDiCaL version: 2.1.3
% 15.47/2.78 % (548977)Termination reason: Refutation not found, incomplete strategy
% 15.47/2.78 % (548977)Time elapsed: 0.006 s
% 15.47/2.78 % (548977)Peak memory usage: 12 MB
% 15.47/2.78 % (548977)Instructions burned: 6 (million)
% 15.47/2.78 % (548977)------------------------------
% 15.47/2.78 % (548977)------------------------------
% 15.47/2.78 % (548965)Instruction limit reached!
% 15.47/2.78 % (548965)------------------------------
% 15.47/2.78 % (548965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.47/2.78 % (548965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.47/2.78 % (548965)CaDiCaL version: 2.1.3
% 15.47/2.78 % (548965)Termination reason: Instruction limit
% 15.47/2.78 % (548965)Termination phase: Saturation
% 15.47/2.78 % (548965)Time elapsed: 0.228 s
% 15.47/2.78 % (548965)Peak memory usage: 12 MB
% 15.47/2.78 % (548965)Instructions burned: 270 (million)
% 15.47/2.78 % (548981)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=2825517957:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2983 on theBenchmark for (2983ds/122Mi)
% 15.47/2.78 % (548981)Refutation not found, incomplete strategy
% 15.47/2.78 % (548981)------------------------------
% 15.47/2.78 % (548981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.47/2.78 % (548981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.47/2.78 % (548981)CaDiCaL version: 2.1.3
% 15.47/2.78 % (548981)Termination reason: Refutation not found, incomplete strategy
% 19.06/3.15 % (548981)Time elapsed: 0.016 s
% 19.06/3.15 % (548981)Peak memory usage: 12 MB
% 19.06/3.15 % (548981)Instructions burned: 20 (million)
% 19.06/3.15 % (548981)------------------------------
% 19.06/3.15 % (548981)------------------------------
% 19.06/3.15 % (548982)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=3404588601:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/136Mi)
% 19.06/3.15 % (548984)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2336144355:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2982 on theBenchmark for (2982ds/232Mi)
% 19.06/3.15 % (548978)Instruction limit reached!
% 19.06/3.15 % (548978)------------------------------
% 19.06/3.15 % (548978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.06/3.15 % (548978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.06/3.15 % (548978)CaDiCaL version: 2.1.3
% 19.06/3.15 % (548978)Termination reason: Instruction limit
% 19.06/3.15 % (548978)Termination phase: Saturation
% 19.06/3.15 % (548978)Time elapsed: 0.094 s
% 19.06/3.15 % (548978)Peak memory usage: 13 MB
% 19.06/3.15 % (548978)Instructions burned: 112 (million)
% 19.06/3.15 % (548987)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=620417069:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2982 on theBenchmark for (2982ds/1254Mi)
% 19.06/3.15 % (548982)Instruction limit reached!
% 19.06/3.15 % (548982)------------------------------
% 19.06/3.15 % (548982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.06/3.15 % (548982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.06/3.15 % (548982)CaDiCaL version: 2.1.3
% 19.06/3.15 % (548982)Termination reason: Instruction limit
% 19.06/3.15 % (548982)Termination phase: Saturation
% 19.06/3.15 % (548982)Time elapsed: 0.123 s
% 19.06/3.15 % (548982)Peak memory usage: 13 MB
% 19.06/3.15 % (548982)Instructions burned: 136 (million)
% 19.06/3.15 % (548962)Instruction limit reached!
% 19.06/3.15 % (548962)------------------------------
% 19.06/3.15 % (548962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.06/3.16 % (548962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.06/3.16 % (548962)CaDiCaL version: 2.1.3
% 19.06/3.16 % (548962)Termination reason: Instruction limit
% 19.06/3.16 % (548962)Termination phase: Saturation
% 19.06/3.16 % (548962)Time elapsed: 0.482 s
% 19.06/3.16 % (548962)Peak memory usage: 14 MB
% 19.06/3.16 % (548962)Instructions burned: 576 (million)
% 19.06/3.16 % (548989)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 19.06/3.16 % (548989)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=3091882002:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2981 on theBenchmark for (2981ds/281Mi)
% 19.06/3.16 % (548990)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2174898714:i=619:add=on:rtra=on_2980 on theBenchmark for (2980ds/619Mi)
% 19.06/3.16 % (548984)Instruction limit reached!
% 19.06/3.16 % (548984)------------------------------
% 19.06/3.16 % (548984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.06/3.16 % (548984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.06/3.16 % (548984)CaDiCaL version: 2.1.3
% 19.06/3.16 % (548984)Termination reason: Instruction limit
% 19.06/3.16 % (548984)Termination phase: Saturation
% 19.06/3.16 % (548984)Time elapsed: 0.195 s
% 19.06/3.16 % (548984)Peak memory usage: 13 MB
% 19.06/3.16 % (548984)Instructions burned: 233 (million)
% 19.06/3.16 % (548993)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=783302600:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/865Mi)
% 19.06/3.16 % (548990)Refutation not found, incomplete strategy
% 19.06/3.16 % (548990)------------------------------
% 19.06/3.16 % (548990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.06/3.16 % (548990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.06/3.16 % (548990)CaDiCaL version: 2.1.3
% 19.06/3.16 % (548990)Termination reason: Refutation not found, incomplete strategy
% 19.06/3.16 % (548990)Time elapsed: 0.115 s
% 20.44/3.43 % (548990)Peak memory usage: 13 MB
% 20.44/3.43 % (548990)Instructions burned: 136 (million)
% 20.44/3.43 % (548990)------------------------------
% 20.44/3.43 % (548990)------------------------------
% 20.44/3.43 % (548995)lrs+10_1_sil=128000:si=on:urr=on:random_seed=393671407:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2979 on theBenchmark for (2979ds/212Mi)
% 20.44/3.43 % (548989)Instruction limit reached!
% 20.44/3.43 % (548989)------------------------------
% 20.44/3.43 % (548989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.44/3.43 % (548989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.43 % (548989)CaDiCaL version: 2.1.3
% 20.44/3.43 % (548989)Termination reason: Instruction limit
% 20.44/3.43 % (548989)Termination phase: Saturation
% 20.44/3.43 % (548989)Time elapsed: 0.240 s
% 20.44/3.43 % (548989)Peak memory usage: 13 MB
% 20.44/3.43 % (548989)Instructions burned: 282 (million)
% 20.44/3.43 % (548997)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=125409467:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2978 on theBenchmark for (2978ds/130Mi)
% 20.44/3.43 % (548997)Refutation not found, incomplete strategy
% 20.44/3.43 % (548997)------------------------------
% 20.44/3.43 % (548997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.44/3.43 % (548997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.43 % (548997)CaDiCaL version: 2.1.3
% 20.44/3.43 % (548997)Termination reason: Refutation not found, incomplete strategy
% 20.44/3.43 % (548997)Time elapsed: 0.010 s
% 20.44/3.43 % (548997)Peak memory usage: 12 MB
% 20.44/3.43 % (548997)Instructions burned: 10 (million)
% 20.44/3.43 % (548997)------------------------------
% 20.44/3.43 % (548997)------------------------------
% 20.44/3.43 % (548999)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=34697870:st=1.5:i=346:rtra=on:ss=axioms_2977 on theBenchmark for (2977ds/346Mi)
% 20.44/3.43 % (548995)Instruction limit reached!
% 20.44/3.43 % (548995)------------------------------
% 20.44/3.43 % (548995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.44/3.43 % (548995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.43 % (548995)CaDiCaL version: 2.1.3
% 20.44/3.43 % (548995)Termination reason: Instruction limit
% 20.44/3.43 % (548995)Termination phase: Saturation
% 20.44/3.43 % (548995)Time elapsed: 0.173 s
% 20.44/3.43 % (548995)Peak memory usage: 13 MB
% 20.44/3.43 % (548995)Instructions burned: 212 (million)
% 20.44/3.43 % (548999)Refutation not found, incomplete strategy
% 20.44/3.43 % (548999)------------------------------
% 20.44/3.43 % (548999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.44/3.43 % (548999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.43 % (548999)CaDiCaL version: 2.1.3
% 20.44/3.43 % (548999)Termination reason: Refutation not found, incomplete strategy
% 20.44/3.43 % (548999)Time elapsed: 0.024 s
% 20.44/3.43 % (548999)Peak memory usage: 12 MB
% 20.44/3.43 % (548999)Instructions burned: 29 (million)
% 20.44/3.43 % (548999)------------------------------
% 20.44/3.43 % (548999)------------------------------
% 20.44/3.43 % (549001)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=729048269:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2977 on theBenchmark for (2977ds/152Mi)
% 20.44/3.43 % (549002)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3335716983:i=75:ep=R:rtra=on:ntd=on_2977 on theBenchmark for (2977ds/75Mi)
% 20.44/3.43 % (549002)Instruction limit reached!
% 20.44/3.43 % (549002)------------------------------
% 20.44/3.43 % (549002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.44/3.43 % (549002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.43 % (549002)CaDiCaL version: 2.1.3
% 20.44/3.43 % (549002)Termination reason: Instruction limit
% 20.44/3.43 % (549002)Termination phase: Saturation
% 20.44/3.43 % (549002)Time elapsed: 0.060 s
% 20.44/3.43 % (549002)Peak memory usage: 12 MB
% 20.44/3.43 % (549002)Instructions burned: 75 (million)
% 20.44/3.43 % (549005)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=3284350510:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2976 on theBenchmark for (2976ds/387Mi)
% 20.44/3.43 % (549001)Instruction limit reached!
% 20.44/3.43 % (549001)------------------------------
% 20.44/3.43 % (549001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 20.44/3.43 % (549001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.65/3.78 % (549001)CaDiCaL version: 2.1.3
% 21.65/3.78 % (549001)Termination reason: Instruction limit
% 21.65/3.78 % (549001)Termination phase: Saturation
% 21.65/3.78 % (549001)Time elapsed: 0.120 s
% 21.65/3.78 % (549001)Peak memory usage: 13 MB
% 21.65/3.78 % (549001)Instructions burned: 153 (million)
% 21.65/3.78 % (549007)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=1314596827:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2975 on theBenchmark for (2975ds/148Mi)
% 21.65/3.78 % (549007)Instruction limit reached!
% 21.65/3.78 % (549007)------------------------------
% 21.65/3.78 % (549007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.65/3.78 % (549007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.65/3.78 % (549007)CaDiCaL version: 2.1.3
% 21.65/3.78 % (549007)Termination reason: Instruction limit
% 21.65/3.78 % (549007)Termination phase: Saturation
% 21.65/3.78 % (549007)Time elapsed: 0.117 s
% 21.65/3.78 % (549007)Peak memory usage: 12 MB
% 21.65/3.78 % (549007)Instructions burned: 149 (million)
% 21.65/3.78 % (549009)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1279729638:i=161:piset=and:rtra=on:ntd=on_2974 on theBenchmark for (2974ds/161Mi)
% 21.65/3.78 % (549005)Instruction limit reached!
% 21.65/3.78 % (549005)------------------------------
% 21.65/3.78 % (549005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.65/3.78 % (549005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.65/3.78 % (549005)CaDiCaL version: 2.1.3
% 21.65/3.78 % (549005)Termination reason: Instruction limit
% 21.65/3.78 % (549005)Termination phase: Saturation
% 21.65/3.78 % (549005)Time elapsed: 0.269 s
% 21.65/3.78 % (549005)Peak memory usage: 12 MB
% 21.65/3.78 % (549005)Instructions burned: 388 (million)
% 21.65/3.78 % (549011)lrs+10_1_sil=128000:si=on:random_seed=1270811599:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2973 on theBenchmark for (2973ds/888Mi)
% 21.65/3.78 % (549009)Instruction limit reached!
% 21.65/3.78 % (549009)------------------------------
% 21.65/3.78 % (549009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.65/3.78 % (549009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.65/3.78 % (549009)CaDiCaL version: 2.1.3
% 21.65/3.78 % (549009)Termination reason: Instruction limit
% 21.65/3.78 % (549009)Termination phase: Saturation
% 21.65/3.78 % (549009)Time elapsed: 0.138 s
% 21.65/3.78 % (549009)Peak memory usage: 13 MB
% 21.65/3.78 % (549009)Instructions burned: 162 (million)
% 21.65/3.78 % (548987)Instruction limit reached!
% 21.65/3.78 % (548987)------------------------------
% 21.65/3.78 % (548987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.65/3.78 % (548987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.65/3.78 % (548987)CaDiCaL version: 2.1.3
% 21.65/3.78 % (548987)Termination reason: Instruction limit
% 21.65/3.78 % (548987)Termination phase: Saturation
% 21.65/3.78 % (548987)Time elapsed: 0.926 s
% 21.65/3.78 % (548987)Peak memory usage: 16 MB
% 21.65/3.78 % (548987)Instructions burned: 1255 (million)
% 21.65/3.78 % (549013)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=269329035:i=136:add=on:ins=4:rtra=on:sup=off_2972 on theBenchmark for (2972ds/136Mi)
% 21.65/3.78 % (549014)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=3365567528:i=88:s2at=3:nm=2:rtra=on:rawr=on_2972 on theBenchmark for (2972ds/88Mi)
% 21.65/3.78 % (548993)Instruction limit reached!
% 21.65/3.78 % (548993)------------------------------
% 21.65/3.78 % (548993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.65/3.78 % (548993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.65/3.78 % (548993)CaDiCaL version: 2.1.3
% 21.65/3.78 % (548993)Termination reason: Instruction limit
% 21.65/3.78 % (548993)Termination phase: Saturation
% 21.65/3.78 % (548993)Time elapsed: 0.770 s
% 21.65/3.78 % (548993)Peak memory usage: 20 MB
% 21.65/3.78 % (548993)Instructions burned: 866 (million)
% 21.65/3.78 % (549013)Refutation not found, incomplete strategy
% 21.65/3.78 % (549013)------------------------------
% 21.65/3.78 % (549013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.65/3.78 % (549013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.66/4.03 % (549013)CaDiCaL version: 2.1.3
% 23.66/4.03 % (549013)Termination reason: Refutation not found, incomplete strategy
% 23.66/4.03 % (549013)Time elapsed: 0.018 s
% 23.66/4.03 % (549013)Peak memory usage: 12 MB
% 23.66/4.03 % (549013)Instructions burned: 23 (million)
% 23.66/4.03 % (549013)------------------------------
% 23.66/4.03 % (549013)------------------------------
% 23.66/4.03 % (549017)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=3006922092:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2972 on theBenchmark for (2972ds/93Mi)
% 23.66/4.03 % (549018)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=71988893:i=2186:rtra=on:ixr=off_2972 on theBenchmark for (2972ds/2186Mi)
% 23.66/4.03 % (548974)Instruction limit reached!
% 23.66/4.03 % (548974)------------------------------
% 23.66/4.03 % (548974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.66/4.03 % (548974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.66/4.03 % (548974)CaDiCaL version: 2.1.3
% 23.66/4.03 % (548974)Termination reason: Instruction limit
% 23.66/4.03 % (548974)Termination phase: Saturation
% 23.66/4.03 % (548974)Time elapsed: 1.206 s
% 23.66/4.03 % (548974)Peak memory usage: 20 MB
% 23.66/4.03 % (548974)Instructions burned: 1440 (million)
% 23.66/4.03 % (549014)Instruction limit reached!
% 23.66/4.03 % (549014)------------------------------
% 23.66/4.03 % (549014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.66/4.03 % (549014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.66/4.03 % (549014)CaDiCaL version: 2.1.3
% 23.66/4.03 % (549014)Termination reason: Instruction limit
% 23.66/4.03 % (549014)Termination phase: Saturation
% 23.66/4.03 % (549014)Time elapsed: 0.068 s
% 23.66/4.03 % (549014)Peak memory usage: 12 MB
% 23.66/4.03 % (549014)Instructions burned: 88 (million)
% 23.66/4.03 % (549021)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1181161791:s2a=on:i=240:rtra=on:ntd=on_2971 on theBenchmark for (2971ds/240Mi)
% 23.66/4.03 % (549022)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=594472985:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2971 on theBenchmark for (2971ds/805Mi)
% 23.66/4.03 % (549017)Instruction limit reached!
% 23.66/4.03 % (549017)------------------------------
% 23.66/4.03 % (549017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.66/4.03 % (549017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.66/4.03 % (549017)CaDiCaL version: 2.1.3
% 23.66/4.03 % (549017)Termination reason: Instruction limit
% 23.66/4.03 % (549017)Termination phase: Saturation
% 23.66/4.03 % (549017)Time elapsed: 0.072 s
% 23.66/4.03 % (549017)Peak memory usage: 12 MB
% 23.66/4.03 % (549017)Instructions burned: 94 (million)
% 23.66/4.03 % (549025)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 23.66/4.03 % (549025)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=954531763:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2971 on theBenchmark for (2971ds/391Mi)
% 23.66/4.03 % (549025)Refutation not found, incomplete strategy
% 23.66/4.03 % (549025)------------------------------
% 23.66/4.03 % (549025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.66/4.03 % (549025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.66/4.03 % (549025)CaDiCaL version: 2.1.3
% 23.66/4.03 % (549025)Termination reason: Refutation not found, incomplete strategy
% 23.66/4.03 % (549025)Time elapsed: 0.021 s
% 23.66/4.03 % (549025)Peak memory usage: 12 MB
% 23.66/4.03 % (549025)Instructions burned: 26 (million)
% 23.66/4.03 % (549025)------------------------------
% 23.66/4.03 % (549025)------------------------------
% 23.66/4.03 % (549027)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=1827616412:i=355:av=off:fsr=off:rtra=on:ixr=off_2970 on theBenchmark for (2970ds/355Mi)
% 23.66/4.03 % (549021)Instruction limit reached!
% 23.66/4.03 % (549021)------------------------------
% 23.66/4.03 % (549021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.66/4.03 % (549021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.66/4.03 % (549021)CaDiCaL version: 2.1.3
% 23.66/4.03 % (549021)Termination reason: Instruction limit
% 26.14/4.10 % (549021)Termination phase: Saturation
% 26.14/4.10 % (549021)Time elapsed: 0.195 s
% 26.14/4.10 % (549021)Peak memory usage: 13 MB
% 26.14/4.10 % (549021)Instructions burned: 241 (million)
% 26.14/4.10 % (549029)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=3423334433:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2969 on theBenchmark for (2969ds/314Mi)
% 26.14/4.10 % (549029)Refutation not found, incomplete strategy
% 26.14/4.10 % (549029)------------------------------
% 26.14/4.10 % (549029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.14/4.10 % (549029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.14/4.10 % (549029)CaDiCaL version: 2.1.3
% 26.14/4.10 % (549029)Termination reason: Refutation not found, incomplete strategy
% 26.14/4.10 % (549029)Time elapsed: 0.007 s
% 26.14/4.10 % (549029)Peak memory usage: 12 MB
% 26.14/4.10 % (549029)Instructions burned: 6 (million)
% 26.14/4.10 % (549029)------------------------------
% 26.14/4.10 % (549029)------------------------------
% 26.14/4.10 % (549031)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=4003573576:s2a=on:i=251:fsr=off:rtra=on_2968 on theBenchmark for (2968ds/251Mi)
% 26.14/4.10 % (549027)Instruction limit reached!
% 26.14/4.10 % (549027)------------------------------
% 26.14/4.10 % (549027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.14/4.10 % (549027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.14/4.10 % (549027)CaDiCaL version: 2.1.3
% 26.14/4.10 % (549027)Termination reason: Instruction limit
% 26.14/4.10 % (549027)Termination phase: Saturation
% 26.14/4.10 % (549027)Time elapsed: 0.275 s
% 26.14/4.10 % (549027)Peak memory usage: 12 MB
% 26.14/4.10 % (549027)Instructions burned: 355 (million)
% 26.14/4.10 % (549033)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=527197827: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_2967 on theBenchmark for (2967ds/2470Mi)
% 26.14/4.10 % (549031)Instruction limit reached!
% 26.14/4.10 % (549031)------------------------------
% 26.14/4.10 % (549031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.14/4.10 % (549031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.14/4.10 % (549031)CaDiCaL version: 2.1.3
% 26.14/4.10 % (549031)Termination reason: Instruction limit
% 26.14/4.10 % (549031)Termination phase: Saturation
% 26.14/4.10 % (549031)Time elapsed: 0.193 s
% 26.14/4.10 % (549031)Peak memory usage: 12 MB
% 26.14/4.10 % (549031)Instructions burned: 251 (million)
% 26.14/4.10 % (548933)Instruction limit reached!
% 26.14/4.10 % (548933)------------------------------
% 26.14/4.10 % (548933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.14/4.10 % (548933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.14/4.10 % (548933)CaDiCaL version: 2.1.3
% 26.14/4.10 % (548933)Termination reason: Instruction limit
% 26.14/4.10 % (548933)Termination phase: Saturation
% 26.14/4.10 % (548933)Time elapsed: 2.467 s
% 26.14/4.10 % (548933)Peak memory usage: 38 MB
% 26.14/4.10 % (548933)Instructions burned: 5756 (million)
% 26.14/4.10 % (549011)Instruction limit reached!
% 26.14/4.10 % (549011)------------------------------
% 26.14/4.10 % (549011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.14/4.10 % (549011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.14/4.10 % (549011)CaDiCaL version: 2.1.3
% 26.14/4.10 % (549011)Termination reason: Instruction limit
% 26.14/4.10 % (549011)Termination phase: Saturation
% 26.14/4.10 % (549011)Time elapsed: 0.671 s
% 26.14/4.10 % (549011)Peak memory usage: 14 MB
% 26.14/4.10 % (549011)Instructions burned: 888 (million)
% 26.14/4.10 % (549036)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1433820577:i=116:ep=RSTC:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/116Mi)
% 26.14/4.10 % (549035)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=2622477498:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2966 on theBenchmark for (2966ds/673Mi)
% 26.14/4.10 % (549038)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2028947038:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2966 on theBenchmark for (2966ds/270Mi)
% 26.14/4.10 % (549036)Instruction limit reached!
% 29.15/4.65 % (549036)------------------------------
% 29.15/4.65 % (549036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.15/4.65 % (549036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.15/4.65 % (549036)CaDiCaL version: 2.1.3
% 29.15/4.65 % (549036)Termination reason: Instruction limit
% 29.15/4.65 % (549036)Termination phase: Saturation
% 29.15/4.65 % (549036)Time elapsed: 0.050 s
% 29.15/4.65 % (549036)Peak memory usage: 13 MB
% 29.15/4.65 % (549036)Instructions burned: 118 (million)
% 29.15/4.65 % (549041)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=2248108250: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)
% 29.15/4.65 % (549041)Instruction limit reached!
% 29.15/4.65 % (549041)------------------------------
% 29.15/4.65 % (549041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.15/4.65 % (549041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.15/4.65 % (549041)CaDiCaL version: 2.1.3
% 29.15/4.65 % (549041)Termination reason: Instruction limit
% 29.15/4.65 % (549041)Termination phase: Saturation
% 29.15/4.65 % (549041)Time elapsed: 0.015 s
% 29.15/4.65 % (549041)Peak memory usage: 12 MB
% 29.15/4.65 % (549041)Instructions burned: 31 (million)
% 29.15/4.65 % (549043)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 29.15/4.65 % (549043)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=1108903440:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2965 on theBenchmark for (2965ds/39Mi)
% 29.15/4.65 % (549043)Instruction limit reached!
% 29.15/4.65 % (549043)------------------------------
% 29.15/4.65 % (549043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.15/4.65 % (549043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.15/4.65 % (549043)CaDiCaL version: 2.1.3
% 29.15/4.65 % (549043)Termination reason: Instruction limit
% 29.15/4.65 % (549043)Termination phase: Saturation
% 29.15/4.65 % (549043)Time elapsed: 0.017 s
% 29.15/4.65 % (549043)Peak memory usage: 12 MB
% 29.15/4.65 % (549043)Instructions burned: 41 (million)
% 29.15/4.65 % (549045)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3982777289:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2965 on theBenchmark for (2965ds/365Mi)
% 29.15/4.65 % (549022)Instruction limit reached!
% 29.15/4.65 % (549022)------------------------------
% 29.15/4.65 % (549022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.15/4.65 % (549022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.15/4.65 % (549022)CaDiCaL version: 2.1.3
% 29.15/4.65 % (549022)Termination reason: Instruction limit
% 29.15/4.65 % (549022)Termination phase: Saturation
% 29.15/4.65 % (549022)Time elapsed: 0.652 s
% 29.15/4.65 % (549022)Peak memory usage: 16 MB
% 29.15/4.65 % (549022)Instructions burned: 805 (million)
% 29.15/4.65 % (549047)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1909639998:i=158:av=off:rtra=on_2964 on theBenchmark for (2964ds/158Mi)
% 29.15/4.65 % (549038)Instruction limit reached!
% 29.15/4.65 % (549038)------------------------------
% 29.15/4.65 % (549038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.15/4.65 % (549038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.15/4.65 % (549038)CaDiCaL version: 2.1.3
% 29.15/4.65 % (549038)Termination reason: Instruction limit
% 29.15/4.65 % (549038)Termination phase: Saturation
% 29.15/4.65 % (549038)Time elapsed: 0.206 s
% 29.15/4.65 % (549038)Peak memory usage: 12 MB
% 29.15/4.65 % (549038)Instructions burned: 271 (million)
% 29.15/4.65 % (549049)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
% 29.15/4.65 % (549049)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=203321758:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2963 on theBenchmark for (2963ds/252Mi)
% 29.15/4.65 % (549049)Refutation not found, incomplete strategy
% 29.15/4.65 % (549049)------------------------------
% 29.15/4.65 % (549049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.40/4.74 % (549049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.40/4.74 % (549049)CaDiCaL version: 2.1.3
% 30.40/4.74 % (549049)Termination reason: Refutation not found, incomplete strategy
% 30.40/4.74 % (549049)Time elapsed: 0.021 s
% 30.40/4.74 % (549049)Peak memory usage: 12 MB
% 30.40/4.74 % (549049)Instructions burned: 26 (million)
% 30.40/4.74 % (549049)------------------------------
% 30.40/4.74 % (549049)------------------------------
% 30.40/4.74 % (549045)Instruction limit reached!
% 30.40/4.74 % (549045)------------------------------
% 30.40/4.74 % (549045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.40/4.74 % (549045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.40/4.74 % (549045)CaDiCaL version: 2.1.3
% 30.40/4.74 % (549045)Termination reason: Instruction limit
% 30.40/4.74 % (549045)Termination phase: Saturation
% 30.40/4.74 % (549045)Time elapsed: 0.158 s
% 30.40/4.74 % (549045)Peak memory usage: 16 MB
% 30.40/4.74 % (549045)Instructions burned: 366 (million)
% 30.40/4.74 % (549052)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=3968903772:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2963 on theBenchmark for (2963ds/160Mi)
% 30.40/4.74 % (549052)Refutation not found, incomplete strategy
% 30.40/4.74 % (549052)------------------------------
% 30.40/4.74 % (549052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.40/4.74 % (549052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.40/4.74 % (549052)CaDiCaL version: 2.1.3
% 30.40/4.74 % (549052)Termination reason: Refutation not found, incomplete strategy
% 30.40/4.74 % (549052)Time elapsed: 0.011 s
% 30.40/4.74 % (549052)Peak memory usage: 12 MB
% 30.40/4.74 % (549052)Instructions burned: 27 (million)
% 30.40/4.74 % (549051)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2886085714:i=213:rtra=on:ss=axioms_2963 on theBenchmark for (2963ds/213Mi)
% 30.40/4.74 % (549052)------------------------------
% 30.40/4.74 % (549052)------------------------------
% 30.40/4.74 % (549047)Instruction limit reached!
% 30.40/4.74 % (549047)------------------------------
% 30.40/4.74 % (549047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.40/4.74 % (549047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.40/4.74 % (549047)CaDiCaL version: 2.1.3
% 30.40/4.74 % (549047)Termination reason: Instruction limit
% 30.40/4.74 % (549047)Termination phase: Saturation
% 30.40/4.74 % (549047)Time elapsed: 0.137 s
% 30.40/4.74 % (549047)Peak memory usage: 12 MB
% 30.40/4.74 % (549047)Instructions burned: 158 (million)
% 30.40/4.74 % (549051)Refutation not found, incomplete strategy
% 30.40/4.74 % (549051)------------------------------
% 30.40/4.74 % (549051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.40/4.74 % (549051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.40/4.74 % (549051)CaDiCaL version: 2.1.3
% 30.40/4.74 % (549051)Termination reason: Refutation not found, incomplete strategy
% 30.40/4.74 % (549051)Time elapsed: 0.006 s
% 30.40/4.74 % (549051)Peak memory usage: 12 MB
% 30.40/4.74 % (549051)Instructions burned: 6 (million)
% 30.40/4.74 % (549051)------------------------------
% 30.40/4.74 % (549051)------------------------------
% 30.40/4.74 % (549055)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=2531248346:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2963 on theBenchmark for (2963ds/763Mi)
% 30.40/4.74 % (549055)Refutation not found, incomplete strategy
% 30.40/4.74 % (549055)------------------------------
% 30.40/4.74 % (549055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.40/4.74 % (549055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.40/4.74 % (549055)CaDiCaL version: 2.1.3
% 30.40/4.74 % (549055)Termination reason: Refutation not found, incomplete strategy
% 30.40/4.74 % (549055)Time elapsed: 0.009 s
% 30.40/4.74 % (549055)Peak memory usage: 12 MB
% 30.40/4.74 % (549055)Instructions burned: 23 (million)
% 30.40/4.74 % (549055)------------------------------
% 30.40/4.74 % (549055)------------------------------
% 30.40/4.74 % (549056)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 30.40/4.74 % (549056)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=3645971381:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2963 on theBenchmark for (2963ds/237Mi)
% 31.00/4.85 % (549057)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=1482598001:s2a=on:i=386:rtra=on:ntd=on_2962 on theBenchmark for (2962ds/386Mi)
% 31.00/4.85 % (549059)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=2217272766:i=300:piset=and:nm=32:rtra=on_2962 on theBenchmark for (2962ds/300Mi)
% 31.00/4.85 % (549059)Instruction limit reached!
% 31.00/4.85 % (549059)------------------------------
% 31.00/4.85 % (549059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.00/4.85 % (549059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.00/4.85 % (549059)CaDiCaL version: 2.1.3
% 31.00/4.85 % (549059)Termination reason: Instruction limit
% 31.00/4.85 % (549059)Termination phase: Saturation
% 31.00/4.85 % (549059)Time elapsed: 0.127 s
% 31.00/4.85 % (549059)Peak memory usage: 13 MB
% 31.00/4.85 % (549059)Instructions burned: 302 (million)
% 31.00/4.85 % (549063)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=3528727496:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2961 on theBenchmark for (2961ds/567Mi)
% 31.00/4.85 % (549056)Instruction limit reached!
% 31.00/4.85 % (549056)------------------------------
% 31.00/4.85 % (549056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.00/4.85 % (549056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.00/4.85 % (549056)CaDiCaL version: 2.1.3
% 31.00/4.85 % (549056)Termination reason: Instruction limit
% 31.00/4.85 % (549056)Termination phase: Saturation
% 31.00/4.85 % (549056)Time elapsed: 0.197 s
% 31.00/4.85 % (549056)Peak memory usage: 13 MB
% 31.00/4.85 % (549056)Instructions burned: 238 (million)
% 31.00/4.85 % (549035)Instruction limit reached!
% 31.00/4.85 % (549035)------------------------------
% 31.00/4.85 % (549035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.00/4.85 % (549035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.00/4.85 % (549035)CaDiCaL version: 2.1.3
% 31.00/4.85 % (549035)Termination reason: Instruction limit
% 31.00/4.85 % (549035)Termination phase: Saturation
% 31.00/4.85 % (549035)Time elapsed: 0.566 s
% 31.00/4.85 % (549035)Peak memory usage: 16 MB
% 31.00/4.85 % (549035)Instructions burned: 674 (million)
% 31.00/4.85 % (549065)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=1769110944:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2960 on theBenchmark for (2960ds/379Mi)
% 31.00/4.85 % (549066)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=151693037:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2960 on theBenchmark for (2960ds/429Mi)
% 31.00/4.85 % (549057)Instruction limit reached!
% 31.00/4.85 % (549057)------------------------------
% 31.00/4.85 % (549057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.00/4.85 % (549057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.00/4.85 % (549057)CaDiCaL version: 2.1.3
% 31.00/4.85 % (549057)Termination reason: Instruction limit
% 31.00/4.85 % (549057)Termination phase: Saturation
% 31.00/4.85 % (549057)Time elapsed: 0.301 s
% 31.00/4.85 % (549057)Peak memory usage: 13 MB
% 31.00/4.85 % (549057)Instructions burned: 387 (million)
% 31.00/4.85 % (549069)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=4035025803:i=478:bd=all:rtra=on_2959 on theBenchmark for (2959ds/478Mi)
% 31.00/4.85 % (549063)Instruction limit reached!
% 31.00/4.85 % (549063)------------------------------
% 31.00/4.85 % (549063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.00/4.85 % (549063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.00/4.85 % (549063)CaDiCaL version: 2.1.3
% 31.00/4.85 % (549063)Termination reason: Instruction limit
% 31.00/4.85 % (549063)Termination phase: Saturation
% 31.00/4.85 % (549063)Time elapsed: 0.225 s
% 31.00/4.85 % (549063)Peak memory usage: 13 MB
% 31.00/4.85 % (549063)Instructions burned: 569 (million)
% 31.00/4.85 % (549071)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3405140502:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2958 on theBenchmark for (2958ds/445Mi)
% 31.00/4.85 % (549065)Instruction limit reached!
% 31.00/4.85 % (549065)------------------------------
% 31.00/4.85 % (549065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.00/4.85 % (549065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.28/5.13 % (549065)CaDiCaL version: 2.1.3
% 33.28/5.13 % (549065)Termination reason: Instruction limit
% 33.28/5.13 % (549065)Termination phase: Saturation
% 33.28/5.13 % (549065)Time elapsed: 0.315 s
% 33.28/5.13 % (549065)Peak memory usage: 14 MB
% 33.28/5.13 % (549065)Instructions burned: 380 (million)
% 33.28/5.13 % (549073)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=271199284:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2957 on theBenchmark for (2957ds/71Mi)
% 33.28/5.13 % (549066)Instruction limit reached!
% 33.28/5.13 % (549066)------------------------------
% 33.28/5.13 % (549066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.28/5.13 % (549066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.28/5.13 % (549066)CaDiCaL version: 2.1.3
% 33.28/5.13 % (549066)Termination reason: Instruction limit
% 33.28/5.13 % (549066)Termination phase: Saturation
% 33.28/5.13 % (549066)Time elapsed: 0.350 s
% 33.28/5.13 % (549066)Peak memory usage: 14 MB
% 33.28/5.13 % (549066)Instructions burned: 429 (million)
% 33.28/5.13 % (549071)Instruction limit reached!
% 33.28/5.13 % (549071)------------------------------
% 33.28/5.13 % (549071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.28/5.13 % (549071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.28/5.13 % (549071)CaDiCaL version: 2.1.3
% 33.28/5.13 % (549071)Termination reason: Instruction limit
% 33.28/5.13 % (549071)Termination phase: Saturation
% 33.28/5.13 % (549071)Time elapsed: 0.192 s
% 33.28/5.13 % (549071)Peak memory usage: 14 MB
% 33.28/5.13 % (549071)Instructions burned: 445 (million)
% 33.28/5.13 % (549076)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=1786595813:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2956 on theBenchmark for (2956ds/4980Mi)
% 33.28/5.13 % (549076)Refutation not found, incomplete strategy
% 33.28/5.13 % (549076)------------------------------
% 33.28/5.13 % (549076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.28/5.13 % (549076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.28/5.13 % (549076)CaDiCaL version: 2.1.3
% 33.28/5.13 % (549076)Termination reason: Refutation not found, incomplete strategy
% 33.28/5.13 % (549076)Time elapsed: 0.005 s
% 33.28/5.13 % (549076)Peak memory usage: 12 MB
% 33.28/5.13 % (549076)Instructions burned: 9 (million)
% 33.28/5.13 % (549076)------------------------------
% 33.28/5.13 % (549076)------------------------------
% 33.28/5.13 % (549075)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3223561650:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2956 on theBenchmark for (2956ds/302Mi)
% 33.28/5.13 % (549075)Refutation not found, incomplete strategy
% 33.28/5.13 % (549075)------------------------------
% 33.28/5.13 % (549075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.28/5.13 % (549075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.28/5.13 % (549075)CaDiCaL version: 2.1.3
% 33.28/5.13 % (549075)Termination reason: Refutation not found, incomplete strategy
% 33.28/5.13 % (549075)Time elapsed: 0.006 s
% 33.28/5.13 % (549075)Peak memory usage: 12 MB
% 33.28/5.13 % (549075)Instructions burned: 6 (million)
% 33.28/5.13 % (549075)------------------------------
% 33.28/5.13 % (549075)------------------------------
% 33.28/5.13 % (549078)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
% 33.28/5.13 % (549078)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 33.28/5.13 % (549078)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2487461472:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2956 on theBenchmark for (2956ds/100Mi)
% 33.28/5.13 % (549073)Instruction limit reached!
% 33.28/5.13 % (549073)------------------------------
% 33.28/5.13 % (549073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.28/5.13 % (549073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.28/5.13 % (549073)CaDiCaL version: 2.1.3
% 33.28/5.13 % (549073)Termination reason: Instruction limit
% 33.28/5.13 % (549073)Termination phase: Saturation
% 33.28/5.13 % (549073)Time elapsed: 0.059 s
% 33.28/5.13 % (549073)Peak memory usage: 12 MB
% 33.28/5.13 % (549073)Instructions burned: 72 (million)
% 35.34/5.43 % (549080)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=3622933282:i=76:piset=equals:rtra=on:ntd=on_2956 on theBenchmark for (2956ds/76Mi)
% 35.34/5.43 % (549082)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=753708777:i=289:rtra=on_2956 on theBenchmark for (2956ds/289Mi)
% 35.34/5.43 % (549078)Instruction limit reached!
% 35.34/5.43 % (549078)------------------------------
% 35.34/5.43 % (549078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.34/5.43 % (549078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.34/5.43 % (549078)CaDiCaL version: 2.1.3
% 35.34/5.43 % (549078)Termination reason: Instruction limit
% 35.34/5.43 % (549078)Termination phase: Saturation
% 35.34/5.43 % (549078)Time elapsed: 0.040 s
% 35.34/5.43 % (549078)Peak memory usage: 12 MB
% 35.34/5.43 % (549078)Instructions burned: 102 (million)
% 35.34/5.43 % (549085)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=485953852:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2955 on theBenchmark for (2955ds/493Mi)
% 35.34/5.43 % (549082)Refutation not found, incomplete strategy
% 35.34/5.43 % (549082)------------------------------
% 35.34/5.43 % (549082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.34/5.43 % (549082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.34/5.43 % (549082)CaDiCaL version: 2.1.3
% 35.34/5.43 % (549082)Termination reason: Refutation not found, incomplete strategy
% 35.34/5.43 % (549082)Time elapsed: 0.020 s
% 35.34/5.43 % (549082)Peak memory usage: 12 MB
% 35.34/5.43 % (549082)Instructions burned: 25 (million)
% 35.34/5.43 % (549082)------------------------------
% 35.34/5.43 % (549082)------------------------------
% 35.34/5.43 % (549087)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=2876567880:cond=on:i=34:hud=10:nm=10:rtra=on_2955 on theBenchmark for (2955ds/34Mi)
% 35.34/5.43 % (549080)Instruction limit reached!
% 35.34/5.43 % (549080)------------------------------
% 35.34/5.43 % (549080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.34/5.43 % (549080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.34/5.43 % (549080)CaDiCaL version: 2.1.3
% 35.34/5.43 % (549080)Termination reason: Instruction limit
% 35.34/5.43 % (549080)Termination phase: Saturation
% 35.34/5.43 % (549080)Time elapsed: 0.064 s
% 35.34/5.43 % (549080)Peak memory usage: 13 MB
% 35.34/5.43 % (549080)Instructions burned: 76 (million)
% 35.34/5.43 % (549069)Instruction limit reached!
% 35.34/5.43 % (549069)------------------------------
% 35.34/5.43 % (549069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.34/5.43 % (549069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.34/5.43 % (549069)CaDiCaL version: 2.1.3
% 35.34/5.43 % (549069)Termination reason: Instruction limit
% 35.34/5.43 % (549069)Termination phase: Saturation
% 35.34/5.43 % (549069)Time elapsed: 0.402 s
% 35.34/5.43 % (549069)Peak memory usage: 14 MB
% 35.34/5.43 % (549069)Instructions burned: 479 (million)
% 35.34/5.43 % (549018)Instruction limit reached!
% 35.34/5.43 % (549018)------------------------------
% 35.34/5.43 % (549018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.34/5.43 % (549018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.34/5.43 % (549018)CaDiCaL version: 2.1.3
% 35.34/5.43 % (549018)Termination reason: Instruction limit
% 35.34/5.43 % (549018)Termination phase: Saturation
% 35.34/5.43 % (549018)Time elapsed: 1.655 s
% 35.34/5.43 % (549018)Peak memory usage: 16 MB
% 35.34/5.43 % (549018)Instructions burned: 2187 (million)
% 35.34/5.43 % (549089)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 35.34/5.43 % (549087)Instruction limit reached!
% 35.34/5.43 % (549087)------------------------------
% 35.34/5.43 % (549087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.34/5.43 % (549087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.34/5.43 % (549087)CaDiCaL version: 2.1.3
% 35.34/5.43 % (549087)Termination reason: Instruction limit
% 35.34/5.43 % (549087)Termination phase: Saturation
% 35.34/5.43 % (549087)Time elapsed: 0.028 s
% 35.34/5.43 % (549087)Peak memory usage: 12 MB
% 35.34/5.43 % (549087)Instructions burned: 34 (million)
% 36.58/5.80 % (549089)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=2370548528:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2955 on theBenchmark for (2955ds/372Mi)
% 36.58/5.80 % (549090)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=705133153:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2955 on theBenchmark for (2955ds/670Mi)
% 36.58/5.80 % (549091)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=338684808:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2955 on theBenchmark for (2955ds/647Mi)
% 36.58/5.80 % (549092)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=900802388:i=857:add=off:kws=frequency:rtra=on:ntd=on_2955 on theBenchmark for (2955ds/857Mi)
% 36.58/5.80 % (549092)Refutation not found, incomplete strategy
% 36.58/5.80 % (549092)------------------------------
% 36.58/5.80 % (549092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.58/5.80 % (549092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.58/5.80 % (549092)CaDiCaL version: 2.1.3
% 36.58/5.80 % (549092)Termination reason: Refutation not found, incomplete strategy
% 36.58/5.80 % (549092)Time elapsed: 0.020 s
% 36.58/5.80 % (549092)Peak memory usage: 12 MB
% 36.58/5.80 % (549092)Instructions burned: 26 (million)
% 36.58/5.80 % (549092)------------------------------
% 36.58/5.80 % (549092)------------------------------
% 36.58/5.80 % (549097)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=2109100074:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2954 on theBenchmark for (2954ds/693Mi)
% 36.58/5.80 % (549085)Instruction limit reached!
% 36.58/5.80 % (549085)------------------------------
% 36.58/5.80 % (549085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.58/5.80 % (549085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.58/5.80 % (549085)CaDiCaL version: 2.1.3
% 36.58/5.80 % (549085)Termination reason: Instruction limit
% 36.58/5.80 % (549085)Termination phase: Saturation
% 36.58/5.80 % (549085)Time elapsed: 0.169 s
% 36.58/5.80 % (549085)Peak memory usage: 12 MB
% 36.58/5.80 % (549085)Instructions burned: 496 (million)
% 36.58/5.80 % (549099)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=4178893064:i=285:hud=10:bd=all:rtra=on:ss=axioms_2954 on theBenchmark for (2954ds/285Mi)
% 36.58/5.80 % (549099)Refutation not found, incomplete strategy
% 36.58/5.80 % (549099)------------------------------
% 36.58/5.80 % (549099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.58/5.80 % (549099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.58/5.80 % (549099)CaDiCaL version: 2.1.3
% 36.58/5.80 % (549099)Termination reason: Refutation not found, incomplete strategy
% 36.58/5.80 % (549099)Time elapsed: 0.004 s
% 36.58/5.80 % (549099)Peak memory usage: 12 MB
% 36.58/5.80 % (549099)Instructions burned: 8 (million)
% 36.58/5.80 % (549099)------------------------------
% 36.58/5.80 % (549099)------------------------------
% 36.58/5.80 % (549101)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 36.58/5.80 % (549101)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=3314906123:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2953 on theBenchmark for (2953ds/52Mi)
% 36.58/5.80 % (549101)Instruction limit reached!
% 36.58/5.80 % (549101)------------------------------
% 36.58/5.80 % (549101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.58/5.80 % (549101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.58/5.80 % (549101)CaDiCaL version: 2.1.3
% 36.58/5.80 % (549101)Termination reason: Instruction limit
% 36.58/5.80 % (549101)Termination phase: Saturation
% 36.58/5.80 % (549101)Time elapsed: 0.022 s
% 36.58/5.80 % (549101)Peak memory usage: 12 MB
% 36.58/5.80 % (549101)Instructions burned: 54 (million)
% 36.58/5.80 % (549103)dis+10_1_si=on:random_seed=559340286:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2953 on theBenchmark for (2953ds/407Mi)
% 36.58/5.80 % (549089)Refutation not found, incomplete strategy
% 41.91/6.40 % (549089)------------------------------
% 41.91/6.40 % (549089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.91/6.40 % (549089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.91/6.40 % (549089)CaDiCaL version: 2.1.3
% 41.91/6.40 % (549089)Termination reason: Refutation not found, incomplete strategy
% 41.91/6.40 % (549089)Time elapsed: 0.270 s
% 41.91/6.40 % (549089)Peak memory usage: 13 MB
% 41.91/6.40 % (549089)Instructions burned: 341 (million)
% 41.91/6.40 % (549089)------------------------------
% 41.91/6.40 % (549089)------------------------------
% 41.91/6.40 % (549105)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=848360939:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2952 on theBenchmark for (2952ds/2240Mi)
% 41.91/6.40 % (549103)Instruction limit reached!
% 41.91/6.40 % (549103)------------------------------
% 41.91/6.40 % (549103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.91/6.40 % (549103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.91/6.40 % (549103)CaDiCaL version: 2.1.3
% 41.91/6.40 % (549103)Termination reason: Instruction limit
% 41.91/6.40 % (549103)Termination phase: Saturation
% 41.91/6.40 % (549103)Time elapsed: 0.169 s
% 41.91/6.40 % (549103)Peak memory usage: 13 MB
% 41.91/6.40 % (549103)Instructions burned: 409 (million)
% 41.91/6.40 % (549107)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=702864053:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2951 on theBenchmark for (2951ds/336Mi)
% 41.91/6.40 % (549107)Refutation not found, incomplete strategy
% 41.91/6.40 % (549107)------------------------------
% 41.91/6.40 % (549107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.91/6.40 % (549107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.91/6.40 % (549107)CaDiCaL version: 2.1.3
% 41.91/6.40 % (549107)Termination reason: Refutation not found, incomplete strategy
% 41.91/6.40 % (549107)Time elapsed: 0.004 s
% 41.91/6.40 % (549107)Peak memory usage: 12 MB
% 41.91/6.40 % (549107)Instructions burned: 9 (million)
% 41.91/6.40 % (549107)------------------------------
% 41.91/6.40 % (549107)------------------------------
% 41.91/6.40 % (549109)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=2693177197:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2951 on theBenchmark for (2951ds/1142Mi)
% 41.91/6.40 % (549109)Refutation not found, incomplete strategy
% 41.91/6.40 % (549109)------------------------------
% 41.91/6.40 % (549109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.91/6.40 % (549109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.91/6.40 % (549109)CaDiCaL version: 2.1.3
% 41.91/6.40 % (549109)Termination reason: Refutation not found, incomplete strategy
% 41.91/6.40 % (549109)Time elapsed: 0.020 s
% 41.91/6.40 % (549109)Peak memory usage: 12 MB
% 41.91/6.40 % (549109)Instructions burned: 37 (million)
% 41.91/6.40 % (549109)------------------------------
% 41.91/6.40 % (549109)------------------------------
% 41.91/6.40 % (549111)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=78753295:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2950 on theBenchmark for (2950ds/376Mi)
% 41.91/6.40 % (549091)Instruction limit reached!
% 41.91/6.40 % (549091)------------------------------
% 41.91/6.40 % (549091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.91/6.40 % (549091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.91/6.40 % (549091)CaDiCaL version: 2.1.3
% 41.91/6.40 % (549091)Termination reason: Instruction limit
% 41.91/6.40 % (549091)Termination phase: Saturation
% 41.91/6.40 % (549091)Time elapsed: 0.523 s
% 41.91/6.40 % (549091)Peak memory usage: 14 MB
% 41.91/6.40 % (549091)Instructions burned: 647 (million)
% 41.91/6.40 % (549090)Instruction limit reached!
% 41.91/6.40 % (549090)------------------------------
% 41.91/6.40 % (549090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.91/6.40 % (549090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.91/6.40 % (549090)CaDiCaL version: 2.1.3
% 41.91/6.40 % (549090)Termination reason: Instruction limit
% 41.91/6.40 % (549090)Termination phase: Saturation
% 41.91/6.40 % (549090)Time elapsed: 0.531 s
% 41.91/6.40 % (549090)Peak memory usage: 16 MB
% 41.91/6.40 % (549090)Instructions burned: 671 (million)
% 41.91/6.40 % (549114)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 43.88/6.60 % (549113)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=4115801836:i=766:bd=all:rtra=on_2949 on theBenchmark for (2949ds/766Mi)
% 43.88/6.60 % (549114)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=3789814621: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_2949 on theBenchmark for (2949ds/959Mi)
% 43.88/6.60 % (549111)Instruction limit reached!
% 43.88/6.60 % (549111)------------------------------
% 43.88/6.60 % (549111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.88/6.60 % (549111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.88/6.60 % (549111)CaDiCaL version: 2.1.3
% 43.88/6.60 % (549111)Termination reason: Instruction limit
% 43.88/6.60 % (549111)Termination phase: Saturation
% 43.88/6.60 % (549111)Time elapsed: 0.167 s
% 43.88/6.60 % (549111)Peak memory usage: 15 MB
% 43.88/6.60 % (549111)Instructions burned: 377 (million)
% 43.88/6.60 % (549117)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=2798717293:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2949 on theBenchmark for (2949ds/6359Mi)
% 43.88/6.60 % (549097)Instruction limit reached!
% 43.88/6.60 % (549097)------------------------------
% 43.88/6.60 % (549097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.88/6.60 % (549097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.88/6.60 % (549097)CaDiCaL version: 2.1.3
% 43.88/6.60 % (549097)Termination reason: Instruction limit
% 43.88/6.60 % (549097)Termination phase: Saturation
% 43.88/6.60 % (549097)Time elapsed: 0.553 s
% 43.88/6.60 % (549097)Peak memory usage: 14 MB
% 43.88/6.60 % (549097)Instructions burned: 693 (million)
% 43.88/6.60 % (549119)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3305602611:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2948 on theBenchmark for (2948ds/35Mi)
% 43.88/6.60 % (549119)Instruction limit reached!
% 43.88/6.60 % (549119)------------------------------
% 43.88/6.60 % (549119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.88/6.60 % (549119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.88/6.60 % (549119)CaDiCaL version: 2.1.3
% 43.88/6.60 % (549119)Termination reason: Instruction limit
% 43.88/6.60 % (549119)Termination phase: Saturation
% 43.88/6.60 % (549119)Time elapsed: 0.028 s
% 43.88/6.60 % (549119)Peak memory usage: 11 MB
% 43.88/6.60 % (549119)Instructions burned: 36 (million)
% 43.88/6.60 % (549121)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=3394603584:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2948 on theBenchmark for (2948ds/53Mi)
% 43.88/6.60 % (549121)Instruction limit reached!
% 43.88/6.60 % (549121)------------------------------
% 43.88/6.60 % (549121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.88/6.60 % (549121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.88/6.60 % (549121)CaDiCaL version: 2.1.3
% 43.88/6.60 % (549121)Termination reason: Instruction limit
% 43.88/6.60 % (549121)Termination phase: Saturation
% 43.88/6.60 % (549121)Time elapsed: 0.043 s
% 43.88/6.60 % (549121)Peak memory usage: 12 MB
% 43.88/6.60 % (549121)Instructions burned: 53 (million)
% 43.88/6.60 % (549123)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=4200148244:s2a=on:i=876:s2at=6:nm=2:rtra=on_2947 on theBenchmark for (2947ds/876Mi)
% 43.88/6.60 % (549033)Instruction limit reached!
% 43.88/6.60 % (549033)------------------------------
% 43.88/6.60 % (549033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 43.88/6.60 % (549033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 43.88/6.60 % (549033)CaDiCaL version: 2.1.3
% 43.88/6.60 % (549033)Termination reason: Instruction limit
% 43.88/6.60 % (549033)Termination phase: Saturation
% 43.88/6.60 % (549033)Time elapsed: 2.071 s
% 43.88/6.60 % (549033)Peak memory usage: 19 MB
% 43.88/6.60 % (549033)Instructions burned: 2470 (million)
% 43.88/6.60 % (549125)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=406578992:i=57:ep=R:rtra=on:ntd=on_2946 on theBenchmark for (2946ds/57Mi)
% 43.88/6.60 % (549125)Instruction limit reached!
% 45.01/6.82 % (549125)------------------------------
% 45.01/6.82 % (549125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.01/6.82 % (549125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.01/6.82 % (549125)CaDiCaL version: 2.1.3
% 45.01/6.82 % (549125)Termination reason: Instruction limit
% 45.01/6.82 % (549125)Termination phase: Saturation
% 45.01/6.82 % (549125)Time elapsed: 0.046 s
% 45.01/6.82 % (549125)Peak memory usage: 12 MB
% 45.01/6.82 % (549125)Instructions burned: 57 (million)
% 45.01/6.82 % (549127)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 45.01/6.82 % (549127)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=2110208066:i=306:bd=all:rtra=on_2945 on theBenchmark for (2945ds/306Mi)
% 45.01/6.82 % (549113)Instruction limit reached!
% 45.01/6.82 % (549113)------------------------------
% 45.01/6.82 % (549113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.01/6.82 % (549113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.01/6.83 % (549113)CaDiCaL version: 2.1.3
% 45.01/6.83 % (549113)Termination reason: Instruction limit
% 45.01/6.83 % (549113)Termination phase: Saturation
% 45.01/6.83 % (549113)Time elapsed: 0.635 s
% 45.01/6.83 % (549113)Peak memory usage: 17 MB
% 45.01/6.83 % (549113)Instructions burned: 767 (million)
% 45.01/6.83 % (549127)Instruction limit reached!
% 45.01/6.83 % (549127)------------------------------
% 45.01/6.83 % (549127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.01/6.83 % (549127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.01/6.83 % (549127)CaDiCaL version: 2.1.3
% 45.01/6.83 % (549127)Termination reason: Instruction limit
% 45.01/6.83 % (549127)Termination phase: Saturation
% 45.01/6.83 % (549127)Time elapsed: 0.259 s
% 45.01/6.83 % (549127)Peak memory usage: 14 MB
% 45.01/6.83 % (549127)Instructions burned: 306 (million)
% 45.01/6.83 % (549129)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=1387847062:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2942 on theBenchmark for (2942ds/262Mi)
% 45.01/6.83 % (549130)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 45.01/6.83 % (549130)ott+1002_16_sil=128000:si=on:random_seed=1485212865:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2942 on theBenchmark for (2942ds/409Mi)
% 45.01/6.83 % (549114)Instruction limit reached!
% 45.01/6.83 % (549114)------------------------------
% 45.01/6.83 % (549114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.01/6.83 % (549114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.01/6.83 % (549114)CaDiCaL version: 2.1.3
% 45.01/6.83 % (549114)Termination reason: Instruction limit
% 45.01/6.83 % (549114)Termination phase: Saturation
% 45.01/6.83 % (549114)Time elapsed: 0.787 s
% 45.01/6.83 % (549114)Peak memory usage: 16 MB
% 45.01/6.83 % (549114)Instructions burned: 959 (million)
% 45.01/6.83 % (549133)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=79631704:s2a=on:i=381:rtra=on_2941 on theBenchmark for (2941ds/381Mi)
% 45.01/6.83 % (549129)Instruction limit reached!
% 45.01/6.83 % (549129)------------------------------
% 45.01/6.83 % (549129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.01/6.83 % (549129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.01/6.83 % (549129)CaDiCaL version: 2.1.3
% 45.01/6.83 % (549129)Termination reason: Instruction limit
% 45.01/6.83 % (549129)Termination phase: Saturation
% 45.01/6.83 % (549129)Time elapsed: 0.191 s
% 45.01/6.83 % (549129)Peak memory usage: 12 MB
% 45.01/6.83 % (549129)Instructions burned: 263 (million)
% 45.01/6.83 % (549135)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=749346259:cond=on:i=324:rtra=on:ntd=on_2940 on theBenchmark for (2940ds/324Mi)
% 45.01/6.83 % (549123)Instruction limit reached!
% 45.01/6.83 % (549123)------------------------------
% 45.01/6.83 % (549123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.01/6.83 % (549123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.01/6.83 % (549123)CaDiCaL version: 2.1.3
% 45.01/6.83 % (549123)Termination reason: Instruction limit
% 45.01/6.83 % (549123)Termination phase: Saturation
% 45.01/6.83 % (549123)Time elapsed: 0.729 s
% 45.01/6.83 % (549123)Peak memory usage: 14 MB
% 45.01/6.83 % (549123)Instructions burned: 877 (million)
% 48.27/7.18 % (549137)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=2010168575:i=240:kws=inv_precedence:rtra=on_2939 on theBenchmark for (2939ds/240Mi)
% 48.27/7.18 % (549137)Refutation not found, incomplete strategy
% 48.27/7.18 % (549137)------------------------------
% 48.27/7.18 % (549137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.27/7.18 % (549137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.27/7.18 % (549137)CaDiCaL version: 2.1.3
% 48.27/7.18 % (549137)Termination reason: Refutation not found, incomplete strategy
% 48.27/7.18 % (549137)Time elapsed: 0.011 s
% 48.27/7.18 % (549137)Peak memory usage: 12 MB
% 48.27/7.18 % (549137)Instructions burned: 11 (million)
% 48.27/7.18 % (549137)------------------------------
% 48.27/7.18 % (549137)------------------------------
% 48.27/7.18 % (549130)Instruction limit reached!
% 48.27/7.18 % (549130)------------------------------
% 48.27/7.18 % (549130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.27/7.18 % (549130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.27/7.18 % (549130)CaDiCaL version: 2.1.3
% 48.27/7.18 % (549130)Termination reason: Instruction limit
% 48.27/7.18 % (549130)Termination phase: Saturation
% 48.27/7.18 % (549130)Time elapsed: 0.343 s
% 48.27/7.18 % (549130)Peak memory usage: 14 MB
% 48.27/7.18 % (549130)Instructions burned: 410 (million)
% 48.27/7.18 % (549139)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 48.27/7.18 % (549139)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=635023883:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2939 on theBenchmark for (2939ds/124Mi)
% 48.27/7.18 % (549140)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=3198960346:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2938 on theBenchmark for (2938ds/223Mi)
% 48.27/7.18 % (549140)Refutation not found, incomplete strategy
% 48.27/7.18 % (549140)------------------------------
% 48.27/7.18 % (549140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.27/7.18 % (549140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.27/7.18 % (549140)CaDiCaL version: 2.1.3
% 48.27/7.18 % (549140)Termination reason: Refutation not found, incomplete strategy
% 48.27/7.18 % (549140)Time elapsed: 0.017 s
% 48.27/7.18 % (549140)Peak memory usage: 12 MB
% 48.27/7.18 % (549140)Instructions burned: 22 (million)
% 48.27/7.18 % (549140)------------------------------
% 48.27/7.18 % (549140)------------------------------
% 48.27/7.18 % (549143)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4197508835:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2938 on theBenchmark for (2938ds/282Mi)
% 48.27/7.18 % (549133)Instruction limit reached!
% 48.27/7.18 % (549133)------------------------------
% 48.27/7.18 % (549133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.27/7.18 % (549133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.27/7.18 % (549133)CaDiCaL version: 2.1.3
% 48.27/7.18 % (549133)Termination reason: Instruction limit
% 48.27/7.18 % (549133)Termination phase: Saturation
% 48.27/7.18 % (549133)Time elapsed: 0.303 s
% 48.27/7.18 % (549133)Peak memory usage: 14 MB
% 48.27/7.18 % (549133)Instructions burned: 382 (million)
% 48.27/7.18 % (549139)Instruction limit reached!
% 48.27/7.18 % (549139)------------------------------
% 48.27/7.18 % (549139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.27/7.18 % (549139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.27/7.18 % (549139)CaDiCaL version: 2.1.3
% 48.27/7.18 % (549139)Termination reason: Instruction limit
% 48.27/7.18 % (549139)Termination phase: Saturation
% 48.27/7.18 % (549139)Time elapsed: 0.097 s
% 48.27/7.18 % (549139)Peak memory usage: 12 MB
% 48.27/7.18 % (549139)Instructions burned: 125 (million)
% 48.27/7.18 % (549145)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=2361089685:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2938 on theBenchmark for (2938ds/464Mi)
% 48.27/7.18 % (549145)Refutation not found, incomplete strategy
% 48.27/7.18 % (549145)------------------------------
% 48.27/7.18 % (549145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 48.27/7.18 % (549145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 48.27/7.18 % (549145)CaDiCaL version: 2.1.3
% 48.27/7.18 % (549145)Termination reason: Refutation not found, incomplete strategy
% 51.13/7.67 % (549145)Time elapsed: 0.008 s
% 51.13/7.67 % (549145)Peak memory usage: 12 MB
% 51.13/7.67 % (549145)Instructions burned: 8 (million)
% 51.13/7.67 % (549145)------------------------------
% 51.13/7.67 % (549145)------------------------------
% 51.13/7.67 % (549135)Instruction limit reached!
% 51.13/7.67 % (549135)------------------------------
% 51.13/7.67 % (549135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.13/7.67 % (549135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.13/7.67 % (549135)CaDiCaL version: 2.1.3
% 51.13/7.67 % (549135)Termination reason: Instruction limit
% 51.13/7.67 % (549135)Termination phase: Saturation
% 51.13/7.67 % (549135)Time elapsed: 0.279 s
% 51.13/7.67 % (549135)Peak memory usage: 13 MB
% 51.13/7.67 % (549135)Instructions burned: 324 (million)
% 51.13/7.67 % (549146)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=3068422002:i=88:s2at=3:nm=2:rtra=on:rawr=on_2937 on theBenchmark for (2937ds/88Mi)
% 51.13/7.67 % (549150)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 51.13/7.67 % (549148)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2305810796:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2937 on theBenchmark for (2937ds/280Mi)
% 51.13/7.67 % (549150)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2126546967:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2937 on theBenchmark for (2937ds/4386Mi)
% 51.13/7.67 % (549146)Instruction limit reached!
% 51.13/7.67 % (549146)------------------------------
% 51.13/7.67 % (549146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.13/7.67 % (549146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.13/7.67 % (549146)CaDiCaL version: 2.1.3
% 51.13/7.67 % (549146)Termination reason: Instruction limit
% 51.13/7.67 % (549146)Termination phase: Saturation
% 51.13/7.67 % (549146)Time elapsed: 0.068 s
% 51.13/7.67 % (549146)Peak memory usage: 12 MB
% 51.13/7.67 % (549146)Instructions burned: 88 (million)
% 51.13/7.67 % (549153)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 51.13/7.67 % (549153)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 51.13/7.67 % (549153)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=1486103376:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2936 on theBenchmark for (2936ds/483Mi)
% 51.13/7.67 % (549153)Refutation not found, incomplete strategy
% 51.13/7.67 % (549153)------------------------------
% 51.13/7.67 % (549153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.13/7.67 % (549153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.13/7.67 % (549153)CaDiCaL version: 2.1.3
% 51.13/7.67 % (549153)Termination reason: Refutation not found, incomplete strategy
% 51.13/7.67 % (549153)Time elapsed: 0.019 s
% 51.13/7.67 % (549153)Peak memory usage: 12 MB
% 51.13/7.67 % (549153)Instructions burned: 24 (million)
% 51.13/7.67 % (549153)------------------------------
% 51.13/7.67 % (549153)------------------------------
% 51.13/7.67 % (549155)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=3903906131:i=73:rtra=on_2936 on theBenchmark for (2936ds/73Mi)
% 51.13/7.67 % (549143)Instruction limit reached!
% 51.13/7.67 % (549143)------------------------------
% 51.13/7.67 % (549143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.13/7.67 % (549143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.13/7.67 % (549143)CaDiCaL version: 2.1.3
% 51.13/7.67 % (549143)Termination reason: Instruction limit
% 51.13/7.67 % (549143)Termination phase: Saturation
% 51.13/7.67 % (549143)Time elapsed: 0.252 s
% 51.13/7.67 % (549143)Peak memory usage: 13 MB
% 51.13/7.67 % (549143)Instructions burned: 282 (million)
% 51.13/7.67 % (549155)Instruction limit reached!
% 51.13/7.67 % (549155)------------------------------
% 51.13/7.67 % (549155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 51.13/7.67 % (549155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 51.13/7.67 % (549155)CaDiCaL version: 2.1.3
% 51.13/7.67 % (549155)Termination reason: Instruction limit
% 55.65/8.29 % (549155)Termination phase: Saturation
% 55.65/8.29 % (549155)Time elapsed: 0.057 s
% 55.65/8.29 % (549155)Peak memory usage: 12 MB
% 55.65/8.29 % (549155)Instructions burned: 73 (million)
% 55.65/8.29 % (549157)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3549270623:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2935 on theBenchmark for (2935ds/176Mi)
% 55.65/8.29 % (549158)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 55.65/8.29 % (549148)Instruction limit reached!
% 55.65/8.29 % (549148)------------------------------
% 55.65/8.29 % (549148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.65/8.29 % (549148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.65/8.29 % (549148)CaDiCaL version: 2.1.3
% 55.65/8.29 % (549148)Termination reason: Instruction limit
% 55.65/8.29 % (549148)Termination phase: Saturation
% 55.65/8.29 % (549148)Time elapsed: 0.215 s
% 55.65/8.29 % (549148)Peak memory usage: 12 MB
% 55.65/8.29 % (549148)Instructions burned: 280 (million)
% 55.65/8.29 % (549158)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3407195320:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2935 on theBenchmark for (2935ds/39Mi)
% 55.65/8.29 % (549160)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2799485619:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2935 on theBenchmark for (2935ds/708Mi)
% 55.65/8.29 % (549158)Instruction limit reached!
% 55.65/8.29 % (549158)------------------------------
% 55.65/8.29 % (549158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.65/8.29 % (549158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.65/8.29 % (549158)CaDiCaL version: 2.1.3
% 55.65/8.29 % (549158)Termination reason: Instruction limit
% 55.65/8.29 % (549158)Termination phase: Saturation
% 55.65/8.29 % (549158)Time elapsed: 0.031 s
% 55.65/8.29 % (549158)Peak memory usage: 12 MB
% 55.65/8.29 % (549158)Instructions burned: 39 (million)
% 55.65/8.29 % (549163)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
% 55.65/8.29 % (549163)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=860461438:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2934 on theBenchmark for (2934ds/252Mi)
% 55.65/8.29 % (549163)Refutation not found, incomplete strategy
% 55.65/8.29 % (549163)------------------------------
% 55.65/8.29 % (549163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.65/8.29 % (549163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.65/8.29 % (549163)CaDiCaL version: 2.1.3
% 55.65/8.29 % (549163)Termination reason: Refutation not found, incomplete strategy
% 55.65/8.29 % (549163)Time elapsed: 0.020 s
% 55.65/8.29 % (549163)Peak memory usage: 12 MB
% 55.65/8.29 % (549163)Instructions burned: 26 (million)
% 55.65/8.29 % (549163)------------------------------
% 55.65/8.29 % (549163)------------------------------
% 55.65/8.29 % (549165)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=2182880275:i=823:fsr=off:rtra=on_2934 on theBenchmark for (2934ds/823Mi)
% 55.65/8.29 % (549157)Instruction limit reached!
% 55.65/8.29 % (549157)------------------------------
% 55.65/8.29 % (549157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 55.65/8.29 % (549157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 55.65/8.29 % (549157)CaDiCaL version: 2.1.3
% 55.65/8.29 % (549157)Termination reason: Instruction limit
% 55.65/8.29 % (549157)Termination phase: Saturation
% 55.65/8.29 % (549157)Time elapsed: 0.137 s
% 55.65/8.29 % (549157)Peak memory usage: 12 MB
% 55.65/8.29 % (549157)Instructions burned: 177 (million)
% 55.65/8.29 % (549167)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 55.65/8.29 % (549167)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=2516366107:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2933 on theBenchmark for (2933ds/16202Mi)
% 55.65/8.29 % (549105)Instruction limit reached!
% 55.65/8.29 % (549105)------------------------------
% 55.65/8.29 % (549105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.05/8.91 % (549105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.05/8.91 % (549105)CaDiCaL version: 2.1.3
% 59.05/8.91 % (549105)Termination reason: Instruction limit
% 59.05/8.91 % (549105)Termination phase: Saturation
% 59.05/8.91 % (549105)Time elapsed: 2.011 s
% 59.05/8.91 % (549105)Peak memory usage: 27 MB
% 59.05/8.91 % (549105)Instructions burned: 2242 (million)
% 59.05/8.91 % (549169)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=2081001519:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2931 on theBenchmark for (2931ds/300Mi)
% 59.05/8.91 % (549169)Instruction limit reached!
% 59.05/8.91 % (549169)------------------------------
% 59.05/8.91 % (549169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.05/8.91 % (549169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.05/8.91 % (549169)CaDiCaL version: 2.1.3
% 59.05/8.91 % (549169)Termination reason: Instruction limit
% 59.05/8.91 % (549169)Termination phase: Saturation
% 59.05/8.91 % (549169)Time elapsed: 0.236 s
% 59.05/8.91 % (549169)Peak memory usage: 13 MB
% 59.05/8.91 % (549169)Instructions burned: 300 (million)
% 59.05/8.91 % (549160)Instruction limit reached!
% 59.05/8.91 % (549160)------------------------------
% 59.05/8.91 % (549160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.05/8.91 % (549160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.05/8.91 % (549160)CaDiCaL version: 2.1.3
% 59.05/8.91 % (549160)Termination reason: Instruction limit
% 59.05/8.91 % (549160)Termination phase: Saturation
% 59.05/8.91 % (549160)Time elapsed: 0.586 s
% 59.05/8.91 % (549160)Peak memory usage: 16 MB
% 59.05/8.91 % (549160)Instructions burned: 708 (million)
% 59.05/8.91 % (549171)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 59.05/8.91 % (549171)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 59.05/8.91 % (549171)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=2651701829:i=177:add=on:bd=preordered:rtra=on:rawr=on_2929 on theBenchmark for (2929ds/177Mi)
% 59.05/8.91 % (549172)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=921359349:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2928 on theBenchmark for (2928ds/715Mi)
% 59.05/8.91 % (549171)Instruction limit reached!
% 59.05/8.91 % (549171)------------------------------
% 59.05/8.91 % (549171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.05/8.91 % (549171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.05/8.91 % (549171)CaDiCaL version: 2.1.3
% 59.05/8.91 % (549171)Termination reason: Instruction limit
% 59.05/8.91 % (549171)Termination phase: Saturation
% 59.05/8.91 % (549171)Time elapsed: 0.145 s
% 59.05/8.91 % (549171)Peak memory usage: 13 MB
% 59.05/8.91 % (549171)Instructions burned: 178 (million)
% 59.05/8.91 % (549165)Instruction limit reached!
% 59.05/8.91 % (549165)------------------------------
% 59.05/8.91 % (549165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.05/8.91 % (549165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.05/8.91 % (549165)CaDiCaL version: 2.1.3
% 59.05/8.91 % (549165)Termination reason: Instruction limit
% 59.05/8.91 % (549165)Termination phase: Saturation
% 59.05/8.91 % (549165)Time elapsed: 0.657 s
% 59.05/8.91 % (549165)Peak memory usage: 14 MB
% 59.05/8.91 % (549165)Instructions burned: 823 (million)
% 59.05/8.91 % (549175)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 59.05/8.91 % (549175)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 59.05/8.91 % (549175)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=416984982:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2927 on theBenchmark for (2927ds/230Mi)
% 59.05/8.91 % (549176)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=2278933869:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2927 on theBenchmark for (2927ds/606Mi)
% 59.05/8.91 % (549175)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 64.10/9.43 % (549175)Instruction limit reached!
% 64.10/9.43 % (549175)------------------------------
% 64.10/9.43 % (549175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.10/9.43 % (549175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.10/9.43 % (549175)CaDiCaL version: 2.1.3
% 64.10/9.43 % (549175)Termination reason: Instruction limit
% 64.10/9.43 % (549175)Termination phase: Saturation
% 64.10/9.43 % (549175)Time elapsed: 0.183 s
% 64.10/9.43 % (549175)Peak memory usage: 13 MB
% 64.10/9.43 % (549175)Instructions burned: 230 (million)
% 64.10/9.43 % (549179)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 64.10/9.43 % (549179)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=1168129941:lrd=on:i=841:nm=0:rtra=on_2925 on theBenchmark for (2925ds/841Mi)
% 64.10/9.43 % (549172)Instruction limit reached!
% 64.10/9.43 % (549172)------------------------------
% 64.10/9.43 % (549172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.10/9.43 % (549172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.10/9.43 % (549172)CaDiCaL version: 2.1.3
% 64.10/9.43 % (549172)Termination reason: Instruction limit
% 64.10/9.43 % (549172)Termination phase: Saturation
% 64.10/9.43 % (549172)Time elapsed: 0.453 s
% 64.10/9.43 % (549172)Peak memory usage: 12 MB
% 64.10/9.43 % (549172)Instructions burned: 716 (million)
% 64.10/9.43 % (549181)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1655863786:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2924 on theBenchmark for (2924ds/445Mi)
% 64.10/9.43 % (549176)Instruction limit reached!
% 64.10/9.43 % (549176)------------------------------
% 64.10/9.43 % (549176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.10/9.43 % (549176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.10/9.43 % (549176)CaDiCaL version: 2.1.3
% 64.10/9.43 % (549176)Termination reason: Instruction limit
% 64.10/9.43 % (549176)Termination phase: Saturation
% 64.10/9.43 % (549176)Time elapsed: 0.493 s
% 64.10/9.43 % (549176)Peak memory usage: 14 MB
% 64.10/9.43 % (549176)Instructions burned: 607 (million)
% 64.10/9.43 % (549183)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=2597158073:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2922 on theBenchmark for (2922ds/71Mi)
% 64.10/9.43 % (549117)Instruction limit reached!
% 64.10/9.43 % (549117)------------------------------
% 64.10/9.43 % (549117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.10/9.43 % (549117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.10/9.43 % (549117)CaDiCaL version: 2.1.3
% 64.10/9.43 % (549117)Termination reason: Instruction limit
% 64.10/9.43 % (549117)Termination phase: Saturation
% 64.10/9.43 % (549117)Time elapsed: 2.751 s
% 64.10/9.43 % (549117)Peak memory usage: 52 MB
% 64.10/9.43 % (549117)Instructions burned: 6361 (million)
% 64.10/9.43 % (549185)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
% 64.10/9.43 % (549185)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 64.10/9.43 % (549183)Instruction limit reached!
% 64.10/9.43 % (549183)------------------------------
% 64.10/9.43 % (549183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 64.10/9.43 % (549183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 64.10/9.43 % (549183)CaDiCaL version: 2.1.3
% 64.10/9.43 % (549183)Termination reason: Instruction limit
% 64.10/9.43 % (549183)Termination phase: Saturation
% 64.10/9.43 % (549183)Time elapsed: 0.059 s
% 64.10/9.43 % (549183)Peak memory usage: 12 MB
% 64.10/9.43 % (549183)Instructions burned: 72 (million)
% 64.10/9.43 % (549185)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3356269368:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2921 on theBenchmark for (2921ds/100Mi)
% 64.10/9.43 % (549186)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 64.10/9.43 % (549186)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=1315915050:i=1352:add=on:aac=none:rtra=on_2921 on theBenchmark for (2921ds/1352Mi)
% 65.35/9.60 % (549185)Instruction limit reached!
% 65.35/9.60 % (549185)------------------------------
% 65.35/9.60 % (549185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.35/9.60 % (549185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.35/9.60 % (549185)CaDiCaL version: 2.1.3
% 65.35/9.60 % (549185)Termination reason: Instruction limit
% 65.35/9.60 % (549185)Termination phase: Saturation
% 65.35/9.60 % (549185)Time elapsed: 0.041 s
% 65.35/9.60 % (549185)Peak memory usage: 12 MB
% 65.35/9.60 % (549185)Instructions burned: 104 (million)
% 65.35/9.60 % (549189)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=3990071561:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2920 on theBenchmark for (2920ds/646Mi)
% 65.35/9.60 % (549181)Instruction limit reached!
% 65.35/9.60 % (549181)------------------------------
% 65.35/9.60 % (549181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.35/9.60 % (549181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.35/9.60 % (549181)CaDiCaL version: 2.1.3
% 65.35/9.60 % (549181)Termination reason: Instruction limit
% 65.35/9.60 % (549181)Termination phase: Saturation
% 65.35/9.60 % (549181)Time elapsed: 0.360 s
% 65.35/9.60 % (549181)Peak memory usage: 14 MB
% 65.35/9.60 % (549181)Instructions burned: 445 (million)
% 65.35/9.60 % (549191)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=1554097656:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2920 on theBenchmark for (2920ds/1924Mi)
% 65.35/9.60 % (549179)Instruction limit reached!
% 65.35/9.60 % (549179)------------------------------
% 65.35/9.60 % (549179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.35/9.60 % (549179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.35/9.60 % (549179)CaDiCaL version: 2.1.3
% 65.35/9.60 % (549179)Termination reason: Instruction limit
% 65.35/9.60 % (549179)Termination phase: Saturation
% 65.35/9.60 % (549179)Time elapsed: 0.599 s
% 65.35/9.60 % (549179)Peak memory usage: 15 MB
% 65.35/9.60 % (549179)Instructions burned: 842 (million)
% 65.35/9.60 % (549193)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3994284263:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2918 on theBenchmark for (2918ds/984Mi)
% 65.35/9.60 % (549189)Instruction limit reached!
% 65.35/9.60 % (549189)------------------------------
% 65.35/9.60 % (549189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.35/9.60 % (549189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.35/9.60 % (549189)CaDiCaL version: 2.1.3
% 65.35/9.60 % (549189)Termination reason: Instruction limit
% 65.35/9.60 % (549189)Termination phase: Saturation
% 65.35/9.60 % (549189)Time elapsed: 0.288 s
% 65.35/9.60 % (549189)Peak memory usage: 16 MB
% 65.35/9.60 % (549189)Instructions burned: 647 (million)
% 65.35/9.60 % (549195)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=99315750:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2917 on theBenchmark for (2917ds/592Mi)
% 65.35/9.60 % (549195)Instruction limit reached!
% 65.35/9.60 % (549195)------------------------------
% 65.35/9.60 % (549195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.35/9.60 % (549195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.35/9.60 % (549195)CaDiCaL version: 2.1.3
% 65.35/9.60 % (549195)Termination reason: Instruction limit
% 65.35/9.60 % (549195)Termination phase: Saturation
% 65.35/9.60 % (549195)Time elapsed: 0.254 s
% 65.35/9.60 % (549195)Peak memory usage: 13 MB
% 65.35/9.60 % (549195)Instructions burned: 592 (million)
% 65.35/9.60 % (549197)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=803130343:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2914 on theBenchmark for (2914ds/872Mi)
% 65.35/9.60 % (549197)Refutation not found, incomplete strategy
% 65.35/9.60 % (549197)------------------------------
% 65.35/9.60 % (549197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 65.35/9.60 % (549197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 65.35/9.60 % (549197)CaDiCaL version: 2.1.3
% 65.35/9.60 % (549197)Termination reason: Refutation not found, incomplete strategy
% 65.35/9.60 % (549197)Time elapsed: 0.006 s
% 65.35/9.60 % (549197)Peak memory usage: 12 MB
% 65.35/9.60 % (549197)Instructions burned: 14 (million)
% 66.34/9.99 % (549197)------------------------------
% 66.34/9.99 % (549197)------------------------------
% 66.34/9.99 % (549199)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 66.34/9.99 % (549199)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=435237949:i=999:add=on:rtra=on_2914 on theBenchmark for (2914ds/999Mi)
% 66.34/9.99 % (549193)Instruction limit reached!
% 66.34/9.99 % (549193)------------------------------
% 66.34/9.99 % (549193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 66.34/9.99 % (549193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 66.34/9.99 % (549193)CaDiCaL version: 2.1.3
% 66.34/9.99 % (549193)Termination reason: Instruction limit
% 66.34/9.99 % (549193)Termination phase: Saturation
% 66.34/9.99 % (549193)Time elapsed: 0.820 s
% 66.34/9.99 % (549193)Peak memory usage: 17 MB
% 66.34/9.99 % (549193)Instructions burned: 985 (million)
% 66.34/9.99 % (549186)Instruction limit reached!
% 66.34/9.99 % (549186)------------------------------
% 66.34/9.99 % (549186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 66.34/9.99 % (549186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 66.34/9.99 % (549186)CaDiCaL version: 2.1.3
% 66.34/9.99 % (549186)Termination reason: Instruction limit
% 66.34/9.99 % (549186)Termination phase: Saturation
% 66.34/9.99 % (549186)Time elapsed: 1.055 s
% 66.34/9.99 % (549186)Peak memory usage: 16 MB
% 66.34/9.99 % (549186)Instructions burned: 1353 (million)
% 66.34/9.99 % (549201)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 66.34/9.99 % (549199)Instruction limit reached!
% 66.34/9.99 % (549199)------------------------------
% 66.34/9.99 % (549199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 66.34/9.99 % (549199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 66.34/9.99 % (549199)CaDiCaL version: 2.1.3
% 66.34/9.99 % (549199)Termination reason: Instruction limit
% 66.34/9.99 % (549199)Termination phase: Saturation
% 66.34/9.99 % (549199)Time elapsed: 0.441 s
% 66.34/9.99 % (549199)Peak memory usage: 16 MB
% 66.34/9.99 % (549199)Instructions burned: 1001 (million)
% 66.34/9.99 % (549201)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=2131256080:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2910 on theBenchmark for (2910ds/244Mi)
% 66.34/9.99 % (549202)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=1864123141:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2910 on theBenchmark for (2910ds/113Mi)
% 66.34/9.99 % (549203)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1634176595:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2910 on theBenchmark for (2910ds/7795Mi)
% 66.34/9.99 % (549203)Refutation not found, incomplete strategy
% 66.34/9.99 % (549203)------------------------------
% 66.34/9.99 % (549203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 66.34/9.99 % (549203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 66.34/9.99 % (549203)CaDiCaL version: 2.1.3
% 66.34/9.99 % (549203)Termination reason: Refutation not found, incomplete strategy
% 66.34/9.99 % (549203)Time elapsed: 0.003 s
% 66.34/9.99 % (549203)Peak memory usage: 12 MB
% 66.34/9.99 % (549203)Instructions burned: 6 (million)
% 66.34/9.99 % (549203)------------------------------
% 66.34/9.99 % (549203)------------------------------
% 66.34/9.99 % (549207)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3678464118:st=2:i=5026:sd=1:rtra=on:ss=axioms_2909 on theBenchmark for (2909ds/5026Mi)
% 66.34/9.99 % (549207)Refutation not found, incomplete strategy
% 66.34/9.99 % (549207)------------------------------
% 66.34/9.99 % (549207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 66.34/9.99 % (549207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 66.34/9.99 % (549207)CaDiCaL version: 2.1.3
% 66.34/9.99 % (549207)Termination reason: Refutation not found, incomplete strategy
% 66.34/9.99 % (549207)Time elapsed: 0.004 s
% 66.34/9.99 % (549207)Peak memory usage: 12 MB
% 66.34/9.99 % (549207)Instructions burned: 8 (million)
% 66.34/9.99 % (549207)------------------------------
% 66.34/9.99 % (549207)------------------------------
% 66.34/9.99 % (549209)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 72.51/10.80 % (549209)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=1253901618:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2909 on theBenchmark for (2909ds/763Mi)
% 72.51/10.80 % (549209)Refutation not found, incomplete strategy
% 72.51/10.80 % (549209)------------------------------
% 72.51/10.80 % (549209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.51/10.80 % (549209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.51/10.80 % (549209)CaDiCaL version: 2.1.3
% 72.51/10.80 % (549209)Termination reason: Refutation not found, incomplete strategy
% 72.51/10.80 % (549209)Time elapsed: 0.003 s
% 72.51/10.80 % (549209)Peak memory usage: 12 MB
% 72.51/10.80 % (549209)Instructions burned: 6 (million)
% 72.51/10.80 % (549209)------------------------------
% 72.51/10.80 % (549209)------------------------------
% 72.51/10.80 % (549211)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=155334854:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2909 on theBenchmark for (2909ds/1144Mi)
% 72.51/10.80 % (549202)Instruction limit reached!
% 72.51/10.80 % (549202)------------------------------
% 72.51/10.80 % (549202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.51/10.80 % (549202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.51/10.80 % (549202)CaDiCaL version: 2.1.3
% 72.51/10.80 % (549202)Termination reason: Instruction limit
% 72.51/10.80 % (549202)Termination phase: Saturation
% 72.51/10.80 % (549202)Time elapsed: 0.093 s
% 72.51/10.80 % (549202)Peak memory usage: 13 MB
% 72.51/10.80 % (549202)Instructions burned: 114 (million)
% 72.51/10.80 % (549213)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 72.51/10.80 % (549213)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=1233835067:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2908 on theBenchmark for (2908ds/52Mi)
% 72.51/10.80 % (549191)Instruction limit reached!
% 72.51/10.80 % (549191)------------------------------
% 72.51/10.80 % (549191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.51/10.80 % (549191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.51/10.80 % (549191)CaDiCaL version: 2.1.3
% 72.51/10.80 % (549191)Termination reason: Instruction limit
% 72.51/10.80 % (549191)Termination phase: Saturation
% 72.51/10.80 % (549191)Time elapsed: 1.136 s
% 72.51/10.80 % (549191)Peak memory usage: 15 MB
% 72.51/10.80 % (549191)Instructions burned: 1924 (million)
% 72.51/10.80 % (549213)Instruction limit reached!
% 72.51/10.80 % (549213)------------------------------
% 72.51/10.80 % (549213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.51/10.80 % (549213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.51/10.80 % (549213)CaDiCaL version: 2.1.3
% 72.51/10.80 % (549213)Termination reason: Instruction limit
% 72.51/10.80 % (549213)Termination phase: Saturation
% 72.51/10.80 % (549213)Time elapsed: 0.041 s
% 72.51/10.80 % (549213)Peak memory usage: 12 MB
% 72.51/10.80 % (549213)Instructions burned: 52 (million)
% 72.51/10.80 % (549215)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=2874351859:i=1724:fsr=off:rtra=on:fe=abstraction_2908 on theBenchmark for (2908ds/1724Mi)
% 72.51/10.80 % (549201)Instruction limit reached!
% 72.51/10.80 % (549201)------------------------------
% 72.51/10.80 % (549201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 72.51/10.80 % (549201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 72.51/10.80 % (549201)CaDiCaL version: 2.1.3
% 72.51/10.80 % (549201)Termination reason: Instruction limit
% 72.51/10.80 % (549201)Termination phase: Saturation
% 72.51/10.80 % (549201)Time elapsed: 0.191 s
% 72.51/10.80 % (549201)Peak memory usage: 12 MB
% 72.51/10.80 % (549201)Instructions burned: 244 (million)
% 72.51/10.80 % (549216)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=3181861722:i=439:add=on:slsql=off:rtra=on:ntd=on_2908 on theBenchmark for (2908ds/439Mi)
% 72.51/10.80 % (549218)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2135130647:i=6395:sd=1:rtra=on:ss=axioms_2908 on theBenchmark for (2908ds/6395Mi)
% 72.51/10.80 % (549218)Refutation not found, incomplete strategy
% 75.99/11.15 % (549218)------------------------------
% 75.99/11.15 % (549218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 75.99/11.15 % (549218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 75.99/11.15 % (549218)CaDiCaL version: 2.1.3
% 75.99/11.15 % (549218)Termination reason: Refutation not found, incomplete strategy
% 75.99/11.15 % (549218)Time elapsed: 0.006 s
% 75.99/11.15 % (549218)Peak memory usage: 12 MB
% 75.99/11.15 % (549218)Instructions burned: 6 (million)
% 75.99/11.15 % (549218)------------------------------
% 75.99/11.15 % (549218)------------------------------
% 75.99/11.15 % (549221)WARNING Broken Constraint: if ho_split_queue_lambda_weight(5) has been set then ho_split_queue(off) is equal to on
% 75.99/11.15 % (549221)ott+2_16:1_sil=128000:si=on:hsqlw=5:sos=on:urr=on:bce=on:uwa=off:random_seed=2655018459:i=6762:add=off:bd=all:rtra=on:ss=axioms:ntd=on_2907 on theBenchmark for (2907ds/6762Mi)
% 75.99/11.15 % (549221)Refutation not found, incomplete strategy
% 75.99/11.15 % (549221)------------------------------
% 75.99/11.15 % (549221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 75.99/11.15 % (549221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 75.99/11.15 % (549221)CaDiCaL version: 2.1.3
% 75.99/11.15 % (549221)Termination reason: Refutation not found, incomplete strategy
% 75.99/11.15 % (549221)Time elapsed: 0.006 s
% 75.99/11.15 % (549221)Peak memory usage: 12 MB
% 75.99/11.15 % (549221)Instructions burned: 6 (million)
% 75.99/11.15 % (549221)------------------------------
% 75.99/11.15 % (549221)------------------------------
% 75.99/11.15 % (549223)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 75.99/11.15 % (549223)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=4196863029:s2a=on:i=376:add=on:rtra=on:fe=axiom:fdi=1024_2907 on theBenchmark for (2907ds/376Mi)
% 75.99/11.15 % (549150)Instruction limit reached!
% 75.99/11.15 % (549150)------------------------------
% 75.99/11.15 % (549150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 75.99/11.15 % (549150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 75.99/11.15 % (549150)CaDiCaL version: 2.1.3
% 75.99/11.15 % (549150)Termination reason: Instruction limit
% 75.99/11.15 % (549150)Termination phase: Saturation
% 75.99/11.15 % (549150)Time elapsed: 3.241 s
% 75.99/11.15 % (549150)Peak memory usage: 15 MB
% 75.99/11.15 % (549150)Instructions burned: 4386 (million)
% 75.99/11.15 % (549225)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=1397658126:i=965:bd=all:ins=4:rtra=on_2904 on theBenchmark for (2904ds/965Mi)
% 75.99/11.15 % (549211)Instruction limit reached!
% 75.99/11.15 % (549211)------------------------------
% 75.99/11.15 % (549211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 75.99/11.15 % (549211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 75.99/11.15 % (549211)CaDiCaL version: 2.1.3
% 75.99/11.15 % (549211)Termination reason: Instruction limit
% 75.99/11.15 % (549211)Termination phase: Saturation
% 75.99/11.15 % (549211)Time elapsed: 0.473 s
% 75.99/11.15 % (549211)Peak memory usage: 15 MB
% 75.99/11.15 % (549211)Instructions burned: 1145 (million)
% 75.99/11.15 % (549216)Instruction limit reached!
% 75.99/11.15 % (549216)------------------------------
% 75.99/11.15 % (549216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 75.99/11.15 % (549216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 75.99/11.15 % (549227)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2669535802:i=5013:sd=1:rtra=on:ss=axioms:sgt=64_2904 on theBenchmark for (2904ds/5013Mi)
% 75.99/11.15 % (549216)CaDiCaL version: 2.1.3
% 75.99/11.15 % (549216)Termination reason: Instruction limit
% 75.99/11.15 % (549216)Termination phase: Saturation
% 75.99/11.15 % (549216)Time elapsed: 0.365 s
% 75.99/11.15 % (549216)Peak memory usage: 16 MB
% 75.99/11.15 % (549216)Instructions burned: 439 (million)
% 75.99/11.15 % (549229)dis+2_1_tgt=full:si=on:uwa=one_side_interpreted:random_seed=899701590:i=1583:kws=inv_frequency:bd=preordered:nm=0:rtra=on_2904 on theBenchmark for (2904ds/1583Mi)
% 75.99/11.15 % (549223)Instruction limit reached!
% 75.99/11.15 % (549223)------------------------------
% 75.99/11.15 % (549223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 75.99/11.15 % (549223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.98/11.66 % (549223)CaDiCaL version: 2.1.3
% 78.98/11.66 % (549223)Termination reason: Instruction limit
% 78.98/11.66 % (549223)Termination phase: Saturation
% 78.98/11.66 % (549223)Time elapsed: 0.309 s
% 78.98/11.66 % (549223)Peak memory usage: 13 MB
% 78.98/11.66 % (549223)Instructions burned: 376 (million)
% 78.98/11.66 % (549231)WARNING Broken Constraint: if sine_level_split_queue_ratios(1,32) has been set then sine_level_split_queue(off) is equal to on
% 78.98/11.66 % (549231)WARNING Broken Constraint: if ho_split_queue_cutoffs(2) has been set then ho_split_queue(off) is equal to on
% 78.98/11.66 % (549231)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
% 78.98/11.66 % (549231)WARNING Broken Constraint: if ho_split_queue_ratios(4,1) has been set then ho_split_queue(off) is equal to on
% 78.98/11.66 % (549231)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=254965407: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_2903 on theBenchmark for (2903ds/1774Mi)
% 78.98/11.66 % (549231)Refutation not found, incomplete strategy
% 78.98/11.66 % (549231)------------------------------
% 78.98/11.66 % (549231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.98/11.66 % (549231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.98/11.66 % (549231)CaDiCaL version: 2.1.3
% 78.98/11.66 % (549231)Termination reason: Refutation not found, incomplete strategy
% 78.98/11.66 % (549231)Time elapsed: 0.007 s
% 78.98/11.66 % (549231)Peak memory usage: 12 MB
% 78.98/11.66 % (549231)Instructions burned: 7 (million)
% 78.98/11.66 % (549231)------------------------------
% 78.98/11.66 % (549231)------------------------------
% 78.98/11.66 % (549233)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1825987167:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2903 on theBenchmark for (2903ds/515Mi)
% 78.98/11.66 % (549233)Refutation not found, incomplete strategy
% 78.98/11.66 % (549233)------------------------------
% 78.98/11.66 % (549233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.98/11.66 % (549233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.98/11.66 % (549233)CaDiCaL version: 2.1.3
% 78.98/11.66 % (549233)Termination reason: Refutation not found, incomplete strategy
% 78.98/11.66 % (549233)Time elapsed: 0.020 s
% 78.98/11.66 % (549233)Peak memory usage: 13 MB
% 78.98/11.66 % (549233)Instructions burned: 24 (million)
% 78.98/11.66 % (549233)------------------------------
% 78.98/11.66 % (549233)------------------------------
% 78.98/11.66 % (549235)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
% 78.98/11.66 % (549235)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=2188331515:avsq=on:i=1297:add=on:avsqr=1,8:rtra=on:fsd=on_2902 on theBenchmark for (2902ds/1297Mi)
% 78.98/11.66 % (548967)Instruction limit reached!
% 78.98/11.66 % (548967)------------------------------
% 78.98/11.66 % (548967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.98/11.66 % (548967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.98/11.66 % (548967)CaDiCaL version: 2.1.3
% 78.98/11.66 % (548967)Termination reason: Instruction limit
% 78.98/11.66 % (548967)Termination phase: Saturation
% 78.98/11.66 % (548967)Time elapsed: 8.421 s
% 78.98/11.66 % (548967)Peak memory usage: 49 MB
% 78.98/11.66 % (548967)Instructions burned: 9841 (million)
% 78.98/11.66 % (549237)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=1834637085:s2a=on:i=611:rtra=on:gsp=on_2900 on theBenchmark for (2900ds/611Mi)
% 78.98/11.66 % (549237)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 78.98/11.66 % (549225)Instruction limit reached!
% 78.98/11.66 % (549225)------------------------------
% 78.98/11.66 % (549225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 78.98/11.66 % (549225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 78.98/11.66 % (549225)CaDiCaL version: 2.1.3
% 86.24/12.51 % (549225)Termination reason: Instruction limit
% 86.24/12.51 % (549225)Termination phase: Saturation
% 86.24/12.51 % (549225)Time elapsed: 0.879 s
% 86.24/12.51 % (549225)Peak memory usage: 22 MB
% 86.24/12.51 % (549225)Instructions burned: 965 (million)
% 86.24/12.51 % (549239)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 86.24/12.51 % (549239)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=84899676:i=72:bd=all:rtra=on_2895 on theBenchmark for (2895ds/72Mi)
% 86.24/12.51 % (549237)Instruction limit reached!
% 86.24/12.51 % (549237)------------------------------
% 86.24/12.51 % (549237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.24/12.51 % (549237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.24/12.51 % (549237)CaDiCaL version: 2.1.3
% 86.24/12.51 % (549237)Termination reason: Instruction limit
% 86.24/12.51 % (549237)Termination phase: Saturation
% 86.24/12.51 % (549237)Time elapsed: 0.510 s
% 86.24/12.51 % (549237)Peak memory usage: 15 MB
% 86.24/12.51 % (549237)Instructions burned: 612 (million)
% 86.24/12.51 % (549239)Instruction limit reached!
% 86.24/12.51 % (549239)------------------------------
% 86.24/12.51 % (549239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.24/12.51 % (549239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.24/12.51 % (549239)CaDiCaL version: 2.1.3
% 86.24/12.51 % (549239)Termination reason: Instruction limit
% 86.24/12.51 % (549239)Termination phase: Saturation
% 86.24/12.51 % (549239)Time elapsed: 0.058 s
% 86.24/12.51 % (549239)Peak memory usage: 12 MB
% 86.24/12.51 % (549239)Instructions burned: 73 (million)
% 86.24/12.51 % (549241)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=2476330508:hsq=on:hsqr=16,1:s2a=on:i=6580:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2894 on theBenchmark for (2894ds/6580Mi)
% 86.24/12.51 % (549242)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=2379996548:i=6209:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2894 on theBenchmark for (2894ds/6209Mi)
% 86.24/12.51 % (549215)Instruction limit reached!
% 86.24/12.51 % (549215)------------------------------
% 86.24/12.51 % (549215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.24/12.51 % (549215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.24/12.51 % (549215)CaDiCaL version: 2.1.3
% 86.24/12.51 % (549215)Termination reason: Instruction limit
% 86.24/12.51 % (549215)Termination phase: Saturation
% 86.24/12.51 % (549215)Time elapsed: 1.452 s
% 86.24/12.51 % (549215)Peak memory usage: 20 MB
% 86.24/12.51 % (549215)Instructions burned: 1725 (million)
% 86.24/12.51 % (549245)lrs+1002_14_sil=128000:e2e=on:si=on:urr=on:nwc=1.2:random_seed=3796116307:cond=fast:i=1003:bd=all:fsr=off:rtra=on:sup=off_2893 on theBenchmark for (2893ds/1003Mi)
% 86.24/12.51 % (549235)Instruction limit reached!
% 86.24/12.51 % (549235)------------------------------
% 86.24/12.51 % (549235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.24/12.51 % (549235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.24/12.51 % (549235)CaDiCaL version: 2.1.3
% 86.24/12.51 % (549235)Termination reason: Instruction limit
% 86.24/12.51 % (549235)Termination phase: Saturation
% 86.24/12.51 % (549235)Time elapsed: 1.019 s
% 86.24/12.51 % (549235)Peak memory usage: 15 MB
% 86.24/12.51 % (549235)Instructions burned: 1298 (million)
% 86.24/12.51 % (549229)Instruction limit reached!
% 86.24/12.51 % (549229)------------------------------
% 86.24/12.51 % (549229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.24/12.51 % (549229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.24/12.51 % (549229)CaDiCaL version: 2.1.3
% 86.24/12.51 % (549229)Termination reason: Instruction limit
% 86.24/12.51 % (549229)Termination phase: Saturation
% 86.24/12.51 % (549229)Time elapsed: 1.164 s
% 86.24/12.51 % (549229)Peak memory usage: 16 MB
% 86.24/12.51 % (549229)Instructions burned: 1584 (million)
% 86.24/12.51 % (549245)Refutation not found, incomplete strategy
% 86.24/12.51 % (549245)------------------------------
% 86.24/12.51 % (549245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 86.24/12.51 % (549245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 86.24/12.51 % (549245)CaDiCaL version: 2.1.3
% 86.24/12.51 % (549245)Termination reason: Refutation not found, incomplete strategy
% 86.24/12.51 % (549245)Time elapsed: 0.096 s
% 87.79/12.89 % (549245)Peak memory usage: 13 MB
% 87.79/12.89 % (549245)Instructions burned: 113 (million)
% 87.79/12.89 % (549245)------------------------------
% 87.79/12.89 % (549245)------------------------------
% 87.79/12.89 % (549247)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 87.79/12.89 % (549247)ott+1002_16_sil=128000:si=on:random_seed=1080491485:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2892 on theBenchmark for (2892ds/409Mi)
% 87.79/12.89 % (549248)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=1112510315:cond=on:i=403:kws=precedence:erml=3:bs=unit_only:bd=all:rtra=on:ss=axioms:er=known:ntd=on_2892 on theBenchmark for (2892ds/403Mi)
% 87.79/12.89 % (549249)lrs+10_1_sil=128000:fde=none:cnfonf=lazy_pi_sigma_gen:si=on:random_seed=1797368254:st=2:i=6843:sd=2:bd=all:rtra=on:sup=off:ss=axioms_2892 on theBenchmark for (2892ds/6843Mi)
% 87.79/12.89 % (549248)Refutation not found, incomplete strategy
% 87.79/12.89 % (549248)------------------------------
% 87.79/12.89 % (549248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549248)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549248)Termination reason: Refutation not found, incomplete strategy
% 87.79/12.89 % (549248)Time elapsed: 0.007 s
% 87.79/12.89 % (549248)Peak memory usage: 12 MB
% 87.79/12.89 % (549248)Instructions burned: 7 (million)
% 87.79/12.89 % (549248)------------------------------
% 87.79/12.89 % (549248)------------------------------
% 87.79/12.89 % (549249)Refutation not found, incomplete strategy
% 87.79/12.89 % (549249)------------------------------
% 87.79/12.89 % (549249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549249)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549249)Termination reason: Refutation not found, incomplete strategy
% 87.79/12.89 % (549249)Time elapsed: 0.019 s
% 87.79/12.89 % (549249)Peak memory usage: 12 MB
% 87.79/12.89 % (549249)Instructions burned: 19 (million)
% 87.79/12.89 % (549249)------------------------------
% 87.79/12.89 % (549249)------------------------------
% 87.79/12.89 % (549253)lrs+10_2:1_si=on:random_seed=538004398:s2a=on:i=506:rtra=on:fe=abstraction_2891 on theBenchmark for (2891ds/506Mi)
% 87.79/12.89 % (549254)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=1199504100:uwa_fpi=on:i=888:doe=on:bd=preordered:rtra=on:fsd=on_2891 on theBenchmark for (2891ds/888Mi)
% 87.79/12.89 % (549247)Instruction limit reached!
% 87.79/12.89 % (549247)------------------------------
% 87.79/12.89 % (549247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549247)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549247)Termination reason: Instruction limit
% 87.79/12.89 % (549247)Termination phase: Saturation
% 87.79/12.89 % (549247)Time elapsed: 0.342 s
% 87.79/12.89 % (549247)Peak memory usage: 14 MB
% 87.79/12.89 % (549247)Instructions burned: 409 (million)
% 87.79/12.89 % (549257)WARNING Broken Constraint: if positive_literal_split_queue_ratios(32,1) has been set then positive_literal_split_queue(off) is equal to on
% 87.79/12.89 % (549257)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=293771528:cond=fast:i=416:fgj=on:bd=preordered:rtra=on_2888 on theBenchmark for (2888ds/416Mi)
% 87.79/12.89 % (549253)Instruction limit reached!
% 87.79/12.89 % (549253)------------------------------
% 87.79/12.89 % (549253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549253)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549253)Termination reason: Instruction limit
% 87.79/12.89 % (549253)Termination phase: Saturation
% 87.79/12.89 % (549253)Time elapsed: 0.405 s
% 87.79/12.89 % (549253)Peak memory usage: 14 MB
% 87.79/12.89 % (549253)Instructions burned: 506 (million)
% 87.79/12.89 % (549259)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=2581529685: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_2887 on theBenchmark for (2887ds/13534Mi)
% 87.79/12.89 % (549227)Instruction limit reached!
% 87.79/12.89 % (549227)------------------------------
% 87.79/12.89 % (549227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549227)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549227)Termination reason: Instruction limit
% 87.79/12.89 % (549227)Termination phase: Saturation
% 87.79/12.89 % (549227)Time elapsed: 1.818 s
% 87.79/12.89 % (549227)Peak memory usage: 15 MB
% 87.79/12.89 % (549227)Instructions burned: 5013 (million)
% 87.79/12.89 % (549261)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(10) has been set then forward_subsumption_demodulation(off) is equal to on
% 87.79/12.89 % (549261)dis+1002_3_tgt=ground:cnfonf=lazy_simp:si=on:sp=unary_first:cbe=off:uwa=ground:updr=off:random_seed=2881859133:i=206:fgj=on:hud=10:nm=30:rtra=on:fsdmm=10_2886 on theBenchmark for (2886ds/206Mi)
% 87.79/12.89 % (549261)Instruction limit reached!
% 87.79/12.89 % (549261)------------------------------
% 87.79/12.89 % (549261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549261)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549261)Termination reason: Instruction limit
% 87.79/12.89 % (549261)Termination phase: Saturation
% 87.79/12.89 % (549261)Time elapsed: 0.081 s
% 87.79/12.89 % (549261)Peak memory usage: 12 MB
% 87.79/12.89 % (549261)Instructions burned: 208 (million)
% 87.79/12.89 % (549257)Instruction limit reached!
% 87.79/12.89 % (549257)------------------------------
% 87.79/12.89 % (549257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549257)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549257)Termination reason: Instruction limit
% 87.79/12.89 % (549257)Termination phase: Saturation
% 87.79/12.89 % (549257)Time elapsed: 0.328 s
% 87.79/12.89 % (549257)Peak memory usage: 13 MB
% 87.79/12.89 % (549257)Instructions burned: 416 (million)
% 87.79/12.89 % (549263)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=2173281879:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2295:avsqr=1,16:aac=none:hud=3:rtra=on_2885 on theBenchmark for (2885ds/2295Mi)
% 87.79/12.89 % (549264)ott+1010_1_to=lpo:sil=128000:fde=none:si=on:sp=unary_first:uwa=off:nwc=1:random_seed=2521590117:i=637:piset=not:ep=RST:bd=all:av=off:rtra=on_2884 on theBenchmark for (2884ds/637Mi)
% 87.79/12.89 % (549254)Instruction limit reached!
% 87.79/12.89 % (549254)------------------------------
% 87.79/12.89 % (549254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549254)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549254)Termination reason: Instruction limit
% 87.79/12.89 % (549254)Termination phase: Saturation
% 87.79/12.89 % (549254)Time elapsed: 0.702 s
% 87.79/12.89 % (549254)Peak memory usage: 13 MB
% 87.79/12.89 % (549254)Instructions burned: 888 (million)
% 87.79/12.89 % (549267)dis+1002_15:31_sil=128000:cnfonf=lazy_not_gen:si=on:cbe=off:uwa=off:random_seed=2471006653:hsq=on:i=667:rtra=on:ixr=off_2884 on theBenchmark for (2884ds/667Mi)
% 87.79/12.89 % (549264)Instruction limit reached!
% 87.79/12.89 % (549264)------------------------------
% 87.79/12.89 % (549264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549264)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549264)Termination reason: Instruction limit
% 87.79/12.89 % (549264)Termination phase: Saturation
% 87.79/12.89 % (549264)Time elapsed: 0.549 s
% 87.79/12.89 % (549264)Peak memory usage: 16 MB
% 87.79/12.89 % (549264)Instructions burned: 637 (million)
% 87.79/12.89 % (549269)lrs-1004_16_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:lma=off:uwa=off:random_seed=1186693247:i=1801:bd=preordered:nm=32:rtra=on:fdi=1024_2879 on theBenchmark for (2879ds/1801Mi)
% 87.79/12.89 % (549267)Instruction limit reached!
% 87.79/12.89 % (549267)------------------------------
% 87.79/12.89 % (549267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549267)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549267)Termination reason: Instruction limit
% 87.79/12.89 % (549267)Termination phase: Saturation
% 87.79/12.89 % (549267)Time elapsed: 0.544 s
% 87.79/12.89 % (549267)Peak memory usage: 15 MB
% 87.79/12.89 % (549267)Instructions burned: 667 (million)
% 87.79/12.89 % (549271)lrs+1002_1024_anc=all_dependent:sil=128000:drc=off:cnfonf=lazy_not_be_gen:si=on:cbe=off:cs=on:random_seed=1646236403:i=555:aac=none:rtra=on:fe=abstraction:ntd=on_2878 on theBenchmark for (2878ds/555Mi)
% 87.79/12.89 % (549269) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-548796-549269"...
% 87.79/12.89 % (549263)Instruction limit reached!
% 87.79/12.89 % (549263)------------------------------
% 87.79/12.89 % (549263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 87.79/12.89 % (549263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 87.79/12.89 % (549263)CaDiCaL version: 2.1.3
% 87.79/12.89 % (549263)Termination reason: Instruction limit
% 87.79/12.89 % (549263)Termination phase: Saturation
% 87.79/12.89 % (549263)Time elapsed: 0.989 s
% 87.79/12.89 % (549263)Peak memory usage: 18 MB
% 87.79/12.89 % (549263)Instructions burned: 2297 (million)
% 87.79/12.89 % (549269)...printing done.
% 87.79/12.89 % (549269)Refutation found. Thanks to Tanya!
% 87.79/12.89 % SZS status Theorem for theBenchmark
% 87.79/12.89 % SZS output start Proof for theBenchmark
% See solution above
% 89.16/12.90 % (549269)------------------------------
% 89.16/12.90 % (549269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 89.16/12.90 % (549269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 89.16/12.90 % (549269)CaDiCaL version: 2.1.3
% 89.16/12.90 % (549269)Termination reason: Refutation
% 89.16/12.90 % (549269)Time elapsed: 0.389 s
% 89.16/12.90 % (549269)Peak memory usage: 14 MB
% 89.16/12.90 % (549269)Instructions burned: 466 (million)
% 89.16/12.90 % (548796)Success in time 12.525 s
% 89.16/12.90 % Vampire exiting
%------------------------------------------------------------------------------