%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN044^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:41:37 AM UTC 2026
% Result : Theorem 1.57s 0.47s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 31
% Syntax : Number of formulae : 292 ( 84 unt; 0 typ; 15 def)
% Number of atoms : 2299 ( 453 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 2660 ( 199 ~; 443 |; 20 &;1664 @)
% ( 15 <=>; 187 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 56 usr; 22 con; 0-4 aty)
% ( 132 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 590 ( 0 sgn 180 !; 0 ?; 590 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
p: $i > $o ).
thf(func_def_22,type,
q: $i > $o ).
thf(func_def_23,type,
r: $i > $o ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_34,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vAND: $o > $o > $o ).
thf(func_def_36,type,
sK0: $i > $i ).
thf(func_def_37,type,
sK1: $i > $i ).
thf(func_def_38,type,
sK2: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ 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,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(f13,axiom,
( ior
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ior) ).
thf(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f16,axiom,
( iequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( iand @ ( iimplies @ X0 @ X1 ) @ ( iimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iequiv) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10_1) ).
thf(f23,axiom,
ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10_2) ).
thf(f24,axiom,
ivalid @ ( iimplies @ ( iatom @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10_3) ).
thf(f25,conjecture,
ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel10) ).
thf(f26,negated_conjecture,
~ ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f28,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f29,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ),
inference(rectify,[],[f22]) ).
thf(f31,plain,
( ( ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ) )
= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f35,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f36,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f38,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f41,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f45,plain,
ivalid @ ( iimplies @ ( iatom @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ),
inference(rectify,[],[f24]) ).
thf(f46,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ) )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f48,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f50,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f51,plain,
ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ),
inference(rectify,[],[f23]) ).
thf(f52,plain,
( ( ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ) )
= $true ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f5]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f56,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f60,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f61,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f62,plain,
~ ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) ),
inference(rectify,[],[f26]) ).
thf(f63,plain,
( ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) )
!= $true ),
inference(fool_elimination,[],[f62]) ).
thf(f65,plain,
( ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) )
!= $true ),
inference(flattening,[],[f63]) ).
thf(f71,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f72,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f73,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f74,plain,
( ( ivalid @ ( iimplies @ ( iatom @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ) )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f75,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f76,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f79,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f80,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f81,plain,
( ( ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ) )
= $true ),
inference(cnf_transformation,[],[f52]) ).
thf(f82,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f83,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f86,plain,
( ( ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) )
!= $true ),
inference(cnf_transformation,[],[f65]) ).
thf(f87,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f88,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f89,plain,
( ( ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ) )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f90,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f93,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,[],[f72,f73,f83]) ).
thf(f96,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f79,f75]) ).
thf(f97,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f90,f73,f87,f87]) ).
thf(f98,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,[],[f88,f93,f87,f87]) ).
thf(f99,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f71,f96,f98,f98]) ).
thf(f101,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [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
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ q )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) ) ) ),
inference(definition_unfolding,[],[f74,f80,f98,f76,f97,f76,f76]) ).
thf(f102,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [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
@ r )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f81,f80,f98,f76,f96,f76,f76]) ).
thf(f103,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p )
@ ( ^ [Y0: $i > $o] : Y0
@ q ) ) ) ),
inference(definition_unfolding,[],[f86,f80,f99,f76,f76]) ).
thf(f104,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [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
@ q )
@ ( ^ [Y0: $i > $o] : Y0
@ r ) ) ) ),
inference(definition_unfolding,[],[f89,f80,f98,f76,f76]) ).
thf(f105,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f106,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) )
@ X2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p @ Y0 ) )
@ ( sK0 @ X1 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f110]) ).
thf(f112,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ ( sK0 @ X1 ) )
=> ( p @ ( sK0 @ X1 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f115,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) )
@ X3 ) )
| ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( q @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( r @ X4 ) ) )
| ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( r @ X4 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( q @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( $true
= ( q @ X3 ) )
| ( $false
= ( irel @ X2 @ X4 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( r @ X4 ) )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p @ ( sK0 @ X1 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f123,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p @ ( sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) )
@ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) )
@ X3 ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( irel @ X2 @ X3 )
=> ( r @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( p @ ( sK0 @ X1 ) ) )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( q @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X2 @ X4 )
=> ( q @ X4 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ X2 @ X4 ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) )
| ( $true
= ( r @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( q @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f130,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( q @ Y0 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( q @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( q @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) )
| ( $false
= ( q @ ( sK1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( r @ X2 ) ) )
| ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f136]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( r @ X2 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( r @ X2 ) )
| ( $false
= ( q @ ( sK1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f137]) ).
thf(f141,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( p @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f142,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( p @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( p @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( p @ Y0 ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( r @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( q @ Y0 )
& ( p @ Y0 ) ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( q @ X2 )
& ( p @ X2 ) ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( r @ ( sK2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( q @ X2 )
& ( p @ X2 ) ) )
| ( $false
= ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( r @ ( sK2 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( r @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( p @ X2 ) ) ),
inference(and_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( ( q @ X2 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ( irel @ X1 @ ( sK2 @ X1 ) )
=> ( r @ ( sK2 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f149]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( q @ X2 )
= $true )
| ( $false
= ( r @ ( sK2 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK2 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( q @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( r @ ( sK2 @ X1 ) ) )
| ( $true
= ( p @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK2 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( p @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f156,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f157,plain,
( $false
= ( ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( ( ( ( irel @ sK3 @ X2 )
=> ( q @ X2 ) )
= $true )
| ( $true
= ( ( irel @ sK3 @ X1 )
=> ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK3 @ X2 ) )
| ( $true
= ( ( irel @ sK3 @ X1 )
=> ( p @ X1 ) ) )
| ( ( q @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( ( q @ X2 )
= $true )
| ( $false
= ( irel @ sK3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f172,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $false
= ( ( irel @ sK3 @ sK4 )
=> ( q @ sK4 ) ) )
| ( $true
= ( ( irel @ sK3 @ X1 )
=> ( q @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( ( irel @ sK3 @ X1 )
=> ( q @ X1 ) ) )
| ( $false
= ( q @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( ( irel @ sK3 @ X1 )
=> ( q @ X1 ) ) )
| ( $true
= ( irel @ sK3 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( irel @ sK3 @ sK4 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( q @ sK4 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( irel @ sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f178,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f179,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK5 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK5 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK5 ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( ( irel @ sK3 @ X1 )
=> ( p @ X1 ) ) )
| ( $false
= ( ( irel @ sK3 @ sK5 )
=> ( p @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ( irel @ sK3 @ sK5 )
=> ( p @ sK5 ) ) )
| ( $false
= ( irel @ sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( ( irel @ sK3 @ sK5 )
= $true )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( irel @ sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( p @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f188,plain,
( ( $false
= ( ( irel @ sK3 @ sK5 )
=> ( p @ sK5 ) ) )
| ( ( ( irel @ sK3 @ sK6 )
=> ( q @ sK6 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( ( $false
= ( p @ sK5 ) )
| ( ( ( irel @ sK3 @ sK6 )
=> ( q @ sK6 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( ( irel @ sK3 @ sK5 )
= $true )
| ( ( ( irel @ sK3 @ sK6 )
=> ( q @ sK6 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $false
= ( q @ sK6 ) )
| ( ( irel @ sK3 @ sK5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $true
= ( irel @ sK3 @ sK6 ) )
| ( ( irel @ sK3 @ sK5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( p @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f194,plain,
( ( $true
= ( irel @ sK3 @ sK6 ) )
| ( $false
= ( p @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f196,definition,
( spl7_1
<=> ! [X1: $i] :
( ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f197,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f199,definition,
( spl7_2
<=> ! [X2: $i] :
( ( ( q @ X2 )
= $true )
| ( $false
= ( irel @ sK3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f200,plain,
( ! [X2: $i] :
( ( $false
= ( irel @ sK3 @ X2 ) )
| ( ( q @ X2 )
= $true ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f201,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f170,f199,f196]) ).
thf(f203,definition,
( spl7_3
<=> ( $true
= ( irel @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f205,plain,
( ( $true
= ( irel @ sK3 @ sK4 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f206,plain,
( spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f176,f199,f203]) ).
thf(f208,definition,
( spl7_4
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f210,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f208]) ).
thf(f211,plain,
( spl7_2
| spl7_4 ),
inference(avatar_split_clause,[],[f177,f208,f199]) ).
thf(f213,definition,
( spl7_5
<=> ( ( irel @ sK3 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f215,plain,
( ( ( irel @ sK3 @ sK5 )
= $true )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f216,plain,
( spl7_1
| spl7_5 ),
inference(avatar_split_clause,[],[f186,f213,f196]) ).
thf(f218,definition,
( spl7_6
<=> ( $false
= ( p @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f220,plain,
( ( $false
= ( p @ sK5 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,plain,
( spl7_1
| spl7_6 ),
inference(avatar_split_clause,[],[f185,f218,f196]) ).
thf(f223,definition,
( spl7_7
<=> ( $true
= ( irel @ sK3 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f225,plain,
( ( $true
= ( irel @ sK3 @ sK6 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f226,plain,
( spl7_5
| spl7_7 ),
inference(avatar_split_clause,[],[f192,f223,f213]) ).
thf(f228,definition,
( spl7_8
<=> ( $false
= ( q @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f230,plain,
( ( $false
= ( q @ sK6 ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl7_5
| spl7_8 ),
inference(avatar_split_clause,[],[f191,f228,f213]) ).
thf(f232,plain,
( spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f194,f223,f218]) ).
thf(f233,plain,
( spl7_8
| spl7_6 ),
inference(avatar_split_clause,[],[f193,f218,f228]) ).
thf(f284,definition,
( spl7_14
<=> ! [X0: $i] :
( ( ( r @ X0 )
= $true )
| ( $false
= ( irel @ sK3 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition]) ).
thf(f285,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK3 @ X0 ) )
| ( ( r @ X0 )
= $true ) )
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f288,definition,
( spl7_15
<=> ( $true
= ( q @ ( sK1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_15])],[avatar_definition]) ).
thf(f290,plain,
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl7_15 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f323,definition,
( spl7_17
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( r @ X2 ) )
| ( $false
= ( irel @ X1 @ X0 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( irel @ sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_17])],[avatar_definition]) ).
thf(f324,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( q @ X0 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X0 ) )
| ( $true
= ( r @ X2 ) ) )
| ~ spl7_17 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f336,plain,
( ! [X0: $i] :
( ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false
= ( irel @ sK3 @ X0 ) )
| ( $false = $true )
| ( ( r @ X0 )
= $true ) )
| ~ spl7_2 ),
inference(superposition,[],[f139,f200]) ).
thf(f340,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK3 @ X0 ) )
| ( $true
= ( q @ ( sK1 @ sK3 ) ) )
| ( ( r @ X0 )
= $true ) )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f348,plain,
( spl7_15
| spl7_14
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f340,f199,f284,f288]) ).
thf(f379,definition,
( spl7_21
<=> ! [X1: $i] :
( ( $false
= ( irel @ X1 @ sK3 ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_21])],[avatar_definition]) ).
thf(f380,plain,
( ! [X1: $i] :
( ( $false
= ( irel @ X1 @ sK3 ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) ) )
| ~ spl7_21 ),
inference(avatar_component_clause,[],[f379]) ).
thf(f450,plain,
( ( $true
= ( q @ sK6 ) )
| ( $false = $true )
| ~ spl7_2
| ~ spl7_7 ),
inference(superposition,[],[f200,f225]) ).
thf(f462,plain,
( ( $true
= ( q @ sK6 ) )
| ~ spl7_2
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f474,plain,
( ( $false = $true )
| ~ spl7_2
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f462,f230]) ).
thf(f475,plain,
( $false
| ~ spl7_2
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f474]) ).
thf(f476,plain,
( ~ spl7_2
| ~ spl7_7
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f475]) ).
thf(f498,plain,
( ( $true
= ( p @ sK5 ) )
| ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ( $false = $true )
| ~ spl7_5 ),
inference(superposition,[],[f154,f215]) ).
thf(f504,plain,
( ( $true
= ( p @ sK5 ) )
| ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f498]) ).
thf(f510,plain,
( ( $false = $true )
| ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_5
| ~ spl7_6 ),
inference(forward_demodulation,[],[f504,f220]) ).
thf(f511,plain,
( ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_5
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f510]) ).
thf(f548,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $true
= ( r @ ( sK2 @ sK3 ) ) )
| ( $true
= ( p @ X0 ) )
| ( $false
= ( irel @ sK3 @ X0 ) ) )
| ~ spl7_14 ),
inference(superposition,[],[f155,f285]) ).
thf(f553,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( q @ ( sK1 @ X0 ) ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false = $true )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( r @ ( sK2 @ X0 ) ) ) ),
inference(superposition,[],[f140,f155]) ).
thf(f558,plain,
( ! [X0: $i] :
( ( $true
= ( r @ ( sK2 @ sK3 ) ) )
| ( $false
= ( irel @ sK3 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f548]) ).
thf(f563,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( q @ ( sK1 @ X0 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( r @ ( sK2 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f553]) ).
thf(f572,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( irel @ sK3 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl7_5
| ~ spl7_6
| ~ spl7_14 ),
inference(forward_demodulation,[],[f558,f511]) ).
thf(f573,plain,
( ! [X0: $i] :
( ( $true
= ( p @ X0 ) )
| ( $false
= ( irel @ sK3 @ X0 ) ) )
| ~ spl7_5
| ~ spl7_6
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f572]) ).
thf(f590,plain,
( spl7_1
| ~ spl7_5
| ~ spl7_6
| ~ spl7_14 ),
inference(avatar_split_clause,[],[f573,f284,f218,f213,f196]) ).
thf(f655,definition,
( spl7_33
<=> ( $false
= ( p @ ( sK0 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_33])],[avatar_definition]) ).
thf(f657,plain,
( ( $false
= ( p @ ( sK0 @ sK3 ) ) )
| ~ spl7_33 ),
inference(avatar_component_clause,[],[f655]) ).
thf(f1141,plain,
( ( $false = $true )
| ( $true
= ( r @ ( sK2 @ sK3 ) ) )
| ( $true
= ( p @ sK5 ) )
| ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ~ spl7_5 ),
inference(superposition,[],[f563,f215]) ).
thf(f1156,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $true
= ( r @ ( sK2 @ sK3 ) ) )
| ( $true
= ( p @ sK5 ) )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f1141]) ).
thf(f1161,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $false = $true )
| ( $true
= ( p @ sK5 ) )
| ~ spl7_5
| ~ spl7_6 ),
inference(forward_demodulation,[],[f1156,f511]) ).
thf(f1162,plain,
( ( $false
= ( q @ ( sK1 @ sK3 ) ) )
| ( $true
= ( p @ sK5 ) )
| ~ spl7_5
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f1161]) ).
thf(f1165,plain,
( ( $true
= ( p @ sK5 ) )
| ( $false = $true )
| ~ spl7_5
| ~ spl7_6
| ~ spl7_15 ),
inference(forward_demodulation,[],[f1162,f290]) ).
thf(f1166,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl7_5
| ~ spl7_6
| ~ spl7_15 ),
inference(trivial_inequality_removal,[],[f1165]) ).
thf(f1168,plain,
( ( $false = $true )
| ~ spl7_5
| ~ spl7_6
| ~ spl7_15 ),
inference(forward_demodulation,[],[f1166,f220]) ).
thf(f1169,plain,
( $false
| ~ spl7_5
| ~ spl7_6
| ~ spl7_15 ),
inference(trivial_inequality_removal,[],[f1168]) ).
thf(f1170,plain,
( ~ spl7_5
| ~ spl7_6
| ~ spl7_15 ),
inference(avatar_contradiction_clause,[],[f1169]) ).
thf(f1175,plain,
( ( $false = $true )
| ( $true
= ( p @ sK5 ) )
| ~ spl7_1
| ~ spl7_5 ),
inference(superposition,[],[f197,f215]) ).
thf(f1177,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( p @ ( sK0 @ sK3 ) ) )
| ( $false = $true )
| ( $false
= ( irel @ X1 @ X0 ) )
| ( $true
= ( q @ X0 ) )
| ( $true
= ( r @ X2 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK3 @ X1 ) ) )
| ~ spl7_1 ),
inference(superposition,[],[f197,f121]) ).
thf(f1187,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( p @ ( sK0 @ sK3 ) ) )
| ( $false
= ( irel @ X1 @ X0 ) )
| ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( q @ X0 ) ) )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f1177]) ).
thf(f1192,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl7_1
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f1175]) ).
thf(f1200,plain,
( ( $false = $true )
| ~ spl7_1
| ~ spl7_5
| ~ spl7_6 ),
inference(forward_demodulation,[],[f1192,f220]) ).
thf(f1201,plain,
( $false
| ~ spl7_1
| ~ spl7_5
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f1200]) ).
thf(f1202,plain,
( ~ spl7_1
| ~ spl7_5
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f1201]) ).
thf(f1212,definition,
( spl7_67
<=> ( $true
= ( r @ ( sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_67])],[avatar_definition]) ).
thf(f1214,plain,
( ( $true
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_67 ),
inference(avatar_component_clause,[],[f1212]) ).
thf(f1235,definition,
( spl7_71
<=> ( $false
= ( r @ ( sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_71])],[avatar_definition]) ).
thf(f1237,plain,
( ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_71 ),
inference(avatar_component_clause,[],[f1235]) ).
thf(f1265,plain,
( ! [X0: $i,X1: $i] :
( ( ( r @ X0 )
= $true )
| ( $false
= ( p @ ( sK0 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ sK3 ) )
| ( $false
= ( irel @ sK3 @ X0 ) )
| ( $true
= ( q @ sK4 ) )
| ( $false = $true ) )
| ~ spl7_3 ),
inference(superposition,[],[f128,f205]) ).
thf(f1267,plain,
( ( $false = $true )
| ( $true
= ( q @ sK4 ) )
| ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_3 ),
inference(superposition,[],[f152,f205]) ).
thf(f1288,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ sK3 @ X0 ) )
| ( $true
= ( q @ sK4 ) )
| ( ( r @ X0 )
= $true )
| ( $false
= ( irel @ X1 @ sK3 ) )
| ( $false
= ( p @ ( sK0 @ X1 ) ) ) )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f1265]) ).
thf(f1293,plain,
( ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f1267]) ).
thf(f1325,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( irel @ sK3 @ X0 ) )
| ( ( r @ X0 )
= $true )
| ( $false
= ( p @ ( sK0 @ X1 ) ) )
| ( $false
= ( irel @ X1 @ sK3 ) ) )
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f1288,f210]) ).
thf(f1326,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( p @ ( sK0 @ X1 ) ) )
| ( $false
= ( irel @ sK3 @ X0 ) )
| ( ( r @ X0 )
= $true )
| ( $false
= ( irel @ X1 @ sK3 ) ) )
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f1325]) ).
thf(f1329,plain,
( ( $false = $true )
| ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_3
| ~ spl7_4 ),
inference(forward_demodulation,[],[f1293,f210]) ).
thf(f1330,plain,
( ( $false
= ( r @ ( sK2 @ sK3 ) ) )
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f1329]) ).
thf(f1352,plain,
( spl7_21
| spl7_14
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f1326,f208,f203,f284,f379]) ).
thf(f1353,plain,
( spl7_71
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f1330,f208,f203,f1235]) ).
thf(f1363,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK3 @ X0 ) )
| ( $false = $true )
| ( $true
= ( q @ X0 ) )
| ( $true
= ( r @ ( sK2 @ sK3 ) ) ) )
| ~ spl7_14 ),
inference(superposition,[],[f285,f153]) ).
thf(f1376,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK3 @ X0 ) )
| ( $true
= ( r @ ( sK2 @ sK3 ) ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl7_14 ),
inference(trivial_inequality_removal,[],[f1363]) ).
thf(f1384,plain,
( spl7_2
| spl7_67
| ~ spl7_14 ),
inference(avatar_split_clause,[],[f1376,f284,f1212,f199]) ).
thf(f1521,plain,
( ( $false = $true )
| ~ spl7_67
| ~ spl7_71 ),
inference(forward_demodulation,[],[f1214,f1237]) ).
thf(f1522,plain,
( $false
| ~ spl7_67
| ~ spl7_71 ),
inference(trivial_inequality_removal,[],[f1521]) ).
thf(f1523,plain,
( ~ spl7_67
| ~ spl7_71 ),
inference(avatar_contradiction_clause,[],[f1522]) ).
thf(f2395,plain,
( ( $false = $true )
| ( $false
= ( p @ ( sK0 @ sK3 ) ) )
| ~ spl7_21 ),
inference(superposition,[],[f82,f380]) ).
thf(f2414,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( irel @ sK3 @ X0 ) )
| ( ( r @ X1 )
= $true ) )
| ~ spl7_17 ),
inference(superposition,[],[f82,f324]) ).
thf(f2533,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ sK3 @ X0 ) )
| ( $true
= ( q @ X0 ) )
| ( ( r @ X1 )
= $true )
| ( $false
= ( irel @ sK3 @ X1 ) ) )
| ~ spl7_17 ),
inference(trivial_inequality_removal,[],[f2414]) ).
thf(f2550,plain,
( ( $false
= ( p @ ( sK0 @ sK3 ) ) )
| ~ spl7_21 ),
inference(trivial_inequality_removal,[],[f2395]) ).
thf(f2616,plain,
( spl7_14
| spl7_2
| ~ spl7_17 ),
inference(avatar_split_clause,[],[f2533,f323,f199,f284]) ).
thf(f2651,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( r @ X2 ) )
| ( $false = $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( irel @ X1 @ X0 ) ) )
| ~ spl7_1
| ~ spl7_33 ),
inference(forward_demodulation,[],[f1187,f657]) ).
thf(f2652,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( r @ X2 ) )
| ( $false
= ( irel @ X1 @ X0 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( irel @ sK3 @ X1 ) ) )
| ~ spl7_1
| ~ spl7_33 ),
inference(trivial_inequality_removal,[],[f2651]) ).
thf(f2684,plain,
( spl7_17
| ~ spl7_1
| ~ spl7_33 ),
inference(avatar_split_clause,[],[f2652,f655,f196,f323]) ).
thf(f2693,plain,
( spl7_33
| ~ spl7_21 ),
inference(avatar_split_clause,[],[f2550,f379,f655]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f201]) ).
cnf(s2,plain,
( spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f206]) ).
cnf(s3,plain,
( spl7_2
| spl7_4 ),
inference(sat_conversion,[],[f211]) ).
cnf(s4,plain,
( spl7_1
| spl7_5 ),
inference(sat_conversion,[],[f216]) ).
cnf(s5,plain,
( spl7_1
| spl7_6 ),
inference(sat_conversion,[],[f221]) ).
cnf(s6,plain,
( spl7_5
| spl7_7 ),
inference(sat_conversion,[],[f226]) ).
cnf(s7,plain,
( spl7_5
| spl7_8 ),
inference(sat_conversion,[],[f231]) ).
cnf(s8,plain,
( spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f232]) ).
cnf(s9,plain,
( spl7_6
| spl7_8 ),
inference(sat_conversion,[],[f233]) ).
cnf(s27,plain,
( ~ spl7_2
| spl7_14
| spl7_15 ),
inference(sat_conversion,[],[f348]) ).
cnf(s44,plain,
( ~ spl7_2
| ~ spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f476]) ).
cnf(s49,plain,
( spl7_1
| ~ spl7_5
| ~ spl7_6
| ~ spl7_14 ),
inference(sat_conversion,[],[f590]) ).
cnf(s105,plain,
( ~ spl7_5
| ~ spl7_6
| ~ spl7_15 ),
inference(sat_conversion,[],[f1170]) ).
cnf(s110,plain,
( ~ spl7_1
| ~ spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f1202]) ).
cnf(s140,plain,
( ~ spl7_3
| ~ spl7_4
| spl7_14
| spl7_21 ),
inference(sat_conversion,[],[f1352]) ).
cnf(s141,plain,
( ~ spl7_3
| ~ spl7_4
| spl7_71 ),
inference(sat_conversion,[],[f1353]) ).
cnf(s149,plain,
( spl7_2
| ~ spl7_14
| spl7_67 ),
inference(sat_conversion,[],[f1384]) ).
cnf(s163,plain,
( ~ spl7_67
| ~ spl7_71 ),
inference(sat_conversion,[],[f1523]) ).
cnf(s220,plain,
( spl7_2
| spl7_14
| ~ spl7_17 ),
inference(sat_conversion,[],[f2616]) ).
cnf(s243,plain,
( ~ spl7_1
| spl7_17
| ~ spl7_33 ),
inference(sat_conversion,[],[f2684]) ).
cnf(s247,plain,
( ~ spl7_21
| spl7_33 ),
inference(sat_conversion,[],[f2693]) ).
cnf(s266,plain,
spl7_1,
inference(rat,[],[s27,s49,s105,s1,s4,s5]) ).
cnf(s267,plain,
( spl7_6
| ~ spl7_2 ),
inference(rat,[],[s44,s8,s9]) ).
cnf(s268,plain,
~ spl7_2,
inference(rat,[],[s44,s6,s7,s110,s267,s266]) ).
cnf(s270,plain,
spl7_4,
inference(rat,[],[s3,s268]) ).
cnf(s271,plain,
spl7_3,
inference(rat,[],[s2,s268]) ).
cnf(s273,plain,
spl7_71,
inference(rat,[],[s141,s271,s270]) ).
cnf(s276,plain,
~ spl7_67,
inference(rat,[],[s163,s273]) ).
cnf(s277,plain,
~ spl7_14,
inference(rat,[],[s149,s268,s276]) ).
cnf(s279,plain,
~ spl7_17,
inference(rat,[],[s220,s268,s277]) ).
cnf(s281,plain,
spl7_21,
inference(rat,[],[s140,s270,s271,s277]) ).
cnf(s284,plain,
~ spl7_33,
inference(rat,[],[s243,s266,s279]) ).
cnf(s285,plain,
$false,
inference(rat,[],[s247,s284,s281]) ).
thf(f2732,plain,
$false,
inference(avatar_sat_refutation,[],[s285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN044^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n018.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:16:11 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.35 % (279004)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (279014)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=321333047:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (279015)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (279015)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (279009)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1410006032:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (279010)lrs+10_16_si=on:nwc=1.5:random_seed=1908345357:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (279011)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=271193094:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (279013)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=98944566:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (279015)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=2095408719:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (279012)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=3642007790:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.35 % (279011)Instruction limit reached!
% 0.20/0.35 % (279011)------------------------------
% 0.20/0.35 % (279011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (279011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (279011)CaDiCaL version: 2.1.3
% 0.20/0.35 % (279011)Termination reason: Instruction limit
% 0.20/0.35 % (279011)Termination phase: Property scanning
% 0.20/0.35 % (279011)Time elapsed: 0.002 s
% 0.20/0.35 % (279011)Peak memory usage: 10 MB
% 0.20/0.35 % (279011)Instructions burned: 4 (million)
% 0.20/0.35 % (279010)Instruction limit reached!
% 0.20/0.35 % (279010)------------------------------
% 0.20/0.35 % (279010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (279010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (279010)CaDiCaL version: 2.1.3
% 0.20/0.35 % (279010)Termination reason: Instruction limit
% 0.20/0.35 % (279010)Termination phase: Saturation
% 0.20/0.35 % (279010)Time elapsed: 0.010 s
% 0.20/0.35 % (279010)Peak memory usage: 12 MB
% 0.20/0.35 % (279010)Instructions burned: 19 (million)
% 0.20/0.35 % (279014)Instruction limit reached!
% 0.20/0.35 % (279014)------------------------------
% 0.20/0.35 % (279014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (279014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (279014)CaDiCaL version: 2.1.3
% 0.20/0.35 % (279014)Termination reason: Instruction limit
% 0.20/0.35 % (279014)Termination phase: Saturation
% 0.20/0.35 % (279014)Time elapsed: 0.020 s
% 0.20/0.35 % (279014)Peak memory usage: 12 MB
% 0.20/0.35 % (279014)Instructions burned: 75 (million)
% 0.20/0.35 % (279013)Instruction limit reached!
% 0.20/0.35 % (279013)------------------------------
% 0.20/0.35 % (279013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (279013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (279013)CaDiCaL version: 2.1.3
% 0.20/0.35 % (279013)Termination reason: Instruction limit
% 0.20/0.35 % (279013)Termination phase: Saturation
% 0.20/0.35 % (279013)Time elapsed: 0.014 s
% 0.20/0.35 % (279013)Peak memory usage: 11 MB
% 0.20/0.35 % (279013)Instructions burned: 25 (million)
% 0.20/0.35 % (279023)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3909819956:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (279025)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (279023)Instruction limit reached!
% 0.84/0.38 % (279023)------------------------------
% 0.84/0.38 % (279023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (279023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (279023)CaDiCaL version: 2.1.3
% 0.84/0.38 % (279025)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1290616517:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.84/0.38 % (279023)Termination reason: Instruction limit
% 0.84/0.38 % (279023)Termination phase: Property scanning
% 0.84/0.38 % (279023)Time elapsed: 0.002 s
% 0.84/0.38 % (279023)Peak memory usage: 10 MB
% 0.84/0.38 % (279023)Instructions burned: 4 (million)
% 0.84/0.38 % (279025)Instruction limit reached!
% 0.84/0.38 % (279025)------------------------------
% 0.84/0.38 % (279025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (279025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (279025)CaDiCaL version: 2.1.3
% 0.84/0.38 % (279025)Termination reason: Instruction limit
% 0.84/0.38 % (279025)Termination phase: Saturation
% 0.84/0.38 % (279025)Time elapsed: 0.002 s
% 0.84/0.38 % (279025)Peak memory usage: 12 MB
% 0.84/0.38 % (279025)Instructions burned: 8 (million)
% 0.84/0.38 % (279024)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3554942726:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.84/0.38 % (279024)Instruction limit reached!
% 0.84/0.38 % (279024)------------------------------
% 0.84/0.38 % (279024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (279024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (279024)CaDiCaL version: 2.1.3
% 0.84/0.38 % (279024)Termination reason: Instruction limit
% 0.84/0.38 % (279024)Termination phase: Saturation
% 0.84/0.38 % (279024)Time elapsed: 0.003 s
% 0.84/0.38 % (279024)Peak memory usage: 11 MB
% 0.84/0.38 % (279024)Instructions burned: 6 (million)
% 0.84/0.38 % (279026)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1781439529:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.84/0.38 % (279030)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=502979628:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.84/0.38 % (279029)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.84/0.38 % (279029)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.84/0.38 % (279026)Instruction limit reached!
% 0.84/0.38 % (279026)------------------------------
% 0.84/0.38 % (279026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (279026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (279026)CaDiCaL version: 2.1.3
% 0.84/0.38 % (279026)Termination reason: Instruction limit
% 0.84/0.38 % (279026)Termination phase: Saturation
% 0.84/0.38 % (279026)Time elapsed: 0.006 s
% 0.84/0.38 % (279026)Peak memory usage: 12 MB
% 0.84/0.38 % (279026)Instructions burned: 12 (million)
% 0.84/0.38 % (279029)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3897837113:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.84/0.38 % (279009)Instruction limit reached!
% 0.84/0.38 % (279009)------------------------------
% 0.84/0.38 % (279009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.38 % (279009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.38 % (279009)CaDiCaL version: 2.1.3
% 0.84/0.38 % (279009)Termination reason: Instruction limit
% 0.84/0.38 % (279009)Termination phase: Saturation
% 0.84/0.38 % (279009)Time elapsed: 0.045 s
% 0.84/0.38 % (279009)Peak memory usage: 12 MB
% 0.84/0.38 % (279009)Instructions burned: 87 (million)
% 0.84/0.38 % (279032)lrs+10_1_si=on:cs=on:random_seed=1337581500:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.84/0.38 % (279035)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.84/0.40 % (279032)Instruction limit reached!
% 0.84/0.40 % (279032)------------------------------
% 0.84/0.40 % (279032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.40 % (279032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.40 % (279032)CaDiCaL version: 2.1.3
% 0.84/0.40 % (279032)Termination reason: Instruction limit
% 0.84/0.40 % (279032)Termination phase: Saturation
% 0.84/0.40 % (279032)Time elapsed: 0.004 s
% 0.84/0.40 % (279032)Peak memory usage: 11 MB
% 0.84/0.40 % (279032)Instructions burned: 8 (million)
% 0.84/0.40 % (279029)Instruction limit reached!
% 0.84/0.40 % (279029)------------------------------
% 0.84/0.40 % (279029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.40 % (279029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.40 % (279029)CaDiCaL version: 2.1.3
% 0.84/0.40 % (279029)Termination reason: Instruction limit
% 0.84/0.40 % (279029)Termination phase: Saturation
% 0.84/0.40 % (279029)Time elapsed: 0.014 s
% 0.84/0.40 % (279029)Peak memory usage: 12 MB
% 0.84/0.40 % (279029)Instructions burned: 29 (million)
% 0.84/0.40 % (279035)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=2901113575:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.84/0.40 % (279035)Instruction limit reached!
% 0.84/0.40 % (279035)------------------------------
% 0.84/0.40 % (279035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.40 % (279035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.40 % (279035)CaDiCaL version: 2.1.3
% 0.84/0.40 % (279035)Termination reason: Instruction limit
% 0.84/0.40 % (279035)Termination phase: Property scanning
% 0.84/0.40 % (279035)Time elapsed: 0.002 s
% 0.84/0.40 % (279035)Peak memory usage: 10 MB
% 0.84/0.40 % (279035)Instructions burned: 4 (million)
% 0.84/0.40 % (279030)Instruction limit reached!
% 0.84/0.40 % (279030)------------------------------
% 0.84/0.40 % (279030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.40 % (279030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.40 % (279030)CaDiCaL version: 2.1.3
% 0.84/0.40 % (279030)Termination reason: Instruction limit
% 0.84/0.40 % (279030)Termination phase: Saturation
% 0.84/0.40 % (279030)Time elapsed: 0.023 s
% 0.84/0.40 % (279030)Peak memory usage: 12 MB
% 0.84/0.40 % (279030)Instructions burned: 87 (million)
% 0.84/0.40 % (279037)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1466247167:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.84/0.40 % (279037)Refutation not found, incomplete strategy
% 0.84/0.40 % (279037)------------------------------
% 0.84/0.40 % (279037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.40 % (279037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.40 % (279037)CaDiCaL version: 2.1.3
% 0.84/0.40 % (279037)Termination reason: Refutation not found, incomplete strategy
% 0.84/0.40 % (279037)Time elapsed: 0.002 s
% 0.84/0.40 % (279037)Peak memory usage: 12 MB
% 0.84/0.40 % (279037)Instructions burned: 3 (million)
% 0.84/0.40 % (279037)------------------------------
% 0.84/0.40 % (279037)------------------------------
% 0.84/0.40 % (279042)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3951342603:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.84/0.40 % (279039)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2231230255:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.84/0.40 % (279042)Instruction limit reached!
% 0.84/0.40 % (279042)------------------------------
% 0.84/0.40 % (279042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.40 % (279042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.40 % (279042)CaDiCaL version: 2.1.3
% 0.84/0.40 % (279042)Termination reason: Instruction limit
% 0.84/0.40 % (279042)Termination phase: Saturation
% 0.84/0.40 % (279042)Time elapsed: 0.004 s
% 0.84/0.40 % (279042)Peak memory usage: 12 MB
% 0.84/0.40 % (279042)Instructions burned: 15 (million)
% 0.84/0.40 % (279039)Refutation not found, incomplete strategy
% 0.84/0.40 % (279039)------------------------------
% 0.84/0.40 % (279039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.45 % (279039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.45 % (279039)CaDiCaL version: 2.1.3
% 0.84/0.45 % (279039)Termination reason: Refutation not found, incomplete strategy
% 0.84/0.45 % (279039)Time elapsed: 0.003 s
% 0.84/0.45 % (279039)Peak memory usage: 12 MB
% 0.84/0.45 % (279039)Instructions burned: 4 (million)
% 0.84/0.45 % (279039)------------------------------
% 0.84/0.45 % (279039)------------------------------
% 0.84/0.45 % (279041)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=122719266:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.84/0.45 % (279043)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=341666808:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.84/0.45 % (279015)Instruction limit reached!
% 0.84/0.45 % (279015)------------------------------
% 0.84/0.45 % (279015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.45 % (279015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.45 % (279015)CaDiCaL version: 2.1.3
% 0.84/0.45 % (279015)Termination reason: Instruction limit
% 0.84/0.45 % (279015)Termination phase: Saturation
% 0.84/0.45 % (279015)Time elapsed: 0.083 s
% 0.84/0.45 % (279015)Peak memory usage: 13 MB
% 0.84/0.45 % (279015)Instructions burned: 158 (million)
% 0.84/0.45 % (279045)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1227509811:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.84/0.45 % (279048)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1527071367: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)
% 0.84/0.45 % (279048)Instruction limit reached!
% 0.84/0.45 % (279048)------------------------------
% 0.84/0.45 % (279048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.45 % (279048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.45 % (279048)CaDiCaL version: 2.1.3
% 0.84/0.45 % (279048)Termination reason: Instruction limit
% 0.84/0.45 % (279048)Termination phase: Function definition elimination
% 0.84/0.45 % (279048)Time elapsed: 0.001 s
% 0.84/0.45 % (279048)Peak memory usage: 10 MB
% 0.84/0.45 % (279048)Instructions burned: 4 (million)
% 0.84/0.45 % (279045)Instruction limit reached!
% 0.84/0.45 % (279045)------------------------------
% 0.84/0.45 % (279045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.45 % (279045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.45 % (279045)CaDiCaL version: 2.1.3
% 0.84/0.45 % (279045)Termination reason: Instruction limit
% 0.84/0.45 % (279045)Termination phase: Saturation
% 0.84/0.45 % (279045)Time elapsed: 0.008 s
% 0.84/0.45 % (279045)Peak memory usage: 12 MB
% 0.84/0.45 % (279045)Instructions burned: 16 (million)
% 0.84/0.45 % (279041)Instruction limit reached!
% 0.84/0.45 % (279041)------------------------------
% 0.84/0.45 % (279041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.45 % (279041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.45 % (279041)CaDiCaL version: 2.1.3
% 0.84/0.45 % (279041)Termination reason: Instruction limit
% 0.84/0.45 % (279041)Termination phase: Saturation
% 0.84/0.45 % (279041)Time elapsed: 0.016 s
% 0.84/0.45 % (279041)Peak memory usage: 12 MB
% 0.84/0.45 % (279041)Instructions burned: 27 (million)
% 0.84/0.45 % (279049)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1083687356:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.84/0.45 % (279055)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1008250991:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.84/0.45 % (279052)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3229420397:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.84/0.45 % (279056)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
% 0.84/0.45 % (279056)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.84/0.45 % (279057)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.57/0.47 % (279049)Instruction limit reached!
% 1.57/0.47 % (279049)------------------------------
% 1.57/0.47 % (279049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279049)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279049)Termination reason: Instruction limit
% 1.57/0.47 % (279049)Termination phase: Saturation
% 1.57/0.47 % (279049)Time elapsed: 0.014 s
% 1.57/0.47 % (279049)Peak memory usage: 12 MB
% 1.57/0.47 % (279049)Instructions burned: 26 (million)
% 1.57/0.47 % (279056)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=2615880355:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.57/0.47 % (279057)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=538762927:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.57/0.47 % (279052)Instruction limit reached!
% 1.57/0.47 % (279052)------------------------------
% 1.57/0.47 % (279052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279052)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279052)Termination reason: Instruction limit
% 1.57/0.47 % (279052)Termination phase: Saturation
% 1.57/0.47 % (279052)Time elapsed: 0.012 s
% 1.57/0.47 % (279052)Peak memory usage: 11 MB
% 1.57/0.47 % (279052)Instructions burned: 25 (million)
% 1.57/0.47 % (279055)Instruction limit reached!
% 1.57/0.47 % (279055)------------------------------
% 1.57/0.47 % (279055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279055)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279055)Termination reason: Instruction limit
% 1.57/0.47 % (279055)Termination phase: Saturation
% 1.57/0.47 % (279055)Time elapsed: 0.017 s
% 1.57/0.47 % (279055)Peak memory usage: 12 MB
% 1.57/0.47 % (279055)Instructions burned: 60 (million)
% 1.57/0.47 % (279057)Instruction limit reached!
% 1.57/0.47 % (279057)------------------------------
% 1.57/0.47 % (279057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279057)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279057)Termination reason: Instruction limit
% 1.57/0.47 % (279057)Termination phase: Saturation
% 1.57/0.47 % (279057)Time elapsed: 0.004 s
% 1.57/0.47 % (279057)Peak memory usage: 11 MB
% 1.57/0.47 % (279057)Instructions burned: 8 (million)
% 1.57/0.47 % (279056)Instruction limit reached!
% 1.57/0.47 % (279056)------------------------------
% 1.57/0.47 % (279056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279056)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279056)Termination reason: Instruction limit
% 1.57/0.47 % (279056)Termination phase: Saturation
% 1.57/0.47 % (279056)Time elapsed: 0.008 s
% 1.57/0.47 % (279056)Peak memory usage: 12 MB
% 1.57/0.47 % (279056)Instructions burned: 15 (million)
% 1.57/0.47 % (279065)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2913436636:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.57/0.47 % (279061)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=3330406914:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.57/0.47 % (279065)Instruction limit reached!
% 1.57/0.47 % (279065)------------------------------
% 1.57/0.47 % (279065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279065)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279065)Termination reason: Instruction limit
% 1.57/0.47 % (279065)Termination phase: Saturation
% 1.57/0.47 % (279065)Time elapsed: 0.005 s
% 1.57/0.47 % (279065)Peak memory usage: 11 MB
% 1.57/0.47 % (279065)Instructions burned: 23 (million)
% 1.57/0.47 % (279064)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2026180332:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.57/0.47 % (279064)Instruction limit reached!
% 1.57/0.47 % (279064)------------------------------
% 1.57/0.47 % (279064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279064)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279064)Termination reason: Instruction limit
% 1.57/0.47 % (279064)Termination phase: Saturation
% 1.57/0.47 % (279064)Time elapsed: 0.004 s
% 1.57/0.47 % (279064)Peak memory usage: 11 MB
% 1.57/0.47 % (279064)Instructions burned: 8 (million)
% 1.57/0.47 % (279066)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=29586516:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.57/0.47 % (279067)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1885951590:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.57/0.47 % (279070)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=609757407:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.57/0.47 % (279061)Instruction limit reached!
% 1.57/0.47 % (279061)------------------------------
% 1.57/0.47 % (279061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279061)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279061)Termination reason: Instruction limit
% 1.57/0.47 % (279061)Termination phase: Saturation
% 1.57/0.47 % (279061)Time elapsed: 0.018 s
% 1.57/0.47 % (279061)Peak memory usage: 12 MB
% 1.57/0.47 % (279061)Instructions burned: 31 (million)
% 1.57/0.47 % (279066)Instruction limit reached!
% 1.57/0.47 % (279066)------------------------------
% 1.57/0.47 % (279066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279066)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279066)Termination reason: Instruction limit
% 1.57/0.47 % (279066)Termination phase: Saturation
% 1.57/0.47 % (279066)Time elapsed: 0.012 s
% 1.57/0.47 % (279066)Peak memory usage: 12 MB
% 1.57/0.47 % (279066)Instructions burned: 21 (million)
% 1.57/0.47 % (279073)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2398448960:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.57/0.47 % (279073)Refutation not found, incomplete strategy
% 1.57/0.47 % (279073)------------------------------
% 1.57/0.47 % (279073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279073)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279073)Termination reason: Refutation not found, incomplete strategy
% 1.57/0.47 % (279073)Time elapsed: 0.004 s
% 1.57/0.47 % (279073)Peak memory usage: 12 MB
% 1.57/0.47 % (279073)Instructions burned: 6 (million)
% 1.57/0.47 % (279073)------------------------------
% 1.57/0.47 % (279073)------------------------------
% 1.57/0.47 % (279077)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.57/0.47 % (279076)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2570433437:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.57/0.47 % (279077)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1371916457:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.57/0.47 % (279077)Instruction limit reached!
% 1.57/0.47 % (279077)------------------------------
% 1.57/0.47 % (279077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279077)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279077)Termination reason: Instruction limit
% 1.57/0.47 % (279077)Termination phase: Saturation
% 1.57/0.47 % (279077)Time elapsed: 0.003 s
% 1.57/0.47 % (279077)Peak memory usage: 11 MB
% 1.57/0.47 % (279077)Instructions burned: 7 (million)
% 1.57/0.47 % (279079)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2754066963:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 1.57/0.47 % (279070)Instruction limit reached!
% 1.57/0.47 % (279070)------------------------------
% 1.57/0.47 % (279070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279070)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279070)Termination reason: Instruction limit
% 1.57/0.47 % (279070)Termination phase: Saturation
% 1.57/0.47 % (279070)Time elapsed: 0.039 s
% 1.57/0.47 % (279070)Peak memory usage: 13 MB
% 1.57/0.47 % (279070)Instructions burned: 146 (million)
% 1.57/0.47 % (279079)Refutation not found, incomplete strategy
% 1.57/0.47 % (279079)------------------------------
% 1.57/0.47 % (279079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279079)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279079)Termination reason: Refutation not found, incomplete strategy
% 1.57/0.47 % (279079)Time elapsed: 0.003 s
% 1.57/0.47 % (279079)Peak memory usage: 12 MB
% 1.57/0.47 % (279079)Instructions burned: 4 (million)
% 1.57/0.47 % (279079)------------------------------
% 1.57/0.47 % (279079)------------------------------
% 1.57/0.47 % (279043) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-279004-279043"...
% 1.57/0.47 % (279084)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.57/0.47 % (279076)Instruction limit reached!
% 1.57/0.47 % (279076)------------------------------
% 1.57/0.47 % (279076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279076)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279076)Termination reason: Instruction limit
% 1.57/0.47 % (279076)Termination phase: Saturation
% 1.57/0.47 % (279076)Time elapsed: 0.023 s
% 1.57/0.47 % (279076)Peak memory usage: 12 MB
% 1.57/0.47 % (279076)Instructions burned: 42 (million)
% 1.57/0.47 % (279082)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=2786765136:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.57/0.47 % (279084)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1431641827:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.57/0.47 % (279084)Instruction limit reached!
% 1.57/0.47 % (279084)------------------------------
% 1.57/0.47 % (279084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279084)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279084)Termination reason: Instruction limit
% 1.57/0.47 % (279084)Termination phase: Property scanning
% 1.57/0.47 % (279084)Time elapsed: 0.001 s
% 1.57/0.47 % (279084)Peak memory usage: 11 MB
% 1.57/0.47 % (279084)Instructions burned: 6 (million)
% 1.57/0.47 % (279082)Refutation not found, incomplete strategy
% 1.57/0.47 % (279082)------------------------------
% 1.57/0.47 % (279082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.47 % (279082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.47 % (279082)CaDiCaL version: 2.1.3
% 1.57/0.47 % (279082)Termination reason: Refutation not found, incomplete strategy
% 1.57/0.47 % (279082)Time elapsed: 0.004 s
% 1.57/0.47 % (279082)Peak memory usage: 12 MB
% 1.57/0.47 % (279082)Instructions burned: 7 (million)
% 1.57/0.47 % (279082)------------------------------
% 1.57/0.47 % (279082)------------------------------
% 1.57/0.47 % (279043)...printing done.
% 1.57/0.47 % (279043)Refutation found. Thanks to Tanya!
% 1.57/0.47 % SZS status Theorem for theBenchmark
% 1.57/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 1.57/0.48 % (279043)------------------------------
% 1.57/0.48 % (279043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.48 % (279043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.48 % (279043)CaDiCaL version: 2.1.3
% 1.57/0.48 % (279043)Termination reason: Refutation
% 1.57/0.48 % (279043)Time elapsed: 0.116 s
% 1.57/0.48 % (279043)Peak memory usage: 13 MB
% 1.57/0.48 % (279043)Instructions burned: 232 (million)
% 1.57/0.48 % (279004)Success in time 0.228 s
% 1.57/0.48 % Vampire exiting
%------------------------------------------------------------------------------