%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO064^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:46:26 AM UTC 2026
% Result : Theorem 1.69s 0.55s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 30
% Syntax : Number of formulae : 268 ( 114 unt; 0 typ; 14 def)
% Number of atoms : 2526 ( 520 equ; 0 cnn)
% Maximal formula atoms : 15 ( 9 avg)
% Number of connectives : 3013 ( 117 ~; 474 |; 42 &;1963 @)
% ( 14 <=>; 209 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 149 ( 149 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 56 usr; 22 con; 0-4 aty)
% ( 194 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 674 ( 0 sgn 261 !; 0 ?; 674 :)
% 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,
a: $i > $o ).
thf(func_def_22,type,
a1: $i > $o ).
thf(func_def_23,type,
a2: $i > $o ).
thf(func_def_24,type,
b: $i > $o ).
thf(func_def_25,type,
b1: $i > $o ).
thf(func_def_26,type,
vAND: $o > $o > $o ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vNOT: $o > $o ).
thf(func_def_37,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
sK6: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X0 @ X1 )
& ( irel @ X1 @ X2 ) )
=> ( irel @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',trans_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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f12,axiom,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(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(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ a2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(f24,axiom,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
thf(f25,conjecture,
ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f26,negated_conjecture,
~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f27,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f28,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f30,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f31,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f34,plain,
~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f35,plain,
( ( ~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f37,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f39,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f40,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X0 @ X1 )
& ( irel @ X1 @ X2 ) )
=> ( irel @ X0 @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f42,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y2 @ Y1 ) )
=> ( irel @ Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f49,plain,
ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ),
inference(rectify,[],[f23]) ).
thf(f50,plain,
( ( ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
ivalid @ ( iatom @ a2 ),
inference(rectify,[],[f22]) ).
thf(f52,plain,
( ( ivalid @ ( iatom @ a2 ) )
= $true ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
inference(rectify,[],[f24]) ).
thf(f54,plain,
( ( ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ) )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f56,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f57,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f60,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f62,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f63,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f65,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f67,plain,
( ( ~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( ior @ ( iand @ ( iatom @ b ) @ ( iatom @ a1 ) ) @ ( iand @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f35]) ).
thf(f68,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f69,plain,
( ( ivalid @ ( iimplies @ ( iatom @ b ) @ ( ior @ ( ior @ ( iatom @ b1 ) @ ( iatom @ a1 ) ) @ ( iatom @ b1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f70,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f71,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y2 @ Y1 ) )
=> ( irel @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f73,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f74,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f78,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f80,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f81,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f82,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f83,plain,
( ( ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ) )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f86,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f87,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f89,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f90,plain,
( ( ivalid @ ( iatom @ a2 ) )
= $true ),
inference(cnf_transformation,[],[f52]) ).
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,[],[f68,f81,f86]) ).
thf(f96,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f73,f70]) ).
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,[],[f74,f81,f82,f82]) ).
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,[],[f78,f93,f82,f82]) ).
thf(f102,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [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
@ a )
@ ( ^ [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,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ b1 )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f67,f89,f97,f87,f97,f96,f87,f87,f96,f87,f87]) ).
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] :
( ( 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
@ b )
@ ( ^ [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,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
@ b1 )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b1 ) ) ) ) ),
inference(definition_unfolding,[],[f69,f89,f98,f87,f97,f97,f87,f87,f87]) ).
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] :
( ( 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,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
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ),
inference(definition_unfolding,[],[f83,f89,f97,f97,f87,f87,f87]) ).
thf(f105,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 ) )
= $true ),
inference(definition_unfolding,[],[f90,f89,f87]) ).
thf(f106,plain,
( ( !! @ $i @ a2 )
= $true ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f108,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
& ( a1 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( b1 @ Y2 )
& ( a2 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f109,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f110,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
& ( a1 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( b1 @ Y2 )
& ( a2 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f108]) ).
thf(f111,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
& ( a1 @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( b1 @ Y2 )
& ( a2 @ Y2 ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a1 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b1 @ Y1 )
& ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f113,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a1 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b1 @ Y1 )
& ( a2 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f112]) ).
thf(f114,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f112]) ).
thf(f115,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f114]) ).
thf(f116,plain,
( ( ( irel @ sK0 @ sK1 )
=> ( a @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f115]) ).
thf(f117,plain,
( $false
= ( a @ sK1 ) ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f118,plain,
( ( irel @ sK0 @ sK1 )
= $true ),
inference(imp_proxy_clausification,[],[f116]) ).
thf(f119,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a1 @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b1 @ Y1 )
& ( a2 @ Y1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f120,plain,
( ( ( irel @ sK0 @ sK2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
& ( a1 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b1 @ Y0 )
& ( a2 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
& ( a1 @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b1 @ Y0 )
& ( a2 @ Y0 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f122,plain,
( ( irel @ sK0 @ sK2 )
= $true ),
inference(imp_proxy_clausification,[],[f120]) ).
thf(f123,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b1 @ Y0 )
& ( a2 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f121]) ).
thf(f124,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
& ( a1 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f121]) ).
thf(f140,plain,
! [X1: $i] :
( $true
= ( a2 @ X1 ) ),
inference(pi_proxy_clausification,[],[f106]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b1 @ Y0 )
& ( a2 @ Y0 ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f123]) ).
thf(f144,plain,
( ( ( irel @ sK2 @ sK3 )
=> ( ( b1 @ sK3 )
& ( a2 @ sK3 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f145,plain,
( ( ( b1 @ sK3 )
& ( a2 @ sK3 ) )
= $false ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( $true
= ( irel @ sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f144]) ).
thf(f147,plain,
( ( ( b1 @ sK3 )
= $false )
| ( $false
= ( a2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f149,definition,
( spl4_1
<=> ( $false
= ( a2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f151,plain,
( ( $false
= ( a2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f153,definition,
( spl4_2
<=> ( ( b1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f155,plain,
( ( ( b1 @ sK3 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f153]) ).
thf(f156,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f147,f153,f149]) ).
thf(f157,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( ( b @ Y0 )
& ( a1 @ Y0 ) ) )
@ sK5 )
= $false ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f160,plain,
( ( ( irel @ sK2 @ sK5 )
=> ( ( b @ sK5 )
& ( a1 @ sK5 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f161,plain,
( ( ( b @ sK5 )
& ( a1 @ sK5 ) )
= $false ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( irel @ sK2 @ sK5 )
= $true ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( ( b @ sK5 )
= $false )
| ( ( a1 @ sK5 )
= $false ) ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f165,definition,
( spl4_3
<=> ( ( b @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f167,plain,
( ( ( b @ sK5 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f169,definition,
( spl4_4
<=> ( ( a1 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f171,plain,
( ( ( a1 @ sK5 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f172,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f163,f169,f165]) ).
thf(f175,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( irel @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f176,plain,
! [X1: $i] :
( $true
= ( irel @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f179,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y0 )
& ( irel @ Y2 @ Y1 ) )
=> ( irel @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f180,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( irel @ Y0 @ X1 )
& ( irel @ Y1 @ Y0 ) )
=> ( irel @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( irel @ Y0 @ X1 )
& ( irel @ Y1 @ Y0 ) )
=> ( irel @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( irel @ X2 @ X1 )
& ( irel @ Y0 @ X2 ) )
=> ( irel @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( irel @ X2 @ X1 )
& ( irel @ Y0 @ X2 ) )
=> ( irel @ Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( irel @ X2 @ X1 )
& ( irel @ X3 @ X2 ) )
=> ( irel @ X3 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X3 @ X1 )
= $true )
| ( $false
= ( ( irel @ X2 @ X1 )
& ( irel @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X3 @ X2 )
= $false )
| ( ( irel @ X2 @ X1 )
= $false )
| ( ( irel @ X3 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f185]) ).
thf(f195,plain,
! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $true )
| ( $true = $false )
| ( ( irel @ sK2 @ X0 )
= $false ) ),
inference(superposition,[],[f122,f186]) ).
thf(f208,plain,
! [X0: $i] :
( ( ( irel @ sK2 @ X0 )
= $false )
| ( ( irel @ sK0 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f220,plain,
( ( $true
= ( irel @ sK0 @ sK5 ) )
| ( $true = $false ) ),
inference(superposition,[],[f208,f162]) ).
thf(f226,plain,
( $true
= ( irel @ sK0 @ sK5 ) ),
inference(trivial_inequality_removal,[],[f220]) ).
thf(f232,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f233,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) )
@ X2 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) )
@ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f248,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( a @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( a @ X3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) )
@ X4 ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( a @ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( a @ X3 )
= $true )
| ( ( ( irel @ X2 @ X4 )
=> ( b @ X4 ) )
= $true )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( a @ X3 )
= $true )
| ( $true
= ( b @ X4 ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f265,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X2 @ X4 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( a @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f266,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ( irel @ X1 @ X5 )
=> ( b @ X5 ) ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( a @ X3 )
= $true )
| ( $true
= ( b @ X4 ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( $true
= ( b @ X4 ) )
| ( $false
= ( irel @ X1 @ X5 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X5 ) )
| ( ( a @ X3 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f277,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( b @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( a @ sK1 ) )
| ( $true = $false )
| ( $true
= ( b @ X2 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ sK0 ) ) ),
inference(superposition,[],[f118,f267]) ).
thf(f294,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( a @ sK1 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ sK0 ) )
| ( $true
= ( b @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f277]) ).
thf(f316,definition,
( spl4_8
<=> ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f317,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f319,definition,
( spl4_9
<=> ! [X2: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ sK0 ) )
| ( $true
= ( b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f320,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ sK0 ) )
| ( $true
= ( b @ X2 ) )
| ( ( irel @ X1 @ X2 )
= $false ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f319]) ).
thf(f334,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( b @ X2 ) )
| ( $true = $false )
| ( $false
= ( irel @ X1 @ sK0 ) )
| ( ( irel @ sK0 @ X0 )
= $false ) ),
inference(forward_demodulation,[],[f294,f117]) ).
thf(f335,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( irel @ X1 @ sK0 ) )
| ( $true
= ( b @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f346,plain,
( spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f335,f319,f316]) ).
thf(f372,plain,
( ( $true = $false )
| ( ( b @ sK5 )
= $true )
| ~ spl4_8 ),
inference(superposition,[],[f317,f226]) ).
thf(f388,plain,
( ( ( b @ sK5 )
= $true )
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f393,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_8 ),
inference(forward_demodulation,[],[f388,f167]) ).
thf(f394,plain,
( $false
| ~ spl4_3
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f395,plain,
( ~ spl4_3
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f394]) ).
thf(f402,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f107]) ).
thf(f403,plain,
! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f402]) ).
thf(f404,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f403]) ).
thf(f405,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f404]) ).
thf(f446,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f405]) ).
thf(f447,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f446]) ).
thf(f448,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f447]) ).
thf(f449,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f448]) ).
thf(f453,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
@ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f449]) ).
thf(f454,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( $true
= ( ( irel @ X2 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f453]) ).
thf(f455,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f454]) ).
thf(f456,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f455]) ).
thf(f471,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b1 @ Y0 ) )
@ X4 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f456]) ).
thf(f472,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( $true
= ( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f471]) ).
thf(f473,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X3 @ X4 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f472]) ).
thf(f475,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a1 @ Y0 ) )
@ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( ( irel @ X3 @ X4 )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f473]) ).
thf(f476,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X3 @ X4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( ( ( irel @ X3 @ X5 )
=> ( a1 @ X5 ) )
= $true )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f475]) ).
thf(f477,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) ) ) )
| ( $false
= ( irel @ X3 @ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( ( a1 @ X5 )
= $true )
| ( $true
= ( b1 @ X4 ) )
| ( ( irel @ X3 @ X4 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b1 @ Y0 ) )
@ X6 )
= $true )
| ( $false
= ( irel @ X3 @ X5 ) )
| ( ( irel @ X3 @ X4 )
= $false )
| ( ( a1 @ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f477]) ).
thf(f479,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( irel @ X2 @ X6 )
=> ( b1 @ X6 ) )
= $true )
| ( $false
= ( irel @ X3 @ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X3 @ X4 )
= $false )
| ( ( a1 @ X5 )
= $true ) ),
inference(beta-eta_normalization,[],[f478]) ).
thf(f480,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( ( irel @ X2 @ X6 )
= $false )
| ( $true
= ( b1 @ X6 ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X3 @ X5 ) )
| ( ( a1 @ X5 )
= $true )
| ( ( irel @ X3 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f479]) ).
thf(f481,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( b1 @ X6 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X3 @ X5 ) )
| ( ( irel @ X3 @ X4 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK6 @ X1 ) ) )
| ( $true
= ( b1 @ X4 ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( a1 @ X5 )
= $true )
| ( ( irel @ X2 @ X6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f480]) ).
thf(f483,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X3 @ X4 )
= $false )
| ( ( irel @ X2 @ X6 )
= $false )
| ( ( a1 @ X5 )
= $true )
| ( $false
= ( ( irel @ X1 @ ( sK6 @ X1 ) )
=> ( b @ ( sK6 @ X1 ) ) ) )
| ( $false
= ( irel @ X3 @ X5 ) )
| ( $true
= ( b1 @ X4 ) )
| ( $true
= ( b1 @ X6 ) )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f481]) ).
thf(f485,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X3 @ X5 ) )
| ( ( irel @ X3 @ X4 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( $false
= ( b @ ( sK6 @ X1 ) ) )
| ( $true
= ( b1 @ X6 ) )
| ( ( a1 @ X5 )
= $true )
| ( $true
= ( b1 @ X4 ) )
| ( ( irel @ X2 @ X6 )
= $false ) ),
inference(imp_proxy_clausification,[],[f483]) ).
thf(f486,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( irel @ X1 @ ( sK6 @ X1 ) ) )
| ( ( irel @ X3 @ X4 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( a1 @ X5 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( ( irel @ X2 @ X6 )
= $false )
| ( $true
= ( b1 @ X6 ) )
| ( $false
= ( irel @ X3 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f483]) ).
thf(f684,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( b1 @ X0 ) )
| ( ( a1 @ sK5 )
= $true )
| ( $false
= ( b @ ( sK6 @ X1 ) ) )
| ( ( irel @ X2 @ sK2 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true = $false )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( ( b1 @ X3 )
= $true ) ),
inference(superposition,[],[f162,f485]) ).
thf(f704,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( b @ ( sK6 @ X1 ) ) )
| ( ( b1 @ X3 )
= $true )
| ( ( irel @ X2 @ sK2 )
= $false )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b1 @ X0 ) )
| ( ( a1 @ sK5 )
= $true )
| ( $false
= ( irel @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f721,definition,
( spl4_20
<=> ! [X0: $i] :
( ( $true
= ( b1 @ X0 ) )
| ( ( irel @ sK2 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_20])],[avatar_definition]) ).
thf(f722,plain,
( ! [X0: $i] :
( ( ( irel @ sK2 @ X0 )
= $false )
| ( $true
= ( b1 @ X0 ) ) )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f721]) ).
thf(f728,definition,
( spl4_22
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( irel @ X2 @ sK2 )
= $false )
| ( $false
= ( b @ ( sK6 @ X1 ) ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( b1 @ X3 )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
thf(f729,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X2 @ sK2 )
= $false )
| ( ( b1 @ X3 )
= $true )
| ( $false
= ( b @ ( sK6 @ X1 ) ) ) )
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f728]) ).
thf(f748,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( b1 @ X0 ) )
| ( $false
= ( b @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( $true = $false )
| ( ( b1 @ X3 )
= $true )
| ( ( irel @ X2 @ sK2 )
= $false )
| ( $false
= ( irel @ X2 @ X3 ) ) )
| ~ spl4_4 ),
inference(forward_demodulation,[],[f704,f171]) ).
thf(f749,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( b @ ( sK6 @ X1 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( ( b1 @ X3 )
= $true )
| ( $true
= ( b1 @ X0 ) )
| ( $false
= ( irel @ X2 @ X3 ) )
| ( ( irel @ X2 @ sK2 )
= $false ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f748]) ).
thf(f755,plain,
( spl4_22
| spl4_20
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f749,f169,f721,f728]) ).
thf(f824,definition,
( spl4_28
<=> ! [X0: $i] :
( ( ( irel @ X0 @ sK2 )
= $false )
| ( $false
= ( b @ ( sK6 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_28])],[avatar_definition]) ).
thf(f825,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ sK2 )
= $false )
| ( $false
= ( b @ ( sK6 @ X0 ) ) ) )
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f824]) ).
thf(f876,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK2 @ X2 ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( ( b1 @ X1 )
= $true )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $false
= ( irel @ X2 @ X0 ) )
| ( ( irel @ sK0 @ ( sK6 @ sK2 ) )
= $true )
| ( ( irel @ X0 @ X3 )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( $true = $false )
| ( $true
= ( a1 @ X3 ) ) ),
inference(superposition,[],[f208,f486]) ).
thf(f915,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ X2 @ X0 ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ sK0 @ ( sK6 @ sK2 ) )
= $true )
| ( ( irel @ X0 @ X1 )
= $false )
| ( ( irel @ X0 @ X3 )
= $false )
| ( ( b1 @ X1 )
= $true )
| ( $true
= ( b1 @ X4 ) )
| ( $false
= ( irel @ sK2 @ X2 ) )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(trivial_inequality_removal,[],[f876]) ).
thf(f940,definition,
( spl4_36
<=> ( ( b @ ( sK6 @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_36])],[avatar_definition]) ).
thf(f942,plain,
( ( ( b @ ( sK6 @ sK2 ) )
= $true )
| ~ spl4_36 ),
inference(avatar_component_clause,[],[f940]) ).
thf(f944,definition,
( spl4_37
<=> ! [X4: $i,X0: $i,X3: $i,X2: $i,X1: $i] :
( ( ( b1 @ X1 )
= $true )
| ( $true
= ( a1 @ X3 ) )
| ( $true
= ( b1 @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X0 @ X3 )
= $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ sK2 @ X2 ) )
| ( $false
= ( irel @ X2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_37])],[avatar_definition]) ).
thf(f945,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( irel @ sK2 @ X2 ) )
| ( ( irel @ X0 @ X3 )
= $false )
| ( ( b1 @ X1 )
= $true )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $true
= ( b1 @ X4 ) )
| ( $true
= ( a1 @ X3 ) )
| ( ( irel @ X2 @ X4 )
= $false )
| ( $false
= ( irel @ X2 @ X0 ) ) )
| ~ spl4_37 ),
inference(avatar_component_clause,[],[f944]) ).
thf(f948,definition,
( spl4_38
<=> ( ( irel @ sK0 @ ( sK6 @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_38])],[avatar_definition]) ).
thf(f950,plain,
( ( ( irel @ sK0 @ ( sK6 @ sK2 ) )
= $true )
| ~ spl4_38 ),
inference(avatar_component_clause,[],[f948]) ).
thf(f981,plain,
( spl4_38
| spl4_37 ),
inference(avatar_split_clause,[],[f915,f944,f948]) ).
thf(f1028,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f151,f140]) ).
thf(f1029,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f1028]) ).
thf(f1030,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f1029]) ).
thf(f1409,definition,
( spl4_52
<=> ( ( b @ ( sK6 @ sK2 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_52])],[avatar_definition]) ).
thf(f1411,plain,
( ( ( b @ ( sK6 @ sK2 ) )
= $false )
| ~ spl4_52 ),
inference(avatar_component_clause,[],[f1409]) ).
thf(f1606,definition,
( spl4_61
<=> ! [X1: $i] :
( ( $true
= ( a1 @ X1 ) )
| ( ( irel @ sK2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_61])],[avatar_definition]) ).
thf(f1607,plain,
( ! [X1: $i] :
( ( ( irel @ sK2 @ X1 )
= $false )
| ( $true
= ( a1 @ X1 ) ) )
| ~ spl4_61 ),
inference(avatar_component_clause,[],[f1606]) ).
thf(f1911,plain,
( ( $true = $false )
| ( ( b1 @ sK3 )
= $true )
| ~ spl4_20 ),
inference(superposition,[],[f722,f146]) ).
thf(f1926,plain,
( ( ( b1 @ sK3 )
= $true )
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f1911]) ).
thf(f1936,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_20 ),
inference(forward_demodulation,[],[f1926,f155]) ).
thf(f1937,plain,
( $false
| ~ spl4_2
| ~ spl4_20 ),
inference(trivial_inequality_removal,[],[f1936]) ).
thf(f1938,plain,
( ~ spl4_2
| ~ spl4_20 ),
inference(avatar_contradiction_clause,[],[f1937]) ).
thf(f2050,plain,
( ( ( b @ ( sK6 @ sK2 ) )
= $false )
| ( $true = $false )
| ~ spl4_28 ),
inference(superposition,[],[f825,f176]) ).
thf(f2056,plain,
( ( ( b @ ( sK6 @ sK2 ) )
= $false )
| ~ spl4_28 ),
inference(trivial_inequality_removal,[],[f2050]) ).
thf(f2360,plain,
( ! [X0: $i] :
( ( ( irel @ sK2 @ sK2 )
= $false )
| ( $true = $false )
| ( ( b1 @ sK3 )
= $true )
| ( $false
= ( b @ ( sK6 @ X0 ) ) )
| ( ( irel @ X0 @ sK2 )
= $false ) )
| ~ spl4_22 ),
inference(superposition,[],[f146,f729]) ).
thf(f2374,plain,
( ! [X0: $i] :
( ( ( irel @ sK2 @ sK2 )
= $false )
| ( ( b1 @ sK3 )
= $true )
| ( ( irel @ X0 @ sK2 )
= $false )
| ( $false
= ( b @ ( sK6 @ X0 ) ) ) )
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f2360]) ).
thf(f2636,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) ) )
| ~ spl4_9 ),
inference(superposition,[],[f176,f320]) ).
thf(f2640,plain,
( ! [X0: $i] :
( ( $true
= ( b @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false ) )
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f2636]) ).
thf(f3245,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( irel @ sK2 @ X2 ) )
| ( ( a1 @ X2 )
= $true )
| ( ( b1 @ X1 )
= $true )
| ( ( irel @ sK2 @ sK2 )
= $false )
| ( $false != $false )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( ( irel @ sK2 @ X1 )
= $false )
| ( $true
= ( b1 @ X0 ) ) )
| ~ spl4_37 ),
inference(equality_factoring,[],[f945]) ).
thf(f3278,plain,
( ( $true = $false )
| ~ spl4_36
| ~ spl4_52 ),
inference(forward_demodulation,[],[f942,f1411]) ).
thf(f3279,plain,
( $false
| ~ spl4_36
| ~ spl4_52 ),
inference(trivial_inequality_removal,[],[f3278]) ).
thf(f3280,plain,
( ~ spl4_36
| ~ spl4_52 ),
inference(avatar_contradiction_clause,[],[f3279]) ).
thf(f3285,plain,
( spl4_52
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f2056,f824,f1409]) ).
thf(f3328,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ sK2 @ X1 )
= $false )
| ( ( a1 @ X2 )
= $true )
| ( ( b1 @ X1 )
= $true )
| ( ( irel @ sK2 @ sK2 )
= $false )
| ( $true
= ( b1 @ X0 ) )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( $false
= ( irel @ sK2 @ X2 ) ) )
| ~ spl4_37 ),
inference(trivial_inequality_removal,[],[f3245]) ).
thf(f3351,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( a1 @ X2 )
= $true )
| ( ( b1 @ X1 )
= $true )
| ( $true
= ( b1 @ X0 ) )
| ( $true = $false )
| ( $false
= ( irel @ sK2 @ X2 ) )
| ( ( irel @ sK2 @ X1 )
= $false )
| ( ( irel @ sK2 @ X0 )
= $false ) )
| ~ spl4_37 ),
inference(forward_demodulation,[],[f3328,f176]) ).
thf(f3352,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( b1 @ X0 ) )
| ( ( b1 @ X1 )
= $true )
| ( ( a1 @ X2 )
= $true )
| ( ( irel @ sK2 @ X0 )
= $false )
| ( ( irel @ sK2 @ X1 )
= $false )
| ( $false
= ( irel @ sK2 @ X2 ) ) )
| ~ spl4_37 ),
inference(trivial_inequality_removal,[],[f3351]) ).
thf(f3362,plain,
( spl4_20
| spl4_20
| spl4_61
| ~ spl4_37 ),
inference(avatar_split_clause,[],[f3352,f944,f1606,f721,f721]) ).
thf(f3364,plain,
( ( ( b @ ( sK6 @ sK2 ) )
= $true )
| ( $true = $false )
| ~ spl4_8
| ~ spl4_38 ),
inference(superposition,[],[f950,f317]) ).
thf(f3456,plain,
( ( ( b @ ( sK6 @ sK2 ) )
= $true )
| ~ spl4_8
| ~ spl4_38 ),
inference(trivial_inequality_removal,[],[f3364]) ).
thf(f3495,plain,
( spl4_36
| ~ spl4_8
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f3456,f948,f316,f940]) ).
thf(f3597,plain,
( ( ( a1 @ sK5 )
= $true )
| ( $true = $false )
| ~ spl4_61 ),
inference(superposition,[],[f162,f1607]) ).
thf(f3606,plain,
( ( ( a1 @ sK5 )
= $true )
| ~ spl4_61 ),
inference(trivial_inequality_removal,[],[f3597]) ).
thf(f3616,plain,
( ( $true = $false )
| ~ spl4_4
| ~ spl4_61 ),
inference(forward_demodulation,[],[f3606,f171]) ).
thf(f3617,plain,
( $false
| ~ spl4_4
| ~ spl4_61 ),
inference(trivial_inequality_removal,[],[f3616]) ).
thf(f3618,plain,
( ~ spl4_4
| ~ spl4_61 ),
inference(avatar_contradiction_clause,[],[f3617]) ).
thf(f3637,plain,
( ! [X0: $i] :
( ( $false
= ( b @ ( sK6 @ X0 ) ) )
| ( $true = $false )
| ( ( irel @ X0 @ sK2 )
= $false )
| ( ( b1 @ sK3 )
= $true ) )
| ~ spl4_22 ),
inference(forward_demodulation,[],[f2374,f176]) ).
thf(f3638,plain,
( ! [X0: $i] :
( ( ( b1 @ sK3 )
= $true )
| ( $false
= ( b @ ( sK6 @ X0 ) ) )
| ( ( irel @ X0 @ sK2 )
= $false ) )
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f3637]) ).
thf(f3641,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( b @ ( sK6 @ X0 ) ) )
| ( ( irel @ X0 @ sK2 )
= $false ) )
| ~ spl4_2
| ~ spl4_22 ),
inference(forward_demodulation,[],[f3638,f155]) ).
thf(f3642,plain,
( ! [X0: $i] :
( ( $false
= ( b @ ( sK6 @ X0 ) ) )
| ( ( irel @ X0 @ sK2 )
= $false ) )
| ~ spl4_2
| ~ spl4_22 ),
inference(trivial_inequality_removal,[],[f3641]) ).
thf(f3645,plain,
( spl4_28
| ~ spl4_2
| ~ spl4_22 ),
inference(avatar_split_clause,[],[f3642,f728,f153,f824]) ).
thf(f3661,plain,
( spl4_8
| ~ spl4_9 ),
inference(avatar_split_clause,[],[f2640,f319,f316]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f156]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f172]) ).
cnf(s13,plain,
( spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f346]) ).
cnf(s18,plain,
( ~ spl4_3
| ~ spl4_8 ),
inference(sat_conversion,[],[f395]) ).
cnf(s49,plain,
( ~ spl4_4
| spl4_20
| spl4_22 ),
inference(sat_conversion,[],[f755]) ).
cnf(s75,plain,
( spl4_37
| spl4_38 ),
inference(sat_conversion,[],[f981]) ).
cnf(s92,plain,
~ spl4_1,
inference(sat_conversion,[],[f1030]) ).
cnf(s228,plain,
( ~ spl4_2
| ~ spl4_20 ),
inference(sat_conversion,[],[f1938]) ).
cnf(s324,plain,
( ~ spl4_36
| ~ spl4_52 ),
inference(sat_conversion,[],[f3280]) ).
cnf(s326,plain,
( ~ spl4_28
| spl4_52 ),
inference(sat_conversion,[],[f3285]) ).
cnf(s367,plain,
( spl4_20
| spl4_20
| ~ spl4_37
| spl4_61 ),
inference(sat_conversion,[],[f3362]) ).
cnf(s368,plain,
( spl4_20
| ~ spl4_37
| spl4_61 ),
inference(rat,[],[s367]) ).
cnf(s371,plain,
( ~ spl4_8
| spl4_36
| ~ spl4_38 ),
inference(sat_conversion,[],[f3495]) ).
cnf(s379,plain,
( ~ spl4_4
| ~ spl4_61 ),
inference(sat_conversion,[],[f3618]) ).
cnf(s384,plain,
( ~ spl4_2
| ~ spl4_22
| spl4_28 ),
inference(sat_conversion,[],[f3645]) ).
cnf(s391,plain,
( spl4_8
| ~ spl4_9 ),
inference(sat_conversion,[],[f3661]) ).
cnf(s406,plain,
spl4_2,
inference(rat,[],[s1,s92]) ).
cnf(s408,plain,
~ spl4_20,
inference(rat,[],[s228,s406]) ).
cnf(s410,plain,
spl4_8,
inference(rat,[],[s13,s391]) ).
cnf(s413,plain,
~ spl4_3,
inference(rat,[],[s18,s410]) ).
cnf(s414,plain,
spl4_4,
inference(rat,[],[s2,s413]) ).
cnf(s415,plain,
~ spl4_61,
inference(rat,[],[s379,s414]) ).
cnf(s418,plain,
spl4_22,
inference(rat,[],[s49,s408,s414]) ).
cnf(s421,plain,
~ spl4_37,
inference(rat,[],[s368,s408,s415]) ).
cnf(s423,plain,
spl4_28,
inference(rat,[],[s384,s406,s418]) ).
cnf(s430,plain,
spl4_38,
inference(rat,[],[s75,s421]) ).
cnf(s432,plain,
spl4_52,
inference(rat,[],[s326,s423]) ).
cnf(s433,plain,
spl4_36,
inference(rat,[],[s371,s410,s430]) ).
cnf(s435,plain,
$false,
inference(rat,[],[s324,s432,s433]) ).
thf(f3682,plain,
$false,
inference(avatar_sat_refutation,[],[s435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO064^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n005.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 16:26:16 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.23 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
% 0.22/0.37 % (1876933)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.37 % (1876938)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=889697805:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.37 % (1876944)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.37 % (1876944)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
% 0.22/0.37 % (1876939)lrs+10_16_si=on:nwc=1.5:random_seed=3447364470:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.37 % (1876940)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3044713792:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.37 % (1876942)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=668748307:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.37 % (1876941)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=369328900: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)
% 0.22/0.37 % (1876944)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=3622092060:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.37 % (1876940)Instruction limit reached!
% 0.22/0.37 % (1876940)------------------------------
% 0.22/0.37 % (1876940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1876940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1876940)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1876940)Termination reason: Instruction limit
% 0.22/0.37 % (1876940)Termination phase: Function definition elimination
% 0.22/0.37 % (1876940)Time elapsed: 0.001 s
% 0.22/0.37 % (1876940)Peak memory usage: 10 MB
% 0.22/0.37 % (1876940)Instructions burned: 3 (million)
% 0.22/0.37 % (1876939)Instruction limit reached!
% 0.22/0.37 % (1876939)------------------------------
% 0.22/0.37 % (1876939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1876939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1876939)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1876939)Termination reason: Instruction limit
% 0.22/0.37 % (1876939)Termination phase: Saturation
% 0.22/0.37 % (1876939)Time elapsed: 0.009 s
% 0.22/0.37 % (1876939)Peak memory usage: 12 MB
% 0.22/0.37 % (1876939)Instructions burned: 18 (million)
% 0.22/0.37 % (1876943)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=404041834:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.37 % (1876942)Instruction limit reached!
% 0.22/0.37 % (1876942)------------------------------
% 0.22/0.37 % (1876942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1876942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1876942)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1876942)Termination reason: Instruction limit
% 0.22/0.37 % (1876942)Termination phase: Saturation
% 0.22/0.37 % (1876942)Time elapsed: 0.014 s
% 0.22/0.37 % (1876942)Peak memory usage: 11 MB
% 0.22/0.37 % (1876942)Instructions burned: 25 (million)
% 0.22/0.37 % (1876938)Instruction limit reached!
% 0.22/0.37 % (1876938)------------------------------
% 0.22/0.37 % (1876938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1876938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1876938)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1876938)Termination reason: Instruction limit
% 0.22/0.37 % (1876938)Termination phase: Saturation
% 0.22/0.37 % (1876938)Time elapsed: 0.023 s
% 0.22/0.37 % (1876938)Peak memory usage: 12 MB
% 0.22/0.37 % (1876938)Instructions burned: 88 (million)
% 0.22/0.37 % (1876952)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3606559075:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.37 % (1876954)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.99/0.39 % (1876952)Instruction limit reached!
% 0.99/0.39 % (1876952)------------------------------
% 0.99/0.39 % (1876952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.39 % (1876952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.39 % (1876952)CaDiCaL version: 2.1.3
% 0.99/0.39 % (1876952)Termination reason: Instruction limit
% 0.99/0.39 % (1876952)Termination phase: Saturation
% 0.99/0.39 % (1876952)Time elapsed: 0.003 s
% 0.99/0.39 % (1876952)Peak memory usage: 11 MB
% 0.99/0.39 % (1876952)Instructions burned: 6 (million)
% 0.99/0.39 % (1876954)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4071337480:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.99/0.39 % (1876955)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1274820815:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.99/0.39 % (1876954)Instruction limit reached!
% 0.99/0.39 % (1876954)------------------------------
% 0.99/0.39 % (1876954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.39 % (1876954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.39 % (1876954)CaDiCaL version: 2.1.3
% 0.99/0.39 % (1876954)Termination reason: Instruction limit
% 0.99/0.39 % (1876954)Termination phase: Saturation
% 0.99/0.39 % (1876954)Time elapsed: 0.004 s
% 0.99/0.39 % (1876954)Peak memory usage: 11 MB
% 0.99/0.39 % (1876954)Instructions burned: 9 (million)
% 0.99/0.39 % (1876957)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
% 0.99/0.39 % (1876957)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.99/0.39 % (1876955)Instruction limit reached!
% 0.99/0.39 % (1876955)------------------------------
% 0.99/0.39 % (1876955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.39 % (1876955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.39 % (1876955)CaDiCaL version: 2.1.3
% 0.99/0.39 % (1876955)Termination reason: Instruction limit
% 0.99/0.39 % (1876955)Termination phase: Saturation
% 0.99/0.39 % (1876955)Time elapsed: 0.006 s
% 0.99/0.39 % (1876955)Peak memory usage: 12 MB
% 0.99/0.39 % (1876955)Instructions burned: 12 (million)
% 0.99/0.39 % (1876957)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3145831822:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.99/0.39 % (1876951)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3178438661:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.99/0.39 % (1876951)Instruction limit reached!
% 0.99/0.39 % (1876951)------------------------------
% 0.99/0.39 % (1876951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.39 % (1876951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.39 % (1876951)CaDiCaL version: 2.1.3
% 0.99/0.39 % (1876951)Termination reason: Instruction limit
% 0.99/0.39 % (1876951)Termination phase: Property scanning
% 0.99/0.39 % (1876951)Time elapsed: 0.002 s
% 0.99/0.39 % (1876951)Peak memory usage: 10 MB
% 0.99/0.39 % (1876951)Instructions burned: 4 (million)
% 0.99/0.39 % (1876957)Instruction limit reached!
% 0.99/0.39 % (1876957)------------------------------
% 0.99/0.39 % (1876957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.39 % (1876957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.39 % (1876957)CaDiCaL version: 2.1.3
% 0.99/0.39 % (1876957)Termination reason: Instruction limit
% 0.99/0.39 % (1876957)Termination phase: Saturation
% 0.99/0.39 % (1876957)Time elapsed: 0.007 s
% 0.99/0.39 % (1876957)Peak memory usage: 12 MB
% 0.99/0.39 % (1876957)Instructions burned: 29 (million)
% 0.99/0.39 % (1876960)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=2368461200:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.99/0.39 % (1876961)lrs+10_1_si=on:cs=on:random_seed=3086221022:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.99/0.39 % (1876965)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1224515301:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.99/0.43 % (1876964)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.99/0.43 % (1876965)Refutation not found, incomplete strategy
% 0.99/0.43 % (1876965)------------------------------
% 0.99/0.43 % (1876965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.43 % (1876965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.43 % (1876965)CaDiCaL version: 2.1.3
% 0.99/0.43 % (1876965)Termination reason: Refutation not found, incomplete strategy
% 0.99/0.43 % (1876965)Time elapsed: 0.001 s
% 0.99/0.43 % (1876965)Peak memory usage: 12 MB
% 0.99/0.43 % (1876965)Instructions burned: 4 (million)
% 0.99/0.43 % (1876965)------------------------------
% 0.99/0.43 % (1876965)------------------------------
% 0.99/0.43 % (1876961)Instruction limit reached!
% 0.99/0.43 % (1876961)------------------------------
% 0.99/0.43 % (1876961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.43 % (1876961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.43 % (1876961)CaDiCaL version: 2.1.3
% 0.99/0.43 % (1876961)Termination reason: Instruction limit
% 0.99/0.43 % (1876961)Termination phase: Saturation
% 0.99/0.43 % (1876961)Time elapsed: 0.004 s
% 0.99/0.43 % (1876961)Peak memory usage: 11 MB
% 0.99/0.43 % (1876961)Instructions burned: 9 (million)
% 0.99/0.43 % (1876964)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=835099222:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.99/0.43 % (1876964)Instruction limit reached!
% 0.99/0.43 % (1876964)------------------------------
% 0.99/0.43 % (1876964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.43 % (1876964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.43 % (1876964)CaDiCaL version: 2.1.3
% 0.99/0.43 % (1876964)Termination reason: Instruction limit
% 0.99/0.43 % (1876964)Termination phase: Saturation
% 0.99/0.43 % (1876964)Time elapsed: 0.004 s
% 0.99/0.43 % (1876964)Peak memory usage: 11 MB
% 0.99/0.43 % (1876964)Instructions burned: 8 (million)
% 0.99/0.43 % (1876969)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1915757412:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.99/0.43 % (1876943)Instruction limit reached!
% 0.99/0.43 % (1876943)------------------------------
% 0.99/0.43 % (1876943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.43 % (1876943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.43 % (1876943)CaDiCaL version: 2.1.3
% 0.99/0.43 % (1876943)Termination reason: Instruction limit
% 0.99/0.43 % (1876943)Termination phase: Saturation
% 0.99/0.43 % (1876943)Time elapsed: 0.065 s
% 0.99/0.43 % (1876943)Peak memory usage: 12 MB
% 0.99/0.43 % (1876943)Instructions burned: 75 (million)
% 0.99/0.43 % (1876969)Refutation not found, incomplete strategy
% 0.99/0.43 % (1876969)------------------------------
% 0.99/0.43 % (1876969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.43 % (1876969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.43 % (1876969)CaDiCaL version: 2.1.3
% 0.99/0.43 % (1876969)Termination reason: Refutation not found, incomplete strategy
% 0.99/0.43 % (1876969)Time elapsed: 0.002 s
% 0.99/0.43 % (1876969)Peak memory usage: 12 MB
% 0.99/0.43 % (1876969)Instructions burned: 5 (million)
% 0.99/0.43 % (1876969)------------------------------
% 0.99/0.43 % (1876969)------------------------------
% 0.99/0.43 % (1876971)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2591230440:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.99/0.43 % (1876972)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1136231565:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.99/0.43 % (1876975)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3674079450:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.99/0.43 % (1876975)Instruction limit reached!
% 0.99/0.43 % (1876975)------------------------------
% 0.99/0.47 % (1876975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.47 % (1876975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.47 % (1876975)CaDiCaL version: 2.1.3
% 0.99/0.47 % (1876975)Termination reason: Instruction limit
% 0.99/0.47 % (1876975)Termination phase: Saturation
% 0.99/0.47 % (1876975)Time elapsed: 0.005 s
% 0.99/0.47 % (1876975)Peak memory usage: 12 MB
% 0.99/0.47 % (1876975)Instructions burned: 16 (million)
% 0.99/0.47 % (1876972)Instruction limit reached!
% 0.99/0.47 % (1876972)------------------------------
% 0.99/0.47 % (1876972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.47 % (1876972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.47 % (1876972)CaDiCaL version: 2.1.3
% 0.99/0.47 % (1876972)Termination reason: Instruction limit
% 0.99/0.47 % (1876972)Termination phase: Saturation
% 0.99/0.47 % (1876972)Time elapsed: 0.007 s
% 0.99/0.47 % (1876972)Peak memory usage: 12 MB
% 0.99/0.47 % (1876972)Instructions burned: 15 (million)
% 0.99/0.47 % (1876960)Instruction limit reached!
% 0.99/0.47 % (1876960)------------------------------
% 0.99/0.47 % (1876960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.47 % (1876960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.47 % (1876960)CaDiCaL version: 2.1.3
% 0.99/0.47 % (1876960)Termination reason: Instruction limit
% 0.99/0.47 % (1876960)Termination phase: Saturation
% 0.99/0.47 % (1876960)Time elapsed: 0.043 s
% 0.99/0.47 % (1876960)Peak memory usage: 12 MB
% 0.99/0.47 % (1876960)Instructions burned: 86 (million)
% 0.99/0.47 % (1876944)Instruction limit reached!
% 0.99/0.47 % (1876944)------------------------------
% 0.99/0.47 % (1876944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.47 % (1876944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.47 % (1876944)CaDiCaL version: 2.1.3
% 0.99/0.47 % (1876944)Termination reason: Instruction limit
% 0.99/0.47 % (1876944)Termination phase: Saturation
% 0.99/0.47 % (1876944)Time elapsed: 0.101 s
% 0.99/0.47 % (1876944)Peak memory usage: 13 MB
% 0.99/0.47 % (1876944)Instructions burned: 157 (million)
% 0.99/0.47 % (1876971)Instruction limit reached!
% 0.99/0.47 % (1876971)------------------------------
% 0.99/0.47 % (1876971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.47 % (1876971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.47 % (1876971)CaDiCaL version: 2.1.3
% 0.99/0.47 % (1876971)Termination reason: Instruction limit
% 0.99/0.47 % (1876971)Termination phase: Saturation
% 0.99/0.47 % (1876971)Time elapsed: 0.018 s
% 0.99/0.47 % (1876971)Peak memory usage: 12 MB
% 0.99/0.47 % (1876971)Instructions burned: 26 (million)
% 0.99/0.47 % (1876979)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1058295229: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)
% 0.99/0.47 % (1876979)Instruction limit reached!
% 0.99/0.47 % (1876979)------------------------------
% 0.99/0.47 % (1876979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.47 % (1876979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.47 % (1876979)CaDiCaL version: 2.1.3
% 0.99/0.47 % (1876979)Termination reason: Instruction limit
% 0.99/0.47 % (1876979)Termination phase: Function definition elimination
% 0.99/0.47 % (1876979)Time elapsed: 0.001 s
% 0.99/0.47 % (1876979)Peak memory usage: 10 MB
% 0.99/0.47 % (1876979)Instructions burned: 3 (million)
% 0.99/0.47 % (1876974)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2431929430:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.99/0.47 % (1876984)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
% 0.99/0.47 % (1876984)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.99/0.47 % (1876984)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=681253439:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.99/0.47 % (1876981)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1723797635:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.69/0.52 % (1876980)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2230720584:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.69/0.52 % (1876982)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3396613346:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.69/0.52 % (1876984)Instruction limit reached!
% 1.69/0.52 % (1876984)------------------------------
% 1.69/0.52 % (1876984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1876984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1876984)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1876984)Termination reason: Instruction limit
% 1.69/0.52 % (1876984)Termination phase: Saturation
% 1.69/0.52 % (1876984)Time elapsed: 0.004 s
% 1.69/0.52 % (1876984)Peak memory usage: 12 MB
% 1.69/0.52 % (1876984)Instructions burned: 14 (million)
% 1.69/0.52 % (1876985)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.69/0.52 % (1876985)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=1336161328:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.69/0.52 % (1876981)Instruction limit reached!
% 1.69/0.52 % (1876981)------------------------------
% 1.69/0.52 % (1876981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1876981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1876981)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1876981)Termination reason: Instruction limit
% 1.69/0.52 % (1876981)Termination phase: Saturation
% 1.69/0.52 % (1876981)Time elapsed: 0.012 s
% 1.69/0.52 % (1876981)Peak memory usage: 11 MB
% 1.69/0.52 % (1876981)Instructions burned: 25 (million)
% 1.69/0.52 % (1876991)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=1139969077:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.69/0.52 % (1876980)Instruction limit reached!
% 1.69/0.52 % (1876980)------------------------------
% 1.69/0.52 % (1876980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1876980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1876980)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1876980)Termination reason: Instruction limit
% 1.69/0.52 % (1876980)Termination phase: Saturation
% 1.69/0.52 % (1876980)Time elapsed: 0.014 s
% 1.69/0.52 % (1876980)Peak memory usage: 12 MB
% 1.69/0.52 % (1876980)Instructions burned: 27 (million)
% 1.69/0.52 % (1876985)Instruction limit reached!
% 1.69/0.52 % (1876985)------------------------------
% 1.69/0.52 % (1876985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1876985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1876985)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1876985)Termination reason: Instruction limit
% 1.69/0.52 % (1876985)Termination phase: Saturation
% 1.69/0.52 % (1876985)Time elapsed: 0.006 s
% 1.69/0.52 % (1876985)Peak memory usage: 11 MB
% 1.69/0.52 % (1876985)Instructions burned: 8 (million)
% 1.69/0.52 % (1876991)Instruction limit reached!
% 1.69/0.52 % (1876991)------------------------------
% 1.69/0.52 % (1876991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.52 % (1876991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.52 % (1876991)CaDiCaL version: 2.1.3
% 1.69/0.52 % (1876991)Termination reason: Instruction limit
% 1.69/0.52 % (1876991)Termination phase: Saturation
% 1.69/0.52 % (1876991)Time elapsed: 0.009 s
% 1.69/0.52 % (1876991)Peak memory usage: 12 MB
% 1.69/0.52 % (1876991)Instructions burned: 32 (million)
% 1.69/0.52 % (1876997)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1055956870:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.69/0.52 % (1876996)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=698228139:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.69/0.52 % (1876982)Instruction limit reached!
% 1.69/0.52 % (1876982)------------------------------
% 1.69/0.52 % (1876982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1876982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1876982)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1876982)Termination reason: Instruction limit
% 1.69/0.55 % (1876982)Termination phase: Saturation
% 1.69/0.55 % (1876982)Time elapsed: 0.032 s
% 1.69/0.55 % (1876982)Peak memory usage: 12 MB
% 1.69/0.55 % (1876982)Instructions burned: 60 (million)
% 1.69/0.55 % (1876993)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3678195260:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.69/0.55 % (1876995)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3919732291:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.69/0.55 % (1876993)Instruction limit reached!
% 1.69/0.55 % (1876993)------------------------------
% 1.69/0.55 % (1876993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1876993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1876993)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1876993)Termination reason: Instruction limit
% 1.69/0.55 % (1876993)Termination phase: Saturation
% 1.69/0.55 % (1876993)Time elapsed: 0.004 s
% 1.69/0.55 % (1876993)Peak memory usage: 12 MB
% 1.69/0.55 % (1876993)Instructions burned: 9 (million)
% 1.69/0.55 % (1876996)Instruction limit reached!
% 1.69/0.55 % (1876996)------------------------------
% 1.69/0.55 % (1876996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1876996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1876996)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1876996)Termination reason: Instruction limit
% 1.69/0.55 % (1876996)Termination phase: Saturation
% 1.69/0.55 % (1876996)Time elapsed: 0.012 s
% 1.69/0.55 % (1876996)Peak memory usage: 12 MB
% 1.69/0.55 % (1876996)Instructions burned: 21 (million)
% 1.69/0.55 % (1876995)Instruction limit reached!
% 1.69/0.55 % (1876995)------------------------------
% 1.69/0.55 % (1876995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1876995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1876995)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1876995)Termination reason: Instruction limit
% 1.69/0.55 % (1876995)Termination phase: Saturation
% 1.69/0.55 % (1876995)Time elapsed: 0.010 s
% 1.69/0.55 % (1876995)Peak memory usage: 11 MB
% 1.69/0.55 % (1876995)Instructions burned: 24 (million)
% 1.69/0.55 % (1877000)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3593593884:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.69/0.55 % (1877003)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1180805921:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.69/0.55 % (1877004)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1270976852:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.69/0.55 % (1877003)Refutation not found, incomplete strategy
% 1.69/0.55 % (1877003)------------------------------
% 1.69/0.55 % (1877003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877003)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877003)Termination reason: Refutation not found, incomplete strategy
% 1.69/0.55 % (1877003)Time elapsed: 0.004 s
% 1.69/0.55 % (1877003)Peak memory usage: 12 MB
% 1.69/0.55 % (1877003)Instructions burned: 7 (million)
% 1.69/0.55 % (1877003)------------------------------
% 1.69/0.55 % (1877003)------------------------------
% 1.69/0.55 % (1877005)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.69/0.55 % (1877005)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2067289403:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.69/0.55 % (1877005)Instruction limit reached!
% 1.69/0.55 % (1877005)------------------------------
% 1.69/0.55 % (1877005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877005)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877005)Termination reason: Instruction limit
% 1.69/0.55 % (1877005)Termination phase: Saturation
% 1.69/0.55 % (1877005)Time elapsed: 0.003 s
% 1.69/0.55 % (1877005)Peak memory usage: 11 MB
% 1.69/0.55 % (1877005)Instructions burned: 7 (million)
% 1.69/0.55 % (1877009)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4173922716:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.69/0.55 % (1877004)Instruction limit reached!
% 1.69/0.55 % (1877004)------------------------------
% 1.69/0.55 % (1877004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877004)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877004)Termination reason: Instruction limit
% 1.69/0.55 % (1877004)Termination phase: Saturation
% 1.69/0.55 % (1877004)Time elapsed: 0.021 s
% 1.69/0.55 % (1877004)Peak memory usage: 12 MB
% 1.69/0.55 % (1877004)Instructions burned: 42 (million)
% 1.69/0.55 % (1877009)Refutation not found, incomplete strategy
% 1.69/0.55 % (1877009)------------------------------
% 1.69/0.55 % (1877009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877009)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877009)Termination reason: Refutation not found, incomplete strategy
% 1.69/0.55 % (1877009)Time elapsed: 0.003 s
% 1.69/0.55 % (1877009)Peak memory usage: 12 MB
% 1.69/0.55 % (1877009)Instructions burned: 5 (million)
% 1.69/0.55 % (1877009)------------------------------
% 1.69/0.55 % (1877009)------------------------------
% 1.69/0.55 % (1877011)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=1829391626: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)
% 1.69/0.55 % (1877013)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.69/0.55 % (1877011)Refutation not found, incomplete strategy
% 1.69/0.55 % (1877011)------------------------------
% 1.69/0.55 % (1877011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877011)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877011)Termination reason: Refutation not found, incomplete strategy
% 1.69/0.55 % (1877011)Time elapsed: 0.007 s
% 1.69/0.55 % (1877011)Peak memory usage: 12 MB
% 1.69/0.55 % (1877011)Instructions burned: 13 (million)
% 1.69/0.55 % (1877011)------------------------------
% 1.69/0.55 % (1877011)------------------------------
% 1.69/0.55 % (1877013)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1243429870:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.69/0.55 % (1877013)Instruction limit reached!
% 1.69/0.55 % (1877013)------------------------------
% 1.69/0.55 % (1877013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877013)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877013)Termination reason: Instruction limit
% 1.69/0.55 % (1877013)Termination phase: Saturation
% 1.69/0.55 % (1877013)Time elapsed: 0.003 s
% 1.69/0.55 % (1877013)Peak memory usage: 11 MB
% 1.69/0.55 % (1877013)Instructions burned: 6 (million)
% 1.69/0.55 % (1877014)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2462407275:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.69/0.55 % (1877016)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3330561023:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.69/0.55 % (1877000)Instruction limit reached!
% 1.69/0.55 % (1877000)------------------------------
% 1.69/0.55 % (1877000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877000)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877000)Termination reason: Instruction limit
% 1.69/0.55 % (1877000)Termination phase: Saturation
% 1.69/0.55 % (1877000)Time elapsed: 0.068 s
% 1.69/0.55 % (1877000)Peak memory usage: 12 MB
% 1.69/0.55 % (1877000)Instructions burned: 144 (million)
% 1.69/0.55 % (1877014)Instruction limit reached!
% 1.69/0.55 % (1877014)------------------------------
% 1.69/0.55 % (1877014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877014)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877014)Termination reason: Instruction limit
% 1.69/0.55 % (1877014)Termination phase: Saturation
% 1.69/0.55 % (1877014)Time elapsed: 0.012 s
% 1.69/0.55 % (1877014)Peak memory usage: 12 MB
% 1.69/0.55 % (1877014)Instructions burned: 23 (million)
% 1.69/0.55 % (1877018)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2345043103:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 1.69/0.55 % (1877016)Refutation not found, incomplete strategy
% 1.69/0.55 % (1877016)------------------------------
% 1.69/0.55 % (1877016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1877016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1877016)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1877016)Termination reason: Refutation not found, incomplete strategy
% 1.69/0.55 % (1877016)Time elapsed: 0.010 s
% 1.69/0.55 % (1877016)Peak memory usage: 12 MB
% 1.69/0.55 % (1877016)Instructions burned: 13 (million)
% 1.69/0.55 % (1877016)------------------------------
% 1.69/0.55 % (1877016)------------------------------
% 1.69/0.55 % (1877021)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=321413990:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 1.69/0.55 % (1877022)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2225189490:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 1.69/0.55 % (1876997) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1876933-1876997"...
% 1.69/0.55 % (1876997)...printing done.
% 1.69/0.55 % (1876997)Refutation found. Thanks to Tanya!
% 1.69/0.55 % SZS status Theorem for theBenchmark
% 1.69/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.69/0.55 % (1876997)------------------------------
% 1.69/0.55 % (1876997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.69/0.55 % (1876997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.55 % (1876997)CaDiCaL version: 2.1.3
% 1.69/0.55 % (1876997)Termination reason: Refutation
% 1.69/0.55 % (1876997)Time elapsed: 0.116 s
% 1.69/0.55 % (1876997)Peak memory usage: 14 MB
% 1.69/0.55 % (1876997)Instructions burned: 474 (million)
% 1.69/0.55 % (1876933)Success in time 0.306 s
% 1.69/0.55 % Vampire exiting
%------------------------------------------------------------------------------