%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN393^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:41:43 AM UTC 2026
% Result : Theorem 2.39s 0.79s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 129 ( 52 unt; 0 typ; 6 def)
% Number of atoms : 1391 ( 107 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 2902 ( 251 ~; 235 |; 66 &;1743 @)
% ( 6 <=>; 304 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 174 ( 174 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 42 usr; 12 con; 0-4 aty)
% ( 297 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 543 ( 0 sgn 8 !; 0 ?; 543 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
a1: $i > $o ).
thf(func_def_22,type,
a2: $i > $o ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( 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,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f12,axiom,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(f14,axiom,
( iimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f16,axiom,
( iequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( iand @ ( iimplies @ X0 @ X1 ) @ ( iimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iequiv) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f27,plain,
~ ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f28,plain,
( ( ~ ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f27]) ).
thf(f32,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f35,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f38,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f40,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f49,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f50,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f51,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f53,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f56,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f57,plain,
( ( ~ ( ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f28]) ).
thf(f58,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f62,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f63,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f64,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f66,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f68,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f69,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f71,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f74,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f77,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f81,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f77,f68,f71]) ).
thf(f84,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f69,f64]) ).
thf(f86,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f58,f81,f74,f74]) ).
thf(f88,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f62,f84,f86,f86]) ).
thf(f90,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
& ( Y5 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a2 )
@ ( ^ [Y0: $i > $o] : Y0
@ a1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f57,f66,f88,f88,f63,f63,f88,f63,f63]) ).
thf(f91,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f94,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f91]) ).
thf(f95,plain,
( $false
= ( ^ [Y0: $i] :
( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f99,definition,
( spl1_1
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f101,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f99]) ).
thf(f103,definition,
( spl1_2
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f105,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f103]) ).
thf(f106,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f97,f103,f99]) ).
thf(f107,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f105]) ).
thf(f108,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f105]) ).
thf(f109,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ sK2 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( ( $false
= ( ( irel @ sK0 @ sK2 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f113,plain,
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f114,plain,
( ( ( irel @ sK0 @ sK2 )
= $true )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f121,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f113]) ).
thf(f123,definition,
( spl1_3
<=> ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f125,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f127,definition,
( spl1_4
<=> ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f129,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f130,plain,
( spl1_3
| spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f121,f103,f127,f123]) ).
thf(f153,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f108]) ).
thf(f161,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f162,plain,
( ! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ spl1_3 ),
inference(or_proxy_clausification,[],[f125]) ).
thf(f164,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ spl1_3 ),
inference(or_proxy_clausification,[],[f125]) ).
thf(f167,plain,
( ( ( $true
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(superposition,[],[f162,f114]) ).
thf(f169,plain,
( ( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f167]) ).
thf(f170,plain,
( ( ( ( ~ $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| $false ) )
= $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f169,f163]) ).
thf(f171,plain,
( ( ( ( ~ $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(boolean_simplification,[],[f170]) ).
thf(f172,plain,
( ( ( ( $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(boolean_simplification,[],[f171]) ).
thf(f173,plain,
( ( ( $true
& ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(boolean_simplification,[],[f172]) ).
thf(f174,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(boolean_simplification,[],[f173]) ).
thf(f175,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f174,f164]) ).
thf(f176,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f175]) ).
thf(f177,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f176]) ).
thf(f178,plain,
( ( ( $false
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
= $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(forward_demodulation,[],[f169,f129]) ).
thf(f179,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(boolean_simplification,[],[f178]) ).
thf(f180,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f181,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f180]) ).
thf(f192,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f101]) ).
thf(f193,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f101]) ).
thf(f202,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) )
@ sK3 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f192]) ).
thf(f203,plain,
( ( $false
= ( ( irel @ sK0 @ sK3 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f206,plain,
( ( $false
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f207,plain,
( ( ( irel @ sK0 @ sK3 )
= $true )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f216,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f224,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f225,plain,
( ! [X1: $i] :
( ( ( irel @ sK0 @ X1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f235,plain,
( ( ( $true
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(superposition,[],[f225,f207]) ).
thf(f236,plain,
( ( $true
= ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f235]) ).
thf(f242,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f206]) ).
thf(f244,definition,
( spl1_7
<=> ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
thf(f246,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f248,definition,
( spl1_8
<=> ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
thf(f250,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,plain,
( spl1_7
| spl1_8
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f242,f99,f248,f244]) ).
thf(f398,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ spl1_8 ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f399,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ spl1_8 ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f532,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f236]) ).
thf(f533,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
= $true )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f236]) ).
thf(f537,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_7 ),
inference(forward_demodulation,[],[f532,f246]) ).
thf(f538,plain,
( $false
| ~ spl1_1
| ~ spl1_7 ),
inference(trivial_inequality_removal,[],[f537]) ).
thf(f539,plain,
( ~ spl1_1
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[],[f538]) ).
thf(f609,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f533]) ).
thf(f610,plain,
( ( $false = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ~ spl1_1
| ~ spl1_8 ),
inference(forward_demodulation,[],[f609,f398]) ).
thf(f611,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
= $true )
| ~ spl1_1
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f610]) ).
thf(f612,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_8 ),
inference(forward_demodulation,[],[f611,f399]) ).
thf(f613,plain,
( $false
| ~ spl1_1
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f614,plain,
( ~ spl1_1
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[],[f613]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f106]) ).
cnf(s2,plain,
( ~ spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f130]) ).
cnf(s3,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f177]) ).
cnf(s4,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(sat_conversion,[],[f181]) ).
cnf(s6,plain,
( ~ spl1_1
| spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f251]) ).
cnf(s12,plain,
( ~ spl1_1
| ~ spl1_7 ),
inference(sat_conversion,[],[f539]) ).
cnf(s15,plain,
( ~ spl1_1
| ~ spl1_8 ),
inference(sat_conversion,[],[f614]) ).
cnf(s16,plain,
~ spl1_2,
inference(rat,[],[s2,s3,s4]) ).
cnf(s17,plain,
spl1_1,
inference(rat,[],[s1,s16]) ).
cnf(s18,plain,
~ spl1_8,
inference(rat,[],[s15,s17]) ).
cnf(s19,plain,
~ spl1_7,
inference(rat,[],[s12,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s6,s18,s19,s17]) ).
thf(f615,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN393^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.26 % Computer : n007.cluster.edu
% 0.21/0.26 % Model : x86_64 x86_64
% 0.21/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.26 % Memory : 8046.5625MB
% 0.21/0.26 % OS : Linux 6.8.0-71-generic
% 0.21/0.26 % CPULimit : 300
% 0.21/0.26 % WCLimit : 300
% 0.21/0.26 % DateTime : Tue Sep 29 16:13:56 UTC 2026
% 0.21/0.27 % CPUTime :
% 0.21/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.30 Running higher-order theorem proving
% 0.21/0.32 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
% 0.94/0.49 % (3569053)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.94/0.49 % (3569064)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.94/0.49 % (3569064)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
% 0.94/0.49 % (3569064)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=1065953258:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.94/0.49 % (3569058)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3786063041:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.94/0.49 % (3569059)lrs+10_16_si=on:nwc=1.5:random_seed=1638063376:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.94/0.49 % (3569060)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=336367310:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.94/0.49 % (3569062)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1108282550:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.94/0.49 % (3569061)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=1206289052: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)
% 0.94/0.49 % (3569063)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=97283366:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.94/0.49 % (3569060)Instruction limit reached!
% 0.94/0.49 % (3569060)------------------------------
% 0.94/0.49 % (3569060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (3569060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (3569060)CaDiCaL version: 2.1.3
% 0.94/0.49 % (3569060)Termination reason: Instruction limit
% 0.94/0.49 % (3569060)Termination phase: Property scanning
% 0.94/0.49 % (3569060)Time elapsed: 0.003 s
% 0.94/0.49 % (3569060)Peak memory usage: 10 MB
% 0.94/0.49 % (3569060)Instructions burned: 3 (million)
% 0.94/0.49 % (3569059)Instruction limit reached!
% 0.94/0.49 % (3569059)------------------------------
% 0.94/0.49 % (3569059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (3569059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (3569059)CaDiCaL version: 2.1.3
% 0.94/0.49 % (3569059)Termination reason: Instruction limit
% 0.94/0.49 % (3569059)Termination phase: Saturation
% 0.94/0.49 % (3569059)Time elapsed: 0.015 s
% 0.94/0.49 % (3569059)Peak memory usage: 11 MB
% 0.94/0.49 % (3569059)Instructions burned: 19 (million)
% 0.94/0.49 % (3569062)Instruction limit reached!
% 0.94/0.49 % (3569062)------------------------------
% 0.94/0.49 % (3569062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (3569062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (3569062)CaDiCaL version: 2.1.3
% 0.94/0.49 % (3569062)Termination reason: Instruction limit
% 0.94/0.49 % (3569062)Termination phase: Saturation
% 0.94/0.49 % (3569062)Time elapsed: 0.023 s
% 0.94/0.49 % (3569062)Peak memory usage: 11 MB
% 0.94/0.49 % (3569062)Instructions burned: 24 (million)
% 0.94/0.49 % (3569072)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4217665907:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.94/0.49 % (3569072)Instruction limit reached!
% 0.94/0.49 % (3569072)------------------------------
% 0.94/0.49 % (3569072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (3569072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (3569072)CaDiCaL version: 2.1.3
% 0.94/0.49 % (3569072)Termination reason: Instruction limit
% 0.94/0.49 % (3569072)Termination phase: Property scanning
% 0.94/0.49 % (3569072)Time elapsed: 0.002 s
% 0.94/0.49 % (3569072)Peak memory usage: 10 MB
% 0.94/0.49 % (3569072)Instructions burned: 4 (million)
% 0.94/0.49 % (3569074)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.54 % (3569073)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2881973597:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.94/0.54 % (3569076)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1201043080:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.94/0.54 % (3569074)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4033241876:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.94/0.54 % (3569073)Instruction limit reached!
% 0.94/0.54 % (3569073)------------------------------
% 0.94/0.54 % (3569073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.54 % (3569073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.54 % (3569073)CaDiCaL version: 2.1.3
% 0.94/0.54 % (3569073)Termination reason: Instruction limit
% 0.94/0.54 % (3569073)Termination phase: Saturation
% 0.94/0.54 % (3569073)Time elapsed: 0.005 s
% 0.94/0.54 % (3569073)Peak memory usage: 11 MB
% 0.94/0.54 % (3569073)Instructions burned: 5 (million)
% 0.94/0.54 % (3569064)Instruction limit reached!
% 0.94/0.54 % (3569064)------------------------------
% 0.94/0.54 % (3569064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.54 % (3569064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.54 % (3569064)CaDiCaL version: 2.1.3
% 0.94/0.54 % (3569064)Termination reason: Instruction limit
% 0.94/0.54 % (3569064)Termination phase: Saturation
% 0.94/0.54 % (3569064)Time elapsed: 0.071 s
% 0.94/0.54 % (3569064)Peak memory usage: 14 MB
% 0.94/0.54 % (3569064)Instructions burned: 157 (million)
% 0.94/0.54 % (3569076)Instruction limit reached!
% 0.94/0.54 % (3569076)------------------------------
% 0.94/0.54 % (3569076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.54 % (3569076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.54 % (3569076)CaDiCaL version: 2.1.3
% 0.94/0.54 % (3569076)Termination reason: Instruction limit
% 0.94/0.54 % (3569076)Termination phase: Saturation
% 0.94/0.54 % (3569076)Time elapsed: 0.008 s
% 0.94/0.54 % (3569076)Peak memory usage: 12 MB
% 0.94/0.54 % (3569076)Instructions burned: 12 (million)
% 0.94/0.54 % (3569074)Instruction limit reached!
% 0.94/0.54 % (3569074)------------------------------
% 0.94/0.54 % (3569074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.54 % (3569074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.54 % (3569074)CaDiCaL version: 2.1.3
% 0.94/0.54 % (3569074)Termination reason: Instruction limit
% 0.94/0.54 % (3569074)Termination phase: Saturation
% 0.94/0.54 % (3569074)Time elapsed: 0.006 s
% 0.94/0.54 % (3569074)Peak memory usage: 11 MB
% 0.94/0.54 % (3569074)Instructions burned: 7 (million)
% 0.94/0.54 % (3569063)Instruction limit reached!
% 0.94/0.54 % (3569063)------------------------------
% 0.94/0.54 % (3569063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.54 % (3569063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.54 % (3569063)CaDiCaL version: 2.1.3
% 0.94/0.54 % (3569063)Termination reason: Instruction limit
% 0.94/0.54 % (3569063)Termination phase: Saturation
% 0.94/0.54 % (3569063)Time elapsed: 0.065 s
% 0.94/0.54 % (3569063)Peak memory usage: 13 MB
% 0.94/0.54 % (3569063)Instructions burned: 77 (million)
% 0.94/0.54 % (3569058)Instruction limit reached!
% 0.94/0.54 % (3569058)------------------------------
% 0.94/0.54 % (3569058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.54 % (3569058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.54 % (3569058)CaDiCaL version: 2.1.3
% 0.94/0.54 % (3569058)Termination reason: Instruction limit
% 0.94/0.54 % (3569058)Termination phase: Saturation
% 0.94/0.54 % (3569058)Time elapsed: 0.075 s
% 0.94/0.54 % (3569058)Peak memory usage: 12 MB
% 0.94/0.54 % (3569058)Instructions burned: 89 (million)
% 0.94/0.54 % (3569080)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
% 0.94/0.54 % (3569080)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.54 % (3569080)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=833658972:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.72/0.59 % (3569083)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.72/0.59 % (3569080)Instruction limit reached!
% 1.72/0.59 % (3569080)------------------------------
% 1.72/0.59 % (3569080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.59 % (3569080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.59 % (3569080)CaDiCaL version: 2.1.3
% 1.72/0.59 % (3569080)Termination reason: Instruction limit
% 1.72/0.59 % (3569080)Termination phase: Saturation
% 1.72/0.59 % (3569080)Time elapsed: 0.012 s
% 1.72/0.59 % (3569080)Peak memory usage: 11 MB
% 1.72/0.59 % (3569080)Instructions burned: 30 (million)
% 1.72/0.59 % (3569081)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=3993106741:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.72/0.59 % (3569082)lrs+10_1_si=on:cs=on:random_seed=874995137:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.72/0.59 % (3569083)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=3445061363:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.72/0.59 % (3569084)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3363601820:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.72/0.59 % (3569083)Instruction limit reached!
% 1.72/0.59 % (3569083)------------------------------
% 1.72/0.59 % (3569083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.59 % (3569083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.59 % (3569083)CaDiCaL version: 2.1.3
% 1.72/0.59 % (3569083)Termination reason: Instruction limit
% 1.72/0.59 % (3569083)Termination phase: Property scanning
% 1.72/0.59 % (3569083)Time elapsed: 0.002 s
% 1.72/0.59 % (3569083)Peak memory usage: 9 MB
% 1.72/0.59 % (3569083)Instructions burned: 2 (million)
% 1.72/0.59 % (3569082)Instruction limit reached!
% 1.72/0.59 % (3569082)------------------------------
% 1.72/0.59 % (3569082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.59 % (3569082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.59 % (3569082)CaDiCaL version: 2.1.3
% 1.72/0.59 % (3569082)Termination reason: Instruction limit
% 1.72/0.59 % (3569082)Termination phase: Saturation
% 1.72/0.59 % (3569082)Time elapsed: 0.007 s
% 1.72/0.59 % (3569082)Peak memory usage: 11 MB
% 1.72/0.59 % (3569082)Instructions burned: 9 (million)
% 1.72/0.59 % (3569084)Refutation not found, incomplete strategy
% 1.72/0.59 % (3569084)------------------------------
% 1.72/0.59 % (3569084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.59 % (3569084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.59 % (3569084)CaDiCaL version: 2.1.3
% 1.72/0.59 % (3569084)Termination reason: Refutation not found, incomplete strategy
% 1.72/0.59 % (3569084)Time elapsed: 0.003 s
% 1.72/0.59 % (3569084)Peak memory usage: 12 MB
% 1.72/0.60 % (3569084)Instructions burned: 2 (million)
% 1.72/0.60 % (3569084)------------------------------
% 1.72/0.60 % (3569084)------------------------------
% 1.72/0.60 % (3569085)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1151760138:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.72/0.60 % (3569089)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1886434935:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.72/0.60 % (3569085)Refutation not found, incomplete strategy
% 1.72/0.60 % (3569085)------------------------------
% 1.72/0.60 % (3569085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.60 % (3569085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.60 % (3569085)CaDiCaL version: 2.1.3
% 1.72/0.60 % (3569085)Termination reason: Refutation not found, incomplete strategy
% 1.72/0.60 % (3569085)Time elapsed: 0.004 s
% 1.72/0.60 % (3569085)Peak memory usage: 12 MB
% 1.72/0.60 % (3569085)Instructions burned: 4 (million)
% 1.72/0.60 % (3569085)------------------------------
% 2.12/0.65 % (3569085)------------------------------
% 2.12/0.65 % (3569094)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1516419787:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.12/0.65 % (3569089)Instruction limit reached!
% 2.12/0.65 % (3569089)------------------------------
% 2.12/0.65 % (3569089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.65 % (3569094)Instruction limit reached!
% 2.12/0.65 % (3569094)------------------------------
% 2.12/0.65 % (3569094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.65 % (3569094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.65 % (3569094)CaDiCaL version: 2.1.3
% 2.12/0.65 % (3569094)Termination reason: Instruction limit
% 2.12/0.65 % (3569094)Termination phase: Saturation
% 2.12/0.65 % (3569094)Time elapsed: 0.006 s
% 2.12/0.65 % (3569094)Peak memory usage: 12 MB
% 2.12/0.65 % (3569094)Instructions burned: 15 (million)
% 2.12/0.65 % (3569089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.65 % (3569089)CaDiCaL version: 2.1.3
% 2.12/0.65 % (3569089)Termination reason: Instruction limit
% 2.12/0.65 % (3569089)Termination phase: Saturation
% 2.12/0.65 % (3569089)Time elapsed: 0.015 s
% 2.12/0.65 % (3569089)Peak memory usage: 12 MB
% 2.12/0.65 % (3569089)Instructions burned: 26 (million)
% 2.12/0.65 % (3569092)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=95832274:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.12/0.65 % (3569093)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=864200600:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.12/0.65 % (3569092)Instruction limit reached!
% 2.12/0.65 % (3569092)------------------------------
% 2.12/0.65 % (3569092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.65 % (3569092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.65 % (3569092)CaDiCaL version: 2.1.3
% 2.12/0.65 % (3569092)Termination reason: Instruction limit
% 2.12/0.65 % (3569092)Termination phase: Saturation
% 2.12/0.65 % (3569092)Time elapsed: 0.011 s
% 2.12/0.65 % (3569092)Peak memory usage: 11 MB
% 2.12/0.65 % (3569092)Instructions burned: 14 (million)
% 2.12/0.65 % (3569099)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2634253692:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.12/0.65 % (3569100)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=967912548:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.12/0.65 % (3569097)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=956999444:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.12/0.65 % (3569097)Instruction limit reached!
% 2.12/0.65 % (3569097)------------------------------
% 2.12/0.65 % (3569097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.65 % (3569097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.65 % (3569097)CaDiCaL version: 2.1.3
% 2.12/0.65 % (3569097)Termination reason: Instruction limit
% 2.12/0.65 % (3569097)Termination phase: Preprocessing 2
% 2.12/0.65 % (3569097)Time elapsed: 0.002 s
% 2.12/0.65 % (3569097)Peak memory usage: 10 MB
% 2.12/0.65 % (3569097)Instructions burned: 2 (million)
% 2.12/0.65 % (3569100)Instruction limit reached!
% 2.12/0.65 % (3569100)------------------------------
% 2.12/0.65 % (3569100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.65 % (3569100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.65 % (3569100)CaDiCaL version: 2.1.3
% 2.12/0.65 % (3569100)Termination reason: Instruction limit
% 2.12/0.65 % (3569100)Termination phase: Saturation
% 2.12/0.65 % (3569100)Time elapsed: 0.009 s
% 2.12/0.65 % (3569100)Peak memory usage: 11 MB
% 2.12/0.65 % (3569100)Instructions burned: 24 (million)
% 2.12/0.65 % (3569099)Instruction limit reached!
% 2.12/0.65 % (3569099)------------------------------
% 2.12/0.65 % (3569099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.65 % (3569099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.65 % (3569099)CaDiCaL version: 2.1.3
% 2.12/0.65 % (3569099)Termination reason: Instruction limit
% 2.39/0.70 % (3569099)Termination phase: Saturation
% 2.39/0.70 % (3569099)Time elapsed: 0.012 s
% 2.39/0.70 % (3569099)Peak memory usage: 12 MB
% 2.39/0.70 % (3569099)Instructions burned: 26 (million)
% 2.39/0.70 % (3569081)Instruction limit reached!
% 2.39/0.70 % (3569081)------------------------------
% 2.39/0.70 % (3569081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.70 % (3569081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.70 % (3569081)CaDiCaL version: 2.1.3
% 2.39/0.70 % (3569081)Termination reason: Instruction limit
% 2.39/0.70 % (3569081)Termination phase: Saturation
% 2.39/0.70 % (3569081)Time elapsed: 0.077 s
% 2.39/0.70 % (3569081)Peak memory usage: 13 MB
% 2.39/0.70 % (3569081)Instructions burned: 86 (million)
% 2.39/0.70 % (3569103)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2803039634:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.39/0.70 % (3569108)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.39/0.70 % (3569110)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2786018586:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.39/0.70 % (3569108)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=1479630844:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.39/0.70 % (3569110)Instruction limit reached!
% 2.39/0.70 % (3569110)------------------------------
% 2.39/0.70 % (3569110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.70 % (3569110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.70 % (3569110)CaDiCaL version: 2.1.3
% 2.39/0.70 % (3569110)Termination reason: Instruction limit
% 2.39/0.70 % (3569110)Termination phase: Saturation
% 2.39/0.70 % (3569110)Time elapsed: 0.003 s
% 2.39/0.70 % (3569110)Peak memory usage: 11 MB
% 2.39/0.70 % (3569110)Instructions burned: 8 (million)
% 2.39/0.70 % (3569107)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.39/0.70 % (3569107)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.39/0.70 % (3569108)Instruction limit reached!
% 2.39/0.70 % (3569108)------------------------------
% 2.39/0.70 % (3569108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.70 % (3569108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.70 % (3569108)CaDiCaL version: 2.1.3
% 2.39/0.70 % (3569108)Termination reason: Instruction limit
% 2.39/0.70 % (3569108)Termination phase: Saturation
% 2.39/0.70 % (3569108)Time elapsed: 0.007 s
% 2.39/0.70 % (3569108)Peak memory usage: 11 MB
% 2.39/0.70 % (3569108)Instructions burned: 8 (million)
% 2.39/0.70 % (3569107)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=219384388:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.39/0.70 % (3569109)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=2616609454:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.39/0.70 % (3569107)Instruction limit reached!
% 2.39/0.70 % (3569107)------------------------------
% 2.39/0.70 % (3569107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.70 % (3569107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.70 % (3569107)CaDiCaL version: 2.1.3
% 2.39/0.70 % (3569107)Termination reason: Instruction limit
% 2.39/0.70 % (3569107)Termination phase: Saturation
% 2.39/0.70 % (3569107)Time elapsed: 0.012 s
% 2.39/0.70 % (3569107)Peak memory usage: 12 MB
% 2.39/0.70 % (3569107)Instructions burned: 14 (million)
% 2.39/0.70 % (3569114)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2985068031:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.39/0.70 % (3569116)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1793929692:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.39/0.79 % (3569114)Instruction limit reached!
% 2.39/0.79 % (3569114)------------------------------
% 2.39/0.79 % (3569114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569114)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569114)Termination reason: Instruction limit
% 2.39/0.79 % (3569114)Termination phase: Saturation
% 2.39/0.79 % (3569114)Time elapsed: 0.009 s
% 2.39/0.79 % (3569114)Peak memory usage: 12 MB
% 2.39/0.79 % (3569114)Instructions burned: 24 (million)
% 2.39/0.79 % (3569103)Instruction limit reached!
% 2.39/0.79 % (3569103)------------------------------
% 2.39/0.79 % (3569103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569103)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569103)Termination reason: Instruction limit
% 2.39/0.79 % (3569103)Termination phase: Saturation
% 2.39/0.79 % (3569103)Time elapsed: 0.056 s
% 2.39/0.79 % (3569103)Peak memory usage: 12 MB
% 2.39/0.79 % (3569103)Instructions burned: 61 (million)
% 2.39/0.79 % (3569116)Instruction limit reached!
% 2.39/0.79 % (3569116)------------------------------
% 2.39/0.79 % (3569116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569116)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569116)Termination reason: Instruction limit
% 2.39/0.79 % (3569116)Termination phase: Saturation
% 2.39/0.79 % (3569116)Time elapsed: 0.019 s
% 2.39/0.79 % (3569116)Peak memory usage: 12 MB
% 2.39/0.79 % (3569116)Instructions burned: 20 (million)
% 2.39/0.79 % (3569109)Instruction limit reached!
% 2.39/0.79 % (3569109)------------------------------
% 2.39/0.79 % (3569109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569109)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569109)Termination reason: Instruction limit
% 2.39/0.79 % (3569109)Termination phase: Saturation
% 2.39/0.79 % (3569109)Time elapsed: 0.030 s
% 2.39/0.79 % (3569109)Peak memory usage: 12 MB
% 2.39/0.79 % (3569109)Instructions burned: 32 (million)
% 2.39/0.79 % (3569121)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=812282311:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.39/0.79 % (3569119)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2234730516:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.39/0.79 % (3569122)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1126773404:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.39/0.79 % (3569122)Refutation not found, incomplete strategy
% 2.39/0.79 % (3569122)------------------------------
% 2.39/0.79 % (3569122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569122)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569122)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.79 % (3569122)Time elapsed: 0.003 s
% 2.39/0.79 % (3569122)Peak memory usage: 12 MB
% 2.39/0.79 % (3569122)Instructions burned: 5 (million)
% 2.39/0.79 % (3569122)------------------------------
% 2.39/0.79 % (3569122)------------------------------
% 2.39/0.79 % (3569123)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=428929086:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.39/0.79 % (3569124)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.39/0.79 % (3569124)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2583123664:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.39/0.79 % (3569128)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3838520381:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.39/0.79 % (3569128)Refutation not found, incomplete strategy
% 2.39/0.79 % (3569128)------------------------------
% 2.39/0.79 % (3569128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569128)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569128)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.79 % (3569128)Time elapsed: 0.002 s
% 2.39/0.79 % (3569128)Peak memory usage: 12 MB
% 2.39/0.79 % (3569128)Instructions burned: 3 (million)
% 2.39/0.79 % (3569128)------------------------------
% 2.39/0.79 % (3569128)------------------------------
% 2.39/0.79 % (3569124)Instruction limit reached!
% 2.39/0.79 % (3569124)------------------------------
% 2.39/0.79 % (3569124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569124)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569124)Termination reason: Instruction limit
% 2.39/0.79 % (3569124)Termination phase: Saturation
% 2.39/0.79 % (3569124)Time elapsed: 0.006 s
% 2.39/0.79 % (3569124)Peak memory usage: 11 MB
% 2.39/0.79 % (3569124)Instructions burned: 7 (million)
% 2.39/0.79 % (3569133)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.39/0.79 % (3569123)Instruction limit reached!
% 2.39/0.79 % (3569123)------------------------------
% 2.39/0.79 % (3569123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569123)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569123)Termination reason: Instruction limit
% 2.39/0.79 % (3569123)Termination phase: Saturation
% 2.39/0.79 % (3569123)Time elapsed: 0.036 s
% 2.39/0.79 % (3569123)Peak memory usage: 12 MB
% 2.39/0.79 % (3569123)Instructions burned: 42 (million)
% 2.39/0.79 % (3569133)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=332356847:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.39/0.79 % (3569132)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=395512544:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 2.39/0.79 % (3569133)Instruction limit reached!
% 2.39/0.79 % (3569133)------------------------------
% 2.39/0.79 % (3569133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569133)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569133)Termination reason: Instruction limit
% 2.39/0.79 % (3569133)Termination phase: Saturation
% 2.39/0.79 % (3569133)Time elapsed: 0.003 s
% 2.39/0.79 % (3569133)Peak memory usage: 11 MB
% 2.39/0.79 % (3569133)Instructions burned: 7 (million)
% 2.39/0.79 % (3569132)Refutation not found, incomplete strategy
% 2.39/0.79 % (3569132)------------------------------
% 2.39/0.79 % (3569132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569132)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569132)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.79 % (3569132)Time elapsed: 0.004 s
% 2.39/0.79 % (3569132)Peak memory usage: 12 MB
% 2.39/0.79 % (3569132)Instructions burned: 8 (million)
% 2.39/0.79 % (3569132)------------------------------
% 2.39/0.79 % (3569132)------------------------------
% 2.39/0.79 % (3569137)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3277003184:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.39/0.79 % (3569138)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=2850058516:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.39/0.79 % (3569137)Instruction limit reached!
% 2.39/0.79 % (3569137)------------------------------
% 2.39/0.79 % (3569137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569137)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569137)Termination reason: Instruction limit
% 2.39/0.79 % (3569137)Termination phase: Saturation
% 2.39/0.79 % (3569137)Time elapsed: 0.009 s
% 2.39/0.79 % (3569137)Peak memory usage: 12 MB
% 2.39/0.79 % (3569137)Instructions burned: 20 (million)
% 2.39/0.79 % (3569135)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=808427291:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.39/0.79 % (3569141)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=4165815949:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.39/0.79 % (3569135)Instruction limit reached!
% 2.39/0.79 % (3569135)------------------------------
% 2.39/0.79 % (3569135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569135)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569135)Termination reason: Instruction limit
% 2.39/0.79 % (3569135)Termination phase: Saturation
% 2.39/0.79 % (3569135)Time elapsed: 0.019 s
% 2.39/0.79 % (3569135)Peak memory usage: 12 MB
% 2.39/0.79 % (3569135)Instructions burned: 22 (million)
% 2.39/0.79 % (3569121)Instruction limit reached!
% 2.39/0.79 % (3569121)------------------------------
% 2.39/0.79 % (3569121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569121)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569121)Termination reason: Instruction limit
% 2.39/0.79 % (3569121)Termination phase: Saturation
% 2.39/0.79 % (3569121)Time elapsed: 0.121 s
% 2.39/0.79 % (3569121)Peak memory usage: 13 MB
% 2.39/0.79 % (3569121)Instructions burned: 143 (million)
% 2.39/0.79 % (3569061)Instruction limit reached!
% 2.39/0.79 % (3569061)------------------------------
% 2.39/0.79 % (3569061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569061)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569061)Termination reason: Instruction limit
% 2.39/0.79 % (3569061)Termination phase: Saturation
% 2.39/0.79 % (3569061)Time elapsed: 0.365 s
% 2.39/0.79 % (3569061)Peak memory usage: 12 MB
% 2.39/0.79 % (3569061)Instructions burned: 636 (million)
% 2.39/0.79 % (3569144)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=3999333132:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 2.39/0.79 % (3569145)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=930318206:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 2.39/0.79 % (3569144)Instruction limit reached!
% 2.39/0.79 % (3569144)------------------------------
% 2.39/0.79 % (3569144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569145)Refutation not found, incomplete strategy
% 2.39/0.79 % (3569145)------------------------------
% 2.39/0.79 % (3569145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569144)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569144)Termination reason: Instruction limit
% 2.39/0.79 % (3569144)Termination phase: Saturation
% 2.39/0.79 % (3569144)Time elapsed: 0.020 s
% 2.39/0.79 % (3569145)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569144)Peak memory usage: 13 MB
% 2.39/0.79 % (3569145)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.79 % (3569145)Time elapsed: 0.003 s
% 2.39/0.79 % (3569145)Peak memory usage: 12 MB
% 2.39/0.79 % (3569144)Instructions burned: 45 (million)
% 2.39/0.79 % (3569145)Instructions burned: 4 (million)
% 2.39/0.79 % (3569145)------------------------------
% 2.39/0.79 % (3569145)------------------------------
% 2.39/0.79 % (3569138) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3569053-3569138"...
% 2.39/0.79 % (3569146)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3331420130:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 2.39/0.79 % (3569093) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3569053-3569093"...
% 2.39/0.79 % (3569138)...printing done.
% 2.39/0.79 % (3569138)Refutation found. Thanks to Tanya!
% 2.39/0.79 % SZS status Theorem for theBenchmark
% 2.39/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/0.79 % (3569138)------------------------------
% 2.39/0.79 % (3569138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.79 % (3569138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.79 % (3569138)CaDiCaL version: 2.1.3
% 2.39/0.79 % (3569138)Termination reason: Refutation
% 2.39/0.79 % (3569138)Time elapsed: 0.080 s
% 2.39/0.79 % (3569138)Peak memory usage: 14 MB
% 2.39/0.79 % (3569138)Instructions burned: 87 (million)
% 2.39/0.79 % (3569053)Success in time 0.463 s
% 2.39/0.79 % Vampire exiting
%------------------------------------------------------------------------------