%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV302^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:38:13 AM UTC 2026
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 11
% Syntax : Number of formulae : 108 ( 20 unt; 0 typ; 9 def)
% Number of atoms : 1009 ( 235 equ; 0 cnn)
% Maximal formula atoms : 13 ( 9 avg)
% Number of connectives : 1003 ( 128 ~; 220 |; 59 &; 499 @)
% ( 9 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 348 ( 348 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 12 con; 0-4 aty)
% ( 26 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 130 ( 0 sgn 85 !; 6 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_1,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
cZERO: ( $i > $o ) > $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
vAND: $o > $o > $o ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_13,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
sK0: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_17,type,
sK1: ( $i > $o ) > $o ).
thf(func_def_18,type,
sK2: ( $i > $o ) > $o ).
thf(func_def_20,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_21,type,
sK5: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(func_def_22,type,
sK6: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(func_def_23,type,
sK7: ( ( $i > $o ) > $o ) > ( $i > $o ) > $i ).
thf(func_def_24,type,
sK8: $i > $o ).
thf(f3,axiom,
( ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1 @ cZERO )
& ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cNAT ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cNAT_def) ).
thf(f4,conjecture,
! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) ) )
& ( X0 @ cZERO ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ( ( X0 @ cZERO )
& ( cNAT @ cZERO )
& ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
& ( X0 @ X1 ) )
=> ( ( cNAT @ ( cSUCC @ X1 ) )
& ( X0 @ ( cSUCC @ X1 ) ) ) ) )
=> ( ( X0 @ X2 )
& ( cNAT @ X2 ) ) )
=> ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX6102_B) ).
thf(f5,negated_conjecture,
~ ! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) ) )
& ( X0 @ cZERO ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ( ( X0 @ cZERO )
& ( cNAT @ cZERO )
& ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
& ( X0 @ X1 ) )
=> ( ( cNAT @ ( cSUCC @ X1 ) )
& ( X0 @ ( cSUCC @ X1 ) ) ) ) )
=> ( ( X0 @ X2 )
& ( cNAT @ X2 ) ) )
=> ( X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( cSUCC @ X1 ) ) ) )
& ( X0 @ cZERO ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ( ( X0 @ cZERO )
& ( cNAT @ cZERO )
& ! [X3: ( $i > $o ) > $o] :
( ( ( cNAT @ X3 )
& ( X0 @ X3 ) )
=> ( ( cNAT @ ( cSUCC @ X3 ) )
& ( X0 @ ( cSUCC @ X3 ) ) ) ) )
=> ( ( X0 @ X2 )
& ( cNAT @ X2 ) ) )
=> ( X0 @ X2 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ! [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ( ( X0 @ cZERO )
= $true )
& ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $true )
=> ( ( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( cSUCC @ X1 ) )
= $true ) ) ) )
=> ! [X2: ( $i > $o ) > $o] :
( ( ( ( ( cNAT @ cZERO )
= $true )
& ! [X3: ( $i > $o ) > $o] :
( ( ( ( X0 @ X3 )
= $true )
& ( $true
= ( cNAT @ X3 ) ) )
=> ( ( $true
= ( cNAT @ ( cSUCC @ X3 ) ) )
& ( ( X0 @ ( cSUCC @ X3 ) )
= $true ) ) )
& ( ( X0 @ cZERO )
= $true ) )
=> ( ( ( cNAT @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) )
=> ( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
! [X1: ( ( $i > $o ) > $o ) > $o] :
( ( ( X1 @ cZERO )
& ! [X2: ( $i > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( cSUCC @ X2 ) ) ) )
=> ( X1 @ X0 ) ) )
= cNAT ),
inference(rectify,[],[f3]) ).
thf(f9,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f14,plain,
? [X0: ( ( $i > $o ) > $o ) > $o] :
( ? [X2: ( $i > $o ) > $o] :
( ( ( X0 @ X2 )
!= $true )
& ( ( ( ( cNAT @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( cNAT @ cZERO )
!= $true )
| ? [X3: ( $i > $o ) > $o] :
( ( ( $true
!= ( cNAT @ ( cSUCC @ X3 ) ) )
| ( ( X0 @ ( cSUCC @ X3 ) )
!= $true ) )
& ( ( X0 @ X3 )
= $true )
& ( $true
= ( cNAT @ X3 ) ) )
| ( ( X0 @ cZERO )
!= $true ) ) )
& ( ( X0 @ cZERO )
= $true )
& ! [X1: ( $i > $o ) > $o] :
( ( ( X0 @ ( cSUCC @ X1 ) )
= $true )
| ( ( X0 @ X1 )
!= $true )
| ( ( cNAT @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f15,plain,
? [X0: ( ( $i > $o ) > $o ) > $o] :
( ( ( X0 @ cZERO )
= $true )
& ! [X1: ( $i > $o ) > $o] :
( ( ( X0 @ X1 )
!= $true )
| ( ( cNAT @ X1 )
!= $true )
| ( ( X0 @ ( cSUCC @ X1 ) )
= $true ) )
& ? [X2: ( $i > $o ) > $o] :
( ( ( ( X0 @ cZERO )
!= $true )
| ( ( cNAT @ cZERO )
!= $true )
| ? [X3: ( $i > $o ) > $o] :
( ( ( X0 @ X3 )
= $true )
& ( ( $true
!= ( cNAT @ ( cSUCC @ X3 ) ) )
| ( ( X0 @ ( cSUCC @ X3 ) )
!= $true ) )
& ( $true
= ( cNAT @ X3 ) ) )
| ( ( ( cNAT @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( X0 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ( sK0 @ cZERO )
= $true )
& ! [X1: ( $i > $o ) > $o] :
( ( ( sK0 @ X1 )
!= $true )
| ( ( cNAT @ X1 )
!= $true )
| ( ( sK0 @ ( cSUCC @ X1 ) )
= $true ) )
& ( ( ( sK0 @ cZERO )
!= $true )
| ( ( cNAT @ cZERO )
!= $true )
| ( ( ( sK0 @ sK2 )
= $true )
& ( ( ( cNAT @ ( cSUCC @ sK2 ) )
!= $true )
| ( $true
!= ( sK0 @ ( cSUCC @ sK2 ) ) ) )
& ( ( cNAT @ sK2 )
= $true ) )
| ( ( ( cNAT @ sK1 )
= $true )
& ( $true
= ( sK0 @ sK1 ) ) ) )
& ( $true
!= ( sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X2,sK1),skolemize(X3,sK2)],[f15]) ).
thf(f18,plain,
( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f20,plain,
( $true
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
( ( ( cNAT @ cZERO )
!= $true )
| ( ( cNAT @ sK2 )
= $true )
| ( $true
= ( sK0 @ sK1 ) )
| ( ( sK0 @ cZERO )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( ( sK0 @ cZERO )
!= $true )
| ( ( cNAT @ cZERO )
!= $true )
| ( $true
!= ( sK0 @ ( cSUCC @ sK2 ) ) )
| ( ( cNAT @ ( cSUCC @ sK2 ) )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f25,plain,
( ( ( cNAT @ cZERO )
!= $true )
| ( ( sK0 @ cZERO )
!= $true )
| ( $true
= ( sK0 @ sK1 ) )
| ( ( sK0 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
! [X1: ( $i > $o ) > $o] :
( ( ( sK0 @ ( cSUCC @ X1 ) )
= $true )
| ( ( sK0 @ X1 )
!= $true )
| ( ( cNAT @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f28,plain,
( ( sK0 @ cZERO )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f32,definition,
( spl3_1
<=> ( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f34,plain,
( ( cNAT
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,plain,
spl3_1,
inference(avatar_split_clause,[],[f18,f32]) ).
thf(f41,definition,
( spl3_3
<=> ( ( cNAT @ cZERO )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f45,definition,
( spl3_4
<=> ( ( sK0 @ cZERO )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f49,definition,
( spl3_5
<=> ( $true
= ( sK0 @ ( cSUCC @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f51,plain,
( ( $true
!= ( sK0 @ ( cSUCC @ sK2 ) ) )
| spl3_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f53,definition,
( spl3_6
<=> ( ( cNAT @ ( cSUCC @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f55,plain,
( ( ( cNAT @ ( cSUCC @ sK2 ) )
!= $true )
| spl3_6 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f63,definition,
( spl3_8
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
thf(f67,definition,
( spl3_9
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
thf(f70,plain,
( ~ spl3_3
| spl3_8
| ~ spl3_4
| spl3_9 ),
inference(avatar_split_clause,[],[f25,f67,f45,f63,f41]) ).
thf(f71,plain,
~ spl3_8,
inference(avatar_split_clause,[],[f20,f63]) ).
thf(f72,plain,
spl3_4,
inference(avatar_split_clause,[],[f28,f45]) ).
thf(f74,definition,
( spl3_10
<=> ( ( cNAT @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
thf(f76,plain,
( ( ( cNAT @ sK2 )
= $true )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f78,plain,
( spl3_8
| ~ spl3_4
| ~ spl3_6
| ~ spl3_5
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f23,f41,f49,f53,f45,f63]) ).
thf(f79,plain,
( spl3_8
| ~ spl3_3
| spl3_10
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f21,f45,f74,f41,f63]) ).
thf(f110,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( cNAT @ X1 )
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) )
| ~ spl3_1 ),
inference(argument_congruence,[],[f34]) ).
thf(f111,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( $false
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) )
| ( ( cNAT @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(iff_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $false )
| ( $true
= ( ^ [Y0: ( $i > $o ) > $o] :
( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y1: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cSUCC @ Y2 ) ) ) )
& ( Y1 @ cZERO ) )
=> ( Y1 @ Y0 ) ) )
@ X1 ) ) )
| ~ spl3_1 ),
inference(iff_proxy_clausification,[],[f110]) ).
thf(f113,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $false )
| ( $true
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cSUCC @ Y1 ) ) ) )
& ( Y0 @ cZERO ) )
=> ( Y0 @ X1 ) ) ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $false )
| ( $true
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cSUCC @ Y1 ) ) ) )
& ( Y0 @ cZERO ) )
=> ( Y0 @ X1 ) )
@ X2 ) ) )
| ~ spl3_1 ),
inference(pi_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X2 @ Y0 )
=> ( X2 @ ( cSUCC @ Y0 ) ) ) )
& ( X2 @ cZERO ) )
=> ( X2 @ X1 ) )
= $true )
| ( ( cNAT @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( X2 @ X1 )
= $true )
| ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X2 @ Y0 )
=> ( X2 @ ( cSUCC @ Y0 ) ) ) )
& ( X2 @ cZERO ) )
= $false )
| ( ( cNAT @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f117,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( X2 @ Y0 )
=> ( X2 @ ( cSUCC @ Y0 ) ) ) )
= $false )
| ( ( cNAT @ X1 )
= $false )
| ( ( X2 @ cZERO )
= $false )
| ( ( X2 @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(and_proxy_clausification,[],[f116]) ).
thf(f118,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( ^ [Y0: ( $i > $o ) > $o] :
( ( X2 @ Y0 )
=> ( X2 @ ( cSUCC @ Y0 ) ) )
@ ( sK5 @ X2 ) )
= $false )
| ( ( cNAT @ X1 )
= $false )
| ( ( X2 @ cZERO )
= $false )
| ( ( X2 @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( X2 @ cZERO )
= $false )
| ( ( cNAT @ X1 )
= $false )
| ( ( X2 @ X1 )
= $true )
| ( ( ( X2 @ ( sK5 @ X2 ) )
=> ( X2 @ ( cSUCC @ ( sK5 @ X2 ) ) ) )
= $false ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( X2 @ ( cSUCC @ ( sK5 @ X2 ) ) )
= $false )
| ( ( X2 @ X1 )
= $true )
| ( ( X2 @ cZERO )
= $false )
| ( ( cNAT @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( ! [X2: ( ( $i > $o ) > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( X2 @ ( sK5 @ X2 ) )
= $true )
| ( ( X2 @ cZERO )
= $false )
| ( ( X2 @ X1 )
= $true )
| ( ( cNAT @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $true )
| ( $false
= ( !! @ ( ( ( $i > $o ) > $o ) > $o )
@ ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cSUCC @ Y1 ) ) ) )
& ( Y0 @ cZERO ) )
=> ( Y0 @ X1 ) ) ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f123,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $true )
| ( $false
= ( ^ [Y0: ( ( $i > $o ) > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y1: ( $i > $o ) > $o] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cSUCC @ Y1 ) ) ) )
& ( Y0 @ cZERO ) )
=> ( Y0 @ X1 ) )
@ ( sK6 @ X1 ) ) ) )
| ~ spl3_1 ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $true )
| ( ( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK6 @ X1 @ Y0 )
=> ( sK6 @ X1 @ ( cSUCC @ Y0 ) ) ) )
& ( sK6 @ X1 @ cZERO ) )
=> ( sK6 @ X1 @ X1 ) )
= $false ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( sK6 @ X1 @ X1 )
= $false )
| ( ( cNAT @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $true )
| ( $true
= ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK6 @ X1 @ Y0 )
=> ( sK6 @ X1 @ ( cSUCC @ Y0 ) ) ) )
& ( sK6 @ X1 @ cZERO ) ) ) )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f127,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( $true
= ( sK6 @ X1 @ cZERO ) )
| ( ( cNAT @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( ! [X1: ( $i > $o ) > $o] :
( ( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( sK6 @ X1 @ Y0 )
=> ( sK6 @ X1 @ ( cSUCC @ Y0 ) ) ) )
= $true )
| ( ( cNAT @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ! [X2: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $true )
| ( $true
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( sK6 @ X1 @ Y0 )
=> ( sK6 @ X1 @ ( cSUCC @ Y0 ) ) )
@ X2 ) ) )
| ~ spl3_1 ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ! [X2: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( $true
= ( ( sK6 @ X1 @ X2 )
=> ( sK6 @ X1 @ ( cSUCC @ X2 ) ) ) )
| ( ( cNAT @ X1 )
= $true ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
( ! [X2: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( $true
= ( sK6 @ X1 @ ( cSUCC @ X2 ) ) )
| ( ( cNAT @ X1 )
= $true )
| ( ( sK6 @ X1 @ X2 )
= $false ) )
| ~ spl3_1 ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f133,plain,
( ( $true = $false )
| ( ( cNAT @ cZERO )
= $true )
| ( ( cNAT @ cZERO )
= $true )
| ~ spl3_1 ),
inference(superposition,[],[f125,f127]) ).
thf(f134,plain,
( ( ( cNAT @ cZERO )
= $true )
| ( $true = $false )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f133]) ).
thf(f135,plain,
( ( ( cNAT @ cZERO )
= $true )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f134]) ).
thf(f142,plain,
( spl3_3
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f135,f32,f41]) ).
thf(f143,plain,
( ( ( cNAT @ sK2 )
!= $true )
| ( ( sK0 @ sK2 )
!= $true )
| ( $true != $true )
| spl3_5 ),
inference(superposition,[],[f51,f27]) ).
thf(f144,plain,
( ( ( cNAT @ sK2 )
!= $true )
| ( ( sK0 @ sK2 )
!= $true )
| spl3_5 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f145,plain,
( ~ spl3_10
| ~ spl3_9
| spl3_5 ),
inference(avatar_split_clause,[],[f144,f49,f67,f74]) ).
thf(f147,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $true = $false )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $false
= ( sK6 @ ( cSUCC @ X0 ) @ X0 ) ) )
| ~ spl3_1 ),
inference(superposition,[],[f125,f131]) ).
thf(f148,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( $true = $false )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $false
= ( sK6 @ ( cSUCC @ X0 ) @ X0 ) ) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f147]) ).
thf(f149,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( $false
= ( sK6 @ ( cSUCC @ X0 ) @ X0 ) )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f148]) ).
thf(f648,plain,
( ! [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true = $false )
| ( ( sK6 @ X0 @ ( sK5 @ ( sK6 @ X0 ) ) )
= $false )
| ( ( cNAT @ X1 )
= $false )
| ( $true
= ( sK6 @ X0 @ X1 ) )
| ( $true
= ( cNAT @ X0 ) ) )
| ~ spl3_1 ),
inference(superposition,[],[f131,f120]) ).
thf(f658,plain,
( ! [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( sK6 @ X0 @ ( sK5 @ ( sK6 @ X0 ) ) )
= $false )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true
= ( cNAT @ X0 ) )
| ( $true
= ( sK6 @ X0 @ X1 ) )
| ( ( cNAT @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f648]) ).
thf(f692,plain,
( ! [X2: ( $i > $o ) > $o,X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $false )
| ( $true
= ( cNAT @ X0 ) )
| ( ( cNAT @ X2 )
= $false )
| ( ( sK6 @ X0 @ X2 )
= $true )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true = $false )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true
= ( sK6 @ X0 @ X1 ) ) )
| ~ spl3_1 ),
inference(superposition,[],[f121,f658]) ).
thf(f694,plain,
( ! [X2: ( $i > $o ) > $o,X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( $true
= ( sK6 @ X0 @ X1 ) )
| ( $true
= ( cNAT @ X0 ) )
| ( $true = $false )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( ( sK6 @ X0 @ X2 )
= $true )
| ( ( cNAT @ X2 )
= $false )
| ( ( cNAT @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f692]) ).
thf(f695,plain,
( ! [X2: ( $i > $o ) > $o,X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( $true
= ( sK6 @ X0 @ X1 ) )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true
= ( cNAT @ X0 ) )
| ( ( sK6 @ X0 @ X2 )
= $true )
| ( ( cNAT @ X1 )
= $false )
| ( ( cNAT @ X2 )
= $false ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f694]) ).
thf(f755,plain,
( ! [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( $true != $true )
| ( ( cNAT @ X1 )
= $false )
| ( ( cNAT @ X1 )
= $false )
| ( $true
= ( cNAT @ X0 ) )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true
= ( sK6 @ X0 @ X1 ) ) )
| ~ spl3_1 ),
inference(equality_factoring,[],[f695]) ).
thf(f864,plain,
( ! [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( ( cNAT @ X1 )
= $false )
| ( $true != $true )
| ( $true
= ( cNAT @ X0 ) )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true
= ( sK6 @ X0 @ X1 ) ) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f755]) ).
thf(f865,plain,
( ! [X0: ( $i > $o ) > $o,X1: ( $i > $o ) > $o] :
( ( $true
= ( sK6 @ X0 @ X1 ) )
| ( ( sK6 @ X0 @ cZERO )
= $false )
| ( $true
= ( cNAT @ X0 ) )
| ( ( cNAT @ X1 )
= $false ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f864]) ).
thf(f905,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( $false
= ( cNAT @ X0 ) )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $false
= ( sK6 @ ( cSUCC @ X0 ) @ cZERO ) )
| ( $true = $false )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true ) )
| ~ spl3_1 ),
inference(superposition,[],[f149,f865]) ).
thf(f960,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( $false
= ( sK6 @ ( cSUCC @ X0 ) @ cZERO ) )
| ( $true = $false )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $false
= ( cNAT @ X0 ) ) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f905]) ).
thf(f961,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( $false
= ( sK6 @ ( cSUCC @ X0 ) @ cZERO ) )
| ( $false
= ( cNAT @ X0 ) )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f960]) ).
thf(f1043,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $true = $false )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $false
= ( cNAT @ X0 ) ) )
| ~ spl3_1 ),
inference(superposition,[],[f961,f127]) ).
thf(f1049,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( $false
= ( cNAT @ X0 ) )
| ( $true = $false )
| ( ( cNAT @ ( cSUCC @ X0 ) )
= $true ) )
| ~ spl3_1 ),
inference(duplicate_literal_removal,[],[f1043]) ).
thf(f1050,plain,
( ! [X0: ( $i > $o ) > $o] :
( ( ( cNAT @ ( cSUCC @ X0 ) )
= $true )
| ( $false
= ( cNAT @ X0 ) ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f1049]) ).
thf(f1089,plain,
( ( $true != $true )
| ( ( cNAT @ sK2 )
= $false )
| ~ spl3_1
| spl3_6 ),
inference(superposition,[],[f55,f1050]) ).
thf(f1091,plain,
( ( ( cNAT @ sK2 )
= $false )
| ~ spl3_1
| spl3_6 ),
inference(trivial_inequality_removal,[],[f1089]) ).
thf(f1093,definition,
( spl3_47
<=> ( ( cNAT @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_47])],[avatar_definition]) ).
thf(f1095,plain,
( ( ( cNAT @ sK2 )
= $false )
| ~ spl3_47 ),
inference(avatar_component_clause,[],[f1093]) ).
thf(f1096,plain,
( spl3_47
| ~ spl3_1
| spl3_6 ),
inference(avatar_split_clause,[],[f1091,f53,f32,f1093]) ).
thf(f1110,plain,
( ( $true = $false )
| ~ spl3_10
| ~ spl3_47 ),
inference(superposition,[],[f76,f1095]) ).
thf(f1113,plain,
( $false
| ~ spl3_10
| ~ spl3_47 ),
inference(trivial_inequality_removal,[],[f1110]) ).
thf(f1114,plain,
( ~ spl3_10
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f1113]) ).
cnf(s1,plain,
spl3_1,
inference(sat_conversion,[],[f35]) ).
cnf(s4,plain,
( ~ spl3_3
| ~ spl3_4
| spl3_8
| spl3_9 ),
inference(sat_conversion,[],[f70]) ).
cnf(s5,plain,
~ spl3_8,
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
spl3_4,
inference(sat_conversion,[],[f72]) ).
cnf(s8,plain,
( ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_6
| spl3_8 ),
inference(sat_conversion,[],[f78]) ).
cnf(s9,plain,
( ~ spl3_3
| ~ spl3_4
| spl3_8
| spl3_10 ),
inference(sat_conversion,[],[f79]) ).
cnf(s15,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f142]) ).
cnf(s17,plain,
( spl3_5
| ~ spl3_9
| ~ spl3_10 ),
inference(sat_conversion,[],[f145]) ).
cnf(s74,plain,
( ~ spl3_1
| spl3_6
| spl3_47 ),
inference(sat_conversion,[],[f1096]) ).
cnf(s76,plain,
( ~ spl3_10
| ~ spl3_47 ),
inference(sat_conversion,[],[f1114]) ).
cnf(s77,plain,
( ~ spl3_3
| spl3_9 ),
inference(rat,[],[s4,s5,s6]) ).
cnf(s105,plain,
spl3_3,
inference(rat,[],[s15,s1]) ).
cnf(s106,plain,
spl3_10,
inference(rat,[],[s9,s5,s6,s105]) ).
cnf(s107,plain,
spl3_9,
inference(rat,[],[s77,s105]) ).
cnf(s108,plain,
~ spl3_47,
inference(rat,[],[s76,s106]) ).
cnf(s109,plain,
spl3_5,
inference(rat,[],[s17,s106,s107]) ).
cnf(s110,plain,
spl3_6,
inference(rat,[],[s74,s1,s108]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s8,s5,s105,s6,s110,s109]) ).
thf(f1115,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV302^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n016.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 15:37:34 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.38 % (490027)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.38 % (490032)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=803214953:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.38 % (490038)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.38 % (490038)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
% 0.21/0.38 % (490033)lrs+10_16_si=on:nwc=1.5:random_seed=1307765160:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (490034)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1276734924:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (490036)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2087243760:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.38 % (490035)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=962848077: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)
% 0.21/0.38 % (490037)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2463967856:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.38 % (490038)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=2087701024:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.38 % (490034)Instruction limit reached!
% 0.21/0.38 % (490034)------------------------------
% 0.21/0.38 % (490034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490034)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490034)Termination reason: Instruction limit
% 0.21/0.38 % (490034)Termination phase: Property scanning
% 0.21/0.38 % (490034)Time elapsed: 0.002 s
% 0.21/0.38 % (490034)Peak memory usage: 10 MB
% 0.21/0.38 % (490034)Instructions burned: 5 (million)
% 0.21/0.38 % (490033)Instruction limit reached!
% 0.21/0.38 % (490033)------------------------------
% 0.21/0.38 % (490033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490033)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490033)Termination reason: Instruction limit
% 0.21/0.38 % (490033)Termination phase: Saturation
% 0.21/0.38 % (490033)Time elapsed: 0.008 s
% 0.21/0.38 % (490033)Peak memory usage: 11 MB
% 0.21/0.38 % (490033)Instructions burned: 18 (million)
% 0.21/0.38 % (490036)Instruction limit reached!
% 0.21/0.38 % (490036)------------------------------
% 0.21/0.38 % (490036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490036)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490036)Termination reason: Instruction limit
% 0.21/0.38 % (490036)Termination phase: Saturation
% 0.21/0.38 % (490036)Time elapsed: 0.014 s
% 0.21/0.38 % (490036)Peak memory usage: 12 MB
% 0.21/0.38 % (490036)Instructions burned: 25 (million)
% 0.21/0.38 % (490032)Instruction limit reached!
% 0.21/0.38 % (490032)------------------------------
% 0.21/0.38 % (490032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490032)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490032)Termination reason: Instruction limit
% 0.21/0.38 % (490032)Termination phase: Saturation
% 0.21/0.38 % (490032)Time elapsed: 0.025 s
% 0.21/0.38 % (490032)Peak memory usage: 13 MB
% 0.21/0.38 % (490032)Instructions burned: 89 (million)
% 0.21/0.38 % (490046)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=288742193:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (490046)Instruction limit reached!
% 0.21/0.38 % (490046)------------------------------
% 0.21/0.38 % (490046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490046)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490046)Termination reason: Instruction limit
% 0.21/0.38 % (490046)Termination phase: Property scanning
% 0.21/0.38 % (490046)Time elapsed: 0.002 s
% 0.21/0.38 % (490046)Peak memory usage: 10 MB
% 0.21/0.38 % (490046)Instructions burned: 4 (million)
% 0.21/0.38 % (490047)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=332545170:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.38 % (490049)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1452797283:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.38 % (490048)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.38 % (490047)Instruction limit reached!
% 0.21/0.38 % (490047)------------------------------
% 0.21/0.38 % (490047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490047)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490047)Termination reason: Instruction limit
% 0.21/0.38 % (490047)Termination phase: Saturation
% 0.21/0.38 % (490047)Time elapsed: 0.003 s
% 0.21/0.38 % (490047)Peak memory usage: 11 MB
% 0.21/0.38 % (490047)Instructions burned: 6 (million)
% 0.21/0.38 % (490049)Instruction limit reached!
% 0.21/0.38 % (490049)------------------------------
% 0.21/0.38 % (490049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490049)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490049)Termination reason: Instruction limit
% 0.21/0.38 % (490049)Termination phase: Saturation
% 0.21/0.38 % (490049)Time elapsed: 0.003 s
% 0.21/0.38 % (490049)Peak memory usage: 11 MB
% 0.21/0.38 % (490049)Instructions burned: 12 (million)
% 0.21/0.38 % (490048)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4010724941:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.38 % (490037)Instruction limit reached!
% 0.21/0.38 % (490037)------------------------------
% 0.21/0.38 % (490037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490037)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490037)Termination reason: Instruction limit
% 0.21/0.38 % (490037)Termination phase: Saturation
% 0.21/0.38 % (490037)Time elapsed: 0.037 s
% 0.21/0.38 % (490037)Peak memory usage: 13 MB
% 0.21/0.38 % (490037)Instructions burned: 77 (million)
% 0.21/0.38 % (490048)Instruction limit reached!
% 0.21/0.38 % (490048)------------------------------
% 0.21/0.38 % (490048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490048)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490048)Termination reason: Instruction limit
% 0.21/0.38 % (490048)Termination phase: Saturation
% 0.21/0.38 % (490048)Time elapsed: 0.004 s
% 0.21/0.38 % (490048)Peak memory usage: 12 MB
% 0.21/0.38 % (490048)Instructions burned: 8 (million)
% 0.21/0.38 % (490052)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
% 0.21/0.38 % (490052)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.38 % (490058)lrs+10_1_si=on:cs=on:random_seed=3346329184:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.38 % (490052)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2793490500:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.38 % (490058)Instruction limit reached!
% 0.21/0.38 % (490058)------------------------------
% 0.21/0.38 % (490058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490058)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490058)Termination reason: Instruction limit
% 0.21/0.38 % (490058)Termination phase: Saturation
% 0.21/0.38 % (490058)Time elapsed: 0.002 s
% 0.21/0.38 % (490058)Peak memory usage: 11 MB
% 0.21/0.38 % (490058)Instructions burned: 8 (million)
% 0.21/0.38 % (490057)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=525068886:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.38 % (490063)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.38 % (490070)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3402610708:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.21/0.38 % (490064)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3025027946:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.38 % (490063)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=3967036924:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (490052)Instruction limit reached!
% 0.21/0.38 % (490052)------------------------------
% 0.21/0.38 % (490052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490052)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490052)Termination reason: Instruction limit
% 0.21/0.38 % (490052)Termination phase: Saturation
% 0.21/0.38 % (490052)Time elapsed: 0.013 s
% 0.21/0.38 % (490052)Peak memory usage: 12 MB
% 0.21/0.38 % (490052)Instructions burned: 29 (million)
% 0.21/0.38 % (490063)Instruction limit reached!
% 0.21/0.38 % (490063)------------------------------
% 0.21/0.38 % (490063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490063)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490063)Termination reason: Instruction limit
% 0.21/0.38 % (490063)Termination phase: Property scanning
% 0.21/0.38 % (490063)Time elapsed: 0.001 s
% 0.21/0.38 % (490063)Peak memory usage: 10 MB
% 0.21/0.38 % (490063)Instructions burned: 2 (million)
% 0.21/0.38 % (490064)Refutation not found, incomplete strategy
% 0.21/0.38 % (490064)------------------------------
% 0.21/0.38 % (490064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490064)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490064)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38 % (490064)Time elapsed: 0.002 s
% 0.21/0.38 % (490064)Peak memory usage: 12 MB
% 0.21/0.38 % (490064)Instructions burned: 3 (million)
% 0.21/0.38 % (490064)------------------------------
% 0.21/0.38 % (490064)------------------------------
% 0.21/0.38 % (490038)Instruction limit reached!
% 0.21/0.38 % (490038)------------------------------
% 0.21/0.38 % (490038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490038)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490038)Termination reason: Instruction limit
% 0.21/0.38 % (490038)Termination phase: Saturation
% 0.21/0.38 % (490038)Time elapsed: 0.074 s
% 0.21/0.38 % (490038)Peak memory usage: 13 MB
% 0.21/0.38 % (490038)Instructions burned: 157 (million)
% 0.21/0.38 % (490082)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3352311643:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.21/0.38 % (490084)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2697522899:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.21/0.38 % (490082)Instruction limit reached!
% 0.21/0.38 % (490082)------------------------------
% 0.21/0.38 % (490082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490082)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490082)Termination reason: Instruction limit
% 0.21/0.38 % (490082)Termination phase: Saturation
% 0.21/0.38 % (490082)Time elapsed: 0.006 s
% 0.21/0.38 % (490082)Peak memory usage: 12 MB
% 0.21/0.38 % (490082)Instructions burned: 14 (million)
% 0.21/0.38 % (490035) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-490027-490035"...
% 0.21/0.38 % (490035)...printing done.
% 0.21/0.38 % (490035)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (490035)------------------------------
% 0.21/0.38 % (490035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (490035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (490035)CaDiCaL version: 2.1.3
% 0.21/0.38 % (490035)Termination reason: Refutation
% 0.21/0.38 % (490035)Time elapsed: 0.087 s
% 0.21/0.38 % (490035)Peak memory usage: 13 MB
% 0.21/0.38 % (490035)Instructions burned: 178 (million)
% 0.21/0.38 % (490027)Success in time 0.131 s
% 0.21/0.38 % Vampire exiting
%------------------------------------------------------------------------------