%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV229^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:38:04 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 120 ( 18 unt; 0 typ; 9 def)
% Number of atoms : 771 ( 158 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 801 ( 83 ~; 195 |; 43 &; 362 @)
% ( 9 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 15 con; 0-4 aty)
% ( 34 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 101 ( 0 sgn 36 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cE: a > $o ).
thf(func_def_1,type,
cD: a > $o ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK0: a > $o ).
thf(func_def_12,type,
sK1: a ).
thf(func_def_13,type,
sK2: a ).
thf(func_def_14,type,
sK3: a ).
thf(f1,conjecture,
( ( ^ [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cD @ X2 ) )
& ! [X2: a] :
( ( X1 @ X2 )
=> ( cE @ X2 ) ) ) )
= ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5209_pme) ).
thf(f2,negated_conjecture,
( ( ^ [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cD @ X2 ) )
& ! [X2: a] :
( ( X1 @ X2 )
=> ( cE @ X2 ) ) ) )
!= ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> ( cD @ X1 ) )
& ! [X2: a] :
( ( X0 @ X2 )
=> ( cE @ X2 ) ) ) )
!= ( ^ [X3: a > $o] :
! [X4: a] :
( ( X3 @ X4 )
=> ( ( cE @ X4 )
& ( cD @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) ) )
!= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) ) )
!= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) ) )
!= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) )
@ sK0 )
!= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f6]) ).
thf(f10,plain,
( ( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) )
@ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f11,plain,
( ( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) )
@ sK0 )
= $false )
| ( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) ) )
@ sK0 )
= $false ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f12,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ sK1 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) )
@ sK2 ) )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) )
@ sK3 )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( ( ( sK0 @ sK2 )
=> ( cD @ sK2 ) )
= $false )
| ( $false
= ( ( sK0 @ sK1 )
=> ( ( cD @ sK1 )
& ( cE @ sK1 ) ) ) )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ( sK0 @ sK1 )
=> ( ( cD @ sK1 )
& ( cE @ sK1 ) ) ) )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( ( cD @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ( sK0 @ sK1 )
=> ( ( cD @ sK1 )
& ( cE @ sK1 ) ) ) )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( ( ( cD @ sK1 )
& ( cE @ sK1 ) )
= $false )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( ( cE @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f21]) ).
thf(f24,plain,
( ( ( cE @ sK1 )
= $false )
| ( $false
= ( cD @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f25,plain,
( ( $false
= ( cD @ sK1 ) )
| ( ( cE @ sK3 )
= $false )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( cE @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( ( cE @ sK1 )
= $false )
| ( $false
= ( cD @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( ( ( cD @ sK1 )
& ( cE @ sK1 ) )
= $false )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( ( cD @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f28,plain,
( ( ( cD @ sK2 )
= $false )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f29,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( ( cE @ sK3 )
= $false )
| ( ( cD @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK1 ) )
| ( ( cD @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( ( $false
= ( cD @ sK1 ) )
| ( ( cE @ sK1 )
= $false )
| ( ( ( sK0 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( ( cD @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f32,plain,
( ( ( cE @ sK3 )
= $false )
| ( ( cE @ sK1 )
= $false )
| ( ( cD @ sK2 )
= $false )
| ( $false
= ( cD @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( $false
= ( cD @ sK1 ) )
| ( ( cD @ sK2 )
= $false )
| ( ( cE @ sK1 )
= $false )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f35,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 )
= $true )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f35]) ).
thf(f38,plain,
! [X2: a,X1: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( sK0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) ) )
| ( $true
= ( ( sK0 @ X2 )
=> ( cE @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( sK0 @ X2 )
=> ( cE @ X2 ) ) )
| ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) )
| ( ( sK0 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( ( cE @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: a,X1: a] :
( ( ( cE @ X2 )
= $true )
| ( ( cE @ X1 )
= $true )
| ( ( sK0 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f44,plain,
! [X2: a,X1: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 )
= $true )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f45,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( sK0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) ) )
| ( ( ( sK0 @ X2 )
=> ( cD @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ( sK0 @ X2 )
=> ( cD @ X2 ) )
= $true )
| ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) )
| ( ( sK0 @ X2 )
= $false )
| ( ( cD @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f49,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK0 @ X2 )
= $false )
| ( ( cD @ X2 )
= $true )
| ( ( cD @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f51,definition,
( spl4_1
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f53,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f55,definition,
( spl4_2
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f57,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f59,definition,
( spl4_3
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f61,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f23,f59,f55,f51]) ).
thf(f64,definition,
( spl4_4
<=> ( ( cE @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f66,plain,
( ( ( cE @ sK3 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f67,plain,
( spl4_2
| spl4_4
| spl4_3 ),
inference(avatar_split_clause,[],[f22,f59,f64,f55]) ).
thf(f69,definition,
( spl4_5
<=> ( ( cE @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f71,plain,
( ( ( cE @ sK1 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f73,definition,
( spl4_6
<=> ( $false
= ( cD @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f75,plain,
( ( $false
= ( cD @ sK1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f76,plain,
( spl4_1
| spl4_3
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f26,f73,f69,f59,f51]) ).
thf(f77,plain,
( spl4_6
| spl4_3
| spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f25,f69,f64,f59,f73]) ).
thf(f79,definition,
( spl4_7
<=> ( ( cD @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f81,plain,
( ( ( cD @ sK2 )
= $false )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f82,plain,
( spl4_1
| spl4_2
| spl4_7 ),
inference(avatar_split_clause,[],[f30,f79,f55,f51]) ).
thf(f83,plain,
( spl4_2
| spl4_7
| spl4_4 ),
inference(avatar_split_clause,[],[f29,f64,f79,f55]) ).
thf(f84,plain,
( spl4_1
| spl4_5
| spl4_7
| spl4_6 ),
inference(avatar_split_clause,[],[f33,f73,f79,f69,f51]) ).
thf(f85,plain,
( spl4_4
| spl4_7
| spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f32,f69,f73,f79,f64]) ).
thf(f87,definition,
( spl4_8
<=> ! [X1: a] :
( ( ( cD @ X1 )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f88,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( cD @ X1 )
= $true ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f90,definition,
( spl4_9
<=> ! [X2: a] :
( ( ( sK0 @ X2 )
= $false )
| ( ( cE @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f91,plain,
( ! [X2: a] :
( ( ( sK0 @ X2 )
= $false )
| ( ( cE @ X2 )
= $true ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f93,plain,
( spl4_9
| spl4_9 ),
inference(avatar_split_clause,[],[f42,f90,f90]) ).
thf(f94,plain,
( spl4_8
| spl4_8 ),
inference(avatar_split_clause,[],[f49,f87,f87]) ).
thf(f97,plain,
( ( $true
= ( cD @ sK1 ) )
| ( $false = $true )
| ~ spl4_2
| ~ spl4_8 ),
inference(constrained_superposition,[],[f88,f57]) ).
thf(f98,plain,
( ( $true
= ( cD @ sK1 ) )
| ~ spl4_2
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f101,plain,
( ( $false = $true )
| ( ( cE @ sK1 )
= $true )
| ~ spl4_2
| ~ spl4_9 ),
inference(constrained_superposition,[],[f57,f91]) ).
thf(f103,plain,
( ( ( cE @ sK1 )
= $true )
| ~ spl4_2
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f107,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(forward_demodulation,[],[f103,f71]) ).
thf(f108,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f109,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f108]) ).
thf(f110,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8 ),
inference(forward_demodulation,[],[f75,f98]) ).
thf(f111,plain,
( $false
| ~ spl4_2
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f112,plain,
( ~ spl4_2
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f111]) ).
thf(f117,plain,
( ( ( cD @ sK2 )
= $true )
| ( $false = $true )
| ~ spl4_3
| ~ spl4_8 ),
inference(constrained_superposition,[],[f88,f61]) ).
thf(f121,plain,
( ( ( cD @ sK2 )
= $true )
| ~ spl4_3
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f125,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_7
| ~ spl4_8 ),
inference(forward_demodulation,[],[f121,f81]) ).
thf(f126,plain,
( $false
| ~ spl4_3
| ~ spl4_7
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f127,plain,
( ~ spl4_3
| ~ spl4_7
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f126]) ).
thf(f131,plain,
( ( $false = $true )
| ( ( cE @ sK3 )
= $true )
| ~ spl4_1
| ~ spl4_9 ),
inference(constrained_superposition,[],[f91,f53]) ).
thf(f135,plain,
( ( ( cE @ sK3 )
= $true )
| ~ spl4_1
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f140,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_9 ),
inference(forward_demodulation,[],[f135,f66]) ).
thf(f141,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f142,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f141]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s2,plain,
( spl4_2
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
( spl4_1
| spl4_3
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s4,plain,
( spl4_3
| spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s5,plain,
( spl4_1
| spl4_2
| spl4_7 ),
inference(sat_conversion,[],[f82]) ).
cnf(s6,plain,
( spl4_2
| spl4_4
| spl4_7 ),
inference(sat_conversion,[],[f83]) ).
cnf(s7,plain,
( spl4_1
| spl4_5
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f84]) ).
cnf(s8,plain,
( spl4_4
| spl4_5
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f85]) ).
cnf(s10,plain,
( spl4_9
| spl4_9 ),
inference(sat_conversion,[],[f93]) ).
cnf(s11,plain,
spl4_9,
inference(rat,[],[s10]) ).
cnf(s12,plain,
( spl4_8
| spl4_8 ),
inference(sat_conversion,[],[f94]) ).
cnf(s13,plain,
spl4_8,
inference(rat,[],[s12]) ).
cnf(s16,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(sat_conversion,[],[f109]) ).
cnf(s17,plain,
( ~ spl4_2
| ~ spl4_6
| ~ spl4_8 ),
inference(sat_conversion,[],[f112]) ).
cnf(s19,plain,
( ~ spl4_3
| ~ spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f127]) ).
cnf(s21,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_9 ),
inference(sat_conversion,[],[f142]) ).
cnf(s22,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s19,s1,s5,s13]) ).
cnf(s23,plain,
( spl4_5
| spl4_6
| spl4_1 ),
inference(rat,[],[s19,s3,s7,s13]) ).
cnf(s24,plain,
spl4_1,
inference(rat,[],[s23,s16,s17,s22,s11,s13]) ).
cnf(s25,plain,
~ spl4_4,
inference(rat,[],[s21,s11,s24]) ).
cnf(s26,plain,
spl4_7,
inference(rat,[],[s8,s16,s17,s6,s25,s11,s13]) ).
cnf(s27,plain,
~ spl4_3,
inference(rat,[],[s19,s13,s26]) ).
cnf(s28,plain,
spl4_2,
inference(rat,[],[s2,s25,s27]) ).
cnf(s29,plain,
~ spl4_6,
inference(rat,[],[s17,s13,s28]) ).
cnf(s30,plain,
~ spl4_5,
inference(rat,[],[s16,s11,s28]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s4,s27,s25,s29,s30]) ).
thf(f143,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV229^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:23:16 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.22/0.27 % (4134135)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (4134144)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1926574307:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.27 % (4134146)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.27 % (4134146)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.27 % (4134144)Instruction limit reached!
% 0.22/0.27 % (4134144)------------------------------
% 0.22/0.27 % (4134144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (4134144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (4134144)CaDiCaL version: 2.1.3
% 0.22/0.27 % (4134144)Termination reason: Instruction limit
% 0.22/0.27 % (4134144)Termination phase: Saturation
% 0.22/0.27 % (4134144)Time elapsed: 0.006 s
% 0.22/0.27 % (4134144)Peak memory usage: 11 MB
% 0.22/0.27 % (4134144)Instructions burned: 27 (million)
% 0.22/0.27 % (4134140)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=597997067:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.27 % (4134141)lrs+10_16_si=on:nwc=1.5:random_seed=2752579545:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.27 % (4134142)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2926849864:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.27 % (4134143)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=1707606853:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.27 % (4134145)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3374381225:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.27 % (4134146)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=2442164208:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.27 % (4134142)Refutation not found, incomplete strategy
% 0.22/0.27 % (4134142)------------------------------
% 0.22/0.27 % (4134142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (4134142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (4134142)CaDiCaL version: 2.1.3
% 0.22/0.27 % (4134142)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.27 % (4134142)Time elapsed: 0.001 s
% 0.22/0.27 % (4134142)Peak memory usage: 12 MB
% 0.22/0.27 % (4134142)Instructions burned: 1 (million)
% 0.22/0.27 % (4134142)------------------------------
% 0.22/0.27 % (4134142)------------------------------
% 0.22/0.27 % (4134140) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4134135-4134140"...
% 0.22/0.27 % (4134141) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4134135-4134141"...
% 0.22/0.27 % (4134145) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4134135-4134145"...
% 0.22/0.27 % (4134143) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4134135-4134143"...
% 0.22/0.27 % (4134146) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4134135-4134146"...
% 0.22/0.27 % (4134140)...printing done.
% 0.22/0.27 % (4134141)...printing done.
% 0.22/0.27 % (4134145)...printing done.
% 0.22/0.27 % (4134140)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (4134140)------------------------------
% 0.22/0.28 % (4134140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (4134140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (4134140)CaDiCaL version: 2.1.3
% 0.22/0.28 % (4134140)Termination reason: Refutation
% 0.22/0.28 % (4134140)Time elapsed: 0.006 s
% 0.22/0.28 % (4134140)Peak memory usage: 13 MB
% 0.22/0.28 % (4134140)Instructions burned: 8 (million)
% 0.22/0.28 % (4134135)Success in time 0.039 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------