%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n006.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 08:39:11 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 118 ( 16 unt; 0 typ; 9 def)
% Number of atoms : 758 ( 155 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 788 ( 81 ~; 193 |; 41 &; 356 @)
% ( 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)
% ( 33 !!; 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
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,
( ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) ) )
= ( ^ [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cE @ X2 ) )
& ! [X2: a] :
( ( X1 @ X2 )
=> ( cD @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5209_pme) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) ) )
!= ( ^ [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cE @ X2 ) )
& ! [X2: a] :
( ( X1 @ X2 )
=> ( cD @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) ) )
!= ( ^ [X2: a > $o] :
( ! [X3: a] :
( ( X2 @ X3 )
=> ( cE @ X3 ) )
& ! [X4: a] :
( ( X2 @ 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 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ 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 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ 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 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f16,plain,
( ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) )
@ sK0 )
!= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f6]) ).
thf(f17,plain,
( ( $true
= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cD @ Y1 )
& ( cE @ Y1 ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) ) ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ sK1 ) )
| ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ sK1 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( ( sK0 @ sK1 )
=> ( ( cD @ sK1 )
& ( cE @ sK1 ) ) ) )
| ( $false
= ( ( sK0 @ sK2 )
=> ( cE @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( ( cD @ sK1 )
& ( cE @ sK1 ) ) )
| ( $false
= ( ( sK0 @ sK2 )
=> ( cE @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $false
= ( ( sK0 @ sK2 )
=> ( cE @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $false
= ( cE @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f26]) ).
thf(f29,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( cD @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $false
= ( cE @ sK2 ) )
| ( $false
= ( cD @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f32,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $false
= ( cE @ sK2 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f33,plain,
( ( $false
= ( cE @ sK1 ) )
| ( $false
= ( ( sK0 @ sK2 )
=> ( cE @ sK2 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) )
| ( $false
= ( cD @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f34,plain,
( ( $false
= ( cE @ sK1 ) )
| ( $false
= ( cE @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) )
| ( $false
= ( cD @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( ( $false
= ( cE @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK3 )
=> ( cD @ sK3 ) ) )
| ( $false
= ( cD @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( $false
= ( cE @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( cD @ sK3 ) )
| ( $false
= ( cD @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f37,plain,
( ( $false
= ( cE @ sK1 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( cD @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f38,plain,
( ( $false
= ( cE @ sK1 ) )
| ( $false
= ( cE @ sK2 ) )
| ( $false
= ( cD @ sK3 ) )
| ( $false
= ( cD @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f39,plain,
( ( $false
= ( cE @ sK1 ) )
| ( $false
= ( cE @ sK2 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( cD @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f40,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) ) ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f41,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f41]) ).
thf(f44,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cD @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( sK0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) ) )
| ( $true
= ( ( sK0 @ X2 )
=> ( cD @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( sK0 @ X2 )
=> ( cD @ X2 ) ) )
| ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) )
| ( ( cD @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f49,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( cD @ X1 )
= $true )
| ( ( cD @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( ( cD @ Y0 )
& ( cE @ Y0 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
=> ( cE @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f51,plain,
! [X2: a,X1: a] :
( ( $true
= ( ( sK0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) ) )
| ( $true
= ( ( sK0 @ X2 )
=> ( cE @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( sK0 @ X2 )
=> ( cE @ X2 ) ) )
| ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( ( cD @ X1 )
& ( cE @ X1 ) ) )
| ( ( cE @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( cE @ X1 )
= $true )
| ( ( cE @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f57,definition,
( spl4_1
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f59,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f61,definition,
( spl4_2
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f63,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f65,definition,
( spl4_3
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f67,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f68,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f30,f65,f61,f57]) ).
thf(f70,definition,
( spl4_4
<=> ( $false
= ( cD @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f72,plain,
( ( $false
= ( cD @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( spl4_4
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f29,f65,f61,f70]) ).
thf(f75,definition,
( spl4_5
<=> ( $false
= ( cE @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f77,plain,
( ( $false
= ( cE @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f78,plain,
( spl4_1
| spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f32,f65,f75,f57]) ).
thf(f79,plain,
( spl4_4
| spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f31,f65,f75,f70]) ).
thf(f81,definition,
( spl4_6
<=> ( $false
= ( cD @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f83,plain,
( ( $false
= ( cD @ sK1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f85,definition,
( spl4_7
<=> ( $false
= ( cE @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f87,plain,
( ( $false
= ( cE @ sK1 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f88,plain,
( spl4_6
| spl4_1
| spl4_2
| spl4_7 ),
inference(avatar_split_clause,[],[f37,f85,f61,f57,f81]) ).
thf(f89,plain,
( spl4_6
| spl4_4
| spl4_2
| spl4_7 ),
inference(avatar_split_clause,[],[f36,f85,f61,f70,f81]) ).
thf(f90,plain,
( spl4_6
| spl4_1
| spl4_5
| spl4_7 ),
inference(avatar_split_clause,[],[f39,f85,f75,f57,f81]) ).
thf(f91,plain,
( spl4_6
| spl4_4
| spl4_5
| spl4_7 ),
inference(avatar_split_clause,[],[f38,f85,f75,f70,f81]) ).
thf(f93,definition,
( spl4_8
<=> ! [X2: a] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( cD @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f94,plain,
( ! [X2: a] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( cD @ X2 )
= $true ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f95,plain,
( spl4_8
| spl4_8 ),
inference(avatar_split_clause,[],[f49,f93,f93]) ).
thf(f97,definition,
( spl4_9
<=> ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( cE @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
thf(f98,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( cE @ X1 )
= $true ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f101,plain,
( spl4_9
| spl4_9 ),
inference(avatar_split_clause,[],[f54,f97,f97]) ).
thf(f109,plain,
( ( $true = $false )
| ( $true
= ( cE @ sK2 ) )
| ~ spl4_2
| ~ spl4_9 ),
inference(constrained_superposition,[],[f98,f63]) ).
thf(f112,plain,
( ( $true
= ( cE @ sK2 ) )
| ~ spl4_2
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f117,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(forward_demodulation,[],[f112,f77]) ).
thf(f118,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f119,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f118]) ).
thf(f121,plain,
( ( $true = $false )
| ( $true
= ( cD @ sK3 ) )
| ~ spl4_1
| ~ spl4_8 ),
inference(constrained_superposition,[],[f59,f94]) ).
thf(f126,plain,
( ( $true
= ( cD @ sK3 ) )
| ~ spl4_1
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f131,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(forward_demodulation,[],[f126,f72]) ).
thf(f132,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f133,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f132]) ).
thf(f135,plain,
( ( $true = $false )
| ( $true
= ( cD @ sK1 ) )
| ~ spl4_3
| ~ spl4_8 ),
inference(constrained_superposition,[],[f67,f94]) ).
thf(f136,plain,
( ( $true = $false )
| ( $true
= ( cE @ sK1 ) )
| ~ spl4_3
| ~ spl4_9 ),
inference(constrained_superposition,[],[f98,f67]) ).
thf(f139,plain,
( ( $true
= ( cE @ sK1 ) )
| ~ spl4_3
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f140,plain,
( ( $true
= ( cD @ sK1 ) )
| ~ spl4_3
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f135]) ).
thf(f145,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(forward_demodulation,[],[f140,f83]) ).
thf(f146,plain,
( $false
| ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f147,plain,
( ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f146]) ).
thf(f156,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_7
| ~ spl4_9 ),
inference(constrained_superposition,[],[f139,f87]) ).
thf(f160,plain,
( $false
| ~ spl4_3
| ~ spl4_7
| ~ spl4_9 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f161,plain,
( ~ spl4_3
| ~ spl4_7
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f160]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f68]) ).
cnf(s2,plain,
( spl4_2
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f73]) ).
cnf(s3,plain,
( spl4_1
| spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f78]) ).
cnf(s4,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f79]) ).
cnf(s5,plain,
( spl4_1
| spl4_2
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f88]) ).
cnf(s6,plain,
( spl4_2
| spl4_4
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f89]) ).
cnf(s7,plain,
( spl4_1
| spl4_5
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f90]) ).
cnf(s8,plain,
( spl4_4
| spl4_5
| spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s9,plain,
( spl4_8
| spl4_8 ),
inference(sat_conversion,[],[f95]) ).
cnf(s10,plain,
spl4_8,
inference(rat,[],[s9]) ).
cnf(s13,plain,
( spl4_9
| spl4_9 ),
inference(sat_conversion,[],[f101]) ).
cnf(s14,plain,
spl4_9,
inference(rat,[],[s13]) ).
cnf(s16,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s18,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_8 ),
inference(sat_conversion,[],[f133]) ).
cnf(s20,plain,
( ~ spl4_3
| ~ spl4_6
| ~ spl4_8 ),
inference(sat_conversion,[],[f147]) ).
cnf(s22,plain,
( ~ spl4_3
| ~ spl4_7
| ~ spl4_9 ),
inference(sat_conversion,[],[f161]) ).
cnf(s23,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s5,s20,s22,s1,s14,s10]) ).
cnf(s24,plain,
( spl4_5
| spl4_1 ),
inference(rat,[],[s7,s20,s22,s3,s14,s10]) ).
cnf(s25,plain,
spl4_1,
inference(rat,[],[s24,s16,s23,s14]) ).
cnf(s26,plain,
~ spl4_4,
inference(rat,[],[s18,s10,s25]) ).
cnf(s27,plain,
( spl4_6
| spl4_7 ),
inference(rat,[],[s16,s8,s6,s26,s14]) ).
cnf(s28,plain,
~ spl4_3,
inference(rat,[],[s27,s20,s22,s10,s14]) ).
cnf(s29,plain,
spl4_2,
inference(rat,[],[s2,s26,s28]) ).
cnf(s30,plain,
spl4_5,
inference(rat,[],[s4,s26,s28]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s16,s14,s30,s29]) ).
thf(f162,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.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:22:54 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (861002)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (861008)% WARNING: option uhcvi not known.
% 0.20/0.27 % (861007)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3628620705_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (861010)dis+10_1_sil=32000:sp=arity:random_seed=638810261:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (861008)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2592508301:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (861009)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3896523977:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (861011)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=370977962:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % Exception at run slice level
% 0.20/0.27 % (861008)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.27 % (861008)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.27 % (861011)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (861010) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-861002-861010"...
% 0.20/0.27 % (861011) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-861002-861011"...
% 0.20/0.27 % (861008) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-861002-861008"...
% 0.20/0.27 % (861008)...printing done.
% 0.20/0.27 % (861010)...printing done.
% 0.20/0.27 % (861011)...printing done.
% 0.20/0.27 % (861009) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-861002-861009"...
% 0.20/0.27 % (861013)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2027578905:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (861011)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (861011)------------------------------
% 0.20/0.27 % (861011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (861011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (861011)CaDiCaL version: 2.1.3
% 0.20/0.27 % (861011)Termination reason: Refutation
% 0.20/0.27 % (861011)Time elapsed: 0.006 s
% 0.20/0.27 % (861011)Peak memory usage: 12 MB
% 0.20/0.27 % (861011)Instructions burned: 9 (million)
% 0.20/0.27 % (861002)Success in time 0.037 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------