%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET582^5 : 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 : n010.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 08:23:17 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 95 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 548 ( 148 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 606 ( 169 ~; 163 |; 49 &; 202 @)
% ( 18 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 28 !; 9 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ~ ( X0 @ X3 )
<=> ( X1 @ X3 ) )
<=> ( X2 @ X3 ) )
=> ( X0
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_25_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ~ ( X0 @ X3 )
<=> ( X1 @ X3 ) )
<=> ( X2 @ X3 ) )
=> ( X0
= ( ^ [X4: a] :
( ( ( X1 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X1 @ X4 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ~ ( X1 @ X3 )
<=> ( X0 @ X3 ) )
<=> ( X2 @ X3 ) )
=> ( X1
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ~ ( X2 @ X4 ) )
| ( ( X2 @ X4 )
& ~ ( X0 @ X4 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( ( X1 @ X3 )
!= $true )
<=> ( ( X0 @ X3 )
= $true ) )
<=> ( ( X2 @ X3 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X1: a > $o,X2: a > $o,X0: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
<=> ( ( ( X0 @ X3 )
= $true )
<=> ( ( X1 @ X3 )
!= $true ) ) )
=> ( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= X1 ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
<=> ( ( ( X0 @ X3 )
= $true )
<=> ( ( X1 @ X3 )
!= $true ) ) )
& ( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= X1 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ! [X3: a] :
( ( ( ( X2 @ X3 )
= $true )
| ( ( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
& ( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ) )
& ( ( ( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
= $true ) )
& ( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) )
| ( ( X2 @ X3 )
!= $true ) ) )
& ( ( ^ [Y0: a] :
( ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) )
| ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= X1 ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( ( X0 @ X3 )
= $true )
| ( ( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ) )
& ( ( ( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
= $true ) )
& ( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
!= $true ) ) )
| ( ( X0 @ X3 )
!= $true ) ) )
& ( ( ^ [Y0: a] :
( ( ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ~ ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= X1 ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ! [X3: a] :
( ( ( ( sK0 @ X3 )
= $true )
| ( ( ( ( sK1 @ X3 )
= $true )
| ( ( sK2 @ X3 )
!= $true ) )
& ( ( ( sK1 @ X3 )
!= $true )
| ( ( sK2 @ X3 )
= $true ) ) ) )
& ( ( ( ( ( sK2 @ X3 )
= $true )
| ( ( sK1 @ X3 )
= $true ) )
& ( ( ( sK1 @ X3 )
!= $true )
| ( ( sK2 @ X3 )
!= $true ) ) )
| ( ( sK0 @ X3 )
!= $true ) ) )
& ( sK1
!= ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
( sK1
!= ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
! [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
!= $true )
| ( ( sK1 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X3: a] :
( ( ( sK0 @ X3 )
!= $true )
| ( ( sK2 @ X3 )
= $true )
| ( ( sK1 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
!= $true )
| ( ( sK0 @ X3 )
= $true )
| ( ( sK2 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK0 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 )
!= ( sK1 @ sK3 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f18,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ^ [Y0: a] :
( ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f26,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f28,plain,
( ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f32,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f33,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f40,definition,
( spl4_1
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f42,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f44,definition,
( spl4_2
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f46,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f48,definition,
( spl4_3
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f50,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f24,f48,f44,f40]) ).
thf(f53,definition,
( spl4_4
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f55,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f57,definition,
( spl4_5
<=> ( ( sK2 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f59,plain,
( ( ( sK2 @ sK3 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f60,plain,
( spl4_4
| spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f26,f40,f57,f53]) ).
thf(f62,definition,
( spl4_6
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f64,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
( spl4_2
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f34,f62,f57,f44]) ).
thf(f66,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f36,f14]) ).
thf(f67,plain,
( spl4_4
| spl4_6 ),
inference(avatar_split_clause,[],[f66,f62,f53]) ).
thf(f68,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f55,f46]) ).
thf(f69,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f70,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f69]) ).
thf(f75,plain,
( ( $true != $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f13,f64]) ).
thf(f76,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f77,plain,
( ( $false = $true )
| ( ( sK2 @ sK3 )
= $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(forward_demodulation,[],[f76,f46]) ).
thf(f78,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f79,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f78,f59]) ).
thf(f80,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f81,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f80]) ).
thf(f82,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f50,f59]) ).
thf(f83,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f84,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f83]) ).
thf(f87,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( $true != $true )
| ( ( sK1 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f12,f55]) ).
thf(f89,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f90,plain,
( ( $false = $true )
| ( ( sK1 @ sK3 )
= $true )
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_demodulation,[],[f89,f59]) ).
thf(f91,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_demodulation,[],[f91,f42]) ).
thf(f93,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f94,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f93]) ).
thf(f95,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_6 ),
inference(forward_demodulation,[],[f64,f42]) ).
thf(f96,plain,
( $false
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f97,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f96]) ).
thf(f100,plain,
( ( ( sK0 @ sK3 )
!= $true )
| ( $true != $true )
| ( ( sK1 @ sK3 )
!= $true )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f11,f50]) ).
thf(f102,plain,
( ( ( sK1 @ sK3 )
!= $true )
| ( ( sK0 @ sK3 )
!= $true )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f103,plain,
( ( ( sK0 @ sK3 )
!= $true )
| ~ spl4_3
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f102,f64]) ).
thf(f104,plain,
( $false
| ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f103,f55]) ).
thf(f105,plain,
( ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f104]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
( spl4_1
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f60]) ).
cnf(s3,plain,
( spl4_2
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
( spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s5,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s6,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f81]) ).
cnf(s7,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f84]) ).
cnf(s8,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f94]) ).
cnf(s9,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(sat_conversion,[],[f97]) ).
cnf(s10,plain,
( ~ spl4_3
| ~ spl4_4
| ~ spl4_6 ),
inference(sat_conversion,[],[f105]) ).
cnf(s11,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s10,s2,s3,s7,s1]) ).
cnf(s12,plain,
spl4_1,
inference(rat,[],[s6,s2,s4,s5,s11]) ).
cnf(s13,plain,
~ spl4_6,
inference(rat,[],[s9,s12]) ).
cnf(s14,plain,
spl4_4,
inference(rat,[],[s4,s13]) ).
cnf(s15,plain,
~ spl4_2,
inference(rat,[],[s5,s14]) ).
cnf(s16,plain,
~ spl4_5,
inference(rat,[],[s8,s12,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s3,s13,s15,s16]) ).
thf(f106,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET582^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n010.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 13:38:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.27 % (2860306)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (2860312)lrs+10_16_si=on:nwc=1.5:random_seed=3048319278:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.27 % (2860312) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2860306-2860312"...
% 0.22/0.27 % (2860312)...printing done.
% 0.22/0.27 % (2860312)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
% 0.22/0.27 % (2860312)------------------------------
% 0.22/0.27 % (2860312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (2860312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (2860312)CaDiCaL version: 2.1.3
% 0.22/0.27 % (2860312)Termination reason: Refutation
% 0.22/0.27 % (2860312)Time elapsed: 0.003 s
% 0.22/0.27 % (2860312)Peak memory usage: 13 MB
% 0.22/0.27 % (2860312)Instructions burned: 6 (million)
% 0.22/0.27 % (2860306)Success in time 0.029 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------