%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET580^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 74 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 662 ( 151 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 564 ( 128 ~; 133 |; 41 &; 246 @)
% ( 15 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 7 con; 0-4 aty)
% Number of variables : 48 ( 0 sgn 15 !; 9 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
vOR: $o > $o > $o ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= excl_union ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',excl_union) ).
thf(f15,conjecture,
! [X0: $i > $o,X2: $i,X1: $i > $o] :
( ( ( X0 @ X2 )
<=> ~ ( X1 @ X2 ) )
<=> ( excl_union @ X0 @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X2: $i,X1: $i > $o] :
( ( ( X0 @ X2 )
<=> ~ ( X1 @ X2 ) )
<=> ( excl_union @ X0 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( ~ ( X1 @ X2 )
& ( X0 @ X2 ) )
| ( ~ ( X0 @ X2 )
& ( X1 @ X2 ) ) ) )
= excl_union ),
inference(rectify,[],[f7]) ).
thf(f18,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) )
| ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f28,plain,
~ ! [X0: $i > $o,X1: $i,X2: $i > $o] :
( ( ( X0 @ X1 )
<=> ~ ( X2 @ X1 ) )
<=> ( excl_union @ X0 @ X2 @ X1 ) ),
inference(rectify,[],[f16]) ).
thf(f29,plain,
~ ! [X0: $i > $o,X1: $i,X2: $i > $o] :
( ( ( ( X0 @ X1 )
= $true )
<=> ( $true
!= ( X2 @ X1 ) ) )
<=> ( ( excl_union @ X0 @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f28]) ).
thf(f41,plain,
~ ! [X0: $i > $o,X2: $i > $o,X1: $i] :
( ( ( excl_union @ X0 @ X2 @ X1 )
= $true )
<=> ( ( $true
!= ( X2 @ X1 ) )
<=> ( ( X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f29]) ).
thf(f42,plain,
? [X2: $i > $o,X1: $i,X0: $i > $o] :
( ( ( $true
!= ( X2 @ X1 ) )
<=> ( ( X0 @ X1 )
= $true ) )
<~> ( ( excl_union @ X0 @ X2 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f41]) ).
thf(f43,plain,
? [X2: $i > $o,X1: $i,X0: $i > $o] :
( ( ( ( excl_union @ X0 @ X2 @ X1 )
!= $true )
| ( ( ( ( X0 @ X1 )
!= $true )
| ( $true
= ( X2 @ X1 ) ) )
& ( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( X2 @ X1 ) ) ) ) )
& ( ( ( excl_union @ X0 @ X2 @ X1 )
= $true )
| ( ( ( $true
!= ( X2 @ X1 ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( ( X0 @ X1 )
= $true )
| ( $true
= ( X2 @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[],[f42]) ).
thf(f44,plain,
? [X0: $i > $o,X1: $i,X2: $i > $o] :
( ( ( $true
!= ( excl_union @ X2 @ X0 @ X1 ) )
| ( ( ( $true
!= ( X2 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) )
& ( ( $true
= ( X2 @ X1 ) )
| ( ( X0 @ X1 )
!= $true ) ) ) )
& ( ( $true
= ( excl_union @ X2 @ X0 @ X1 ) )
| ( ( ( ( X0 @ X1 )
!= $true )
| ( $true
!= ( X2 @ X1 ) ) )
& ( ( $true
= ( X2 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f45,plain,
( ( ( $true
!= ( excl_union @ sK2 @ sK0 @ sK1 ) )
| ( ( ( $true
!= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) )
& ( ( $true
= ( sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) ) ) ) )
& ( ( $true
= ( excl_union @ sK2 @ sK0 @ sK1 ) )
| ( ( ( $true
!= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) ) )
& ( ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f44]) ).
thf(f48,plain,
( ( $true
= ( excl_union @ sK2 @ sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f49,plain,
( ( $true
= ( excl_union @ sK2 @ sK0 @ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f50,plain,
( ( $true
!= ( excl_union @ sK2 @ sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f51,plain,
( ( $true
!= ( excl_union @ sK2 @ sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f63,plain,
( excl_union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) )
| ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f67,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) )
| ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) )
@ sK2
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f51,f63]) ).
thf(f68,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) )
| ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) )
@ sK2
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f50,f63]) ).
thf(f69,plain,
( ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) )
| ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) )
@ sK2
@ sK0
@ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) ) ),
inference(definition_unfolding,[],[f49,f63]) ).
thf(f70,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( ( Y1 @ Y2 )
& ~ ( Y0 @ Y2 ) )
| ( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) )
@ sK2
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f48,f63]) ).
thf(f71,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) )
| ( $true
= ( ( ( sK0 @ sK1 )
& ~ ( sK2 @ sK1 ) )
| ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f72,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK1 )
& ~ ( sK2 @ sK1 ) ) )
| ( ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) )
= $true )
| ( $true
!= ( sK2 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) )
| ( ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) )
= $true )
| ( ( ~ ( sK2 @ sK1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f78,plain,
( ( ( ~ ( sK2 @ sK1 ) )
= $true )
| ( $true
!= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) )
| ( ( ~ ( sK0 @ sK1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f81,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( ( ~ ( sK0 @ sK1 ) )
= $true )
| ( $true
!= ( sK2 @ sK1 ) )
| ( $false
= ( sK2 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f78]) ).
thf(f82,plain,
( ( $true
!= ( sK2 @ sK1 ) )
| ( ( sK0 @ sK1 )
= $false )
| ( $false
= ( sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) )
| ( $true
!= ( ( ( sK0 @ sK1 )
& ~ ( sK2 @ sK1 ) )
| ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f85,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) )
| ( ( ( sK0 @ sK1 )
& ~ ( sK2 @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ( $true
!= ( sK0 @ sK1 ) )
| ( ( ~ ( sK2 @ sK1 ) )
= $false )
| ( ( sK0 @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( ( sK0 @ sK1 )
= $false )
| ( $true
= ( sK2 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f86]) ).
thf(f88,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( ( sK0 @ sK1 )
= $false ) ),
inference(duplicate_literal_removal,[],[f87]) ).
thf(f91,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( ( ( sK0 @ sK1 )
& ~ ( sK2 @ sK1 ) )
| ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) ) ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f92,plain,
( ( $true
= ( ( sK0 @ sK1 )
& ~ ( sK2 @ sK1 ) ) )
| ( $true
= ( sK0 @ sK1 ) )
| ( ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) )
= $true )
| ( $true
= ( sK2 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f91]) ).
thf(f94,plain,
( ( ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) )
= $true )
| ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f92]) ).
thf(f96,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f97,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK2 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f96]) ).
thf(f105,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) )
| ( $true
!= ( ( ( sK0 @ sK1 )
& ~ ( sK2 @ sK1 ) )
| ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f106,plain,
( ( ( ( sK2 @ sK1 )
& ~ ( sK0 @ sK1 ) )
= $false )
| ( $true
!= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f105]) ).
thf(f110,plain,
( ( $true
!= ( sK2 @ sK1 ) )
| ( ( ~ ( sK0 @ sK1 ) )
= $false )
| ( $false
= ( sK2 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f111,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK0 @ sK1 ) )
| ( $false
= ( sK2 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
!= ( sK2 @ sK1 ) )
| ( $false
= ( sK2 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f111]) ).
thf(f114,definition,
( spl3_1
<=> ( ( sK0 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f116,plain,
( ( ( sK0 @ sK1 )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f118,definition,
( spl3_2
<=> ( $false
= ( sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f120,plain,
( ( $false
= ( sK2 @ sK1 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f122,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f123,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f126,definition,
( spl3_4
<=> ( $true
= ( sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f127,plain,
( ( $true
= ( sK2 @ sK1 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f129,plain,
( spl3_1
| spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f82,f126,f122,f118,f114]) ).
thf(f130,plain,
( spl3_1
| ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f88,f126,f122,f114]) ).
thf(f131,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f97,f122,f126]) ).
thf(f132,plain,
( spl3_2
| spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f112,f126,f122,f118]) ).
thf(f133,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f120,f127]) ).
thf(f134,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f135,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f134]) ).
thf(f137,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[],[f116,f123]) ).
thf(f138,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f137]) ).
thf(f139,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f138]) ).
cnf(s1,plain,
( spl3_1
| spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f129]) ).
cnf(s2,plain,
( spl3_1
| ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f130]) ).
cnf(s3,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f131]) ).
cnf(s4,plain,
( spl3_2
| spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f132]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f135]) ).
cnf(s6,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f139]) ).
cnf(s7,plain,
( spl3_3
| spl3_2 ),
inference(rat,[],[s4,s3]) ).
cnf(s8,plain,
( spl3_2
| spl3_1 ),
inference(rat,[],[s1,s2,s7]) ).
cnf(s9,plain,
spl3_1,
inference(rat,[],[s2,s3,s5,s8]) ).
cnf(s10,plain,
~ spl3_3,
inference(rat,[],[s6,s9]) ).
cnf(s11,plain,
spl3_4,
inference(rat,[],[s3,s10]) ).
cnf(s12,plain,
spl3_2,
inference(rat,[],[s7,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s5,s11,s12]) ).
thf(f140,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET580^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.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 13:37:45 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
% 0.09/0.24 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
% 0.22/0.29 % (2664243)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (2664251)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=2432101762: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)
% 0.22/0.29 % (2664254)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (2664254)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
% 0.22/0.29 % (2664250)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3045008985:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (2664248)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=976905327:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (2664249)lrs+10_16_si=on:nwc=1.5:random_seed=951462902:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (2664252)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3732096146:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (2664253)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=717635921:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (2664254)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=4156823408:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (2664250)Instruction limit reached!
% 0.22/0.29 % (2664250)------------------------------
% 0.22/0.29 % (2664250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2664250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2664250)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2664250)Termination reason: Instruction limit
% 0.22/0.29 % (2664250)Termination phase: Saturation
% 0.22/0.29 % (2664250)Time elapsed: 0.002 s
% 0.22/0.29 % (2664250)Peak memory usage: 11 MB
% 0.22/0.29 % (2664250)Instructions burned: 3 (million)
% 0.22/0.29 % (2664248) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2664243-2664248"...
% 0.22/0.29 % (2664249) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2664243-2664249"...
% 0.22/0.29 % (2664253) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2664243-2664253"...
% 0.22/0.29 % (2664248)...printing done.
% 0.22/0.29 % (2664249)...printing done.
% 0.22/0.29 % (2664253)...printing done.
% 0.22/0.29 % (2664248)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (2664248)------------------------------
% 0.22/0.29 % (2664248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2664248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2664248)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2664248)Termination reason: Refutation
% 0.22/0.29 % (2664248)Time elapsed: 0.005 s
% 0.22/0.29 % (2664248)Peak memory usage: 12 MB
% 0.22/0.29 % (2664248)Instructions burned: 7 (million)
% 0.22/0.29 % (2664243)Success in time 0.045 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------