%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET615^3 : 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 : n012.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 08:23:22 AM UTC 2026
% Result : Theorem 0.06s 0.19s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 27 unt; 0 typ; 6 def)
% Number of atoms : 631 ( 115 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 518 ( 94 ~; 114 |; 43 &; 261 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 9 con; 0-4 aty)
% Number of variables : 59 ( 0 sgn 9 !; 3 ?; 59 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(func_def_26,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f6,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union) ).
thf(f9,axiom,
( setminus
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',setminus) ).
thf(f15,conjecture,
! [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( setminus @ ( union @ X0 @ X1 ) @ X2 )
= ( union @ ( setminus @ X0 @ X2 ) @ ( setminus @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( setminus @ ( union @ X0 @ X1 ) @ X2 )
= ( union @ ( setminus @ X0 @ X2 ) @ ( setminus @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f19,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f20,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f37,plain,
( setminus
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f38,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
~ ! [X2: $i > $o,X0: $i > $o,X1: $i > $o] :
( ( setminus @ ( union @ X2 @ X0 ) @ X1 )
= ( union @ ( setminus @ X2 @ X1 ) @ ( setminus @ X0 @ X1 ) ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( setminus @ ( union @ X2 @ X0 ) @ X1 )
!= ( union @ ( setminus @ X2 @ X1 ) @ ( setminus @ X0 @ X1 ) ) ),
inference(ennf_transformation,[],[f39]) ).
thf(f41,plain,
( ( setminus @ ( union @ sK2 @ sK0 ) @ sK1 )
!= ( union @ ( setminus @ sK2 @ sK1 ) @ ( setminus @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
thf(f43,plain,
( ( setminus @ ( union @ sK2 @ sK0 ) @ sK1 )
!= ( union @ ( setminus @ sK2 @ sK1 ) @ ( setminus @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f47,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f51,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f60,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ sK2
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ sK0
@ sK1 ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK2
@ sK0 )
@ sK1 ) ),
inference(definition_unfolding,[],[f43,f47,f51,f51,f47,f47]) ).
thf(f61,plain,
( ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ~ ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ~ ( sK1 @ Y0 ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f61]) ).
thf(f63,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ~ ( sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK2 @ Y0 )
| ( sK0 @ Y0 ) )
& ~ ( sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f65,plain,
( ( $false
= ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ( $false
= ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f70,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f68]) ).
thf(f71,plain,
( ( $false
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f73]) ).
thf(f79,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f67]) ).
thf(f80,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f85,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f86,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f86]) ).
thf(f88,plain,
( ( $true
= ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f89,plain,
( ( ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ~ ( sK1 @ sK3 ) ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ~ ( sK1 @ sK3 ) ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f91,plain,
( ( $true
= ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ~ ( sK1 @ sK3 ) ) )
| ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f93,plain,
( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f95,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f93]) ).
thf(f96,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f96]) ).
thf(f106,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $true
= ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ~ ( sK1 @ sK3 ) ) )
| ( ( ~ ( sK1 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f90]) ).
thf(f115,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK2 @ sK3 )
| ( sK0 @ sK3 ) )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f106]) ).
thf(f116,plain,
( ( ( ~ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f115]) ).
thf(f120,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f116]) ).
thf(f121,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f120]) ).
thf(f123,definition,
( spl4_1
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f124,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f126,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f127,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f128,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f74,f126,f123]) ).
thf(f130,definition,
( spl4_3
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f131,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f134,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f87,f126,f130]) ).
thf(f136,definition,
( spl4_4
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f137,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f139,definition,
( spl4_5
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f140,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f139]) ).
thf(f141,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f97,f139,f136]) ).
thf(f143,definition,
( spl4_6
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f144,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f151,plain,
spl4_6,
inference(avatar_split_clause,[],[f121,f143]) ).
thf(f152,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(backward_demodulation,[],[f127,f144]) ).
thf(f153,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f154,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f153]) ).
thf(f155,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4 ),
inference(backward_demodulation,[],[f137,f124]) ).
thf(f156,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f155]) ).
thf(f157,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f156]) ).
thf(f158,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f140,f131]) ).
thf(f159,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f158]) ).
thf(f160,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f159]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f128]) ).
cnf(s4,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f134]) ).
cnf(s5,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f141]) ).
cnf(s12,plain,
spl4_6,
inference(sat_conversion,[],[f151]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s14,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f157]) ).
cnf(s15,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f160]) ).
cnf(s16,plain,
~ spl4_2,
inference(rat,[],[s13,s12]) ).
cnf(s17,plain,
spl4_3,
inference(rat,[],[s4,s16]) ).
cnf(s18,plain,
~ spl4_5,
inference(rat,[],[s15,s17]) ).
cnf(s19,plain,
spl4_4,
inference(rat,[],[s5,s18]) ).
cnf(s20,plain,
~ spl4_1,
inference(rat,[],[s14,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s16,s20]) ).
thf(f161,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET615^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 13:39:04 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.14 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
% 0.06/0.19 % (113083)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.19 % (113094)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.06/0.19 % (113094)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
% 0.06/0.19 % (113094)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=956166265:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.06/0.19 % (113088)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1338616423:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.19 % (113092)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2335105825:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.06/0.19 % (113093)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3937371075:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.06/0.19 % (113091)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=348178218: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)
% 0.06/0.19 % (113089)lrs+10_16_si=on:nwc=1.5:random_seed=2555442904:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.19 % (113090)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=474791608:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.19 % (113088) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113083-113088"...
% 0.06/0.19 % (113093) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113083-113093"...
% 0.06/0.19 % (113094) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113083-113094"...
% 0.06/0.19 % (113090)Instruction limit reached!
% 0.06/0.19 % (113090)------------------------------
% 0.06/0.19 % (113090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (113090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (113090)CaDiCaL version: 2.1.3
% 0.06/0.19 % (113090)Termination reason: Instruction limit
% 0.06/0.19 % (113090)Termination phase: Saturation
% 0.06/0.19 % (113090)Time elapsed: 0.001 s
% 0.06/0.19 % (113090)Peak memory usage: 11 MB
% 0.06/0.19 % (113090)Instructions burned: 3 (million)
% 0.06/0.19 % (113088)...printing done.
% 0.06/0.19 % (113093)...printing done.
% 0.06/0.19 % (113089) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-113083-113089"...
% 0.06/0.19 % (113094)...printing done.
% 0.06/0.19 % (113093)Refutation found. Thanks to Tanya!
% 0.06/0.19 % SZS status Theorem for theBenchmark
% 0.06/0.19 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.19 % (113093)------------------------------
% 0.06/0.19 % (113093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.19 % (113093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.19 % (113093)CaDiCaL version: 2.1.3
% 0.06/0.19 % (113093)Termination reason: Refutation
% 0.06/0.19 % (113093)Time elapsed: 0.003 s
% 0.06/0.19 % (113093)Peak memory usage: 13 MB
% 0.06/0.19 % (113093)Instructions burned: 8 (million)
% 0.06/0.19 % (113083)Success in time 0.037 s
% 0.06/0.19 % Vampire exiting
%------------------------------------------------------------------------------