%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS144+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 : Tue Sep 29 11:41:45 AM UTC 2026
% Result : Theorem 2.93s 1.26s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 23
% Syntax : Number of formulae : 145 ( 15 unt; 19 def)
% Number of atoms : 566 ( 66 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 678 ( 257 ~; 293 |; 90 &)
% ( 22 <=>; 13 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 19 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 141 ( 0 sgn 92 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
fof(f9,axiom,
! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f10,axiom,
! [X0] :
( cc(X0)
=> ( ? [X1,X2] :
( rp(X0,X1)
& rp(X0,X2)
& X1 != X2 )
& ! [X1,X2,X3] :
( ( rp(X0,X1)
& rp(X0,X2)
& rp(X0,X3) )
=> ( X1 = X2
| X1 = X3
| X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f11,conjecture,
( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cc(X0)
=> ! [X1,X2,X3] :
( ( rp(X0,X1)
& rp(X0,X2)
& rp(X0,X3) )
=> ( X1 = X2
| X1 = X3
| X2 = X3 ) ) )
& ! [X0] :
( cc(X0)
=> ? [X1,X2] :
( rp(X0,X1)
& rp(X0,X2)
& X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
fof(f12,negated_conjecture,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) )
& ! [X0] :
( cc(X0)
=> ! [X1,X2,X3] :
( ( rp(X0,X1)
& rp(X0,X2)
& rp(X0,X3) )
=> ( X1 = X2
| X1 = X3
| X2 = X3 ) ) )
& ! [X0] :
( cc(X0)
=> ? [X1,X2] :
( rp(X0,X1)
& rp(X0,X2)
& X1 != X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0] :
( cc(X0)
=> ( ? [X1,X2] :
( rp(X0,X1)
& rp(X0,X2)
& X1 != X2 )
& ! [X3,X4,X5] :
( ( rp(X0,X3)
& rp(X0,X4)
& rp(X0,X5) )
=> ( X3 = X4
| X3 = X5
| X4 = X5 ) ) ) ),
inference(rectify,[],[f10]) ).
fof(f14,plain,
~ ( ! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) )
& ! [X1] :
( xsd_string(X1)
<=> ~ xsd_integer(X1) )
& ! [X2] :
( cc(X2)
=> ! [X3,X4,X5] :
( ( rp(X2,X3)
& rp(X2,X4)
& rp(X2,X5) )
=> ( X3 = X4
| X3 = X5
| X4 = X5 ) ) )
& ! [X6] :
( cc(X6)
=> ? [X7,X8] :
( rp(X6,X7)
& rp(X6,X8)
& X7 != X8 ) ) ),
inference(rectify,[],[f12]) ).
fof(f29,plain,
! [X0] :
( ( ? [X1,X2] :
( rp(X0,X1)
& rp(X0,X2)
& X1 != X2 )
& ! [X3,X4,X5] :
( X3 = X4
| X3 = X5
| X4 = X5
| ~ rp(X0,X3)
| ~ rp(X0,X4)
| ~ rp(X0,X5) ) )
| ~ cc(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0] :
( ( ? [X1,X2] :
( rp(X0,X1)
& rp(X0,X2)
& X1 != X2 )
& ! [X3,X4,X5] :
( X3 = X4
| X3 = X5
| X4 = X5
| ~ rp(X0,X3)
| ~ rp(X0,X4)
| ~ rp(X0,X5) ) )
| ~ cc(X0) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( ? [X3,X4,X5] :
( X3 != X4
& X3 != X5
& X4 != X5
& rp(X2,X3)
& rp(X2,X4)
& rp(X2,X5) )
& cc(X2) )
| ? [X6] :
( ! [X7,X8] :
( ~ rp(X6,X7)
| ~ rp(X6,X8)
| X7 = X8 )
& cc(X6) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f32,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| ? [X2] :
( ? [X3,X4,X5] :
( X3 != X4
& X3 != X5
& X4 != X5
& rp(X2,X3)
& rp(X2,X4)
& rp(X2,X5) )
& cc(X2) )
| ? [X6] :
( ! [X7,X8] :
( ~ rp(X6,X7)
| ~ rp(X6,X8)
| X7 = X8 )
& cc(X6) ) ),
inference(flattening,[],[f31]) ).
fof(f33,definition,
( ? [X2] :
( ? [X3,X4,X5] :
( X3 != X4
& X3 != X5
& X4 != X5
& rp(X2,X3)
& rp(X2,X4)
& rp(X2,X5) )
& cc(X2) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f34,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( xsd_string(X1)
<~> ~ xsd_integer(X1) )
| sP0
| ? [X6] :
( ! [X7,X8] :
( ~ rp(X6,X7)
| ~ rp(X6,X8)
| X7 = X8 )
& cc(X6) ) ),
inference(definition_folding,[],[f32,f33]) ).
fof(f35,plain,
! [X0] :
( ( xsd_string(X0)
| xsd_integer(X0) )
& ( ~ xsd_integer(X0)
| ~ xsd_string(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0] :
( ( rp(X0,sK1(X0))
& rp(X0,sK2(X0))
& sK1(X0) != sK2(X0)
& ! [X3,X4,X5] :
( X3 = X4
| X3 = X5
| X4 = X5
| ~ rp(X0,X3)
| ~ rp(X0,X4)
| ~ rp(X0,X5) ) )
| ~ cc(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f30]) ).
fof(f37,plain,
( ? [X2] :
( ? [X3,X4,X5] :
( X3 != X4
& X3 != X5
& X4 != X5
& rp(X2,X3)
& rp(X2,X4)
& rp(X2,X5) )
& cc(X2) )
| ~ sP0 ),
inference(nnf_transformation,[],[f33]) ).
fof(f38,plain,
( ? [X0] :
( ? [X1,X2,X3] :
( X1 != X2
& X1 != X3
& X2 != X3
& rp(X0,X1)
& rp(X0,X2)
& rp(X0,X3) )
& cc(X0) )
| ~ sP0 ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
( ( sK4 != sK5
& sK4 != sK6
& sK5 != sK6
& rp(sK3,sK4)
& rp(sK3,sK5)
& rp(sK3,sK6)
& cc(sK3) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f38]) ).
fof(f40,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| sP0
| ? [X6] :
( ! [X7,X8] :
( ~ rp(X6,X7)
| ~ rp(X6,X8)
| X7 = X8 )
& cc(X6) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f41,plain,
( ? [X0] :
( ~ cowlThing(X0)
| cowlNothing(X0) )
| ? [X1] :
( ( xsd_integer(X1)
| ~ xsd_string(X1) )
& ( ~ xsd_integer(X1)
| xsd_string(X1) ) )
| sP0
| ? [X2] :
( ! [X3,X4] :
( ~ rp(X2,X3)
| ~ rp(X2,X4)
| X3 = X4 )
& cc(X2) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| ( ( xsd_integer(sK8)
| ~ xsd_string(sK8) )
& ( ~ xsd_integer(sK8)
| xsd_string(sK8) ) )
| sP0
| ( ! [X3,X4] :
( ~ rp(sK9,X3)
| ~ rp(sK9,X4)
| X3 = X4 )
& cc(sK9) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f41]) ).
fof(f50,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f52,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
! [X0] :
( xsd_string(X0)
| xsd_integer(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X3,X0,X4,X5] :
( X3 = X4
| X3 = X5
| X4 = X5
| ~ rp(X0,X3)
| ~ rp(X0,X4)
| ~ rp(X0,X5)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| ~ cc(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0] :
( ~ cc(X0)
| rp(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0] :
( ~ cc(X0)
| rp(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
( cc(sK3)
| ~ sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
( rp(sK3,sK6)
| ~ sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
( rp(sK3,sK5)
| ~ sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
( rp(sK3,sK4)
| ~ sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f62,plain,
( sK5 != sK6
| ~ sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f63,plain,
( sK4 != sK6
| ~ sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
( sK4 != sK5
| ~ sP0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f65,plain,
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| ~ xsd_integer(sK8)
| xsd_string(sK8)
| sP0
| cc(sK9) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
! [X3,X4] :
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| ~ xsd_integer(sK8)
| xsd_string(sK8)
| sP0
| ~ rp(sK9,X3)
| ~ rp(sK9,X4)
| X3 = X4 ),
inference(cnf_transformation,[],[f42]) ).
fof(f67,plain,
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| xsd_integer(sK8)
| ~ xsd_string(sK8)
| sP0
| cc(sK9) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X3,X4] :
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| xsd_integer(sK8)
| ~ xsd_string(sK8)
| sP0
| ~ rp(sK9,X3)
| ~ rp(sK9,X4)
| X3 = X4 ),
inference(cnf_transformation,[],[f42]) ).
fof(f76,definition,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ10_eqProxy])],[equality_proxy_definition]) ).
fof(f77,plain,
! [X0] :
( ~ sQ10_eqProxy(sK1(X0),sK2(X0))
| ~ cc(X0) ),
inference(equality_proxy_replacement,[],[f55,f76]) ).
fof(f78,plain,
! [X3,X0,X4,X5] :
( sQ10_eqProxy(X4,X5)
| sQ10_eqProxy(X3,X5)
| sQ10_eqProxy(X3,X4)
| ~ rp(X0,X3)
| ~ rp(X0,X4)
| ~ rp(X0,X5)
| ~ cc(X0) ),
inference(equality_proxy_replacement,[],[f54,f76,f76,f76]) ).
fof(f79,plain,
( ~ sQ10_eqProxy(sK4,sK5)
| ~ sP0 ),
inference(equality_proxy_replacement,[],[f64,f76]) ).
fof(f80,plain,
( ~ sQ10_eqProxy(sK4,sK6)
| ~ sP0 ),
inference(equality_proxy_replacement,[],[f63,f76]) ).
fof(f81,plain,
( ~ sQ10_eqProxy(sK5,sK6)
| ~ sP0 ),
inference(equality_proxy_replacement,[],[f62,f76]) ).
fof(f82,plain,
! [X3,X4] :
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| xsd_integer(sK8)
| ~ xsd_string(sK8)
| sP0
| ~ rp(sK9,X3)
| ~ rp(sK9,X4)
| sQ10_eqProxy(X3,X4) ),
inference(equality_proxy_replacement,[],[f68,f76]) ).
fof(f83,plain,
! [X3,X4] :
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| ~ xsd_integer(sK8)
| xsd_string(sK8)
| sP0
| ~ rp(sK9,X3)
| ~ rp(sK9,X4)
| sQ10_eqProxy(X3,X4) ),
inference(equality_proxy_replacement,[],[f66,f76]) ).
fof(f87,definition,
( spl11_1
<=> cc(sK9) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f88,plain,
( cc(sK9)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl11_2
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f93,definition,
( spl11_3
<=> xsd_string(sK8) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f94,plain,
( xsd_string(sK8)
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl11_4
<=> xsd_integer(sK8) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f99,definition,
( spl11_5
<=> cowlNothing(sK7) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f100,plain,
( cowlNothing(sK7)
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl11_6
<=> cowlThing(sK7) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f103,plain,
( ~ cowlThing(sK7)
| spl11_6 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( spl11_1
| spl11_2
| spl11_3
| ~ spl11_4
| spl11_5
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f65,f102,f99,f96,f93,f90,f87]) ).
fof(f106,definition,
( spl11_7
<=> ! [X4,X3] :
( ~ rp(sK9,X3)
| sQ10_eqProxy(X3,X4)
| ~ rp(sK9,X4) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
fof(f107,plain,
( ! [X3,X4] :
( sQ10_eqProxy(X3,X4)
| ~ rp(sK9,X3)
| ~ rp(sK9,X4) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f108,plain,
( spl11_7
| spl11_2
| spl11_3
| ~ spl11_4
| spl11_5
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f83,f102,f99,f96,f93,f90,f106]) ).
fof(f109,plain,
( ~ xsd_string(sK8)
| spl11_3 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f111,plain,
( spl11_1
| spl11_2
| ~ spl11_3
| spl11_4
| spl11_5
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f67,f102,f99,f96,f93,f90,f87]) ).
fof(f112,plain,
( spl11_7
| spl11_2
| ~ spl11_3
| spl11_4
| spl11_5
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f82,f102,f99,f96,f93,f90,f106]) ).
fof(f115,definition,
( spl11_8
<=> cc(sK3) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f116,plain,
( cc(sK3)
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f117,plain,
( ~ spl11_2
| spl11_8 ),
inference(avatar_split_clause,[],[f58,f115,f90]) ).
fof(f119,definition,
( spl11_9
<=> rp(sK3,sK6) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f121,plain,
( ~ spl11_2
| spl11_9 ),
inference(avatar_split_clause,[],[f59,f119,f90]) ).
fof(f123,definition,
( spl11_10
<=> rp(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
fof(f125,plain,
( ~ spl11_2
| spl11_10 ),
inference(avatar_split_clause,[],[f60,f123,f90]) ).
fof(f127,definition,
( spl11_11
<=> rp(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
fof(f129,plain,
( ~ spl11_2
| spl11_11 ),
inference(avatar_split_clause,[],[f61,f127,f90]) ).
fof(f131,definition,
( spl11_12
<=> sQ10_eqProxy(sK5,sK6) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
fof(f132,plain,
( ~ sQ10_eqProxy(sK5,sK6)
| spl11_12 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( ~ spl11_2
| ~ spl11_12 ),
inference(avatar_split_clause,[],[f81,f131,f90]) ).
fof(f135,definition,
( spl11_13
<=> sQ10_eqProxy(sK4,sK6) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
fof(f136,plain,
( ~ sQ10_eqProxy(sK4,sK6)
| spl11_13 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( ~ spl11_2
| ~ spl11_13 ),
inference(avatar_split_clause,[],[f80,f135,f90]) ).
fof(f139,definition,
( spl11_14
<=> sQ10_eqProxy(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
fof(f141,plain,
( ~ spl11_2
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f79,f139,f90]) ).
fof(f142,plain,
( $false
| spl11_6 ),
inference(resolution,[],[f51,f103]) ).
fof(f143,plain,
spl11_6,
inference(avatar_contradiction_clause,[],[f142]) ).
fof(f144,plain,
( xsd_integer(sK8)
| spl11_3 ),
inference(resolution,[],[f53,f109]) ).
fof(f146,plain,
( spl11_4
| spl11_3 ),
inference(avatar_split_clause,[],[f144,f93,f96]) ).
fof(f147,plain,
( ~ xsd_integer(sK8)
| ~ spl11_3 ),
inference(resolution,[],[f94,f52]) ).
fof(f148,plain,
( $false
| ~ spl11_5 ),
inference(resolution,[],[f100,f50]) ).
fof(f149,plain,
~ spl11_5,
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f150,plain,
( ~ spl11_4
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f147,f93,f96]) ).
fof(f165,plain,
( ! [X0,X1] :
( sQ10_eqProxy(X0,sK6)
| sQ10_eqProxy(X0,sK5)
| ~ rp(X1,X0)
| ~ rp(X1,sK5)
| ~ rp(X1,sK6)
| ~ cc(X1) )
| spl11_12 ),
inference(resolution,[],[f78,f132]) ).
fof(f171,definition,
( spl11_15
<=> ! [X0] :
( ~ rp(X0,sK6)
| ~ cc(X0)
| ~ rp(X0,sK5)
| ~ rp(X0,sK4) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
fof(f172,plain,
( ! [X0] :
( ~ cc(X0)
| ~ rp(X0,sK6)
| ~ rp(X0,sK5)
| ~ rp(X0,sK4) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f178,plain,
( ! [X0] :
( sQ10_eqProxy(sK4,sK5)
| ~ rp(X0,sK4)
| ~ rp(X0,sK5)
| ~ rp(X0,sK6)
| ~ cc(X0) )
| spl11_12
| spl11_13 ),
inference(resolution,[],[f165,f136]) ).
fof(f181,plain,
( spl11_15
| spl11_14
| spl11_12
| spl11_13 ),
inference(avatar_split_clause,[],[f178,f135,f131,f139,f171]) ).
fof(f182,plain,
( ~ rp(sK3,sK6)
| ~ rp(sK3,sK5)
| ~ rp(sK3,sK4)
| ~ spl11_8
| ~ spl11_15 ),
inference(resolution,[],[f172,f116]) ).
fof(f186,plain,
( ~ spl11_11
| ~ spl11_10
| ~ spl11_9
| ~ spl11_8
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f182,f171,f115,f119,f123,f127]) ).
fof(f190,plain,
( rp(sK9,sK1(sK9))
| ~ spl11_1 ),
inference(resolution,[],[f88,f57]) ).
fof(f191,plain,
( rp(sK9,sK2(sK9))
| ~ spl11_1 ),
inference(resolution,[],[f88,f56]) ).
fof(f203,plain,
( ! [X0] :
( ~ cc(X0)
| ~ rp(sK9,sK2(X0))
| ~ rp(sK9,sK1(X0)) )
| ~ spl11_7 ),
inference(resolution,[],[f107,f77]) ).
fof(f217,plain,
( ~ rp(sK9,sK2(sK9))
| ~ rp(sK9,sK1(sK9))
| ~ spl11_1
| ~ spl11_7 ),
inference(resolution,[],[f203,f88]) ).
fof(f219,definition,
( spl11_20
<=> rp(sK9,sK1(sK9)) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
fof(f220,plain,
( ~ rp(sK9,sK1(sK9))
| spl11_20 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,definition,
( spl11_21
<=> rp(sK9,sK2(sK9)) ),
introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition]) ).
fof(f223,plain,
( ~ rp(sK9,sK2(sK9))
| spl11_21 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ spl11_20
| ~ spl11_21
| ~ spl11_1
| ~ spl11_7 ),
inference(avatar_split_clause,[],[f217,f106,f87,f222,f219]) ).
fof(f235,plain,
( $false
| ~ spl11_1
| spl11_20 ),
inference(resolution,[],[f220,f190]) ).
fof(f236,plain,
( ~ spl11_1
| spl11_20 ),
inference(avatar_contradiction_clause,[],[f235]) ).
fof(f237,plain,
( $false
| ~ spl11_1
| spl11_21 ),
inference(resolution,[],[f223,f191]) ).
fof(f238,plain,
( ~ spl11_1
| spl11_21 ),
inference(avatar_contradiction_clause,[],[f237]) ).
cnf(s1,plain,
( spl11_1
| spl11_2
| spl11_3
| ~ spl11_4
| spl11_5
| ~ spl11_6 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl11_2
| spl11_3
| ~ spl11_4
| spl11_5
| ~ spl11_6
| spl11_7 ),
inference(sat_conversion,[],[f108]) ).
cnf(s3,plain,
( spl11_1
| spl11_2
| ~ spl11_3
| spl11_4
| spl11_5
| ~ spl11_6 ),
inference(sat_conversion,[],[f111]) ).
cnf(s4,plain,
( spl11_2
| ~ spl11_3
| spl11_4
| spl11_5
| ~ spl11_6
| spl11_7 ),
inference(sat_conversion,[],[f112]) ).
cnf(s5,plain,
( ~ spl11_2
| spl11_8 ),
inference(sat_conversion,[],[f117]) ).
cnf(s6,plain,
( ~ spl11_2
| spl11_9 ),
inference(sat_conversion,[],[f121]) ).
cnf(s7,plain,
( ~ spl11_2
| spl11_10 ),
inference(sat_conversion,[],[f125]) ).
cnf(s8,plain,
( ~ spl11_2
| spl11_11 ),
inference(sat_conversion,[],[f129]) ).
cnf(s9,plain,
( ~ spl11_2
| ~ spl11_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s10,plain,
( ~ spl11_2
| ~ spl11_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s11,plain,
( ~ spl11_2
| ~ spl11_14 ),
inference(sat_conversion,[],[f141]) ).
cnf(s12,plain,
spl11_6,
inference(sat_conversion,[],[f143]) ).
cnf(s13,plain,
( spl11_3
| spl11_4 ),
inference(sat_conversion,[],[f146]) ).
cnf(s14,plain,
~ spl11_5,
inference(sat_conversion,[],[f149]) ).
cnf(s15,plain,
( ~ spl11_3
| ~ spl11_4 ),
inference(sat_conversion,[],[f150]) ).
cnf(s17,plain,
( spl11_12
| spl11_13
| spl11_14
| spl11_15 ),
inference(sat_conversion,[],[f181]) ).
cnf(s18,plain,
( ~ spl11_8
| ~ spl11_9
| ~ spl11_10
| ~ spl11_11
| ~ spl11_15 ),
inference(sat_conversion,[],[f186]) ).
cnf(s26,plain,
( ~ spl11_1
| ~ spl11_7
| ~ spl11_20
| ~ spl11_21 ),
inference(sat_conversion,[],[f224]) ).
cnf(s28,plain,
( ~ spl11_1
| spl11_20 ),
inference(sat_conversion,[],[f236]) ).
cnf(s29,plain,
( ~ spl11_1
| spl11_21 ),
inference(sat_conversion,[],[f238]) ).
cnf(s30,plain,
( spl11_2
| ~ spl11_3
| spl11_4
| spl11_7 ),
inference(rat,[],[s4,s12,s14]) ).
cnf(s31,plain,
( spl11_1
| spl11_2
| ~ spl11_3
| spl11_4 ),
inference(rat,[],[s3,s12,s14]) ).
cnf(s32,plain,
( spl11_2
| spl11_3
| ~ spl11_4
| spl11_7 ),
inference(rat,[],[s2,s12,s14]) ).
cnf(s33,plain,
( spl11_1
| spl11_2
| spl11_3
| ~ spl11_4 ),
inference(rat,[],[s1,s12,s14]) ).
cnf(s34,plain,
( spl11_3
| spl11_2
| spl11_1 ),
inference(rat,[],[s33,s13]) ).
cnf(s35,plain,
( spl11_2
| spl11_1 ),
inference(rat,[],[s31,s15,s34]) ).
cnf(s36,plain,
~ spl11_2,
inference(rat,[],[s18,s17,s5,s6,s7,s8,s9,s10,s11]) ).
cnf(s37,plain,
spl11_1,
inference(rat,[],[s35,s36]) ).
cnf(s38,plain,
spl11_21,
inference(rat,[],[s29,s37]) ).
cnf(s39,plain,
spl11_20,
inference(rat,[],[s28,s37]) ).
cnf(s40,plain,
~ spl11_7,
inference(rat,[],[s26,s38,s39,s37]) ).
cnf(s41,plain,
spl11_3,
inference(rat,[],[s32,s13,s36,s40]) ).
cnf(s42,plain,
~ spl11_4,
inference(rat,[],[s15,s41]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s30,s40,s36,s41,s42]) ).
fof(f239,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS144+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:29:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/1.26 % (2411946)Detected formulas, will run a generic FOF schedule.
% 2.93/1.26 % (2411952)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1510246467:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.93/1.26 % (2411957)dis-21_1_sil=8000:lcm=predicate:random_seed=1106498163:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.93/1.26 % (2411953)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1332930368:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.93/1.26 % (2411954)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2446507776:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.93/1.26 % (2411951)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1451110275:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.93/1.26 % (2411956)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=829740178:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.93/1.26 % (2411955)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2693738202:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.93/1.26 % (2411954)Refutation not found, incomplete strategy
% 2.93/1.26 % (2411954)------------------------------
% 2.93/1.26 % (2411954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.26 % (2411954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.26 % (2411954)CaDiCaL version: 2.1.3
% 2.93/1.26 % (2411954)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.26 % (2411954)Time elapsed: 0.002 s
% 2.93/1.26 % (2411954)Peak memory usage: 88 MB
% 2.93/1.26 % (2411954)Instructions burned: 2 (million)
% 2.93/1.26 % (2411957)First to succeed.
% 2.93/1.26 % (2411955)Also succeeded, but the first one will report.
% 2.93/1.26 % (2411956)Also succeeded, but the first one will report.
% 2.93/1.26 % (2411957)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2411946"
% 2.93/1.26 % (2411954)------------------------------
% 2.93/1.26 % (2411954)------------------------------
% 2.93/1.26 % (2411957)Refutation found. Thanks to Tanya!
% 2.93/1.26 % SZS status Theorem for theBenchmark
% 2.93/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.46 % (2411957)------------------------------
% 3.54/1.46 % (2411957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.46 % (2411957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.46 % (2411957)CaDiCaL version: 2.1.3
% 3.54/1.46 % (2411957)Termination reason: Refutation
% 3.54/1.46 % (2411957)Time elapsed: 0.005 s
% 3.54/1.46 % (2411957)Peak memory usage: 89 MB
% 3.54/1.46 % (2411957)Instructions burned: 6 (million)
% 3.54/1.46 % (2411957)------------------------------
% 3.54/1.46 % (2411957)------------------------------
% 3.54/1.46 % (2411946)Success in time 0.417 s
% 3.54/1.46 % Vampire exiting
%------------------------------------------------------------------------------