%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS144+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 11:42:22 AM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 183 ( 13 unt; 23 def)
% Number of atoms : 693 ( 127 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 773 ( 263 ~; 378 |; 90 &)
% ( 26 <=>; 13 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 24 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 155 ( 0 sgn 106 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( cowlThing(X0)
& ~ cowlNothing(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
fof(f9,axiom,
! [X0] :
( xsd_string(X0)
<=> ~ xsd_integer(X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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_integer(X0)
| ~ xsd_string(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] :
( rp(X0,sK2(X0))
| ~ cc(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0] :
( rp(X0,sK1(X0))
| ~ cc(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(f80,plain,
! [X0] :
( xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f81,plain,
! [X0] :
( ~ xsd_string(X0)
| xsd_integer(X0) ),
inference(consistent_polarity_flipping,[],[f52]) ).
fof(f82,plain,
! [X0] :
( ~ rp(X0,sK1(X0))
| cc(X0) ),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f83,plain,
! [X0] :
( ~ rp(X0,sK2(X0))
| cc(X0) ),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f84,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| cc(X0) ),
inference(consistent_polarity_flipping,[],[f55]) ).
fof(f85,plain,
! [X3,X0,X4,X5] :
( cc(X0)
| X3 = X5
| X4 = X5
| rp(X0,X3)
| rp(X0,X4)
| rp(X0,X5)
| X3 = X4 ),
inference(consistent_polarity_flipping,[],[f54]) ).
fof(f86,plain,
( sK4 != sK5
| sP0 ),
inference(consistent_polarity_flipping,[],[f64]) ).
fof(f87,plain,
( sK4 != sK6
| sP0 ),
inference(consistent_polarity_flipping,[],[f63]) ).
fof(f88,plain,
( sK5 != sK6
| sP0 ),
inference(consistent_polarity_flipping,[],[f62]) ).
fof(f89,plain,
( ~ rp(sK3,sK4)
| sP0 ),
inference(consistent_polarity_flipping,[],[f61]) ).
fof(f90,plain,
( ~ rp(sK3,sK5)
| sP0 ),
inference(consistent_polarity_flipping,[],[f60]) ).
fof(f91,plain,
( ~ rp(sK3,sK6)
| sP0 ),
inference(consistent_polarity_flipping,[],[f59]) ).
fof(f92,plain,
( ~ cc(sK3)
| sP0 ),
inference(consistent_polarity_flipping,[],[f58]) ).
fof(f93,plain,
! [X3,X4] :
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| ~ xsd_integer(sK8)
| ~ xsd_string(sK8)
| ~ sP0
| rp(sK9,X3)
| rp(sK9,X4)
| X3 = X4 ),
inference(consistent_polarity_flipping,[],[f68]) ).
fof(f94,plain,
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| ~ xsd_integer(sK8)
| ~ xsd_string(sK8)
| ~ sP0
| ~ cc(sK9) ),
inference(consistent_polarity_flipping,[],[f67]) ).
fof(f95,plain,
! [X3,X4] :
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| xsd_integer(sK8)
| xsd_string(sK8)
| ~ sP0
| rp(sK9,X3)
| rp(sK9,X4)
| X3 = X4 ),
inference(consistent_polarity_flipping,[],[f66]) ).
fof(f96,plain,
( ~ cowlThing(sK7)
| cowlNothing(sK7)
| xsd_integer(sK8)
| xsd_string(sK8)
| ~ sP0
| ~ cc(sK9) ),
inference(consistent_polarity_flipping,[],[f65]) ).
fof(f98,definition,
( spl10_1
<=> cc(sK9) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f102,definition,
( spl10_2
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f106,definition,
( spl10_3
<=> xsd_string(sK8) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f107,plain,
( ~ xsd_string(sK8)
| spl10_3 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f108,plain,
( xsd_string(sK8)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl10_4
<=> xsd_integer(sK8) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f114,definition,
( spl10_5
<=> cowlNothing(sK7) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f116,plain,
( cowlNothing(sK7)
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl10_6
<=> cowlThing(sK7) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f120,plain,
( ~ cowlThing(sK7)
| spl10_6 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( ~ spl10_1
| ~ spl10_2
| spl10_3
| spl10_4
| spl10_5
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f96,f118,f114,f110,f106,f102,f98]) ).
fof(f123,definition,
( spl10_7
<=> ! [X4,X3] :
( rp(sK9,X3)
| X3 = X4
| rp(sK9,X4) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
fof(f124,plain,
( ! [X3,X4] :
( rp(sK9,X4)
| X3 = X4
| rp(sK9,X3) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( spl10_7
| ~ spl10_2
| spl10_3
| spl10_4
| spl10_5
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f95,f118,f114,f110,f106,f102,f123]) ).
fof(f126,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_3
| ~ spl10_4
| spl10_5
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f94,f118,f114,f110,f106,f102,f98]) ).
fof(f127,plain,
( spl10_7
| ~ spl10_2
| ~ spl10_3
| ~ spl10_4
| spl10_5
| ~ spl10_6 ),
inference(avatar_split_clause,[],[f93,f118,f114,f110,f106,f102,f123]) ).
fof(f129,definition,
( spl10_8
<=> cc(sK3) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
fof(f131,plain,
( ~ cc(sK3)
| spl10_8 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl10_2
| ~ spl10_8 ),
inference(avatar_split_clause,[],[f92,f129,f102]) ).
fof(f134,definition,
( spl10_9
<=> rp(sK3,sK6) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
fof(f136,plain,
( ~ rp(sK3,sK6)
| spl10_9 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl10_2
| ~ spl10_9 ),
inference(avatar_split_clause,[],[f91,f134,f102]) ).
fof(f139,definition,
( spl10_10
<=> rp(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
fof(f141,plain,
( ~ rp(sK3,sK5)
| spl10_10 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl10_2
| ~ spl10_10 ),
inference(avatar_split_clause,[],[f90,f139,f102]) ).
fof(f144,definition,
( spl10_11
<=> rp(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
fof(f146,plain,
( ~ rp(sK3,sK4)
| spl10_11 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl10_2
| ~ spl10_11 ),
inference(avatar_split_clause,[],[f89,f144,f102]) ).
fof(f149,definition,
( spl10_12
<=> sK5 = sK6 ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
fof(f152,plain,
( spl10_2
| ~ spl10_12 ),
inference(avatar_split_clause,[],[f88,f149,f102]) ).
fof(f154,definition,
( spl10_13
<=> sK4 = sK6 ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
fof(f157,plain,
( spl10_2
| ~ spl10_13 ),
inference(avatar_split_clause,[],[f87,f154,f102]) ).
fof(f159,definition,
( spl10_14
<=> sK4 = sK5 ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
fof(f162,plain,
( spl10_2
| ~ spl10_14 ),
inference(avatar_split_clause,[],[f86,f159,f102]) ).
fof(f163,plain,
( $false
| spl10_6 ),
inference(resolution,[],[f51,f120]) ).
fof(f164,plain,
spl10_6,
inference(avatar_contradiction_clause,[],[f163]) ).
fof(f165,plain,
( ~ xsd_integer(sK8)
| spl10_3 ),
inference(resolution,[],[f80,f107]) ).
fof(f168,plain,
( ! [X2,X0,X1] :
( rp(sK3,X2)
| X1 = X2
| rp(sK3,X0)
| X0 = X1
| rp(sK3,X1)
| X0 = X2 )
| spl10_8 ),
inference(resolution,[],[f85,f131]) ).
fof(f183,plain,
( ! [X0,X1] :
( sK2(sK3) = X0
| rp(sK3,X1)
| X0 = X1
| rp(sK3,X0)
| sK2(sK3) = X1
| cc(sK3) )
| spl10_8 ),
inference(resolution,[],[f168,f83]) ).
fof(f185,definition,
( spl10_17
<=> ! [X0,X1] :
( sK2(sK3) = X0
| sK2(sK3) = X1
| rp(sK3,X0)
| X0 = X1
| rp(sK3,X1) ) ),
introduced(definition,[new_symbols(definition,[spl10_17])],[avatar_definition]) ).
fof(f186,plain,
( ! [X0,X1] :
( rp(sK3,X1)
| sK2(sK3) = X1
| rp(sK3,X0)
| X0 = X1
| sK2(sK3) = X0 )
| ~ spl10_17 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f187,plain,
( spl10_8
| spl10_17
| spl10_8 ),
inference(avatar_split_clause,[],[f183,f129,f185,f129]) ).
fof(f192,plain,
( xsd_integer(sK8)
| ~ spl10_3 ),
inference(resolution,[],[f108,f81]) ).
fof(f193,plain,
( spl10_4
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f192,f106,f110]) ).
fof(f194,plain,
( $false
| ~ spl10_5 ),
inference(resolution,[],[f116,f50]) ).
fof(f195,plain,
~ spl10_5,
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f212,definition,
( spl10_21
<=> ! [X0] :
( rp(sK3,X0)
| sK2(sK3) = X0
| sK4 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl10_21])],[avatar_definition]) ).
fof(f213,plain,
( ! [X0] :
( rp(sK3,X0)
| sK2(sK3) = X0
| sK4 = X0 )
| ~ spl10_21 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,definition,
( spl10_22
<=> sK4 = sK2(sK3) ),
introduced(definition,[new_symbols(definition,[spl10_22])],[avatar_definition]) ).
fof(f217,plain,
( sK4 = sK2(sK3)
| ~ spl10_22 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f220,definition,
( spl10_23
<=> ! [X0] :
( rp(sK3,X0)
| sK2(sK3) = X0
| sK5 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl10_23])],[avatar_definition]) ).
fof(f221,plain,
( ! [X0] :
( rp(sK3,X0)
| sK2(sK3) = X0
| sK5 = X0 )
| ~ spl10_23 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f223,definition,
( spl10_24
<=> sK5 = sK2(sK3) ),
introduced(definition,[new_symbols(definition,[spl10_24])],[avatar_definition]) ).
fof(f225,plain,
( sK5 = sK2(sK3)
| ~ spl10_24 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f231,definition,
( spl10_26
<=> sK6 = sK2(sK3) ),
introduced(definition,[new_symbols(definition,[spl10_26])],[avatar_definition]) ).
fof(f233,plain,
( sK6 = sK2(sK3)
| ~ spl10_26 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,plain,
( ~ spl10_4
| spl10_3 ),
inference(avatar_split_clause,[],[f165,f106,f110]) ).
fof(f242,plain,
( ! [X0] :
( sK5 = sK2(sK3)
| rp(sK3,X0)
| sK5 = X0
| sK2(sK3) = X0 )
| spl10_10
| ~ spl10_17 ),
inference(resolution,[],[f141,f186]) ).
fof(f243,plain,
( ! [X0] :
( sK4 = sK2(sK3)
| rp(sK3,X0)
| sK4 = X0
| sK2(sK3) = X0 )
| spl10_11
| ~ spl10_17 ),
inference(resolution,[],[f146,f186]) ).
fof(f244,plain,
( sK6 = sK2(sK3)
| sK4 = sK6
| spl10_9
| ~ spl10_21 ),
inference(resolution,[],[f213,f136]) ).
fof(f245,plain,
( sK5 = sK2(sK3)
| sK4 = sK5
| spl10_10
| ~ spl10_21 ),
inference(resolution,[],[f213,f141]) ).
fof(f254,plain,
( spl10_14
| spl10_24
| spl10_10
| ~ spl10_21 ),
inference(avatar_split_clause,[],[f245,f212,f139,f223,f159]) ).
fof(f261,plain,
( sK6 = sK2(sK3)
| sK5 = sK6
| spl10_9
| ~ spl10_23 ),
inference(resolution,[],[f221,f136]) ).
fof(f271,plain,
( spl10_12
| spl10_26
| spl10_9
| ~ spl10_23 ),
inference(avatar_split_clause,[],[f261,f220,f134,f231,f149]) ).
fof(f273,plain,
( sK4 = sK5
| ~ spl10_22
| ~ spl10_24 ),
inference(superposition,[],[f217,f225]) ).
fof(f278,plain,
( spl10_14
| ~ spl10_22
| ~ spl10_24 ),
inference(avatar_split_clause,[],[f273,f223,f215,f159]) ).
fof(f279,plain,
( spl10_13
| spl10_26
| spl10_9
| ~ spl10_21 ),
inference(avatar_split_clause,[],[f244,f212,f134,f231,f154]) ).
fof(f283,plain,
( sK5 = sK6
| ~ spl10_24
| ~ spl10_26 ),
inference(superposition,[],[f225,f233]) ).
fof(f291,plain,
( spl10_12
| ~ spl10_24
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f283,f231,f223,f149]) ).
fof(f294,plain,
( ! [X0] :
( sK2(sK9) = X0
| rp(sK9,X0)
| cc(sK9) )
| ~ spl10_7 ),
inference(resolution,[],[f124,f83]) ).
fof(f296,definition,
( spl10_30
<=> ! [X0] :
( sK2(sK9) = X0
| rp(sK9,X0) ) ),
introduced(definition,[new_symbols(definition,[spl10_30])],[avatar_definition]) ).
fof(f297,plain,
( ! [X0] :
( rp(sK9,X0)
| sK2(sK9) = X0 )
| ~ spl10_30 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( spl10_1
| spl10_30
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f294,f123,f296,f98]) ).
fof(f303,plain,
( sK1(sK9) = sK2(sK9)
| cc(sK9)
| ~ spl10_30 ),
inference(resolution,[],[f297,f82]) ).
fof(f306,definition,
( spl10_32
<=> sK1(sK9) = sK2(sK9) ),
introduced(definition,[new_symbols(definition,[spl10_32])],[avatar_definition]) ).
fof(f308,plain,
( sK1(sK9) = sK2(sK9)
| ~ spl10_32 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f309,plain,
( spl10_1
| spl10_32
| ~ spl10_30 ),
inference(avatar_split_clause,[],[f303,f296,f306,f98]) ).
fof(f310,plain,
( sK1(sK9) != sK1(sK9)
| cc(sK9)
| ~ spl10_32 ),
inference(superposition,[],[f84,f308]) ).
fof(f312,plain,
( cc(sK9)
| ~ spl10_32 ),
inference(trivial_inequality_removal,[],[f310]) ).
fof(f313,plain,
( spl10_1
| ~ spl10_32 ),
inference(avatar_split_clause,[],[f312,f306,f98]) ).
fof(f316,plain,
( spl10_23
| spl10_24
| spl10_10
| ~ spl10_17 ),
inference(avatar_split_clause,[],[f242,f185,f139,f223,f220]) ).
fof(f317,plain,
( spl10_21
| spl10_22
| spl10_11
| ~ spl10_17 ),
inference(avatar_split_clause,[],[f243,f185,f144,f215,f212]) ).
fof(f337,plain,
( sK4 = sK6
| ~ spl10_22
| ~ spl10_26 ),
inference(superposition,[],[f233,f217]) ).
fof(f340,plain,
( spl10_13
| ~ spl10_22
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f337,f231,f215,f154]) ).
cnf(s1,plain,
( ~ spl10_1
| ~ spl10_2
| spl10_3
| spl10_4
| spl10_5
| ~ spl10_6 ),
inference(sat_conversion,[],[f121]) ).
cnf(s2,plain,
( ~ spl10_2
| spl10_3
| spl10_4
| spl10_5
| ~ spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f125]) ).
cnf(s3,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_3
| ~ spl10_4
| spl10_5
| ~ spl10_6 ),
inference(sat_conversion,[],[f126]) ).
cnf(s4,plain,
( ~ spl10_2
| ~ spl10_3
| ~ spl10_4
| spl10_5
| ~ spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
( spl10_2
| ~ spl10_8 ),
inference(sat_conversion,[],[f132]) ).
cnf(s6,plain,
( spl10_2
| ~ spl10_9 ),
inference(sat_conversion,[],[f137]) ).
cnf(s7,plain,
( spl10_2
| ~ spl10_10 ),
inference(sat_conversion,[],[f142]) ).
cnf(s8,plain,
( spl10_2
| ~ spl10_11 ),
inference(sat_conversion,[],[f147]) ).
cnf(s9,plain,
( spl10_2
| ~ spl10_12 ),
inference(sat_conversion,[],[f152]) ).
cnf(s10,plain,
( spl10_2
| ~ spl10_13 ),
inference(sat_conversion,[],[f157]) ).
cnf(s11,plain,
( spl10_2
| ~ spl10_14 ),
inference(sat_conversion,[],[f162]) ).
cnf(s12,plain,
spl10_6,
inference(sat_conversion,[],[f164]) ).
cnf(s17,plain,
( spl10_8
| spl10_8
| spl10_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s18,plain,
( spl10_8
| spl10_17 ),
inference(rat,[],[s17]) ).
cnf(s21,plain,
( ~ spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f193]) ).
cnf(s22,plain,
~ spl10_5,
inference(sat_conversion,[],[f195]) ).
cnf(s27,plain,
( spl10_3
| ~ spl10_4 ),
inference(sat_conversion,[],[f235]) ).
cnf(s32,plain,
( spl10_10
| spl10_14
| ~ spl10_21
| spl10_24 ),
inference(sat_conversion,[],[f254]) ).
cnf(s35,plain,
( spl10_9
| spl10_12
| ~ spl10_23
| spl10_26 ),
inference(sat_conversion,[],[f271]) ).
cnf(s36,plain,
( spl10_14
| ~ spl10_22
| ~ spl10_24 ),
inference(sat_conversion,[],[f278]) ).
cnf(s38,plain,
( spl10_9
| spl10_13
| ~ spl10_21
| spl10_26 ),
inference(sat_conversion,[],[f279]) ).
cnf(s40,plain,
( spl10_12
| ~ spl10_24
| ~ spl10_26 ),
inference(sat_conversion,[],[f291]) ).
cnf(s42,plain,
( spl10_1
| ~ spl10_7
| spl10_30 ),
inference(sat_conversion,[],[f298]) ).
cnf(s44,plain,
( spl10_1
| ~ spl10_30
| spl10_32 ),
inference(sat_conversion,[],[f309]) ).
cnf(s45,plain,
( spl10_1
| ~ spl10_32 ),
inference(sat_conversion,[],[f313]) ).
cnf(s48,plain,
( spl10_10
| ~ spl10_17
| spl10_23
| spl10_24 ),
inference(sat_conversion,[],[f316]) ).
cnf(s49,plain,
( spl10_11
| ~ spl10_17
| spl10_21
| spl10_22 ),
inference(sat_conversion,[],[f317]) ).
cnf(s52,plain,
( spl10_13
| ~ spl10_22
| ~ spl10_26 ),
inference(sat_conversion,[],[f340]) ).
cnf(s54,plain,
( ~ spl10_2
| ~ spl10_3
| ~ spl10_4
| spl10_7 ),
inference(rat,[],[s4,s12,s22]) ).
cnf(s55,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_3
| ~ spl10_4 ),
inference(rat,[],[s3,s12,s22]) ).
cnf(s56,plain,
( ~ spl10_2
| spl10_3
| spl10_4
| spl10_7 ),
inference(rat,[],[s2,s12,s22]) ).
cnf(s57,plain,
( ~ spl10_1
| ~ spl10_2
| spl10_3
| spl10_4 ),
inference(rat,[],[s1,s12,s22]) ).
cnf(s58,plain,
( ~ spl10_22
| spl10_2 ),
inference(rat,[],[s48,s35,s36,s52,s11,s10,s9,s7,s6,s18,s5]) ).
cnf(s59,plain,
spl10_2,
inference(rat,[],[s40,s38,s32,s49,s58,s18,s5,s6,s7,s8,s9,s10,s11]) ).
cnf(s63,plain,
( spl10_3
| spl10_7 ),
inference(rat,[],[s56,s27,s59]) ).
cnf(s64,plain,
spl10_7,
inference(rat,[],[s54,s21,s63,s59]) ).
cnf(s65,plain,
( spl10_1
| spl10_32 ),
inference(rat,[],[s42,s44,s64]) ).
cnf(s66,plain,
spl10_1,
inference(rat,[],[s65,s45]) ).
cnf(s67,plain,
spl10_3,
inference(rat,[],[s57,s27,s66,s59]) ).
cnf(s68,plain,
spl10_4,
inference(rat,[],[s21,s67]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s55,s59,s66,s68,s67]) ).
fof(f341,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 13:28:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.43 % (231879)Will run a generic schedule for satisfiability detection.
% 0.11/0.43 % (231890)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4189722784:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.43 % (231885)% WARNING: option uhcvi not known.
% 0.11/0.43 % (231890) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-231879-231890"...
% 0.11/0.43 % (231890)...printing done.
% 0.11/0.43 % (231890)Refutation found. Thanks to Tanya!
% 0.11/0.43 % SZS status Theorem for theBenchmark
% 0.11/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.43 % (231890)------------------------------
% 0.11/0.43 % (231890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.43 % (231890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.43 % (231890)CaDiCaL version: 2.1.3
% 0.11/0.43 % (231890)Termination reason: Refutation
% 0.11/0.43 % (231890)Time elapsed: 0.005 s
% 0.11/0.43 % (231890)Peak memory usage: 12 MB
% 0.11/0.43 % (231890)Instructions burned: 11 (million)
% 0.11/0.43 % (231879)Success in time 0.029 s
% 0.11/0.43 % Vampire exiting
%------------------------------------------------------------------------------