%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC412+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 01:05:56 PM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 155 ( 14 unt; 10 def)
% Number of atoms : 484 ( 80 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 537 ( 208 ~; 262 |; 35 &)
% ( 10 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 133 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X3 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) ) )
& ( ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(app(cons(X11,nil),X12),cons(X10,nil)) != X2
& app(app(cons(X10,nil),X12),cons(X11,nil)) = X3 ) ) )
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssItem(X14)
=> ! [X15] :
( ssList(X15)
=> app(app(cons(X13,nil),cons(X14,nil)),X15) != X1 ) ) )
| ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ~ ssList(X18)
| app(app(cons(X16,nil),X18),cons(X17,nil)) != X1
| app(app(cons(X17,nil),X18),cons(X16,nil)) = X0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(app(cons(X4,nil),cons(X5,nil)),X6) = X3 ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> app(app(cons(X7,nil),cons(X8,nil)),X9) != X1 ) ) ) )
& ( ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(app(cons(X11,nil),X12),cons(X10,nil)) != X2
& app(app(cons(X10,nil),X12),cons(X11,nil)) = X3 ) ) )
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssItem(X14)
=> ! [X15] :
( ssList(X15)
=> app(app(cons(X13,nil),cons(X14,nil)),X15) != X1 ) ) )
| ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssItem(X17)
=> ! [X18] :
( ~ ssList(X18)
| app(app(cons(X16,nil),X18),cons(X17,nil)) != X1
| app(app(cons(X17,nil),X18),cons(X16,nil)) = X0 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ( ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(cons(X4,nil),cons(X5,nil)),X6) != X3 ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
& ssList(X9) )
& ssItem(X8) )
& ssItem(X7) ) )
| ( ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssItem(X11)
| ! [X12] :
( ~ ssList(X12)
| app(app(cons(X11,nil),X12),cons(X10,nil)) = X2
| app(app(cons(X10,nil),X12),cons(X11,nil)) != X3 ) ) )
& ? [X13] :
( ? [X14] :
( ? [X15] :
( app(app(cons(X13,nil),cons(X14,nil)),X15) = X1
& ssList(X15) )
& ssItem(X14) )
& ssItem(X13) )
& ? [X16] :
( ? [X17] :
( ? [X18] :
( ssList(X18)
& app(app(cons(X16,nil),X18),cons(X17,nil)) = X1
& app(app(cons(X17,nil),X18),cons(X16,nil)) != X0 )
& ssItem(X17) )
& ssItem(X16) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f410,plain,
! [X3,X6,X4,X5] :
( app(app(cons(X4,nil),cons(X5,nil)),X6) != X3
| ~ ssList(X6)
| ~ sP61(X6,X5,X4,X3) ),
inference(cnf_transformation,[],[f221]) ).
fof(f411,plain,
! [X1,X8,X9,X7] :
( ssList(X9)
| ~ sP60(X9,X8,X7,X1) ),
inference(cnf_transformation,[],[f221]) ).
fof(f412,plain,
! [X1,X8,X9,X7] :
( app(app(cons(X7,nil),cons(X8,nil)),X9) = X1
| ~ sP60(X9,X8,X7,X1) ),
inference(cnf_transformation,[],[f221]) ).
fof(f413,plain,
! [X10,X11,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssItem(X10)
| ssItem(sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f414,plain,
! [X10,X11,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssItem(X10)
| sP60(sK59,sK56,sK53,sK48) ),
inference(cnf_transformation,[],[f221]) ).
fof(f415,plain,
! [X10,X11,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssItem(X10)
| ssItem(sK56) ),
inference(cnf_transformation,[],[f221]) ).
fof(f416,plain,
! [X10,X11,X6,X4,X5,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssItem(X10)
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f425,plain,
( sK47 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ssItem(sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f426,plain,
( sK48 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| ssItem(sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f427,plain,
( ssList(sK57)
| ssItem(sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f428,plain,
( sK47 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| sP60(sK59,sK56,sK53,sK48) ),
inference(cnf_transformation,[],[f221]) ).
fof(f429,plain,
( sK48 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| sP60(sK59,sK56,sK53,sK48) ),
inference(cnf_transformation,[],[f221]) ).
fof(f430,plain,
( ssList(sK57)
| sP60(sK59,sK56,sK53,sK48) ),
inference(cnf_transformation,[],[f221]) ).
fof(f431,plain,
( sK47 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ssItem(sK56) ),
inference(cnf_transformation,[],[f221]) ).
fof(f432,plain,
( sK48 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| ssItem(sK56) ),
inference(cnf_transformation,[],[f221]) ).
fof(f433,plain,
( ssList(sK57)
| ssItem(sK56) ),
inference(cnf_transformation,[],[f221]) ).
fof(f434,plain,
! [X6,X4,X5] :
( sK47 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f435,plain,
! [X6,X4,X5] :
( sK48 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f436,plain,
! [X6,X4,X5] :
( ssList(sK57)
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f438,plain,
! [X6,X4,X5] :
( ssItem(sK51)
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f439,plain,
! [X6,X4,X5] :
( ssItem(sK54)
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f443,plain,
( ssItem(sK51)
| ssItem(sK56) ),
inference(cnf_transformation,[],[f221]) ).
fof(f444,plain,
( ssItem(sK51)
| sP60(sK59,sK56,sK53,sK48) ),
inference(cnf_transformation,[],[f221]) ).
fof(f445,plain,
( ssItem(sK54)
| ssItem(sK56) ),
inference(cnf_transformation,[],[f221]) ).
fof(f446,plain,
( ssItem(sK54)
| sP60(sK59,sK56,sK53,sK48) ),
inference(cnf_transformation,[],[f221]) ).
fof(f450,plain,
( ssItem(sK54)
| ssItem(sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f451,plain,
( ssItem(sK51)
| ssItem(sK53) ),
inference(cnf_transformation,[],[f221]) ).
fof(f453,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f221]) ).
fof(f454,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f221]) ).
fof(f462,plain,
( ssItem(sK54)
| sP60(sK59,sK56,sK53,sK50) ),
inference(definition_unfolding,[],[f446,f454]) ).
fof(f463,plain,
( ssItem(sK51)
| sP60(sK59,sK56,sK53,sK50) ),
inference(definition_unfolding,[],[f444,f454]) ).
fof(f465,plain,
! [X6,X4,X5] :
( sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f435,f454]) ).
fof(f466,plain,
! [X6,X4,X5] :
( sK49 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f434,f453]) ).
fof(f467,plain,
( sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| ssItem(sK56) ),
inference(definition_unfolding,[],[f432,f454]) ).
fof(f468,plain,
( sK49 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ssItem(sK56) ),
inference(definition_unfolding,[],[f431,f453]) ).
fof(f469,plain,
( ssList(sK57)
| sP60(sK59,sK56,sK53,sK50) ),
inference(definition_unfolding,[],[f430,f454]) ).
fof(f470,plain,
( sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| sP60(sK59,sK56,sK53,sK50) ),
inference(definition_unfolding,[],[f429,f454,f454]) ).
fof(f471,plain,
( sK49 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| sP60(sK59,sK56,sK53,sK50) ),
inference(definition_unfolding,[],[f428,f453,f454]) ).
fof(f472,plain,
( sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| ssItem(sK53) ),
inference(definition_unfolding,[],[f426,f454]) ).
fof(f473,plain,
( sK49 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ssItem(sK53) ),
inference(definition_unfolding,[],[f425,f453]) ).
fof(f479,plain,
! [X10,X11,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssItem(X10)
| sP60(sK59,sK56,sK53,sK50) ),
inference(definition_unfolding,[],[f414,f454]) ).
fof(f505,plain,
! [X6,X4,X5] :
( ~ ssList(X6)
| ~ sP61(X6,X5,X4,app(app(cons(X4,nil),cons(X5,nil)),X6)) ),
inference(equality_resolution,[],[f410]) ).
fof(f559,plain,
( ssItem(sK54)
| ~ sP60(sK59,sK56,sK53,sK50) ),
inference(consistent_polarity_flipping,[],[f462]) ).
fof(f560,plain,
( ssItem(sK51)
| ~ sP60(sK59,sK56,sK53,sK50) ),
inference(consistent_polarity_flipping,[],[f463]) ).
fof(f563,plain,
! [X6,X4,X5] :
( ssItem(sK54)
| ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f439]) ).
fof(f564,plain,
! [X6,X4,X5] :
( ssItem(sK51)
| ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f438]) ).
fof(f566,plain,
! [X6,X4,X5] :
( ssList(sK57)
| ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f436]) ).
fof(f567,plain,
! [X6,X4,X5] :
( sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f465]) ).
fof(f568,plain,
! [X6,X4,X5] :
( sK49 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f466]) ).
fof(f569,plain,
( ssList(sK57)
| ~ sP60(sK59,sK56,sK53,sK50) ),
inference(consistent_polarity_flipping,[],[f469]) ).
fof(f570,plain,
( sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| ~ sP60(sK59,sK56,sK53,sK50) ),
inference(consistent_polarity_flipping,[],[f470]) ).
fof(f571,plain,
( sK49 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ~ sP60(sK59,sK56,sK53,sK50) ),
inference(consistent_polarity_flipping,[],[f471]) ).
fof(f576,plain,
! [X10,X11,X6,X4,X5,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssItem(X10)
| ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f416]) ).
fof(f577,plain,
! [X10,X11,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssItem(X10)
| ~ sP60(sK59,sK56,sK53,sK50) ),
inference(consistent_polarity_flipping,[],[f479]) ).
fof(f578,plain,
! [X1,X8,X9,X7] :
( sP60(X9,X8,X7,X1)
| app(app(cons(X7,nil),cons(X8,nil)),X9) = X1 ),
inference(consistent_polarity_flipping,[],[f412]) ).
fof(f579,plain,
! [X1,X8,X9,X7] :
( sP60(X9,X8,X7,X1)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f411]) ).
fof(f580,plain,
! [X6,X4,X5] :
( sP61(X6,X5,X4,app(app(cons(X4,nil),cons(X5,nil)),X6))
| ~ ssList(X6) ),
inference(consistent_polarity_flipping,[],[f505]) ).
fof(f589,definition,
( spl62_1
<=> ssItem(sK53) ),
introduced(definition,[new_symbols(definition,[spl62_1])],[avatar_definition]) ).
fof(f591,plain,
( ssItem(sK53)
| ~ spl62_1 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f593,definition,
( spl62_2
<=> ! [X12,X11,X10] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| ~ ssItem(X10)
| ~ ssItem(X11)
| ~ ssList(X12)
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49 ) ),
introduced(definition,[new_symbols(definition,[spl62_2])],[avatar_definition]) ).
fof(f594,plain,
( ! [X10,X11,X12] :
( app(app(cons(X10,nil),X12),cons(X11,nil)) != sK50
| ~ ssItem(X10)
| ~ ssItem(X11)
| ~ ssList(X12)
| app(app(cons(X11,nil),X12),cons(X10,nil)) = sK49 )
| ~ spl62_2 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f595,plain,
( spl62_1
| spl62_2 ),
inference(avatar_split_clause,[],[f413,f593,f589]) ).
fof(f597,definition,
( spl62_3
<=> sP60(sK59,sK56,sK53,sK50) ),
introduced(definition,[new_symbols(definition,[spl62_3])],[avatar_definition]) ).
fof(f599,plain,
( ~ sP60(sK59,sK56,sK53,sK50)
| spl62_3 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f600,plain,
( ~ spl62_3
| spl62_2 ),
inference(avatar_split_clause,[],[f577,f593,f597]) ).
fof(f602,definition,
( spl62_4
<=> ssItem(sK56) ),
introduced(definition,[new_symbols(definition,[spl62_4])],[avatar_definition]) ).
fof(f604,plain,
( ssItem(sK56)
| ~ spl62_4 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f605,plain,
( spl62_4
| spl62_2 ),
inference(avatar_split_clause,[],[f415,f593,f602]) ).
fof(f607,definition,
( spl62_5
<=> ! [X6,X4,X5] :
( ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X4)
| ~ ssItem(X5) ) ),
introduced(definition,[new_symbols(definition,[spl62_5])],[avatar_definition]) ).
fof(f608,plain,
( ! [X6,X4,X5] :
( ~ sP61(X6,X5,X4,sK50)
| ~ ssItem(X4)
| ~ ssItem(X5) )
| ~ spl62_5 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f609,plain,
( spl62_5
| spl62_2 ),
inference(avatar_split_clause,[],[f576,f593,f607]) ).
fof(f627,definition,
( spl62_8
<=> sK49 = app(app(cons(sK54,nil),sK57),cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl62_8])],[avatar_definition]) ).
fof(f629,plain,
( sK49 != app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| spl62_8 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f630,plain,
( spl62_1
| ~ spl62_8 ),
inference(avatar_split_clause,[],[f473,f627,f589]) ).
fof(f632,definition,
( spl62_9
<=> sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil)) ),
introduced(definition,[new_symbols(definition,[spl62_9])],[avatar_definition]) ).
fof(f634,plain,
( sK50 = app(app(cons(sK51,nil),sK57),cons(sK54,nil))
| ~ spl62_9 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f635,plain,
( spl62_1
| spl62_9 ),
inference(avatar_split_clause,[],[f472,f632,f589]) ).
fof(f637,definition,
( spl62_10
<=> ssList(sK57) ),
introduced(definition,[new_symbols(definition,[spl62_10])],[avatar_definition]) ).
fof(f639,plain,
( ssList(sK57)
| ~ spl62_10 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f640,plain,
( spl62_1
| spl62_10 ),
inference(avatar_split_clause,[],[f427,f637,f589]) ).
fof(f641,plain,
( ~ spl62_3
| ~ spl62_8 ),
inference(avatar_split_clause,[],[f571,f627,f597]) ).
fof(f642,plain,
( ~ spl62_3
| spl62_9 ),
inference(avatar_split_clause,[],[f570,f632,f597]) ).
fof(f643,plain,
( ~ spl62_3
| spl62_10 ),
inference(avatar_split_clause,[],[f569,f637,f597]) ).
fof(f644,plain,
( spl62_4
| ~ spl62_8 ),
inference(avatar_split_clause,[],[f468,f627,f602]) ).
fof(f645,plain,
( spl62_4
| spl62_9 ),
inference(avatar_split_clause,[],[f467,f632,f602]) ).
fof(f646,plain,
( spl62_4
| spl62_10 ),
inference(avatar_split_clause,[],[f433,f637,f602]) ).
fof(f647,plain,
( spl62_5
| ~ spl62_8 ),
inference(avatar_split_clause,[],[f568,f627,f607]) ).
fof(f648,plain,
( spl62_5
| spl62_9 ),
inference(avatar_split_clause,[],[f567,f632,f607]) ).
fof(f649,plain,
( spl62_5
| spl62_10 ),
inference(avatar_split_clause,[],[f566,f637,f607]) ).
fof(f656,definition,
( spl62_12
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl62_12])],[avatar_definition]) ).
fof(f658,plain,
( ssItem(sK51)
| ~ spl62_12 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f659,plain,
( spl62_5
| spl62_12 ),
inference(avatar_split_clause,[],[f564,f656,f607]) ).
fof(f661,definition,
( spl62_13
<=> ssItem(sK54) ),
introduced(definition,[new_symbols(definition,[spl62_13])],[avatar_definition]) ).
fof(f664,plain,
( spl62_5
| spl62_13 ),
inference(avatar_split_clause,[],[f563,f661,f607]) ).
fof(f672,plain,
( spl62_4
| spl62_12 ),
inference(avatar_split_clause,[],[f443,f656,f602]) ).
fof(f673,plain,
( ~ spl62_3
| spl62_12 ),
inference(avatar_split_clause,[],[f560,f656,f597]) ).
fof(f674,plain,
( spl62_4
| spl62_13 ),
inference(avatar_split_clause,[],[f445,f661,f602]) ).
fof(f675,plain,
( ~ spl62_3
| spl62_13 ),
inference(avatar_split_clause,[],[f559,f661,f597]) ).
fof(f679,plain,
( spl62_1
| spl62_13 ),
inference(avatar_split_clause,[],[f450,f661,f589]) ).
fof(f680,plain,
( spl62_1
| spl62_12 ),
inference(avatar_split_clause,[],[f451,f656,f589]) ).
fof(f717,plain,
( ssList(sK59)
| spl62_3 ),
inference(resolution,[],[f579,f599]) ).
fof(f720,plain,
( sK50 = app(app(cons(sK53,nil),cons(sK56,nil)),sK59)
| spl62_3 ),
inference(resolution,[],[f578,f599]) ).
fof(f721,plain,
( sP61(sK59,sK56,sK53,sK50)
| ~ ssList(sK59)
| spl62_3 ),
inference(superposition,[],[f580,f720]) ).
fof(f722,plain,
( sP61(sK59,sK56,sK53,sK50)
| spl62_3 ),
inference(forward_subsumption_resolution,[],[f721,f717]) ).
fof(f723,plain,
( sK50 != sK50
| ~ ssItem(sK51)
| ~ ssItem(sK54)
| ~ ssList(sK57)
| sK49 = app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ~ spl62_2
| ~ spl62_9 ),
inference(superposition,[],[f594,f634]) ).
fof(f724,plain,
( ~ ssItem(sK51)
| ~ ssItem(sK54)
| ~ ssList(sK57)
| sK49 = app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ~ spl62_2
| ~ spl62_9 ),
inference(trivial_inequality_removal,[],[f723]) ).
fof(f725,plain,
( ~ ssItem(sK54)
| ~ ssList(sK57)
| sK49 = app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ~ spl62_2
| ~ spl62_9
| ~ spl62_12 ),
inference(forward_subsumption_resolution,[],[f724,f658]) ).
fof(f730,plain,
( ~ ssItem(sK54)
| sK49 = app(app(cons(sK54,nil),sK57),cons(sK51,nil))
| ~ spl62_2
| ~ spl62_9
| ~ spl62_10
| ~ spl62_12 ),
inference(forward_subsumption_resolution,[],[f725,f639]) ).
fof(f731,plain,
( ~ ssItem(sK54)
| ~ spl62_2
| spl62_8
| ~ spl62_9
| ~ spl62_10
| ~ spl62_12 ),
inference(forward_subsumption_resolution,[],[f730,f629]) ).
fof(f732,plain,
( ~ spl62_13
| ~ spl62_2
| spl62_8
| ~ spl62_9
| ~ spl62_10
| ~ spl62_12 ),
inference(avatar_split_clause,[],[f731,f656,f637,f632,f627,f593,f661]) ).
fof(f734,plain,
( ~ ssItem(sK53)
| ~ ssItem(sK56)
| spl62_3
| ~ spl62_5 ),
inference(resolution,[],[f608,f722]) ).
fof(f735,plain,
( ~ ssItem(sK56)
| ~ spl62_1
| spl62_3
| ~ spl62_5 ),
inference(forward_subsumption_resolution,[],[f734,f591]) ).
fof(f737,plain,
( $false
| ~ spl62_1
| spl62_3
| ~ spl62_4
| ~ spl62_5 ),
inference(forward_subsumption_resolution,[],[f735,f604]) ).
fof(f738,plain,
( ~ spl62_1
| spl62_3
| ~ spl62_4
| ~ spl62_5 ),
inference(avatar_contradiction_clause,[],[f737]) ).
cnf(s1,plain,
( spl62_1
| spl62_2 ),
inference(sat_conversion,[],[f595]) ).
cnf(s2,plain,
( spl62_2
| ~ spl62_3 ),
inference(sat_conversion,[],[f600]) ).
cnf(s3,plain,
( spl62_2
| spl62_4 ),
inference(sat_conversion,[],[f605]) ).
cnf(s4,plain,
( spl62_2
| spl62_5 ),
inference(sat_conversion,[],[f609]) ).
cnf(s13,plain,
( spl62_1
| ~ spl62_8 ),
inference(sat_conversion,[],[f630]) ).
cnf(s14,plain,
( spl62_1
| spl62_9 ),
inference(sat_conversion,[],[f635]) ).
cnf(s15,plain,
( spl62_1
| spl62_10 ),
inference(sat_conversion,[],[f640]) ).
cnf(s16,plain,
( ~ spl62_3
| ~ spl62_8 ),
inference(sat_conversion,[],[f641]) ).
cnf(s17,plain,
( ~ spl62_3
| spl62_9 ),
inference(sat_conversion,[],[f642]) ).
cnf(s18,plain,
( ~ spl62_3
| spl62_10 ),
inference(sat_conversion,[],[f643]) ).
cnf(s19,plain,
( spl62_4
| ~ spl62_8 ),
inference(sat_conversion,[],[f644]) ).
cnf(s20,plain,
( spl62_4
| spl62_9 ),
inference(sat_conversion,[],[f645]) ).
cnf(s21,plain,
( spl62_4
| spl62_10 ),
inference(sat_conversion,[],[f646]) ).
cnf(s22,plain,
( spl62_5
| ~ spl62_8 ),
inference(sat_conversion,[],[f647]) ).
cnf(s23,plain,
( spl62_5
| spl62_9 ),
inference(sat_conversion,[],[f648]) ).
cnf(s24,plain,
( spl62_5
| spl62_10 ),
inference(sat_conversion,[],[f649]) ).
cnf(s26,plain,
( spl62_5
| spl62_12 ),
inference(sat_conversion,[],[f659]) ).
cnf(s27,plain,
( spl62_5
| spl62_13 ),
inference(sat_conversion,[],[f664]) ).
cnf(s31,plain,
( spl62_4
| spl62_12 ),
inference(sat_conversion,[],[f672]) ).
cnf(s32,plain,
( ~ spl62_3
| spl62_12 ),
inference(sat_conversion,[],[f673]) ).
cnf(s33,plain,
( spl62_4
| spl62_13 ),
inference(sat_conversion,[],[f674]) ).
cnf(s34,plain,
( ~ spl62_3
| spl62_13 ),
inference(sat_conversion,[],[f675]) ).
cnf(s38,plain,
( spl62_1
| spl62_13 ),
inference(sat_conversion,[],[f679]) ).
cnf(s39,plain,
( spl62_1
| spl62_12 ),
inference(sat_conversion,[],[f680]) ).
cnf(s51,plain,
( ~ spl62_2
| spl62_8
| ~ spl62_9
| ~ spl62_10
| ~ spl62_12
| ~ spl62_13 ),
inference(sat_conversion,[],[f732]) ).
cnf(s52,plain,
( ~ spl62_1
| spl62_3
| ~ spl62_4
| ~ spl62_5 ),
inference(sat_conversion,[],[f738]) ).
cnf(s58,plain,
spl62_1,
inference(rat,[],[s51,s1,s13,s14,s15,s38,s39]) ).
cnf(s59,plain,
spl62_2,
inference(rat,[],[s52,s2,s3,s4,s58]) ).
cnf(s60,plain,
spl62_5,
inference(rat,[],[s51,s22,s23,s24,s26,s27,s59]) ).
cnf(s61,plain,
spl62_4,
inference(rat,[],[s51,s19,s20,s21,s31,s33,s59]) ).
cnf(s62,plain,
spl62_3,
inference(rat,[],[s52,s60,s58,s61]) ).
cnf(s64,plain,
spl62_13,
inference(rat,[],[s34,s62]) ).
cnf(s65,plain,
spl62_12,
inference(rat,[],[s32,s62]) ).
cnf(s67,plain,
spl62_10,
inference(rat,[],[s18,s62]) ).
cnf(s68,plain,
spl62_9,
inference(rat,[],[s17,s62]) ).
cnf(s69,plain,
~ spl62_8,
inference(rat,[],[s16,s62]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s51,s64,s65,s67,s59,s68,s69]) ).
fof(f741,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC412+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 09:29:55 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.28 % (2267444)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (2267451)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4217335395:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (2267450)% WARNING: option uhcvi not known.
% 0.19/0.28 % (2267449)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2021399588_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (2267450)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3694978111:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (2267452)dis+10_1_sil=32000:sp=arity:random_seed=3390510414:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (2267453)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4010594000:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (2267454)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1269412175:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (2267455)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2187887358:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (2267450) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2267444-2267450"...
% 0.19/0.28 % (2267450)...printing done.
% 0.19/0.28 % (2267450)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (2267450)------------------------------
% 0.19/0.29 % (2267450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2267450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2267450)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2267450)Termination reason: Refutation
% 0.19/0.29 % (2267450)Time elapsed: 0.011 s
% 0.19/0.29 % (2267450)Peak memory usage: 13 MB
% 0.19/0.29 % (2267450)Instructions burned: 17 (million)
% 0.19/0.29 % (2267444)Success in time 0.05 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------