%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC327+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 01:05:33 PM UTC 2026
% Result : Theorem 0.12s 0.29s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 172 ( 17 unt; 11 def)
% Number of atoms : 734 ( 204 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 998 ( 436 ~; 485 |; 50 &)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 92 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ? [X8] :
( ssList(X8)
& app(X0,X8) = X1
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(cons(X9,nil),X10) != X8
| ! [X11] :
( ssList(X11)
=> app(X11,cons(X9,nil)) != X0 ) ) ) )
& equalelemsP(X0) )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ equalelemsP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssList(X7)
& app(X7,cons(X5,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ? [X8] :
( ssList(X8)
& app(X0,X8) = X1
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ( app(cons(X9,nil),X10) != X8
| ! [X11] :
( ssList(X11)
=> app(X11,cons(X9,nil)) != X0 ) ) ) )
& equalelemsP(X0) )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ! [X8] :
( ~ ssList(X8)
| app(X0,X8) != X1
| ? [X9] :
( ? [X10] :
( app(cons(X9,nil),X10) = X8
& ? [X11] :
( app(X11,cons(X9,nil)) = X0
& ssList(X11) )
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X0) )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( app(X2,X4) = X3
& equalelemsP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X5,nil)) != X2 ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ! [X8] :
( ~ ssList(X8)
| app(X0,X8) != X1
| ? [X9] :
( ? [X10] :
( app(cons(X9,nil),X10) = X8
& ? [X11] :
( app(X11,cons(X9,nil)) = X0
& ssList(X11) )
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X0) )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f411,plain,
! [X8] :
( nil != sK48
| ~ equalelemsP(sK47)
| ssList(sK54(X8))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f412,plain,
! [X8] :
( nil != sK48
| ~ equalelemsP(sK47)
| sK47 = app(sK54(X8),cons(sK52(X8),nil))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
! [X8] :
( nil = sK47
| ~ equalelemsP(sK47)
| ssList(sK54(X8))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
! [X8] :
( nil = sK47
| ~ equalelemsP(sK47)
| sK47 = app(sK54(X8),cons(sK52(X8),nil))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
! [X6,X7,X5] :
( app(X7,cons(X5,nil)) != sK49
| ~ ssList(X7)
| app(cons(X5,nil),X6) != sK51
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
! [X8] :
( nil = sK47
| ~ equalelemsP(sK47)
| ssList(sK53(X8))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
! [X8] :
( nil = sK47
| ~ equalelemsP(sK47)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
! [X8] :
( nil != sK48
| ~ equalelemsP(sK47)
| ssList(sK53(X8))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
! [X8] :
( nil != sK48
| ~ equalelemsP(sK47)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
! [X8] :
( nil != sK48
| ~ equalelemsP(sK47)
| ssItem(sK52(X8))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
! [X8] :
( nil = sK47
| ~ equalelemsP(sK47)
| ssItem(sK52(X8))
| sK48 != app(sK47,X8)
| ~ ssList(X8) ),
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
ssList(sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
equalelemsP(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
sK50 = app(sK49,sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
( nil != sK49
| nil = sK50 ),
inference(cnf_transformation,[],[f222]) ).
fof(f427,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f428,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f434,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| ssItem(sK52(X8))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f421,f427,f427,f428,f427]) ).
fof(f435,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| ssItem(sK52(X8))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f420,f428,f427,f428,f427]) ).
fof(f436,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f419,f428,f427,f428,f427]) ).
fof(f437,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| ssList(sK53(X8))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f418,f428,f427,f428,f427]) ).
fof(f438,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f417,f427,f427,f428,f427]) ).
fof(f439,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| ssList(sK53(X8))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f416,f427,f427,f428,f427]) ).
fof(f440,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| sK49 = app(sK54(X8),cons(sK52(X8),nil))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f414,f427,f427,f427,f428,f427]) ).
fof(f441,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| ssList(sK54(X8))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f413,f427,f427,f428,f427]) ).
fof(f442,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| sK49 = app(sK54(X8),cons(sK52(X8),nil))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f412,f428,f427,f427,f428,f427]) ).
fof(f443,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| ssList(sK54(X8))
| sK50 != app(sK49,X8)
| ~ ssList(X8) ),
inference(definition_unfolding,[],[f411,f428,f427,f428,f427]) ).
fof(f656,plain,
~ ssList(sK51),
inference(consistent_polarity_flipping,[],[f422]) ).
fof(f657,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| ~ ssItem(sK52(X8))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f434]) ).
fof(f658,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| ~ ssItem(sK52(X8))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f435]) ).
fof(f659,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f436]) ).
fof(f660,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| ~ ssList(sK53(X8))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f437]) ).
fof(f661,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f438]) ).
fof(f662,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| ~ ssList(sK53(X8))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f439]) ).
fof(f663,plain,
! [X6,X7,X5] :
( app(cons(X5,nil),X6) != sK51
| ssList(X7)
| app(X7,cons(X5,nil)) != sK49
| ssList(X6)
| ssItem(X5) ),
inference(consistent_polarity_flipping,[],[f415]) ).
fof(f664,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| sK49 = app(sK54(X8),cons(sK52(X8),nil))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f440]) ).
fof(f665,plain,
! [X8] :
( nil = sK49
| ~ equalelemsP(sK49)
| ~ ssList(sK54(X8))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f441]) ).
fof(f666,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| sK49 = app(sK54(X8),cons(sK52(X8),nil))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f442]) ).
fof(f667,plain,
! [X8] :
( nil != sK50
| ~ equalelemsP(sK49)
| ~ ssList(sK54(X8))
| sK50 != app(sK49,X8)
| ssList(X8) ),
inference(consistent_polarity_flipping,[],[f443]) ).
fof(f676,definition,
( spl55_1
<=> ! [X8] :
( ~ ssList(sK54(X8))
| ssList(X8)
| sK50 != app(sK49,X8) ) ),
introduced(definition,[new_symbols(definition,[spl55_1])],[avatar_definition]) ).
fof(f677,plain,
( ! [X8] :
( ~ ssList(sK54(X8))
| ssList(X8)
| sK50 != app(sK49,X8) )
| ~ spl55_1 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f679,definition,
( spl55_2
<=> equalelemsP(sK49) ),
introduced(definition,[new_symbols(definition,[spl55_2])],[avatar_definition]) ).
fof(f683,definition,
( spl55_3
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl55_3])],[avatar_definition]) ).
fof(f684,plain,
( nil = sK50
| ~ spl55_3 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f686,plain,
( spl55_1
| ~ spl55_2
| ~ spl55_3 ),
inference(avatar_split_clause,[],[f667,f683,f679,f676]) ).
fof(f688,definition,
( spl55_4
<=> ! [X8] :
( sK49 = app(sK54(X8),cons(sK52(X8),nil))
| ssList(X8)
| sK50 != app(sK49,X8) ) ),
introduced(definition,[new_symbols(definition,[spl55_4])],[avatar_definition]) ).
fof(f689,plain,
( ! [X8] :
( sK50 != app(sK49,X8)
| ssList(X8)
| sK49 = app(sK54(X8),cons(sK52(X8),nil)) )
| ~ spl55_4 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f690,plain,
( spl55_4
| ~ spl55_2
| ~ spl55_3 ),
inference(avatar_split_clause,[],[f666,f683,f679,f688]) ).
fof(f692,definition,
( spl55_5
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl55_5])],[avatar_definition]) ).
fof(f694,plain,
( nil = sK49
| ~ spl55_5 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f695,plain,
( spl55_1
| ~ spl55_2
| spl55_5 ),
inference(avatar_split_clause,[],[f665,f692,f679,f676]) ).
fof(f696,plain,
( spl55_4
| ~ spl55_2
| spl55_5 ),
inference(avatar_split_clause,[],[f664,f692,f679,f688]) ).
fof(f698,definition,
( spl55_6
<=> ! [X8] :
( ~ ssList(sK53(X8))
| ssList(X8)
| sK50 != app(sK49,X8) ) ),
introduced(definition,[new_symbols(definition,[spl55_6])],[avatar_definition]) ).
fof(f699,plain,
( ! [X8] :
( ~ ssList(sK53(X8))
| ssList(X8)
| sK50 != app(sK49,X8) )
| ~ spl55_6 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f700,plain,
( spl55_6
| ~ spl55_2
| spl55_5 ),
inference(avatar_split_clause,[],[f662,f692,f679,f698]) ).
fof(f702,definition,
( spl55_7
<=> ! [X8] :
( app(cons(sK52(X8),nil),sK53(X8)) = X8
| ssList(X8)
| sK50 != app(sK49,X8) ) ),
introduced(definition,[new_symbols(definition,[spl55_7])],[avatar_definition]) ).
fof(f703,plain,
( ! [X8] :
( sK50 != app(sK49,X8)
| ssList(X8)
| app(cons(sK52(X8),nil),sK53(X8)) = X8 )
| ~ spl55_7 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f704,plain,
( spl55_7
| ~ spl55_2
| spl55_5 ),
inference(avatar_split_clause,[],[f661,f692,f679,f702]) ).
fof(f705,plain,
( spl55_6
| ~ spl55_2
| ~ spl55_3 ),
inference(avatar_split_clause,[],[f660,f683,f679,f698]) ).
fof(f706,plain,
( spl55_7
| ~ spl55_2
| ~ spl55_3 ),
inference(avatar_split_clause,[],[f659,f683,f679,f702]) ).
fof(f708,definition,
( spl55_8
<=> ! [X8] :
( ~ ssItem(sK52(X8))
| ssList(X8)
| sK50 != app(sK49,X8) ) ),
introduced(definition,[new_symbols(definition,[spl55_8])],[avatar_definition]) ).
fof(f709,plain,
( ! [X8] :
( ~ ssItem(sK52(X8))
| ssList(X8)
| sK50 != app(sK49,X8) )
| ~ spl55_8 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f710,plain,
( spl55_8
| ~ spl55_2
| ~ spl55_3 ),
inference(avatar_split_clause,[],[f658,f683,f679,f708]) ).
fof(f711,plain,
( spl55_8
| ~ spl55_2
| spl55_5 ),
inference(avatar_split_clause,[],[f657,f692,f679,f708]) ).
fof(f712,plain,
spl55_2,
inference(avatar_split_clause,[],[f423,f679]) ).
fof(f713,plain,
( spl55_3
| ~ spl55_5 ),
inference(avatar_split_clause,[],[f425,f692,f683]) ).
fof(f754,plain,
( sK50 = app(nil,sK51)
| ~ spl55_5 ),
inference(forward_demodulation,[],[f424,f694]) ).
fof(f755,plain,
( nil = app(nil,sK51)
| ~ spl55_3
| ~ spl55_5 ),
inference(forward_demodulation,[],[f754,f684]) ).
fof(f756,plain,
( ! [X8] :
( sK50 != app(nil,X8)
| ~ ssList(sK54(X8))
| ssList(X8) )
| ~ spl55_1
| ~ spl55_5 ),
inference(forward_demodulation,[],[f677,f694]) ).
fof(f757,plain,
( ! [X8] :
( nil != app(nil,X8)
| ~ ssList(sK54(X8))
| ssList(X8) )
| ~ spl55_1
| ~ spl55_3
| ~ spl55_5 ),
inference(forward_demodulation,[],[f756,f684]) ).
fof(f758,plain,
( ! [X8] :
( sK50 != app(nil,X8)
| ~ ssList(sK53(X8))
| ssList(X8) )
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_demodulation,[],[f699,f694]) ).
fof(f759,plain,
( ! [X8] :
( nil != app(nil,X8)
| ~ ssList(sK53(X8))
| ssList(X8) )
| ~ spl55_3
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_demodulation,[],[f758,f684]) ).
fof(f760,plain,
( ! [X8] :
( sK50 != app(nil,X8)
| ~ ssItem(sK52(X8))
| ssList(X8) )
| ~ spl55_5
| ~ spl55_8 ),
inference(forward_demodulation,[],[f709,f694]) ).
fof(f761,plain,
( ! [X8] :
( nil != app(nil,X8)
| ~ ssItem(sK52(X8))
| ssList(X8) )
| ~ spl55_3
| ~ spl55_5
| ~ spl55_8 ),
inference(forward_demodulation,[],[f760,f684]) ).
fof(f762,plain,
( nil != nil
| ~ ssList(sK54(sK51))
| ssList(sK51)
| ~ spl55_1
| ~ spl55_3
| ~ spl55_5 ),
inference(superposition,[],[f757,f755]) ).
fof(f763,plain,
( ~ ssList(sK54(sK51))
| ssList(sK51)
| ~ spl55_1
| ~ spl55_3
| ~ spl55_5 ),
inference(trivial_inequality_removal,[],[f762]) ).
fof(f764,plain,
( ~ ssList(sK54(sK51))
| ~ spl55_1
| ~ spl55_3
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f763,f656]) ).
fof(f765,plain,
( nil != nil
| ~ ssList(sK53(sK51))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_5
| ~ spl55_6 ),
inference(superposition,[],[f759,f755]) ).
fof(f766,plain,
( ~ ssList(sK53(sK51))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_5
| ~ spl55_6 ),
inference(trivial_inequality_removal,[],[f765]) ).
fof(f767,plain,
( ~ ssList(sK53(sK51))
| ~ spl55_3
| ~ spl55_5
| ~ spl55_6 ),
inference(forward_subsumption_resolution,[],[f766,f656]) ).
fof(f768,plain,
( nil != nil
| ~ ssItem(sK52(sK51))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_5
| ~ spl55_8 ),
inference(superposition,[],[f761,f755]) ).
fof(f769,plain,
( ~ ssItem(sK52(sK51))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_5
| ~ spl55_8 ),
inference(trivial_inequality_removal,[],[f768]) ).
fof(f770,plain,
( ~ ssItem(sK52(sK51))
| ~ spl55_3
| ~ spl55_5
| ~ spl55_8 ),
inference(forward_subsumption_resolution,[],[f769,f656]) ).
fof(f771,plain,
( ! [X8] :
( nil = app(sK54(X8),cons(sK52(X8),nil))
| ssList(X8)
| sK50 != app(sK49,X8) )
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_demodulation,[],[f689,f694]) ).
fof(f772,plain,
( ! [X8] :
( sK50 != app(nil,X8)
| nil = app(sK54(X8),cons(sK52(X8),nil))
| ssList(X8) )
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_demodulation,[],[f771,f694]) ).
fof(f773,plain,
( ! [X8] :
( nil != app(nil,X8)
| nil = app(sK54(X8),cons(sK52(X8),nil))
| ssList(X8) )
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_demodulation,[],[f772,f684]) ).
fof(f774,plain,
( ! [X8] :
( sK50 != app(nil,X8)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| ssList(X8) )
| ~ spl55_5
| ~ spl55_7 ),
inference(forward_demodulation,[],[f703,f694]) ).
fof(f775,plain,
( ! [X8] :
( nil != app(nil,X8)
| app(cons(sK52(X8),nil),sK53(X8)) = X8
| ssList(X8) )
| ~ spl55_3
| ~ spl55_5
| ~ spl55_7 ),
inference(forward_demodulation,[],[f774,f684]) ).
fof(f776,plain,
( nil != nil
| nil = app(sK54(sK51),cons(sK52(sK51),nil))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(superposition,[],[f773,f755]) ).
fof(f777,plain,
( nil = app(sK54(sK51),cons(sK52(sK51),nil))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(trivial_inequality_removal,[],[f776]) ).
fof(f778,plain,
( nil = app(sK54(sK51),cons(sK52(sK51),nil))
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f777,f656]) ).
fof(f779,plain,
( nil != nil
| sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_5
| ~ spl55_7 ),
inference(superposition,[],[f775,f755]) ).
fof(f780,plain,
( sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ssList(sK51)
| ~ spl55_3
| ~ spl55_5
| ~ spl55_7 ),
inference(trivial_inequality_removal,[],[f779]) ).
fof(f781,plain,
( sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ~ spl55_3
| ~ spl55_5
| ~ spl55_7 ),
inference(forward_subsumption_resolution,[],[f780,f656]) ).
fof(f782,plain,
( ! [X6,X7,X5] :
( nil != app(X7,cons(X5,nil))
| ssList(X7)
| app(cons(X5,nil),X6) != sK51
| ssList(X6)
| ssItem(X5) )
| ~ spl55_5 ),
inference(forward_demodulation,[],[f663,f694]) ).
fof(f783,plain,
( ! [X0] :
( nil != nil
| ssList(sK54(sK51))
| sK51 != app(cons(sK52(sK51),nil),X0)
| ssList(X0)
| ssItem(sK52(sK51)) )
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(superposition,[],[f782,f778]) ).
fof(f784,plain,
( ! [X0] :
( ssList(sK54(sK51))
| sK51 != app(cons(sK52(sK51),nil),X0)
| ssList(X0)
| ssItem(sK52(sK51)) )
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(trivial_inequality_removal,[],[f783]) ).
fof(f785,plain,
( ! [X0] :
( sK51 != app(cons(sK52(sK51),nil),X0)
| ssList(X0)
| ssItem(sK52(sK51)) )
| ~ spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f784,f764]) ).
fof(f786,plain,
( ! [X0] :
( sK51 != app(cons(sK52(sK51),nil),X0)
| ssList(X0) )
| ~ spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_8 ),
inference(forward_subsumption_resolution,[],[f785,f770]) ).
fof(f787,plain,
( sK51 != sK51
| ssList(sK53(sK51))
| ~ spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_7
| ~ spl55_8 ),
inference(superposition,[],[f786,f781]) ).
fof(f788,plain,
( ssList(sK53(sK51))
| ~ spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_7
| ~ spl55_8 ),
inference(trivial_inequality_removal,[],[f787]) ).
fof(f789,plain,
( $false
| ~ spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6
| ~ spl55_7
| ~ spl55_8 ),
inference(forward_subsumption_resolution,[],[f788,f767]) ).
fof(f790,plain,
( ~ spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6
| ~ spl55_7
| ~ spl55_8 ),
inference(avatar_contradiction_clause,[],[f789]) ).
fof(f806,definition,
( spl55_16
<=> ssItem(sK52(sK51)) ),
introduced(definition,[new_symbols(definition,[spl55_16])],[avatar_definition]) ).
fof(f808,plain,
( ssItem(sK52(sK51))
| ~ spl55_16 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f810,definition,
( spl55_17
<=> ssList(sK53(sK51)) ),
introduced(definition,[new_symbols(definition,[spl55_17])],[avatar_definition]) ).
fof(f812,plain,
( ssList(sK53(sK51))
| ~ spl55_17 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f814,definition,
( spl55_18
<=> ! [X0] :
( ssList(X0)
| sK49 != app(X0,cons(sK52(sK51),nil)) ) ),
introduced(definition,[new_symbols(definition,[spl55_18])],[avatar_definition]) ).
fof(f815,plain,
( ! [X0] :
( sK49 != app(X0,cons(sK52(sK51),nil))
| ssList(X0) )
| ~ spl55_18 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f831,plain,
( sK50 != sK50
| ssList(sK51)
| sK49 = app(sK54(sK51),cons(sK52(sK51),nil))
| ~ spl55_4 ),
inference(superposition,[],[f689,f424]) ).
fof(f832,plain,
( ssList(sK51)
| sK49 = app(sK54(sK51),cons(sK52(sK51),nil))
| ~ spl55_4 ),
inference(trivial_inequality_removal,[],[f831]) ).
fof(f833,plain,
( sK49 = app(sK54(sK51),cons(sK52(sK51),nil))
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f832,f656]) ).
fof(f834,plain,
( sK50 != sK50
| ssList(sK51)
| sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ~ spl55_7 ),
inference(superposition,[],[f703,f424]) ).
fof(f835,plain,
( ssList(sK51)
| sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ~ spl55_7 ),
inference(trivial_inequality_removal,[],[f834]) ).
fof(f836,plain,
( sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ~ spl55_7 ),
inference(forward_subsumption_resolution,[],[f835,f656]) ).
fof(f837,plain,
( ! [X0] :
( sK51 != sK51
| ssList(X0)
| sK49 != app(X0,cons(sK52(sK51),nil))
| ssList(sK53(sK51))
| ssItem(sK52(sK51)) )
| ~ spl55_7 ),
inference(superposition,[],[f663,f836]) ).
fof(f838,plain,
( ! [X0] :
( ssList(X0)
| sK49 != app(X0,cons(sK52(sK51),nil))
| ssList(sK53(sK51))
| ssItem(sK52(sK51)) )
| ~ spl55_7 ),
inference(trivial_inequality_removal,[],[f837]) ).
fof(f841,plain,
( sK49 != sK49
| ssList(sK54(sK51))
| ~ spl55_4
| ~ spl55_18 ),
inference(superposition,[],[f815,f833]) ).
fof(f842,plain,
( ssList(sK54(sK51))
| ~ spl55_4
| ~ spl55_18 ),
inference(trivial_inequality_removal,[],[f841]) ).
fof(f843,plain,
( ssList(sK51)
| sK50 != app(sK49,sK51)
| ~ spl55_1
| ~ spl55_4
| ~ spl55_18 ),
inference(resolution,[],[f842,f677]) ).
fof(f844,plain,
( sK50 != app(sK49,sK51)
| ~ spl55_1
| ~ spl55_4
| ~ spl55_18 ),
inference(forward_subsumption_resolution,[],[f843,f656]) ).
fof(f845,plain,
( $false
| ~ spl55_1
| ~ spl55_4
| ~ spl55_18 ),
inference(forward_subsumption_resolution,[],[f844,f424]) ).
fof(f846,plain,
( ~ spl55_1
| ~ spl55_4
| ~ spl55_18 ),
inference(avatar_contradiction_clause,[],[f845]) ).
fof(f847,plain,
( ssList(sK51)
| sK50 != app(sK49,sK51)
| ~ spl55_6
| ~ spl55_17 ),
inference(resolution,[],[f812,f699]) ).
fof(f848,plain,
( sK50 != app(sK49,sK51)
| ~ spl55_6
| ~ spl55_17 ),
inference(forward_subsumption_resolution,[],[f847,f656]) ).
fof(f849,plain,
( $false
| ~ spl55_6
| ~ spl55_17 ),
inference(forward_subsumption_resolution,[],[f848,f424]) ).
fof(f850,plain,
( ~ spl55_6
| ~ spl55_17 ),
inference(avatar_contradiction_clause,[],[f849]) ).
fof(f851,plain,
( spl55_16
| spl55_17
| spl55_18
| ~ spl55_7 ),
inference(avatar_split_clause,[],[f838,f702,f814,f810,f806]) ).
fof(f852,plain,
( ssList(sK51)
| sK50 != app(sK49,sK51)
| ~ spl55_8
| ~ spl55_16 ),
inference(resolution,[],[f808,f709]) ).
fof(f853,plain,
( sK50 != app(sK49,sK51)
| ~ spl55_8
| ~ spl55_16 ),
inference(forward_subsumption_resolution,[],[f852,f656]) ).
fof(f854,plain,
( $false
| ~ spl55_8
| ~ spl55_16 ),
inference(forward_subsumption_resolution,[],[f853,f424]) ).
fof(f855,plain,
( ~ spl55_8
| ~ spl55_16 ),
inference(avatar_contradiction_clause,[],[f854]) ).
cnf(s1,plain,
( spl55_1
| ~ spl55_2
| ~ spl55_3 ),
inference(sat_conversion,[],[f686]) ).
cnf(s2,plain,
( ~ spl55_2
| ~ spl55_3
| spl55_4 ),
inference(sat_conversion,[],[f690]) ).
cnf(s3,plain,
( spl55_1
| ~ spl55_2
| spl55_5 ),
inference(sat_conversion,[],[f695]) ).
cnf(s4,plain,
( ~ spl55_2
| spl55_4
| spl55_5 ),
inference(sat_conversion,[],[f696]) ).
cnf(s5,plain,
( ~ spl55_2
| spl55_5
| spl55_6 ),
inference(sat_conversion,[],[f700]) ).
cnf(s6,plain,
( ~ spl55_2
| spl55_5
| spl55_7 ),
inference(sat_conversion,[],[f704]) ).
cnf(s7,plain,
( ~ spl55_2
| ~ spl55_3
| spl55_6 ),
inference(sat_conversion,[],[f705]) ).
cnf(s8,plain,
( ~ spl55_2
| ~ spl55_3
| spl55_7 ),
inference(sat_conversion,[],[f706]) ).
cnf(s9,plain,
( ~ spl55_2
| ~ spl55_3
| spl55_8 ),
inference(sat_conversion,[],[f710]) ).
cnf(s10,plain,
( ~ spl55_2
| spl55_5
| spl55_8 ),
inference(sat_conversion,[],[f711]) ).
cnf(s11,plain,
spl55_2,
inference(sat_conversion,[],[f712]) ).
cnf(s12,plain,
( spl55_3
| ~ spl55_5 ),
inference(sat_conversion,[],[f713]) ).
cnf(s24,plain,
( ~ spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_5
| ~ spl55_6
| ~ spl55_7
| ~ spl55_8 ),
inference(sat_conversion,[],[f790]) ).
cnf(s30,plain,
( ~ spl55_1
| ~ spl55_4
| ~ spl55_18 ),
inference(sat_conversion,[],[f846]) ).
cnf(s31,plain,
( ~ spl55_6
| ~ spl55_17 ),
inference(sat_conversion,[],[f850]) ).
cnf(s32,plain,
( ~ spl55_7
| spl55_16
| spl55_17
| spl55_18 ),
inference(sat_conversion,[],[f851]) ).
cnf(s33,plain,
( ~ spl55_8
| ~ spl55_16 ),
inference(sat_conversion,[],[f855]) ).
cnf(s38,plain,
( spl55_5
| spl55_8 ),
inference(rat,[],[s10,s11]) ).
cnf(s39,plain,
( ~ spl55_3
| spl55_8 ),
inference(rat,[],[s9,s11]) ).
cnf(s40,plain,
( ~ spl55_3
| spl55_7 ),
inference(rat,[],[s8,s11]) ).
cnf(s41,plain,
( ~ spl55_3
| spl55_6 ),
inference(rat,[],[s7,s11]) ).
cnf(s42,plain,
( spl55_5
| spl55_7 ),
inference(rat,[],[s6,s11]) ).
cnf(s43,plain,
( spl55_5
| spl55_6 ),
inference(rat,[],[s5,s11]) ).
cnf(s44,plain,
( spl55_4
| spl55_5 ),
inference(rat,[],[s4,s11]) ).
cnf(s45,plain,
( spl55_1
| spl55_5 ),
inference(rat,[],[s3,s11]) ).
cnf(s46,plain,
( ~ spl55_3
| spl55_4 ),
inference(rat,[],[s2,s11]) ).
cnf(s47,plain,
( spl55_1
| ~ spl55_3 ),
inference(rat,[],[s1,s11]) ).
cnf(s48,plain,
spl55_1,
inference(rat,[],[s12,s47,s45]) ).
cnf(s49,plain,
spl55_5,
inference(rat,[],[s32,s30,s31,s33,s44,s43,s42,s38,s48]) ).
cnf(s50,plain,
spl55_3,
inference(rat,[],[s12,s49]) ).
cnf(s51,plain,
spl55_8,
inference(rat,[],[s39,s50]) ).
cnf(s52,plain,
spl55_7,
inference(rat,[],[s40,s50]) ).
cnf(s53,plain,
spl55_6,
inference(rat,[],[s41,s50]) ).
cnf(s54,plain,
spl55_4,
inference(rat,[],[s46,s50]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s24,s51,s52,s49,s50,s48,s53,s54]) ).
fof(f856,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC327+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.19 % Computer : n008.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Mon Sep 28 09:06:55 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.22 Running first-order model finding
% 0.12/0.22 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
% 0.12/0.29 % (2114563)Will run a generic schedule for satisfiability detection.
% 0.12/0.29 % (2114571)dis+10_1_sil=32000:sp=arity:random_seed=1868220244:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.29 % (2114569)% WARNING: option uhcvi not known.
% 0.12/0.29 % (2114570)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1301076620:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.29 % (2114569)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3405719125:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.29 % (2114572)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=898090867:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.29 % (2114573)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2309274268:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.29 % (2114574)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1368057948:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.29 % (2114569) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2114563-2114569"...
% 0.12/0.29 % (2114568)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1248305681_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.29 % (2114569)...printing done.
% 0.12/0.29 % (2114569)Refutation found. Thanks to Tanya!
% 0.12/0.29 % SZS status Theorem for theBenchmark
% 0.12/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.30 % (2114569)------------------------------
% 0.12/0.30 % (2114569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.30 % (2114569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.30 % (2114569)CaDiCaL version: 2.1.3
% 0.12/0.30 % (2114569)Termination reason: Refutation
% 0.12/0.30 % (2114569)Time elapsed: 0.017 s
% 0.12/0.30 % (2114569)Peak memory usage: 13 MB
% 0.12/0.30 % (2114569)Instructions burned: 21 (million)
% 0.12/0.30 % (2114563)Success in time 0.067 s
% 0.12/0.30 % Vampire exiting
%------------------------------------------------------------------------------