%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC343+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 : n017.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 01:05:37 PM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 162 ( 20 unt; 10 def)
% Number of atoms : 687 ( 192 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 861 ( 336 ~; 439 |; 58 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 100 !; 28 ?)
% 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
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ? [X9] :
( ssList(X9)
& app(X0,X9) = X1
& ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(cons(X10,nil),X11) != X9
| ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssList(X13)
=> ( app(X13,cons(X12,nil)) != X0
| ~ lt(X12,X10) ) ) ) ) ) )
& strictorderedP(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
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ? [X9] :
( ssList(X9)
& app(X0,X9) = X1
& ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(cons(X10,nil),X11) != X9
| ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssList(X13)
=> ( app(X13,cons(X12,nil)) != X0
| ~ lt(X12,X10) ) ) ) ) ) )
& strictorderedP(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
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ! [X9] :
( ~ ssList(X9)
| app(X0,X9) != X1
| ? [X10] :
( ? [X11] :
( app(cons(X10,nil),X11) = X9
& ? [X12] :
( ? [X13] :
( app(X13,cons(X12,nil)) = X0
& lt(X12,X10)
& ssList(X13) )
& ssItem(X12) )
& ssList(X11) )
& ssItem(X10) )
| ~ strictorderedP(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
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ! [X9] :
( ~ ssList(X9)
| app(X0,X9) != X1
| ? [X10] :
( ? [X11] :
( app(cons(X10,nil),X11) = X9
& ? [X12] :
( ? [X13] :
( app(X13,cons(X12,nil)) = X0
& lt(X12,X10)
& ssList(X13) )
& ssItem(X12) )
& ssList(X11) )
& ssItem(X10) )
| ~ strictorderedP(X0) )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f411,plain,
! [X9] :
( nil = sK47
| ~ strictorderedP(sK47)
| ssList(sK55(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f412,plain,
! [X9] :
( nil = sK47
| ~ strictorderedP(sK47)
| lt(sK54(X9),sK52(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
! [X9] :
( nil = sK47
| ~ strictorderedP(sK47)
| sK47 = app(sK55(X9),cons(sK54(X9),nil))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
! [X9] :
( nil != sK48
| ~ strictorderedP(sK47)
| ssList(sK55(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
! [X9] :
( nil != sK48
| ~ strictorderedP(sK47)
| lt(sK54(X9),sK52(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f416,plain,
! [X9] :
( nil != sK48
| ~ strictorderedP(sK47)
| sK47 = app(sK55(X9),cons(sK54(X9),nil))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
! [X8,X6,X7,X5] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != sK49
| ~ ssList(X8)
| ~ ssItem(X7)
| app(cons(X5,nil),X6) != sK51
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
! [X9] :
( nil != sK48
| ~ strictorderedP(sK47)
| ssItem(sK54(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
! [X9] :
( nil = sK47
| ~ strictorderedP(sK47)
| ssItem(sK54(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
! [X9] :
( nil = sK47
| ~ strictorderedP(sK47)
| ssList(sK53(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
! [X9] :
( nil = sK47
| ~ strictorderedP(sK47)
| app(cons(sK52(X9),nil),sK53(X9)) = X9
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
! [X9] :
( nil != sK48
| ~ strictorderedP(sK47)
| ssList(sK53(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
! [X9] :
( nil != sK48
| ~ strictorderedP(sK47)
| app(cons(sK52(X9),nil),sK53(X9)) = X9
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
! [X9] :
( nil != sK48
| ~ strictorderedP(sK47)
| ssItem(sK52(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
! [X9] :
( nil = sK47
| ~ strictorderedP(sK47)
| ssItem(sK52(X9))
| sK48 != app(sK47,X9)
| ~ ssList(X9) ),
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
ssList(sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f427,plain,
strictorderedP(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f428,plain,
sK50 = app(sK49,sK51),
inference(cnf_transformation,[],[f222]) ).
fof(f429,plain,
( nil != sK49
| nil = sK50 ),
inference(cnf_transformation,[],[f222]) ).
fof(f431,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f432,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f438,plain,
! [X9] :
( nil = sK49
| ~ strictorderedP(sK49)
| ssItem(sK52(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f425,f431,f431,f432,f431]) ).
fof(f439,plain,
! [X9] :
( nil != sK50
| ~ strictorderedP(sK49)
| ssItem(sK52(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f424,f432,f431,f432,f431]) ).
fof(f440,plain,
! [X9] :
( nil != sK50
| ~ strictorderedP(sK49)
| app(cons(sK52(X9),nil),sK53(X9)) = X9
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f423,f432,f431,f432,f431]) ).
fof(f441,plain,
! [X9] :
( nil != sK50
| ~ strictorderedP(sK49)
| ssList(sK53(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f422,f432,f431,f432,f431]) ).
fof(f442,plain,
! [X9] :
( nil = sK49
| ~ strictorderedP(sK49)
| app(cons(sK52(X9),nil),sK53(X9)) = X9
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f421,f431,f431,f432,f431]) ).
fof(f443,plain,
! [X9] :
( nil = sK49
| ~ strictorderedP(sK49)
| ssList(sK53(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f420,f431,f431,f432,f431]) ).
fof(f444,plain,
! [X9] :
( nil = sK49
| ~ strictorderedP(sK49)
| ssItem(sK54(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f419,f431,f431,f432,f431]) ).
fof(f445,plain,
! [X9] :
( nil != sK50
| ~ strictorderedP(sK49)
| ssItem(sK54(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f418,f432,f431,f432,f431]) ).
fof(f446,plain,
! [X9] :
( nil != sK50
| ~ strictorderedP(sK49)
| sK49 = app(sK55(X9),cons(sK54(X9),nil))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f416,f432,f431,f431,f432,f431]) ).
fof(f447,plain,
! [X9] :
( nil != sK50
| ~ strictorderedP(sK49)
| lt(sK54(X9),sK52(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f415,f432,f431,f432,f431]) ).
fof(f448,plain,
! [X9] :
( nil != sK50
| ~ strictorderedP(sK49)
| ssList(sK55(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f414,f432,f431,f432,f431]) ).
fof(f449,plain,
! [X9] :
( nil = sK49
| ~ strictorderedP(sK49)
| sK49 = app(sK55(X9),cons(sK54(X9),nil))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f413,f431,f431,f431,f432,f431]) ).
fof(f450,plain,
! [X9] :
( nil = sK49
| ~ strictorderedP(sK49)
| lt(sK54(X9),sK52(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f412,f431,f431,f432,f431]) ).
fof(f451,plain,
! [X9] :
( nil = sK49
| ~ strictorderedP(sK49)
| ssList(sK55(X9))
| sK50 != app(sK49,X9)
| ~ ssList(X9) ),
inference(definition_unfolding,[],[f411,f431,f431,f432,f431]) ).
fof(f664,plain,
~ strictorderedP(sK49),
inference(consistent_polarity_flipping,[],[f427]) ).
fof(f665,plain,
~ ssList(sK51),
inference(consistent_polarity_flipping,[],[f426]) ).
fof(f666,plain,
! [X9] :
( nil = sK49
| strictorderedP(sK49)
| ~ ssItem(sK52(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f438]) ).
fof(f667,plain,
! [X9] :
( nil != sK50
| strictorderedP(sK49)
| ~ ssItem(sK52(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f439]) ).
fof(f668,plain,
! [X9] :
( nil != sK50
| strictorderedP(sK49)
| app(cons(sK52(X9),nil),sK53(X9)) = X9
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f440]) ).
fof(f669,plain,
! [X9] :
( nil != sK50
| strictorderedP(sK49)
| ~ ssList(sK53(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f441]) ).
fof(f670,plain,
! [X9] :
( nil = sK49
| strictorderedP(sK49)
| app(cons(sK52(X9),nil),sK53(X9)) = X9
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f442]) ).
fof(f671,plain,
! [X9] :
( nil = sK49
| strictorderedP(sK49)
| ~ ssList(sK53(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f443]) ).
fof(f672,plain,
! [X9] :
( nil = sK49
| strictorderedP(sK49)
| ~ ssItem(sK54(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f444]) ).
fof(f673,plain,
! [X9] :
( nil != sK50
| strictorderedP(sK49)
| ~ ssItem(sK54(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f445]) ).
fof(f674,plain,
! [X8,X6,X7,X5] :
( app(cons(X5,nil),X6) != sK51
| app(X8,cons(X7,nil)) != sK49
| ssList(X8)
| ssItem(X7)
| lt(X7,X5)
| ssList(X6)
| ssItem(X5) ),
inference(consistent_polarity_flipping,[],[f417]) ).
fof(f675,plain,
! [X9] :
( nil != sK50
| strictorderedP(sK49)
| sK49 = app(sK55(X9),cons(sK54(X9),nil))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f446]) ).
fof(f676,plain,
! [X9] :
( nil != sK50
| strictorderedP(sK49)
| ~ lt(sK54(X9),sK52(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f447]) ).
fof(f677,plain,
! [X9] :
( nil != sK50
| strictorderedP(sK49)
| ~ ssList(sK55(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f448]) ).
fof(f678,plain,
! [X9] :
( nil = sK49
| strictorderedP(sK49)
| sK49 = app(sK55(X9),cons(sK54(X9),nil))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f449]) ).
fof(f679,plain,
! [X9] :
( nil = sK49
| strictorderedP(sK49)
| ~ lt(sK54(X9),sK52(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f450]) ).
fof(f680,plain,
! [X9] :
( nil = sK49
| strictorderedP(sK49)
| ~ ssList(sK55(X9))
| sK50 != app(sK49,X9)
| ssList(X9) ),
inference(consistent_polarity_flipping,[],[f451]) ).
fof(f689,definition,
( spl56_1
<=> ! [X9] :
( ~ ssList(sK55(X9))
| ssList(X9)
| sK50 != app(sK49,X9) ) ),
introduced(definition,[new_symbols(definition,[spl56_1])],[avatar_definition]) ).
fof(f690,plain,
( ! [X9] :
( sK50 != app(sK49,X9)
| ssList(X9)
| ~ ssList(sK55(X9)) )
| ~ spl56_1 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f692,definition,
( spl56_2
<=> strictorderedP(sK49) ),
introduced(definition,[new_symbols(definition,[spl56_2])],[avatar_definition]) ).
fof(f696,definition,
( spl56_3
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl56_3])],[avatar_definition]) ).
fof(f699,plain,
( spl56_1
| spl56_2
| spl56_3 ),
inference(avatar_split_clause,[],[f680,f696,f692,f689]) ).
fof(f701,definition,
( spl56_4
<=> ! [X9] :
( ~ lt(sK54(X9),sK52(X9))
| ssList(X9)
| sK50 != app(sK49,X9) ) ),
introduced(definition,[new_symbols(definition,[spl56_4])],[avatar_definition]) ).
fof(f702,plain,
( ! [X9] :
( sK50 != app(sK49,X9)
| ssList(X9)
| ~ lt(sK54(X9),sK52(X9)) )
| ~ spl56_4 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f703,plain,
( spl56_4
| spl56_2
| spl56_3 ),
inference(avatar_split_clause,[],[f679,f696,f692,f701]) ).
fof(f705,definition,
( spl56_5
<=> ! [X9] :
( sK49 = app(sK55(X9),cons(sK54(X9),nil))
| ssList(X9)
| sK50 != app(sK49,X9) ) ),
introduced(definition,[new_symbols(definition,[spl56_5])],[avatar_definition]) ).
fof(f706,plain,
( ! [X9] :
( sK50 != app(sK49,X9)
| ssList(X9)
| sK49 = app(sK55(X9),cons(sK54(X9),nil)) )
| ~ spl56_5 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f707,plain,
( spl56_5
| spl56_2
| spl56_3 ),
inference(avatar_split_clause,[],[f678,f696,f692,f705]) ).
fof(f709,definition,
( spl56_6
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl56_6])],[avatar_definition]) ).
fof(f712,plain,
( spl56_1
| spl56_2
| ~ spl56_6 ),
inference(avatar_split_clause,[],[f677,f709,f692,f689]) ).
fof(f713,plain,
( spl56_4
| spl56_2
| ~ spl56_6 ),
inference(avatar_split_clause,[],[f676,f709,f692,f701]) ).
fof(f714,plain,
( spl56_5
| spl56_2
| ~ spl56_6 ),
inference(avatar_split_clause,[],[f675,f709,f692,f705]) ).
fof(f716,definition,
( spl56_7
<=> ! [X9] :
( ~ ssItem(sK54(X9))
| ssList(X9)
| sK50 != app(sK49,X9) ) ),
introduced(definition,[new_symbols(definition,[spl56_7])],[avatar_definition]) ).
fof(f717,plain,
( ! [X9] :
( sK50 != app(sK49,X9)
| ssList(X9)
| ~ ssItem(sK54(X9)) )
| ~ spl56_7 ),
inference(avatar_component_clause,[],[f716]) ).
fof(f718,plain,
( spl56_7
| spl56_2
| ~ spl56_6 ),
inference(avatar_split_clause,[],[f673,f709,f692,f716]) ).
fof(f719,plain,
( spl56_7
| spl56_2
| spl56_3 ),
inference(avatar_split_clause,[],[f672,f696,f692,f716]) ).
fof(f721,definition,
( spl56_8
<=> ! [X9] :
( ~ ssList(sK53(X9))
| ssList(X9)
| sK50 != app(sK49,X9) ) ),
introduced(definition,[new_symbols(definition,[spl56_8])],[avatar_definition]) ).
fof(f722,plain,
( ! [X9] :
( sK50 != app(sK49,X9)
| ssList(X9)
| ~ ssList(sK53(X9)) )
| ~ spl56_8 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f723,plain,
( spl56_8
| spl56_2
| spl56_3 ),
inference(avatar_split_clause,[],[f671,f696,f692,f721]) ).
fof(f725,definition,
( spl56_9
<=> ! [X9] :
( app(cons(sK52(X9),nil),sK53(X9)) = X9
| ssList(X9)
| sK50 != app(sK49,X9) ) ),
introduced(definition,[new_symbols(definition,[spl56_9])],[avatar_definition]) ).
fof(f726,plain,
( ! [X9] :
( sK50 != app(sK49,X9)
| ssList(X9)
| app(cons(sK52(X9),nil),sK53(X9)) = X9 )
| ~ spl56_9 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f727,plain,
( spl56_9
| spl56_2
| spl56_3 ),
inference(avatar_split_clause,[],[f670,f696,f692,f725]) ).
fof(f728,plain,
( spl56_8
| spl56_2
| ~ spl56_6 ),
inference(avatar_split_clause,[],[f669,f709,f692,f721]) ).
fof(f729,plain,
( spl56_9
| spl56_2
| ~ spl56_6 ),
inference(avatar_split_clause,[],[f668,f709,f692,f725]) ).
fof(f731,definition,
( spl56_10
<=> ! [X9] :
( ~ ssItem(sK52(X9))
| ssList(X9)
| sK50 != app(sK49,X9) ) ),
introduced(definition,[new_symbols(definition,[spl56_10])],[avatar_definition]) ).
fof(f732,plain,
( ! [X9] :
( sK50 != app(sK49,X9)
| ssList(X9)
| ~ ssItem(sK52(X9)) )
| ~ spl56_10 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f733,plain,
( spl56_10
| spl56_2
| ~ spl56_6 ),
inference(avatar_split_clause,[],[f667,f709,f692,f731]) ).
fof(f734,plain,
( spl56_10
| spl56_2
| spl56_3 ),
inference(avatar_split_clause,[],[f666,f696,f692,f731]) ).
fof(f735,plain,
~ spl56_2,
inference(avatar_split_clause,[],[f664,f692]) ).
fof(f736,plain,
( spl56_6
| ~ spl56_3 ),
inference(avatar_split_clause,[],[f429,f696,f709]) ).
fof(f772,plain,
( sK50 != sK50
| ssList(sK51)
| ~ ssList(sK55(sK51))
| ~ spl56_1 ),
inference(superposition,[],[f690,f428]) ).
fof(f773,plain,
( ssList(sK51)
| ~ ssList(sK55(sK51))
| ~ spl56_1 ),
inference(trivial_inequality_removal,[],[f772]) ).
fof(f774,plain,
( ~ ssList(sK55(sK51))
| ~ spl56_1 ),
inference(forward_subsumption_resolution,[],[f773,f665]) ).
fof(f775,plain,
( sK50 != sK50
| ssList(sK51)
| ~ ssItem(sK54(sK51))
| ~ spl56_7 ),
inference(superposition,[],[f717,f428]) ).
fof(f776,plain,
( ssList(sK51)
| ~ ssItem(sK54(sK51))
| ~ spl56_7 ),
inference(trivial_inequality_removal,[],[f775]) ).
fof(f777,plain,
( ~ ssItem(sK54(sK51))
| ~ spl56_7 ),
inference(forward_subsumption_resolution,[],[f776,f665]) ).
fof(f778,plain,
( sK50 != sK50
| ssList(sK51)
| ~ ssList(sK53(sK51))
| ~ spl56_8 ),
inference(superposition,[],[f722,f428]) ).
fof(f779,plain,
( ssList(sK51)
| ~ ssList(sK53(sK51))
| ~ spl56_8 ),
inference(trivial_inequality_removal,[],[f778]) ).
fof(f780,plain,
( ~ ssList(sK53(sK51))
| ~ spl56_8 ),
inference(forward_subsumption_resolution,[],[f779,f665]) ).
fof(f781,plain,
( sK50 != sK50
| ssList(sK51)
| ~ ssItem(sK52(sK51))
| ~ spl56_10 ),
inference(superposition,[],[f732,f428]) ).
fof(f782,plain,
( ssList(sK51)
| ~ ssItem(sK52(sK51))
| ~ spl56_10 ),
inference(trivial_inequality_removal,[],[f781]) ).
fof(f783,plain,
( ~ ssItem(sK52(sK51))
| ~ spl56_10 ),
inference(forward_subsumption_resolution,[],[f782,f665]) ).
fof(f784,plain,
( sK50 != sK50
| ssList(sK51)
| ~ lt(sK54(sK51),sK52(sK51))
| ~ spl56_4 ),
inference(superposition,[],[f702,f428]) ).
fof(f785,plain,
( ssList(sK51)
| ~ lt(sK54(sK51),sK52(sK51))
| ~ spl56_4 ),
inference(trivial_inequality_removal,[],[f784]) ).
fof(f786,plain,
( ~ lt(sK54(sK51),sK52(sK51))
| ~ spl56_4 ),
inference(forward_subsumption_resolution,[],[f785,f665]) ).
fof(f787,plain,
( sK50 != sK50
| ssList(sK51)
| sK49 = app(sK55(sK51),cons(sK54(sK51),nil))
| ~ spl56_5 ),
inference(superposition,[],[f706,f428]) ).
fof(f788,plain,
( ssList(sK51)
| sK49 = app(sK55(sK51),cons(sK54(sK51),nil))
| ~ spl56_5 ),
inference(trivial_inequality_removal,[],[f787]) ).
fof(f789,plain,
( sK49 = app(sK55(sK51),cons(sK54(sK51),nil))
| ~ spl56_5 ),
inference(forward_subsumption_resolution,[],[f788,f665]) ).
fof(f790,plain,
( sK50 != sK50
| ssList(sK51)
| sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ~ spl56_9 ),
inference(superposition,[],[f726,f428]) ).
fof(f791,plain,
( ssList(sK51)
| sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ~ spl56_9 ),
inference(trivial_inequality_removal,[],[f790]) ).
fof(f792,plain,
( sK51 = app(cons(sK52(sK51),nil),sK53(sK51))
| ~ spl56_9 ),
inference(forward_subsumption_resolution,[],[f791,f665]) ).
fof(f793,plain,
( ! [X0,X1] :
( sK51 != sK51
| sK49 != app(X0,cons(X1,nil))
| ssList(X0)
| ssItem(X1)
| lt(X1,sK52(sK51))
| ssList(sK53(sK51))
| ssItem(sK52(sK51)) )
| ~ spl56_9 ),
inference(superposition,[],[f674,f792]) ).
fof(f794,plain,
( ! [X0,X1] :
( sK49 != app(X0,cons(X1,nil))
| ssList(X0)
| ssItem(X1)
| lt(X1,sK52(sK51))
| ssList(sK53(sK51))
| ssItem(sK52(sK51)) )
| ~ spl56_9 ),
inference(trivial_inequality_removal,[],[f793]) ).
fof(f795,plain,
( ! [X0,X1] :
( sK49 != app(X0,cons(X1,nil))
| ssList(X0)
| ssItem(X1)
| lt(X1,sK52(sK51))
| ssItem(sK52(sK51)) )
| ~ spl56_8
| ~ spl56_9 ),
inference(forward_subsumption_resolution,[],[f794,f780]) ).
fof(f796,plain,
( ! [X0,X1] :
( sK49 != app(X0,cons(X1,nil))
| ssList(X0)
| ssItem(X1)
| lt(X1,sK52(sK51)) )
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(forward_subsumption_resolution,[],[f795,f783]) ).
fof(f797,plain,
( sK49 != sK49
| ssList(sK55(sK51))
| ssItem(sK54(sK51))
| lt(sK54(sK51),sK52(sK51))
| ~ spl56_5
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(superposition,[],[f796,f789]) ).
fof(f798,plain,
( ssList(sK55(sK51))
| ssItem(sK54(sK51))
| lt(sK54(sK51),sK52(sK51))
| ~ spl56_5
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(trivial_inequality_removal,[],[f797]) ).
fof(f799,plain,
( ssItem(sK54(sK51))
| lt(sK54(sK51),sK52(sK51))
| ~ spl56_1
| ~ spl56_5
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(forward_subsumption_resolution,[],[f798,f774]) ).
fof(f800,plain,
( lt(sK54(sK51),sK52(sK51))
| ~ spl56_1
| ~ spl56_5
| ~ spl56_7
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(forward_subsumption_resolution,[],[f799,f777]) ).
fof(f801,plain,
( $false
| ~ spl56_1
| ~ spl56_4
| ~ spl56_5
| ~ spl56_7
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(forward_subsumption_resolution,[],[f800,f786]) ).
fof(f802,plain,
( ~ spl56_1
| ~ spl56_4
| ~ spl56_5
| ~ spl56_7
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(avatar_contradiction_clause,[],[f801]) ).
cnf(s1,plain,
( spl56_1
| spl56_2
| spl56_3 ),
inference(sat_conversion,[],[f699]) ).
cnf(s2,plain,
( spl56_2
| spl56_3
| spl56_4 ),
inference(sat_conversion,[],[f703]) ).
cnf(s3,plain,
( spl56_2
| spl56_3
| spl56_5 ),
inference(sat_conversion,[],[f707]) ).
cnf(s4,plain,
( spl56_1
| spl56_2
| ~ spl56_6 ),
inference(sat_conversion,[],[f712]) ).
cnf(s5,plain,
( spl56_2
| spl56_4
| ~ spl56_6 ),
inference(sat_conversion,[],[f713]) ).
cnf(s6,plain,
( spl56_2
| spl56_5
| ~ spl56_6 ),
inference(sat_conversion,[],[f714]) ).
cnf(s7,plain,
( spl56_2
| ~ spl56_6
| spl56_7 ),
inference(sat_conversion,[],[f718]) ).
cnf(s8,plain,
( spl56_2
| spl56_3
| spl56_7 ),
inference(sat_conversion,[],[f719]) ).
cnf(s9,plain,
( spl56_2
| spl56_3
| spl56_8 ),
inference(sat_conversion,[],[f723]) ).
cnf(s10,plain,
( spl56_2
| spl56_3
| spl56_9 ),
inference(sat_conversion,[],[f727]) ).
cnf(s11,plain,
( spl56_2
| ~ spl56_6
| spl56_8 ),
inference(sat_conversion,[],[f728]) ).
cnf(s12,plain,
( spl56_2
| ~ spl56_6
| spl56_9 ),
inference(sat_conversion,[],[f729]) ).
cnf(s13,plain,
( spl56_2
| ~ spl56_6
| spl56_10 ),
inference(sat_conversion,[],[f733]) ).
cnf(s14,plain,
( spl56_2
| spl56_3
| spl56_10 ),
inference(sat_conversion,[],[f734]) ).
cnf(s15,plain,
~ spl56_2,
inference(sat_conversion,[],[f735]) ).
cnf(s16,plain,
( ~ spl56_3
| spl56_6 ),
inference(sat_conversion,[],[f736]) ).
cnf(s26,plain,
( ~ spl56_1
| ~ spl56_4
| ~ spl56_5
| ~ spl56_7
| ~ spl56_8
| ~ spl56_9
| ~ spl56_10 ),
inference(sat_conversion,[],[f802]) ).
cnf(s31,plain,
( spl56_3
| spl56_10 ),
inference(rat,[],[s14,s15]) ).
cnf(s32,plain,
( ~ spl56_6
| spl56_10 ),
inference(rat,[],[s13,s15]) ).
cnf(s33,plain,
( ~ spl56_6
| spl56_9 ),
inference(rat,[],[s12,s15]) ).
cnf(s34,plain,
( ~ spl56_6
| spl56_8 ),
inference(rat,[],[s11,s15]) ).
cnf(s35,plain,
( spl56_3
| spl56_9 ),
inference(rat,[],[s10,s15]) ).
cnf(s36,plain,
( spl56_3
| spl56_8 ),
inference(rat,[],[s9,s15]) ).
cnf(s37,plain,
( spl56_3
| spl56_7 ),
inference(rat,[],[s8,s15]) ).
cnf(s38,plain,
( ~ spl56_6
| spl56_7 ),
inference(rat,[],[s7,s15]) ).
cnf(s39,plain,
( spl56_5
| ~ spl56_6 ),
inference(rat,[],[s6,s15]) ).
cnf(s40,plain,
( spl56_4
| ~ spl56_6 ),
inference(rat,[],[s5,s15]) ).
cnf(s41,plain,
( spl56_1
| ~ spl56_6 ),
inference(rat,[],[s4,s15]) ).
cnf(s42,plain,
( spl56_3
| spl56_5 ),
inference(rat,[],[s3,s15]) ).
cnf(s43,plain,
( spl56_3
| spl56_4 ),
inference(rat,[],[s2,s15]) ).
cnf(s44,plain,
( spl56_1
| spl56_3 ),
inference(rat,[],[s1,s15]) ).
cnf(s45,plain,
spl56_1,
inference(rat,[],[s16,s44,s41]) ).
cnf(s46,plain,
spl56_3,
inference(rat,[],[s26,s43,s42,s37,s36,s35,s31,s45]) ).
cnf(s47,plain,
spl56_6,
inference(rat,[],[s16,s46]) ).
cnf(s48,plain,
spl56_10,
inference(rat,[],[s32,s47]) ).
cnf(s49,plain,
spl56_9,
inference(rat,[],[s33,s47]) ).
cnf(s50,plain,
spl56_8,
inference(rat,[],[s34,s47]) ).
cnf(s51,plain,
spl56_7,
inference(rat,[],[s38,s47]) ).
cnf(s52,plain,
spl56_5,
inference(rat,[],[s39,s47]) ).
cnf(s53,plain,
spl56_4,
inference(rat,[],[s40,s47]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s26,s48,s49,s50,s51,s45,s52,s53]) ).
fof(f803,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC343+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 % Computer : n017.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Mon Sep 28 09:06:51 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.25 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
% 0.22/0.30 % (3416952)Will run a generic schedule for satisfiability detection.
% 0.22/0.30 % (3416957)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1715283372_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.30 % (3416958)% WARNING: option uhcvi not known.
% 0.22/0.30 % (3416959)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=349658206:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.30 % (3416958)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2593487062:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.30 % (3416960)dis+10_1_sil=32000:sp=arity:random_seed=4024180257:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.30 % (3416961)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4272621383:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.30 % (3416963)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2347916688:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.30 % (3416962)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2839144255:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.30 % TRYING [1]
% 0.22/0.30 % TRYING [2]
% 0.22/0.30 % TRYING [3]
% 0.22/0.30 % (3416958) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3416952-3416958"...
% 0.22/0.30 % (3416958)...printing done.
% 0.22/0.30 % (3416958)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (3416958)------------------------------
% 0.22/0.30 % (3416958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3416958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3416958)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3416958)Termination reason: Refutation
% 0.22/0.30 % (3416958)Time elapsed: 0.010 s
% 0.22/0.30 % (3416958)Peak memory usage: 13 MB
% 0.22/0.30 % (3416958)Instructions burned: 16 (million)
% 0.22/0.30 % (3416952)Success in time 0.048 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------