%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n016.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 01:03:33 PM UTC 2026
% Result : Unsatisfiable 0.64s 0.96s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 40
% Syntax : Number of formulae : 196 ( 30 unt; 19 def)
% Number of atoms : 657 ( 107 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 861 ( 400 ~; 442 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 19 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f207]) ).
fof(f209,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk5
| ~ ssItem(X2)
| ~ ssList(X3)
| app(X3,cons(X2,nil)) != sk3
| ~ lt(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk5
| ~ ssItem(X2)
| ~ ssList(X3)
| sk3 != app(X3,cons(X2,nil))
| ~ lt(X2,X0) ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f216,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f215]) ).
fof(f217,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f218,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f217]) ).
fof(f219,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f220,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f219]) ).
fof(f221,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f222,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f221]) ).
fof(f223,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f224,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f223]) ).
fof(f225,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(sk9(X0),cons(sk8(X0),nil)) = sk1
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f226,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| sk1 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f225]) ).
fof(f227,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f228,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f227]) ).
fof(f229,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f230,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f229]) ).
fof(f231,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_21) ).
fof(f232,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f231]) ).
fof(f233,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_22) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f233]) ).
fof(f235,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_23) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f235]) ).
fof(f237,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(sk9(X0),cons(sk8(X0),nil)) = sk1
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_24) ).
fof(f238,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| sk1 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f237]) ).
fof(f239,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_25) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f239]) ).
fof(f243,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f214,f204,f205,f205,f205]) ).
fof(f244,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f216,f204,f205,f205,f204]) ).
fof(f245,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f218,f204,f205,f205,f205]) ).
fof(f246,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f220,f204,f205,f205,f205]) ).
fof(f247,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f222,f204,f205,f205,f205]) ).
fof(f248,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f224,f204,f205,f205,f205]) ).
fof(f249,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f226,f204,f205,f205,f205,f205]) ).
fof(f250,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f228,f204,f205,f205,f205]) ).
fof(f251,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f230,f204,f205,f205,f204]) ).
fof(f252,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f232,f204,f205,f205,f204]) ).
fof(f253,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f234,f204,f205,f205,f204]) ).
fof(f254,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f236,f204,f205,f205,f204]) ).
fof(f255,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f238,f204,f205,f205,f205,f204]) ).
fof(f256,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f240,f204,f205,f205,f204]) ).
fof(f270,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f271,plain,
sQ0_eqProxy(sk4,app(sk3,sk5)),
inference(equality_proxy_replacement,[],[f208,f270]) ).
fof(f272,plain,
! [X2,X3,X0,X1] :
( ~ sQ0_eqProxy(app(cons(X0,nil),X1),sk5)
| ~ sQ0_eqProxy(sk3,app(X3,cons(X2,nil)))
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ lt(X2,X0) ),
inference(equality_proxy_replacement,[],[f211,f270,f270]) ).
fof(f273,plain,
( sQ0_eqProxy(nil,sk4)
| ~ sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f212,f270,f270]) ).
fof(f274,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f243,f270,f270]) ).
fof(f275,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f244,f270,f270]) ).
fof(f276,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssList(sk7(X0))
| ~ strictorderedP(sk3)
| sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f245,f270,f270]) ).
fof(f277,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| sQ0_eqProxy(app(cons(sk6(X0),nil),sk7(X0)),X0)
| ~ strictorderedP(sk3)
| sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f246,f270,f270,f270]) ).
fof(f278,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f247,f270,f270]) ).
fof(f279,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssList(sk9(X0))
| ~ strictorderedP(sk3)
| sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f248,f270,f270]) ).
fof(f280,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| sQ0_eqProxy(sk3,app(sk9(X0),cons(sk8(X0),nil)))
| ~ strictorderedP(sk3)
| sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f249,f270,f270,f270]) ).
fof(f281,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| sQ0_eqProxy(nil,sk3) ),
inference(equality_proxy_replacement,[],[f250,f270,f270]) ).
fof(f282,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssList(sk7(X0))
| ~ strictorderedP(sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f251,f270,f270]) ).
fof(f283,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| sQ0_eqProxy(app(cons(sk6(X0),nil),sk7(X0)),X0)
| ~ strictorderedP(sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f252,f270,f270,f270]) ).
fof(f284,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f253,f270,f270]) ).
fof(f285,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssList(sk9(X0))
| ~ strictorderedP(sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f254,f270,f270]) ).
fof(f286,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| sQ0_eqProxy(sk3,app(sk9(X0),cons(sk8(X0),nil)))
| ~ strictorderedP(sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f255,f270,f270,f270]) ).
fof(f287,plain,
! [X0] :
( ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0))
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| ~ sQ0_eqProxy(nil,sk4) ),
inference(equality_proxy_replacement,[],[f256,f270,f270]) ).
fof(f354,definition,
( spl1_6
<=> sQ0_eqProxy(nil,sk4) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f357,definition,
( spl1_7
<=> strictorderedP(sk3) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f358,plain,
( ~ strictorderedP(sk3)
| spl1_7 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f360,definition,
( spl1_8
<=> ! [X0] :
( ~ ssList(X0)
| lt(sk8(X0),sk6(X0))
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f361,plain,
( ! [X0] :
( ~ sQ0_eqProxy(sk4,app(sk3,X0))
| lt(sk8(X0),sk6(X0))
| ~ ssList(X0) )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f362,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f287,f360,f357,f354]) ).
fof(f364,definition,
( spl1_9
<=> ! [X0] :
( ~ ssList(X0)
| sQ0_eqProxy(sk3,app(sk9(X0),cons(sk8(X0),nil)))
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f365,plain,
( ! [X0] :
( sQ0_eqProxy(sk3,app(sk9(X0),cons(sk8(X0),nil)))
| ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f366,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_9 ),
inference(avatar_split_clause,[],[f286,f364,f357,f354]) ).
fof(f368,definition,
( spl1_10
<=> ! [X0] :
( ~ ssList(X0)
| ssList(sk9(X0))
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f369,plain,
( ! [X0] :
( ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssList(sk9(X0))
| ~ ssList(X0) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f370,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_10 ),
inference(avatar_split_clause,[],[f285,f368,f357,f354]) ).
fof(f372,definition,
( spl1_11
<=> ! [X0] :
( ~ ssList(X0)
| ssItem(sk8(X0))
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f373,plain,
( ! [X0] :
( ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssItem(sk8(X0))
| ~ ssList(X0) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f374,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_11 ),
inference(avatar_split_clause,[],[f284,f372,f357,f354]) ).
fof(f376,definition,
( spl1_12
<=> ! [X0] :
( ~ ssList(X0)
| sQ0_eqProxy(app(cons(sk6(X0),nil),sk7(X0)),X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f377,plain,
( ! [X0] :
( sQ0_eqProxy(app(cons(sk6(X0),nil),sk7(X0)),X0)
| ~ ssList(X0)
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_12 ),
inference(avatar_split_clause,[],[f283,f376,f357,f354]) ).
fof(f380,definition,
( spl1_13
<=> ! [X0] :
( ~ ssList(X0)
| ssList(sk7(X0))
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f381,plain,
( ! [X0] :
( ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssList(sk7(X0))
| ~ ssList(X0) )
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f382,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_13 ),
inference(avatar_split_clause,[],[f282,f380,f357,f354]) ).
fof(f384,definition,
( spl1_14
<=> sQ0_eqProxy(nil,sk3) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f386,plain,
( spl1_14
| ~ spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f281,f360,f357,f384]) ).
fof(f387,plain,
( spl1_14
| ~ spl1_7
| spl1_9 ),
inference(avatar_split_clause,[],[f280,f364,f357,f384]) ).
fof(f388,plain,
( spl1_14
| ~ spl1_7
| spl1_10 ),
inference(avatar_split_clause,[],[f279,f368,f357,f384]) ).
fof(f389,plain,
( spl1_14
| ~ spl1_7
| spl1_11 ),
inference(avatar_split_clause,[],[f278,f372,f357,f384]) ).
fof(f390,plain,
( spl1_14
| ~ spl1_7
| spl1_12 ),
inference(avatar_split_clause,[],[f277,f376,f357,f384]) ).
fof(f391,plain,
( spl1_14
| ~ spl1_7
| spl1_13 ),
inference(avatar_split_clause,[],[f276,f380,f357,f384]) ).
fof(f393,definition,
( spl1_15
<=> ! [X0] :
( ~ ssList(X0)
| ssItem(sk6(X0))
| ~ sQ0_eqProxy(sk4,app(sk3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f394,plain,
( ! [X0] :
( ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ssItem(sk6(X0))
| ~ ssList(X0) )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f395,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_15 ),
inference(avatar_split_clause,[],[f275,f393,f357,f354]) ).
fof(f396,plain,
( spl1_14
| ~ spl1_7
| spl1_15 ),
inference(avatar_split_clause,[],[f274,f393,f357,f384]) ).
fof(f399,plain,
( ~ spl1_14
| spl1_6 ),
inference(avatar_split_clause,[],[f273,f354,f384]) ).
fof(f400,plain,
( $false
| spl1_7 ),
inference(resolution,[],[f209,f358]) ).
fof(f401,plain,
spl1_7,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f402,plain,
( lt(sk8(sk5),sk6(sk5))
| ~ ssList(sk5)
| ~ spl1_8 ),
inference(resolution,[],[f271,f361]) ).
fof(f403,plain,
( ssItem(sk6(sk5))
| ~ ssList(sk5)
| ~ spl1_15 ),
inference(resolution,[],[f271,f394]) ).
fof(f404,plain,
( ssList(sk7(sk5))
| ~ ssList(sk5)
| ~ spl1_13 ),
inference(resolution,[],[f271,f381]) ).
fof(f405,plain,
( ssItem(sk8(sk5))
| ~ ssList(sk5)
| ~ spl1_11 ),
inference(resolution,[],[f271,f373]) ).
fof(f406,plain,
( ssList(sk9(sk5))
| ~ ssList(sk5)
| ~ spl1_10 ),
inference(resolution,[],[f271,f369]) ).
fof(f408,definition,
( spl1_16
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f409,plain,
( ~ ssList(sk5)
| spl1_16 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f411,definition,
( spl1_17
<=> ssList(sk9(sk5)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f413,plain,
( ~ spl1_16
| spl1_17
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f406,f368,f411,f408]) ).
fof(f415,definition,
( spl1_18
<=> ssItem(sk8(sk5)) ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f417,plain,
( ~ spl1_16
| spl1_18
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f405,f372,f415,f408]) ).
fof(f419,definition,
( spl1_19
<=> ssList(sk7(sk5)) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f421,plain,
( ~ spl1_16
| spl1_19
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f404,f380,f419,f408]) ).
fof(f423,definition,
( spl1_20
<=> ssItem(sk6(sk5)) ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
fof(f425,plain,
( ~ spl1_16
| spl1_20
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f403,f393,f423,f408]) ).
fof(f427,definition,
( spl1_21
<=> lt(sk8(sk5),sk6(sk5)) ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f429,plain,
( ~ spl1_16
| spl1_21
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f402,f360,f427,f408]) ).
fof(f430,plain,
( $false
| spl1_16 ),
inference(resolution,[],[f409,f206]) ).
fof(f431,plain,
spl1_16,
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f434,plain,
( ! [X0,X1] :
( ~ sQ0_eqProxy(sk3,app(X0,cons(X1,nil)))
| ~ ssItem(sk6(sk5))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(sk7(sk5))
| ~ lt(X1,sk6(sk5))
| ~ ssList(sk5)
| ~ sQ0_eqProxy(sk4,app(sk3,sk5)) )
| ~ spl1_12 ),
inference(resolution,[],[f272,f377]) ).
fof(f437,definition,
( spl1_22
<=> sQ0_eqProxy(sk4,app(sk3,sk5)) ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f438,plain,
( ~ sQ0_eqProxy(sk4,app(sk3,sk5))
| spl1_22 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f442,definition,
( spl1_23
<=> ! [X0,X1] :
( ~ sQ0_eqProxy(sk3,app(X0,cons(X1,nil)))
| ~ lt(X1,sk6(sk5))
| ~ ssList(X0)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_23])],[avatar_definition]) ).
fof(f443,plain,
( ! [X0,X1] :
( ~ sQ0_eqProxy(sk3,app(X0,cons(X1,nil)))
| ~ lt(X1,sk6(sk5))
| ~ ssList(X0)
| ~ ssItem(X1) )
| ~ spl1_23 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f444,plain,
( ~ spl1_22
| ~ spl1_16
| ~ spl1_19
| ~ spl1_20
| spl1_23
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f434,f376,f442,f423,f419,f408,f437]) ).
fof(f445,plain,
( $false
| spl1_22 ),
inference(resolution,[],[f438,f271]) ).
fof(f446,plain,
spl1_22,
inference(avatar_contradiction_clause,[],[f445]) ).
fof(f447,plain,
( ! [X0] :
( ~ sQ0_eqProxy(sk4,app(sk3,X0))
| ~ ssList(sk9(X0))
| ~ ssItem(sk8(X0))
| ~ ssList(X0)
| ~ lt(sk8(X0),sk6(sk5)) )
| ~ spl1_9
| ~ spl1_23 ),
inference(resolution,[],[f443,f365]) ).
fof(f448,plain,
( ~ ssList(sk9(sk5))
| ~ ssItem(sk8(sk5))
| ~ ssList(sk5)
| ~ lt(sk8(sk5),sk6(sk5))
| ~ spl1_9
| ~ spl1_23 ),
inference(resolution,[],[f447,f271]) ).
fof(f452,plain,
( ~ spl1_21
| ~ spl1_16
| ~ spl1_18
| ~ spl1_17
| ~ spl1_9
| ~ spl1_23 ),
inference(avatar_split_clause,[],[f448,f442,f364,f411,f415,f408,f427]) ).
cnf(s5,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f362]) ).
cnf(s6,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_9 ),
inference(sat_conversion,[],[f366]) ).
cnf(s7,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_10 ),
inference(sat_conversion,[],[f370]) ).
cnf(s8,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_11 ),
inference(sat_conversion,[],[f374]) ).
cnf(s9,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_12 ),
inference(sat_conversion,[],[f378]) ).
cnf(s10,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_13 ),
inference(sat_conversion,[],[f382]) ).
cnf(s11,plain,
( ~ spl1_7
| spl1_8
| spl1_14 ),
inference(sat_conversion,[],[f386]) ).
cnf(s12,plain,
( ~ spl1_7
| spl1_9
| spl1_14 ),
inference(sat_conversion,[],[f387]) ).
cnf(s13,plain,
( ~ spl1_7
| spl1_10
| spl1_14 ),
inference(sat_conversion,[],[f388]) ).
cnf(s14,plain,
( ~ spl1_7
| spl1_11
| spl1_14 ),
inference(sat_conversion,[],[f389]) ).
cnf(s15,plain,
( ~ spl1_7
| spl1_12
| spl1_14 ),
inference(sat_conversion,[],[f390]) ).
cnf(s16,plain,
( ~ spl1_7
| spl1_13
| spl1_14 ),
inference(sat_conversion,[],[f391]) ).
cnf(s17,plain,
( ~ spl1_6
| ~ spl1_7
| spl1_15 ),
inference(sat_conversion,[],[f395]) ).
cnf(s18,plain,
( ~ spl1_7
| spl1_14
| spl1_15 ),
inference(sat_conversion,[],[f396]) ).
cnf(s19,plain,
( spl1_6
| ~ spl1_14 ),
inference(sat_conversion,[],[f399]) ).
cnf(s20,plain,
spl1_7,
inference(sat_conversion,[],[f401]) ).
cnf(s21,plain,
( ~ spl1_10
| ~ spl1_16
| spl1_17 ),
inference(sat_conversion,[],[f413]) ).
cnf(s22,plain,
( ~ spl1_11
| ~ spl1_16
| spl1_18 ),
inference(sat_conversion,[],[f417]) ).
cnf(s23,plain,
( ~ spl1_13
| ~ spl1_16
| spl1_19 ),
inference(sat_conversion,[],[f421]) ).
cnf(s24,plain,
( ~ spl1_15
| ~ spl1_16
| spl1_20 ),
inference(sat_conversion,[],[f425]) ).
cnf(s25,plain,
( ~ spl1_8
| ~ spl1_16
| spl1_21 ),
inference(sat_conversion,[],[f429]) ).
cnf(s26,plain,
spl1_16,
inference(sat_conversion,[],[f431]) ).
cnf(s28,plain,
( ~ spl1_12
| ~ spl1_16
| ~ spl1_19
| ~ spl1_20
| ~ spl1_22
| spl1_23 ),
inference(sat_conversion,[],[f444]) ).
cnf(s29,plain,
spl1_22,
inference(sat_conversion,[],[f446]) ).
cnf(s30,plain,
( ~ spl1_9
| ~ spl1_16
| ~ spl1_17
| ~ spl1_18
| ~ spl1_21
| ~ spl1_23 ),
inference(sat_conversion,[],[f452]) ).
cnf(s31,plain,
( ~ spl1_12
| ~ spl1_16
| ~ spl1_19
| ~ spl1_20
| spl1_23 ),
inference(rat,[],[s28,s29]) ).
cnf(s32,plain,
( ~ spl1_8
| spl1_21 ),
inference(rat,[],[s25,s26]) ).
cnf(s33,plain,
( ~ spl1_15
| spl1_20 ),
inference(rat,[],[s24,s26]) ).
cnf(s34,plain,
( ~ spl1_13
| spl1_19 ),
inference(rat,[],[s23,s26]) ).
cnf(s35,plain,
( ~ spl1_11
| spl1_18 ),
inference(rat,[],[s22,s26]) ).
cnf(s36,plain,
( ~ spl1_10
| spl1_17 ),
inference(rat,[],[s21,s26]) ).
cnf(s37,plain,
( spl1_14
| spl1_15 ),
inference(rat,[],[s18,s20]) ).
cnf(s38,plain,
( ~ spl1_6
| spl1_15 ),
inference(rat,[],[s17,s20]) ).
cnf(s39,plain,
( spl1_13
| spl1_14 ),
inference(rat,[],[s16,s20]) ).
cnf(s40,plain,
( spl1_12
| spl1_14 ),
inference(rat,[],[s15,s20]) ).
cnf(s41,plain,
( spl1_11
| spl1_14 ),
inference(rat,[],[s14,s20]) ).
cnf(s42,plain,
( spl1_10
| spl1_14 ),
inference(rat,[],[s13,s20]) ).
cnf(s43,plain,
( spl1_9
| spl1_14 ),
inference(rat,[],[s12,s20]) ).
cnf(s44,plain,
( spl1_8
| spl1_14 ),
inference(rat,[],[s11,s20]) ).
cnf(s45,plain,
( ~ spl1_6
| spl1_13 ),
inference(rat,[],[s10,s20]) ).
cnf(s46,plain,
( ~ spl1_6
| spl1_12 ),
inference(rat,[],[s9,s20]) ).
cnf(s47,plain,
( ~ spl1_6
| spl1_11 ),
inference(rat,[],[s8,s20]) ).
cnf(s48,plain,
( ~ spl1_6
| spl1_10 ),
inference(rat,[],[s7,s20]) ).
cnf(s49,plain,
( ~ spl1_6
| spl1_9 ),
inference(rat,[],[s6,s20]) ).
cnf(s50,plain,
( ~ spl1_6
| spl1_8 ),
inference(rat,[],[s5,s20]) ).
cnf(s55,plain,
spl1_14,
inference(rat,[],[s30,s31,s32,s36,s35,s34,s33,s44,s43,s42,s41,s40,s39,s37,s26]) ).
cnf(s56,plain,
spl1_6,
inference(rat,[],[s19,s55]) ).
cnf(s57,plain,
spl1_15,
inference(rat,[],[s38,s56]) ).
cnf(s58,plain,
spl1_13,
inference(rat,[],[s45,s56]) ).
cnf(s59,plain,
spl1_12,
inference(rat,[],[s46,s56]) ).
cnf(s60,plain,
spl1_11,
inference(rat,[],[s47,s56]) ).
cnf(s61,plain,
spl1_10,
inference(rat,[],[s48,s56]) ).
cnf(s62,plain,
spl1_9,
inference(rat,[],[s49,s56]) ).
cnf(s63,plain,
spl1_8,
inference(rat,[],[s50,s56]) ).
cnf(s64,plain,
spl1_20,
inference(rat,[],[s33,s57]) ).
cnf(s65,plain,
spl1_19,
inference(rat,[],[s34,s58]) ).
cnf(s66,plain,
spl1_18,
inference(rat,[],[s35,s60]) ).
cnf(s67,plain,
spl1_17,
inference(rat,[],[s36,s61]) ).
cnf(s68,plain,
spl1_21,
inference(rat,[],[s32,s63]) ).
cnf(s69,plain,
spl1_23,
inference(rat,[],[s31,s59,s64,s26,s65]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s30,s69,s62,s66,s26,s68,s67]) ).
fof(f453,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC343-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 09:16:03 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.96 % (3499358)Input is clausal, will run a generic CNF schedule.
% 0.64/0.96 % (3499369)dis-21_1_sil=8000:lcm=predicate:random_seed=1033695421:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.64/0.96 % (3499369)First to succeed.
% 0.64/0.96 % (3499369)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3499358"
% 0.64/0.96 % (3499366)lrs+10_1_sil=8000:sp=occurrence:random_seed=2319855833:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.64/0.96 % (3499367)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1837151711:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.64/0.96 % (3499365)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2789396286:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.64/0.96 % (3499363)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1162228496:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.64/0.96 % (3499364)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2576302355:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.64/0.96 % (3499366)Also succeeded, but the first one will report.
% 0.64/0.96 % (3499368)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1671749614:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.64/0.96 % (3499368)Also succeeded, but the first one will report.
% 0.64/0.96 % (3499367)Instruction limit reached!
% 0.64/0.96 % (3499367)------------------------------
% 0.64/0.96 % (3499367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.64/0.96 % (3499367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.96 % (3499367)CaDiCaL version: 2.1.3
% 0.64/0.96 % (3499367)Termination reason: Instruction limit
% 0.64/0.96 % (3499367)Termination phase: Saturation
% 0.64/0.96 % (3499367)Time elapsed: 0.065 s
% 0.64/0.96 % (3499367)Peak memory usage: 89 MB
% 0.64/0.96 % (3499367)Instructions burned: 115 (million)
% 0.64/0.96 % (3499369)Refutation found. Thanks to Tanya!
% 0.64/0.96 % SZS status Unsatisfiable for theBenchmark
% 0.64/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.06 % (3499369)------------------------------
% 2.65/1.06 % (3499369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.06 % (3499369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.06 % (3499369)CaDiCaL version: 2.1.3
% 2.65/1.06 % (3499369)Termination reason: Refutation
% 2.65/1.06 % (3499369)Time elapsed: 0.004 s
% 2.65/1.06 % (3499369)Peak memory usage: 89 MB
% 2.65/1.06 % (3499369)Instructions burned: 10 (million)
% 2.65/1.06 % (3499369)------------------------------
% 2.65/1.06 % (3499369)------------------------------
% 2.65/1.06 % (3499358)Success in time 0.3 s
% 2.65/1.06 % Vampire exiting
%------------------------------------------------------------------------------