%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC413-1 : 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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:03:53 PM UTC 2026
% Result : Unsatisfiable 1.88s 0.79s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 172 ( 12 unt; 12 def)
% Number of atoms : 487 ( 74 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 535 ( 220 ~; 303 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 107 !; 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,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| app(app(cons(X3,nil),cons(X4,nil)),X5) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk2 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk1 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| sk4 != app(app(cons(X3,nil),cons(X4,nil)),X5) ),
inference(reorient_equations,[],[f206]) ).
fof(f212,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk2 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk1 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| ssList(sk13) ),
inference(reorient_equations,[],[f212]) ).
fof(f214,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| app(app(cons(X1,nil),cons(X0,nil)),X2) != sk1
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f215,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk2 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk1 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(reorient_equations,[],[f214]) ).
fof(f224,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk8)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f225,plain,
! [X2,X0,X1] :
( ssItem(sk8)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2) ),
inference(reorient_equations,[],[f224]) ).
fof(f226,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk9)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f227,plain,
! [X2,X0,X1] :
( ssItem(sk9)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2) ),
inference(reorient_equations,[],[f226]) ).
fof(f228,negated_conjecture,
! [X2,X0,X1] :
( ssList(sk10)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f229,plain,
! [X2,X0,X1] :
( ssList(sk10)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2) ),
inference(reorient_equations,[],[f228]) ).
fof(f230,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f231,plain,
! [X2,X0,X1] :
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2) ),
inference(reorient_equations,[],[f230]) ).
fof(f232,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f233,plain,
! [X2,X0,X1] :
( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2) ),
inference(reorient_equations,[],[f232]) ).
fof(f257,negated_conjecture,
( ssItem(sk8)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_37) ).
fof(f258,negated_conjecture,
( ssItem(sk9)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_38) ).
fof(f259,negated_conjecture,
( ssList(sk10)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_39) ).
fof(f260,negated_conjecture,
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_40) ).
fof(f261,plain,
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| ssItem(sk11) ),
inference(reorient_equations,[],[f260]) ).
fof(f262,negated_conjecture,
( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_41) ).
fof(f263,plain,
( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ssItem(sk11) ),
inference(reorient_equations,[],[f262]) ).
fof(f264,negated_conjecture,
( ssItem(sk8)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_42) ).
fof(f265,negated_conjecture,
( ssItem(sk8)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_43) ).
fof(f266,negated_conjecture,
( ssItem(sk8)
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_44) ).
fof(f267,plain,
( ssItem(sk8)
| sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(reorient_equations,[],[f266]) ).
fof(f268,negated_conjecture,
( ssItem(sk9)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_45) ).
fof(f269,negated_conjecture,
( ssList(sk10)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_46) ).
fof(f270,negated_conjecture,
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_47) ).
fof(f271,plain,
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| ssItem(sk12) ),
inference(reorient_equations,[],[f270]) ).
fof(f272,negated_conjecture,
( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_48) ).
fof(f273,plain,
( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ssItem(sk12) ),
inference(reorient_equations,[],[f272]) ).
fof(f274,negated_conjecture,
( ssItem(sk9)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_49) ).
fof(f275,negated_conjecture,
( ssItem(sk9)
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_50) ).
fof(f276,plain,
( ssItem(sk9)
| sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(reorient_equations,[],[f275]) ).
fof(f277,negated_conjecture,
( ssList(sk10)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_51) ).
fof(f278,negated_conjecture,
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_52) ).
fof(f279,plain,
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| ssList(sk13) ),
inference(reorient_equations,[],[f278]) ).
fof(f280,negated_conjecture,
( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_53) ).
fof(f281,plain,
( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ssList(sk13) ),
inference(reorient_equations,[],[f280]) ).
fof(f282,negated_conjecture,
( ssList(sk10)
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_54) ).
fof(f283,plain,
( ssList(sk10)
| sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(reorient_equations,[],[f282]) ).
fof(f284,negated_conjecture,
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_55) ).
fof(f285,plain,
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(reorient_equations,[],[f284]) ).
fof(f286,negated_conjecture,
( app(app(cons(sk9,nil),cons(sk8,nil)),sk10) = sk3
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_56) ).
fof(f287,plain,
( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| sk2 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(reorient_equations,[],[f286]) ).
fof(f290,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| sk4 != app(app(cons(X3,nil),cons(X4,nil)),X5) ),
inference(definition_unfolding,[],[f207,f204,f205]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| ssList(sk13) ),
inference(definition_unfolding,[],[f213,f204,f205]) ).
fof(f294,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(definition_unfolding,[],[f215,f204,f205,f204]) ).
fof(f303,plain,
( ssItem(sk8)
| sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(definition_unfolding,[],[f267,f204]) ).
fof(f304,plain,
( ssItem(sk9)
| sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(definition_unfolding,[],[f276,f204]) ).
fof(f305,plain,
( ssList(sk10)
| sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(definition_unfolding,[],[f283,f204]) ).
fof(f306,plain,
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(definition_unfolding,[],[f285,f204]) ).
fof(f307,plain,
( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
inference(definition_unfolding,[],[f287,f204]) ).
fof(f310,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f311,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ sQ0_eqProxy(sk3,app(app(cons(X1,nil),cons(X0,nil)),X2))
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| ~ sQ0_eqProxy(sk4,app(app(cons(X3,nil),cons(X4,nil)),X5)) ),
inference(equality_proxy_replacement,[],[f290,f310,f310,f310]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ sQ0_eqProxy(sk3,app(app(cons(X1,nil),cons(X0,nil)),X2))
| ssList(sk13) ),
inference(equality_proxy_replacement,[],[f293,f310,f310]) ).
fof(f315,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ sQ0_eqProxy(sk3,app(app(cons(X1,nil),cons(X0,nil)),X2))
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
inference(equality_proxy_replacement,[],[f294,f310,f310,f310]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ssItem(sk8)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2)) ),
inference(equality_proxy_replacement,[],[f225,f310]) ).
fof(f321,plain,
! [X2,X0,X1] :
( ssItem(sk9)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2)) ),
inference(equality_proxy_replacement,[],[f227,f310]) ).
fof(f322,plain,
! [X2,X0,X1] :
( ssList(sk10)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2)) ),
inference(equality_proxy_replacement,[],[f229,f310]) ).
fof(f323,plain,
! [X2,X0,X1] :
( sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2)) ),
inference(equality_proxy_replacement,[],[f231,f310,f310]) ).
fof(f324,plain,
! [X2,X0,X1] :
( sQ0_eqProxy(sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2)) ),
inference(equality_proxy_replacement,[],[f233,f310,f310]) ).
fof(f332,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
| ssItem(sk11) ),
inference(equality_proxy_replacement,[],[f261,f310]) ).
fof(f333,plain,
( sQ0_eqProxy(sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
| ssItem(sk11) ),
inference(equality_proxy_replacement,[],[f263,f310]) ).
fof(f334,plain,
( ssItem(sk8)
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
inference(equality_proxy_replacement,[],[f303,f310]) ).
fof(f335,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
| ssItem(sk12) ),
inference(equality_proxy_replacement,[],[f271,f310]) ).
fof(f336,plain,
( sQ0_eqProxy(sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
| ssItem(sk12) ),
inference(equality_proxy_replacement,[],[f273,f310]) ).
fof(f337,plain,
( ssItem(sk9)
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
inference(equality_proxy_replacement,[],[f304,f310]) ).
fof(f338,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
| ssList(sk13) ),
inference(equality_proxy_replacement,[],[f279,f310]) ).
fof(f339,plain,
( sQ0_eqProxy(sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
| ssList(sk13) ),
inference(equality_proxy_replacement,[],[f281,f310]) ).
fof(f340,plain,
( ssList(sk10)
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
inference(equality_proxy_replacement,[],[f305,f310]) ).
fof(f341,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
inference(equality_proxy_replacement,[],[f306,f310,f310]) ).
fof(f342,plain,
( sQ0_eqProxy(sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
inference(equality_proxy_replacement,[],[f307,f310,f310]) ).
fof(f368,definition,
( spl1_3
<=> sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f369,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk11,nil),cons(sk12,nil)),sk13))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f371,definition,
( spl1_4
<=> sQ0_eqProxy(sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f372,plain,
( sQ0_eqProxy(sk3,app(app(cons(sk9,nil),cons(sk8,nil)),sk10))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f373,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f342,f371,f368]) ).
fof(f375,definition,
( spl1_5
<=> sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f376,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f377,plain,
( spl1_3
| spl1_5 ),
inference(avatar_split_clause,[],[f341,f375,f368]) ).
fof(f379,definition,
( spl1_6
<=> ssList(sk10) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f381,plain,
( spl1_3
| spl1_6 ),
inference(avatar_split_clause,[],[f340,f379,f368]) ).
fof(f383,definition,
( spl1_7
<=> ssList(sk13) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f385,plain,
( spl1_7
| spl1_4 ),
inference(avatar_split_clause,[],[f339,f371,f383]) ).
fof(f386,plain,
( spl1_7
| spl1_5 ),
inference(avatar_split_clause,[],[f338,f375,f383]) ).
fof(f387,plain,
( spl1_7
| spl1_6 ),
inference(avatar_split_clause,[],[f277,f379,f383]) ).
fof(f389,definition,
( spl1_8
<=> ssItem(sk9) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f391,plain,
( spl1_3
| spl1_8 ),
inference(avatar_split_clause,[],[f337,f389,f368]) ).
fof(f392,plain,
( spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f274,f389,f383]) ).
fof(f394,definition,
( spl1_9
<=> ssItem(sk12) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f396,plain,
( spl1_9
| spl1_4 ),
inference(avatar_split_clause,[],[f336,f371,f394]) ).
fof(f397,plain,
( spl1_9
| spl1_5 ),
inference(avatar_split_clause,[],[f335,f375,f394]) ).
fof(f398,plain,
( spl1_9
| spl1_6 ),
inference(avatar_split_clause,[],[f269,f379,f394]) ).
fof(f399,plain,
( spl1_9
| spl1_8 ),
inference(avatar_split_clause,[],[f268,f389,f394]) ).
fof(f401,definition,
( spl1_10
<=> ssItem(sk8) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f403,plain,
( spl1_3
| spl1_10 ),
inference(avatar_split_clause,[],[f334,f401,f368]) ).
fof(f404,plain,
( spl1_7
| spl1_10 ),
inference(avatar_split_clause,[],[f265,f401,f383]) ).
fof(f405,plain,
( spl1_9
| spl1_10 ),
inference(avatar_split_clause,[],[f264,f401,f394]) ).
fof(f407,definition,
( spl1_11
<=> ssItem(sk11) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f409,plain,
( spl1_11
| spl1_4 ),
inference(avatar_split_clause,[],[f333,f371,f407]) ).
fof(f410,plain,
( spl1_11
| spl1_5 ),
inference(avatar_split_clause,[],[f332,f375,f407]) ).
fof(f411,plain,
( spl1_11
| spl1_6 ),
inference(avatar_split_clause,[],[f259,f379,f407]) ).
fof(f412,plain,
( spl1_11
| spl1_8 ),
inference(avatar_split_clause,[],[f258,f389,f407]) ).
fof(f413,plain,
( spl1_11
| spl1_10 ),
inference(avatar_split_clause,[],[f257,f401,f407]) ).
fof(f443,definition,
( spl1_16
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f444,plain,
( ! [X2,X0,X1] :
( ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( spl1_16
| spl1_4 ),
inference(avatar_split_clause,[],[f324,f371,f443]) ).
fof(f446,plain,
( spl1_16
| spl1_5 ),
inference(avatar_split_clause,[],[f323,f375,f443]) ).
fof(f447,plain,
( spl1_16
| spl1_6 ),
inference(avatar_split_clause,[],[f322,f379,f443]) ).
fof(f448,plain,
( spl1_16
| spl1_8 ),
inference(avatar_split_clause,[],[f321,f389,f443]) ).
fof(f449,plain,
( spl1_16
| spl1_10 ),
inference(avatar_split_clause,[],[f320,f401,f443]) ).
fof(f455,definition,
( spl1_17
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ sQ0_eqProxy(sk3,app(app(cons(X1,nil),cons(X0,nil)),X2))
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f456,plain,
( ! [X2,X0,X1] :
( ~ sQ0_eqProxy(sk3,app(app(cons(X1,nil),cons(X0,nil)),X2))
| ~ ssItem(X0)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f457,plain,
( spl1_3
| spl1_17 ),
inference(avatar_split_clause,[],[f315,f455,f368]) ).
fof(f458,plain,
( spl1_7
| spl1_17 ),
inference(avatar_split_clause,[],[f314,f455,f383]) ).
fof(f461,plain,
( spl1_16
| spl1_17 ),
inference(avatar_split_clause,[],[f311,f455,f443]) ).
fof(f462,plain,
( ~ ssItem(sk11)
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ spl1_3
| ~ spl1_16 ),
inference(resolution,[],[f444,f369]) ).
fof(f466,plain,
( ~ spl1_9
| ~ spl1_7
| ~ spl1_11
| ~ spl1_3
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f462,f443,f368,f407,f383,f394]) ).
fof(f467,plain,
( ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl1_5
| ~ spl1_16 ),
inference(resolution,[],[f376,f444]) ).
fof(f471,plain,
( ~ spl1_8
| ~ spl1_6
| ~ spl1_10
| ~ spl1_5
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f467,f443,f375,f401,f379,f389]) ).
fof(f472,plain,
( ~ ssItem(sk8)
| ~ sQ0_eqProxy(sk4,app(app(cons(sk8,nil),cons(sk9,nil)),sk10))
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl1_4
| ~ spl1_17 ),
inference(resolution,[],[f456,f372]) ).
fof(f474,plain,
( ~ spl1_8
| ~ spl1_6
| ~ spl1_5
| ~ spl1_10
| ~ spl1_4
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f472,f455,f371,f401,f375,f379,f389]) ).
cnf(s2,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f373]) ).
cnf(s3,plain,
( spl1_3
| spl1_5 ),
inference(sat_conversion,[],[f377]) ).
cnf(s4,plain,
( spl1_3
| spl1_6 ),
inference(sat_conversion,[],[f381]) ).
cnf(s5,plain,
( spl1_4
| spl1_7 ),
inference(sat_conversion,[],[f385]) ).
cnf(s6,plain,
( spl1_5
| spl1_7 ),
inference(sat_conversion,[],[f386]) ).
cnf(s7,plain,
( spl1_6
| spl1_7 ),
inference(sat_conversion,[],[f387]) ).
cnf(s8,plain,
( spl1_3
| spl1_8 ),
inference(sat_conversion,[],[f391]) ).
cnf(s9,plain,
( spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f392]) ).
cnf(s10,plain,
( spl1_4
| spl1_9 ),
inference(sat_conversion,[],[f396]) ).
cnf(s11,plain,
( spl1_5
| spl1_9 ),
inference(sat_conversion,[],[f397]) ).
cnf(s12,plain,
( spl1_6
| spl1_9 ),
inference(sat_conversion,[],[f398]) ).
cnf(s13,plain,
( spl1_8
| spl1_9 ),
inference(sat_conversion,[],[f399]) ).
cnf(s14,plain,
( spl1_3
| spl1_10 ),
inference(sat_conversion,[],[f403]) ).
cnf(s15,plain,
( spl1_7
| spl1_10 ),
inference(sat_conversion,[],[f404]) ).
cnf(s16,plain,
( spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f405]) ).
cnf(s17,plain,
( spl1_4
| spl1_11 ),
inference(sat_conversion,[],[f409]) ).
cnf(s18,plain,
( spl1_5
| spl1_11 ),
inference(sat_conversion,[],[f410]) ).
cnf(s19,plain,
( spl1_6
| spl1_11 ),
inference(sat_conversion,[],[f411]) ).
cnf(s20,plain,
( spl1_8
| spl1_11 ),
inference(sat_conversion,[],[f412]) ).
cnf(s21,plain,
( spl1_10
| spl1_11 ),
inference(sat_conversion,[],[f413]) ).
cnf(s38,plain,
( spl1_4
| spl1_16 ),
inference(sat_conversion,[],[f445]) ).
cnf(s39,plain,
( spl1_5
| spl1_16 ),
inference(sat_conversion,[],[f446]) ).
cnf(s40,plain,
( spl1_6
| spl1_16 ),
inference(sat_conversion,[],[f447]) ).
cnf(s41,plain,
( spl1_8
| spl1_16 ),
inference(sat_conversion,[],[f448]) ).
cnf(s42,plain,
( spl1_10
| spl1_16 ),
inference(sat_conversion,[],[f449]) ).
cnf(s47,plain,
( spl1_3
| spl1_17 ),
inference(sat_conversion,[],[f457]) ).
cnf(s48,plain,
( spl1_7
| spl1_17 ),
inference(sat_conversion,[],[f458]) ).
cnf(s51,plain,
( spl1_16
| spl1_17 ),
inference(sat_conversion,[],[f461]) ).
cnf(s52,plain,
( ~ spl1_3
| ~ spl1_7
| ~ spl1_9
| ~ spl1_11
| ~ spl1_16 ),
inference(sat_conversion,[],[f466]) ).
cnf(s53,plain,
( ~ spl1_5
| ~ spl1_6
| ~ spl1_8
| ~ spl1_10
| ~ spl1_16 ),
inference(sat_conversion,[],[f471]) ).
cnf(s54,plain,
( ~ spl1_4
| ~ spl1_5
| ~ spl1_6
| ~ spl1_8
| ~ spl1_10
| ~ spl1_17 ),
inference(sat_conversion,[],[f474]) ).
cnf(s55,plain,
spl1_3,
inference(rat,[],[s54,s2,s3,s4,s8,s14,s47]) ).
cnf(s56,plain,
( spl1_7
| ~ spl1_6
| ~ spl1_5
| ~ spl1_4 ),
inference(rat,[],[s54,s9,s15,s48]) ).
cnf(s57,plain,
( ~ spl1_10
| ~ spl1_8
| ~ spl1_6
| ~ spl1_5
| ~ spl1_4 ),
inference(rat,[],[s51,s54,s53]) ).
cnf(s58,plain,
( spl1_10
| ~ spl1_7 ),
inference(rat,[],[s52,s16,s21,s42,s55]) ).
cnf(s59,plain,
( ~ spl1_6
| ~ spl1_5
| ~ spl1_4 ),
inference(rat,[],[s52,s13,s20,s41,s57,s58,s56,s55]) ).
cnf(s60,plain,
spl1_6,
inference(rat,[],[s52,s7,s12,s19,s40,s55]) ).
cnf(s61,plain,
spl1_5,
inference(rat,[],[s52,s6,s11,s18,s39,s55]) ).
cnf(s62,plain,
~ spl1_4,
inference(rat,[],[s59,s60,s61]) ).
cnf(s63,plain,
spl1_16,
inference(rat,[],[s38,s62]) ).
cnf(s64,plain,
spl1_11,
inference(rat,[],[s17,s62]) ).
cnf(s65,plain,
spl1_9,
inference(rat,[],[s10,s62]) ).
cnf(s66,plain,
spl1_7,
inference(rat,[],[s5,s62]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s52,s66,s55,s64,s63,s65]) ).
fof(f475,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC413-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n013.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Mon Sep 28 09:31:51 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 1.88/0.79 % (1049103)Input is clausal, will run a generic CNF schedule.
% 1.88/0.79 % (1049185)dis-21_1_sil=8000:lcm=predicate:random_seed=3656496310: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)
% 1.88/0.79 % (1049185)First to succeed.
% 1.88/0.79 % (1049185)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1049103"
% 1.88/0.79 % (1049179)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=3360123537:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.88/0.79 % (1049183)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1627608351:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.88/0.79 % (1049181)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=749713748:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.88/0.79 % (1049184)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=522444804:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.88/0.79 % (1049180)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4284433620:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.88/0.79 % (1049183)Also succeeded, but the first one will report.
% 1.88/0.79 % (1049184)Also succeeded, but the first one will report.
% 1.88/0.79 % (1049182)lrs+10_1_sil=8000:sp=occurrence:random_seed=4038485744:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.88/0.79 % (1049182)Also succeeded, but the first one will report.
% 1.88/0.79 % (1049185)Refutation found. Thanks to Tanya!
% 1.88/0.79 % SZS status Unsatisfiable for theBenchmark
% 1.88/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/0.89 % (1049185)------------------------------
% 2.54/0.89 % (1049185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/0.89 % (1049185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.89 % (1049185)CaDiCaL version: 2.1.3
% 2.54/0.89 % (1049185)Termination reason: Refutation
% 2.54/0.89 % (1049185)Time elapsed: 0.004 s
% 2.54/0.89 % (1049185)Peak memory usage: 89 MB
% 2.54/0.89 % (1049185)Instructions burned: 9 (million)
% 2.54/0.89 % (1049185)------------------------------
% 2.54/0.89 % (1049185)------------------------------
% 2.54/0.89 % (1049103)Success in time 0.324 s
% 2.54/0.89 % Vampire exiting
%------------------------------------------------------------------------------