%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n003.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 01:05:57 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 41
% Syntax : Number of formulae : 171 ( 12 unt; 11 def)
% Number of atoms : 502 ( 90 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 589 ( 258 ~; 320 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 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(f339,definition,
( spl0_1
<=> sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f341,plain,
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f343,definition,
( spl0_2
<=> sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f345,plain,
( sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f346,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f307,f343,f339]) ).
fof(f348,definition,
( spl0_3
<=> sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f350,plain,
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f351,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f306,f348,f339]) ).
fof(f353,definition,
( spl0_4
<=> ssList(sk10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f355,plain,
( ssList(sk10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f356,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f305,f353,f339]) ).
fof(f358,definition,
( spl0_5
<=> ssList(sk13) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f360,plain,
( ssList(sk13)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f361,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f281,f343,f358]) ).
fof(f362,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f279,f348,f358]) ).
fof(f363,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f277,f353,f358]) ).
fof(f365,definition,
( spl0_6
<=> ssItem(sk9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f367,plain,
( ssItem(sk9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f368,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f304,f365,f339]) ).
fof(f369,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f274,f365,f358]) ).
fof(f371,definition,
( spl0_7
<=> ssItem(sk12) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f373,plain,
( ssItem(sk12)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f374,plain,
( spl0_7
| spl0_2 ),
inference(avatar_split_clause,[],[f273,f343,f371]) ).
fof(f375,plain,
( spl0_7
| spl0_3 ),
inference(avatar_split_clause,[],[f271,f348,f371]) ).
fof(f376,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f269,f353,f371]) ).
fof(f377,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f268,f365,f371]) ).
fof(f379,definition,
( spl0_8
<=> ssItem(sk8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f381,plain,
( ssItem(sk8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f382,plain,
( spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f303,f379,f339]) ).
fof(f383,plain,
( spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f265,f379,f358]) ).
fof(f384,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f264,f379,f371]) ).
fof(f386,definition,
( spl0_9
<=> ssItem(sk11) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f388,plain,
( ssItem(sk11)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f389,plain,
( spl0_9
| spl0_2 ),
inference(avatar_split_clause,[],[f263,f343,f386]) ).
fof(f390,plain,
( spl0_9
| spl0_3 ),
inference(avatar_split_clause,[],[f261,f348,f386]) ).
fof(f391,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f259,f353,f386]) ).
fof(f392,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f258,f365,f386]) ).
fof(f393,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f257,f379,f386]) ).
fof(f427,definition,
( spl0_14
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f428,plain,
( ! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f429,plain,
( spl0_14
| spl0_2 ),
inference(avatar_split_clause,[],[f233,f343,f427]) ).
fof(f430,plain,
( spl0_14
| spl0_3 ),
inference(avatar_split_clause,[],[f231,f348,f427]) ).
fof(f431,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f229,f353,f427]) ).
fof(f432,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f227,f365,f427]) ).
fof(f433,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f225,f379,f427]) ).
fof(f439,definition,
( spl0_15
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f440,plain,
( ! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk3 != app(app(cons(X1,nil),cons(X0,nil)),X2)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f441,plain,
( spl0_1
| spl0_15 ),
inference(avatar_split_clause,[],[f294,f439,f339]) ).
fof(f442,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f293,f439,f358]) ).
fof(f445,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f290,f439,f427]) ).
fof(f503,plain,
( sk4 != sk4
| sk3 != app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f440,f350]) ).
fof(f506,plain,
( sk3 != app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f503]) ).
fof(f508,plain,
( ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f506,f345]) ).
fof(f511,plain,
( ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f508,f381]) ).
fof(f514,plain,
( ~ ssItem(sk9)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f511,f355]) ).
fof(f516,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f514,f367]) ).
fof(f517,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f516]) ).
fof(f521,plain,
( sk4 != sk4
| ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f428,f350]) ).
fof(f523,plain,
( sk4 != sk4
| ~ ssItem(sk11)
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f428,f341]) ).
fof(f524,plain,
( ~ ssItem(sk11)
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f523]) ).
fof(f526,plain,
( ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f521]) ).
fof(f527,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f524,f388]) ).
fof(f529,plain,
( ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f526,f381]) ).
fof(f531,plain,
( ~ ssItem(sk12)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f527,f360]) ).
fof(f533,plain,
( ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f529,f355]) ).
fof(f535,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f531,f373]) ).
fof(f536,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f535]) ).
fof(f539,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f533,f367]) ).
fof(f540,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f539]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f346]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f351]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f356]) ).
cnf(s4,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f361]) ).
cnf(s5,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f362]) ).
cnf(s6,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f363]) ).
cnf(s7,plain,
( spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f368]) ).
cnf(s8,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f369]) ).
cnf(s9,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f374]) ).
cnf(s10,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f375]) ).
cnf(s11,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f376]) ).
cnf(s12,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f377]) ).
cnf(s13,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f382]) ).
cnf(s14,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f383]) ).
cnf(s15,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f384]) ).
cnf(s16,plain,
( spl0_2
| spl0_9 ),
inference(sat_conversion,[],[f389]) ).
cnf(s17,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f390]) ).
cnf(s18,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f391]) ).
cnf(s19,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f392]) ).
cnf(s20,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f393]) ).
cnf(s37,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f429]) ).
cnf(s38,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f430]) ).
cnf(s39,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f431]) ).
cnf(s40,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f432]) ).
cnf(s41,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f433]) ).
cnf(s46,plain,
( spl0_1
| spl0_15 ),
inference(sat_conversion,[],[f441]) ).
cnf(s47,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f442]) ).
cnf(s50,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f445]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(sat_conversion,[],[f517]) ).
cnf(s63,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(sat_conversion,[],[f536]) ).
cnf(s65,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(sat_conversion,[],[f540]) ).
cnf(s70,plain,
spl0_1,
inference(rat,[],[s62,s1,s2,s3,s7,s13,s46]) ).
cnf(s71,plain,
spl0_2,
inference(rat,[],[s63,s4,s9,s16,s37,s70]) ).
cnf(s72,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_3
| ~ spl0_4 ),
inference(rat,[],[s50,s62,s65,s71]) ).
cnf(s73,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s15,s63,s20,s41,s70]) ).
cnf(s74,plain,
( ~ spl0_5
| ~ spl0_4
| ~ spl0_3 ),
inference(rat,[],[s63,s12,s19,s40,s72,s73,s70]) ).
cnf(s75,plain,
( ~ spl0_4
| ~ spl0_3 ),
inference(rat,[],[s62,s8,s14,s47,s74,s71]) ).
cnf(s76,plain,
spl0_4,
inference(rat,[],[s63,s6,s11,s18,s39,s70]) ).
cnf(s77,plain,
~ spl0_3,
inference(rat,[],[s75,s76]) ).
cnf(s78,plain,
spl0_14,
inference(rat,[],[s38,s77]) ).
cnf(s79,plain,
spl0_9,
inference(rat,[],[s17,s77]) ).
cnf(s80,plain,
spl0_7,
inference(rat,[],[s10,s77]) ).
cnf(s81,plain,
spl0_5,
inference(rat,[],[s5,s77]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s63,s79,s81,s70,s78,s80]) ).
fof(f542,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.20 % Computer : n003.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 09:34:12 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.19/0.29 % (1461629)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (1461639)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=202863140:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (1461635)% WARNING: option uhcvi not known.
% 0.19/0.29 % (1461634)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2828274706_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (1461636)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3073461545:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (1461635)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2490394372:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (1461637)dis+10_1_sil=32000:sp=arity:random_seed=2354457673:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (1461638)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1679604029:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (1461640)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=726917135:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (1461637) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1461629-1461637"...
% 0.19/0.29 % (1461635) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1461629-1461635"...
% 0.19/0.29 % (1461640) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1461629-1461640"...
% 0.19/0.29 % (1461637)...printing done.
% 0.19/0.29 % (1461635)...printing done.
% 0.19/0.29 % (1461637)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (1461637)------------------------------
% 0.19/0.30 % (1461637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1461637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1461637)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1461637)Termination reason: Refutation
% 0.19/0.30 % (1461637)Time elapsed: 0.008 s
% 0.19/0.30 % (1461637)Peak memory usage: 12 MB
% 0.19/0.30 % (1461637)Instructions burned: 12 (million)
% 0.19/0.30 % (1461629)Success in time 0.058 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------