%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC414-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 01:05:57 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 50
% Syntax : Number of formulae : 188 ( 15 unt; 17 def)
% Number of atoms : 543 ( 105 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 632 ( 277 ~; 338 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 18 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk2
| app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4) != sk1
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ ssList(X7)
| app(app(cons(X5,nil),cons(X6,nil)),X7) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| sk2 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| sk1 != app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4)
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ ssList(X7)
| sk4 != app(app(cons(X5,nil),cons(X6,nil)),X7) ),
inference(reorient_equations,[],[f206]) ).
fof(f214,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4) != sk2
| app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4) != sk1
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f215,plain,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| sk2 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| sk1 != app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4)
| 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',co1_37) ).
fof(f258,negated_conjecture,
( ssItem(sk9)
| ssItem(sk11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_38) ).
fof(f259,negated_conjecture,
( ssList(sk10)
| ssItem(sk11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_39) ).
fof(f260,negated_conjecture,
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| ssItem(sk11) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',co1_42) ).
fof(f265,negated_conjecture,
( ssItem(sk8)
| ssList(sk13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_43) ).
fof(f266,negated_conjecture,
( ssItem(sk8)
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',co1_45) ).
fof(f269,negated_conjecture,
( ssList(sk10)
| ssItem(sk12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_46) ).
fof(f270,negated_conjecture,
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| ssItem(sk12) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',co1_49) ).
fof(f275,negated_conjecture,
( ssItem(sk9)
| app(app(cons(sk11,nil),cons(sk12,nil)),sk13) = sk2 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',co1_51) ).
fof(f278,negated_conjecture,
( app(app(cons(sk8,nil),cons(sk9,nil)),sk10) = sk4
| ssList(sk13) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,X6,X7,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| sk4 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| sk3 != app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4)
| ~ ssItem(X5)
| ~ ssItem(X6)
| ~ ssList(X7)
| sk4 != app(app(cons(X5,nil),cons(X6,nil)),X7) ),
inference(definition_unfolding,[],[f207,f204,f205]) ).
fof(f294,plain,
! [X2,X3,X0,X1,X4] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| sk4 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| sk3 != app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4)
| 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(f394,definition,
( spl0_1
<=> sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f396,plain,
( sk4 = app(app(cons(sk11,nil),cons(sk12,nil)),sk13)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f398,definition,
( spl0_2
<=> sk3 = app(app(cons(sk9,nil),cons(sk8,nil)),sk10) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f401,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f307,f398,f394]) ).
fof(f403,definition,
( spl0_3
<=> sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f405,plain,
( sk4 = app(app(cons(sk8,nil),cons(sk9,nil)),sk10)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f406,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f306,f403,f394]) ).
fof(f408,definition,
( spl0_4
<=> ssList(sk10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f411,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f305,f408,f394]) ).
fof(f413,definition,
( spl0_5
<=> ssList(sk13) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f416,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f281,f398,f413]) ).
fof(f417,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f279,f403,f413]) ).
fof(f418,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f277,f408,f413]) ).
fof(f420,definition,
( spl0_6
<=> ssItem(sk9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f423,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f304,f420,f394]) ).
fof(f424,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f274,f420,f413]) ).
fof(f426,definition,
( spl0_7
<=> ssItem(sk12) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f429,plain,
( spl0_7
| spl0_2 ),
inference(avatar_split_clause,[],[f273,f398,f426]) ).
fof(f430,plain,
( spl0_7
| spl0_3 ),
inference(avatar_split_clause,[],[f271,f403,f426]) ).
fof(f431,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f269,f408,f426]) ).
fof(f432,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f268,f420,f426]) ).
fof(f434,definition,
( spl0_8
<=> ssItem(sk8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f437,plain,
( spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f303,f434,f394]) ).
fof(f438,plain,
( spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f265,f434,f413]) ).
fof(f439,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f264,f434,f426]) ).
fof(f441,definition,
( spl0_9
<=> ssItem(sk11) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f444,plain,
( spl0_9
| spl0_2 ),
inference(avatar_split_clause,[],[f263,f398,f441]) ).
fof(f445,plain,
( spl0_9
| spl0_3 ),
inference(avatar_split_clause,[],[f261,f403,f441]) ).
fof(f446,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f259,f408,f441]) ).
fof(f447,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f258,f420,f441]) ).
fof(f448,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f257,f434,f441]) ).
fof(f482,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(f483,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,[],[f482]) ).
fof(f484,plain,
( spl0_14
| spl0_2 ),
inference(avatar_split_clause,[],[f233,f398,f482]) ).
fof(f485,plain,
( spl0_14
| spl0_3 ),
inference(avatar_split_clause,[],[f231,f403,f482]) ).
fof(f486,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f229,f408,f482]) ).
fof(f487,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f227,f420,f482]) ).
fof(f488,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f225,f434,f482]) ).
fof(f494,definition,
( spl0_15
<=> ! [X2,X4,X0,X3,X1] :
( ~ ssItem(X0)
| sk3 != app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4)
| sk4 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f495,plain,
( ! [X2,X3,X0,X1,X4] :
( sk4 != app(app(app(app(X2,cons(X0,nil)),X3),cons(X1,nil)),X4)
| sk3 != app(app(app(app(X2,cons(X1,nil)),X3),cons(X0,nil)),X4)
| ~ ssItem(X0)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f496,plain,
( spl0_1
| spl0_15 ),
inference(avatar_split_clause,[],[f294,f494,f394]) ).
fof(f500,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f290,f494,f482]) ).
fof(f506,definition,
( spl0_17
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f542,plain,
spl0_17,
inference(avatar_split_clause,[],[f8,f506]) ).
fof(f559,definition,
( spl0_27
<=> ssList(cons(sk8,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f560,plain,
( ssList(cons(sk8,nil))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f561,plain,
( ~ ssList(cons(sk8,nil))
| spl0_27 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f567,definition,
( spl0_29
<=> ssList(cons(sk9,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f568,plain,
( ssList(cons(sk9,nil))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f569,plain,
( ~ ssList(cons(sk9,nil))
| spl0_29 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f710,plain,
( ~ ssList(nil)
| ~ ssItem(sk8)
| spl0_27 ),
inference(resolution,[],[f86,f561]) ).
fof(f711,plain,
( ~ ssList(nil)
| ~ ssItem(sk9)
| spl0_29 ),
inference(resolution,[],[f86,f569]) ).
fof(f714,plain,
( ~ spl0_6
| ~ spl0_17
| spl0_29 ),
inference(avatar_split_clause,[],[f711,f567,f506,f420]) ).
fof(f715,plain,
( ~ spl0_8
| ~ spl0_17
| spl0_27 ),
inference(avatar_split_clause,[],[f710,f559,f506,f434]) ).
fof(f719,plain,
( cons(sk8,nil) = app(nil,cons(sk8,nil))
| ~ spl0_27 ),
inference(resolution,[],[f560,f74]) ).
fof(f720,plain,
( cons(sk8,nil) = app(cons(sk8,nil),nil)
| ~ spl0_27 ),
inference(resolution,[],[f560,f73]) ).
fof(f726,plain,
( cons(sk9,nil) = app(nil,cons(sk9,nil))
| ~ spl0_29 ),
inference(resolution,[],[f568,f74]) ).
fof(f727,plain,
( cons(sk9,nil) = app(cons(sk9,nil),nil)
| ~ spl0_29 ),
inference(resolution,[],[f568,f73]) ).
fof(f741,plain,
( ! [X2,X0,X1] :
( sk4 != app(app(app(cons(sk8,nil),X0),cons(X1,nil)),X2)
| sk3 != app(app(app(app(nil,cons(X1,nil)),X0),cons(sk8,nil)),X2)
| ~ ssItem(sk8)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(X1) )
| ~ spl0_15
| ~ spl0_27 ),
inference(superposition,[],[f495,f719]) ).
fof(f744,definition,
( spl0_32
<=> ! [X2,X0,X1] :
( sk4 != app(app(app(cons(sk8,nil),X0),cons(X1,nil)),X2)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| sk3 != app(app(app(app(nil,cons(X1,nil)),X0),cons(sk8,nil)),X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f745,plain,
( ! [X2,X0,X1] :
( sk4 != app(app(app(cons(sk8,nil),X0),cons(X1,nil)),X2)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| sk3 != app(app(app(app(nil,cons(X1,nil)),X0),cons(sk8,nil)),X2) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f746,plain,
( ~ spl0_17
| ~ spl0_8
| spl0_32
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f741,f559,f494,f744,f434,f506]) ).
fof(f777,plain,
( sk4 != sk4
| ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f483,f405]) ).
fof(f779,plain,
( sk4 != sk4
| ~ ssItem(sk11)
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ spl0_1
| ~ spl0_14 ),
inference(superposition,[],[f483,f396]) ).
fof(f780,plain,
( ~ ssItem(sk11)
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ spl0_1
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f779]) ).
fof(f782,plain,
( ~ ssItem(sk8)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f777]) ).
fof(f783,plain,
( ~ spl0_7
| ~ spl0_5
| ~ spl0_9
| ~ spl0_1
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f780,f482,f394,f441,f413,f426]) ).
fof(f785,plain,
( ~ spl0_6
| ~ spl0_4
| ~ spl0_8
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f782,f482,f403,f434,f408,f420]) ).
fof(f842,plain,
( ! [X0,X1] :
( sk4 != app(app(cons(sk8,nil),cons(X0,nil)),X1)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| sk3 != app(app(app(app(nil,cons(X0,nil)),nil),cons(sk8,nil)),X1) )
| ~ spl0_27
| ~ spl0_32 ),
inference(superposition,[],[f745,f720]) ).
fof(f844,definition,
( spl0_40
<=> ! [X0,X1] :
( sk4 != app(app(cons(sk8,nil),cons(X0,nil)),X1)
| sk3 != app(app(app(app(nil,cons(X0,nil)),nil),cons(sk8,nil)),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f845,plain,
( ! [X0,X1] :
( sk4 != app(app(cons(sk8,nil),cons(X0,nil)),X1)
| sk3 != app(app(app(app(nil,cons(X0,nil)),nil),cons(sk8,nil)),X1)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f846,plain,
( ~ spl0_17
| spl0_40
| ~ spl0_27
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f842,f744,f559,f844,f506]) ).
fof(f847,plain,
( sk4 != sk4
| sk3 != app(app(app(app(nil,cons(sk9,nil)),nil),cons(sk8,nil)),sk10)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_40 ),
inference(superposition,[],[f845,f405]) ).
fof(f848,plain,
( sk3 != app(app(app(app(nil,cons(sk9,nil)),nil),cons(sk8,nil)),sk10)
| ~ ssList(sk10)
| ~ ssItem(sk9)
| ~ spl0_3
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f847]) ).
fof(f850,definition,
( spl0_41
<=> sk3 = app(app(app(app(nil,cons(sk9,nil)),nil),cons(sk8,nil)),sk10) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f852,plain,
( sk3 != app(app(app(app(nil,cons(sk9,nil)),nil),cons(sk8,nil)),sk10)
| spl0_41 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f853,plain,
( ~ spl0_6
| ~ spl0_4
| ~ spl0_41
| ~ spl0_3
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f848,f844,f403,f850,f408,f420]) ).
fof(f854,plain,
( sk3 != app(app(app(cons(sk9,nil),nil),cons(sk8,nil)),sk10)
| ~ spl0_29
| spl0_41 ),
inference(superposition,[],[f852,f726]) ).
fof(f855,plain,
( sk3 != app(app(cons(sk9,nil),cons(sk8,nil)),sk10)
| ~ spl0_29
| spl0_41 ),
inference(superposition,[],[f854,f727]) ).
fof(f856,plain,
( ~ spl0_2
| ~ spl0_29
| spl0_41 ),
inference(avatar_split_clause,[],[f855,f850,f567,f398]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f401]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f406]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f411]) ).
cnf(s4,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f416]) ).
cnf(s5,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f417]) ).
cnf(s6,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f418]) ).
cnf(s7,plain,
( spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f423]) ).
cnf(s8,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f424]) ).
cnf(s9,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f429]) ).
cnf(s10,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f430]) ).
cnf(s11,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f431]) ).
cnf(s12,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f432]) ).
cnf(s13,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f437]) ).
cnf(s14,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f438]) ).
cnf(s15,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f439]) ).
cnf(s16,plain,
( spl0_2
| spl0_9 ),
inference(sat_conversion,[],[f444]) ).
cnf(s17,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f445]) ).
cnf(s18,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f446]) ).
cnf(s19,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f447]) ).
cnf(s20,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f448]) ).
cnf(s37,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f484]) ).
cnf(s38,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f485]) ).
cnf(s39,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f486]) ).
cnf(s40,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f487]) ).
cnf(s41,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f488]) ).
cnf(s46,plain,
( spl0_1
| spl0_15 ),
inference(sat_conversion,[],[f496]) ).
cnf(s50,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f500]) ).
cnf(s60,plain,
spl0_17,
inference(sat_conversion,[],[f542]) ).
cnf(s66,plain,
( ~ spl0_6
| ~ spl0_17
| spl0_29 ),
inference(sat_conversion,[],[f714]) ).
cnf(s67,plain,
( ~ spl0_8
| ~ spl0_17
| spl0_27 ),
inference(sat_conversion,[],[f715]) ).
cnf(s71,plain,
( ~ spl0_8
| ~ spl0_15
| ~ spl0_17
| ~ spl0_27
| spl0_32 ),
inference(sat_conversion,[],[f746]) ).
cnf(s76,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_14 ),
inference(sat_conversion,[],[f783]) ).
cnf(s78,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(sat_conversion,[],[f785]) ).
cnf(s82,plain,
( ~ spl0_17
| ~ spl0_27
| ~ spl0_32
| spl0_40 ),
inference(sat_conversion,[],[f846]) ).
cnf(s83,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_40
| ~ spl0_41 ),
inference(sat_conversion,[],[f853]) ).
cnf(s84,plain,
( ~ spl0_2
| ~ spl0_29
| spl0_41 ),
inference(sat_conversion,[],[f856]) ).
cnf(s89,plain,
spl0_1,
inference(rat,[],[s83,s82,s84,s71,s66,s67,s1,s2,s3,s7,s13,s46,s60]) ).
cnf(s90,plain,
spl0_2,
inference(rat,[],[s76,s4,s9,s16,s37,s89]) ).
cnf(s91,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_4
| ~ spl0_3 ),
inference(rat,[],[s71,s50,s82,s78,s67,s83,s84,s66,s60,s90]) ).
cnf(s92,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s15,s76,s20,s41,s89]) ).
cnf(s93,plain,
( ~ spl0_5
| ~ spl0_4
| ~ spl0_3 ),
inference(rat,[],[s76,s12,s19,s40,s91,s92,s89]) ).
cnf(s94,plain,
( ~ spl0_4
| ~ spl0_3 ),
inference(rat,[],[s91,s8,s14,s93]) ).
cnf(s95,plain,
spl0_4,
inference(rat,[],[s76,s6,s11,s18,s39,s89]) ).
cnf(s96,plain,
~ spl0_3,
inference(rat,[],[s94,s95]) ).
cnf(s97,plain,
spl0_14,
inference(rat,[],[s38,s96]) ).
cnf(s98,plain,
spl0_9,
inference(rat,[],[s17,s96]) ).
cnf(s99,plain,
spl0_7,
inference(rat,[],[s10,s96]) ).
cnf(s100,plain,
spl0_5,
inference(rat,[],[s5,s96]) ).
cnf(s102,plain,
$false,
inference(rat,[],[s76,s100,s89,s97,s98,s99]) ).
fof(f857,plain,
$false,
inference(avatar_sat_refutation,[],[s102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC414-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n017.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 09:27:51 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.30 % (3428087)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (3428096)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3611226027:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (3428093)% WARNING: option uhcvi not known.
% 0.19/0.30 % (3428094)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2893351543:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (3428092)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2269740527_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (3428093)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3494363562:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (3428095)dis+10_1_sil=32000:sp=arity:random_seed=371035955:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (3428097)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2768192076:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (3428098)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2006024379:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (3428098) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3428087-3428098"...
% 0.19/0.30 % TRYING [1]
% 0.19/0.30 % (3428098)...printing done.
% 0.19/0.30 % TRYING [2]
% 0.19/0.30 % (3428098)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (3428098)------------------------------
% 0.19/0.30 % (3428098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3428098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3428098)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3428098)Termination reason: Refutation
% 0.19/0.30 % (3428098)Time elapsed: 0.019 s
% 0.19/0.30 % (3428098)Peak memory usage: 13 MB
% 0.19/0.30 % (3428098)Instructions burned: 29 (million)
% 0.19/0.30 % (3428087)Success in time 0.057 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------