%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC412-1 : 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 : 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 01:05:56 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 43
% Syntax : Number of formulae : 177 ( 10 unt; 11 def)
% Number of atoms : 501 ( 105 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 557 ( 233 ~; 313 |; 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 : 87 ( 0 sgn 87 !; 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) != sk4
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| app(app(cons(X4,nil),X5),cons(X3,nil)) = sk3
| app(app(cons(X3,nil),X5),cons(X4,nil)) != 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)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| sk3 = app(app(cons(X4,nil),X5),cons(X3,nil))
| sk4 != app(app(cons(X3,nil),X5),cons(X4,nil)) ),
inference(reorient_equations,[],[f206]) ).
fof(f216,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ssItem(sk11) ),
inference(reorient_equations,[],[f216]) ).
fof(f218,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ssItem(sk12) ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ssList(sk13) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f222]) ).
fof(f224,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f225,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f224]) ).
fof(f226,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f227,plain,
! [X2,X0,X1] :
( ssItem(sk5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f226]) ).
fof(f228,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk6)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f229,plain,
! [X2,X0,X1] :
( ssItem(sk6)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f228]) ).
fof(f230,negated_conjecture,
! [X2,X0,X1] :
( ssList(sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f231,plain,
! [X2,X0,X1] :
( ssList(sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f230]) ).
fof(f232,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f233,plain,
! [X2,X0,X1] :
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f232]) ).
fof(f239,negated_conjecture,
( ssItem(sk5)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_25) ).
fof(f240,negated_conjecture,
( ssItem(sk5)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_26) ).
fof(f241,negated_conjecture,
( ssItem(sk5)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_27) ).
fof(f242,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_28) ).
fof(f243,plain,
( ssItem(sk5)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f242]) ).
fof(f244,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_29) ).
fof(f245,plain,
( ssItem(sk5)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f244]) ).
fof(f264,negated_conjecture,
( ssItem(sk6)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_42) ).
fof(f265,negated_conjecture,
( ssItem(sk6)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_43) ).
fof(f266,negated_conjecture,
( ssItem(sk6)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_44) ).
fof(f267,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_45) ).
fof(f268,plain,
( ssItem(sk6)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f267]) ).
fof(f269,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_46) ).
fof(f270,plain,
( ssItem(sk6)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f269]) ).
fof(f271,negated_conjecture,
( ssList(sk7)
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_47) ).
fof(f272,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_48) ).
fof(f273,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk11) ),
inference(reorient_equations,[],[f272]) ).
fof(f274,negated_conjecture,
( ssList(sk7)
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_49) ).
fof(f275,negated_conjecture,
( ssList(sk7)
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_50) ).
fof(f276,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_51) ).
fof(f277,plain,
( ssList(sk7)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f276]) ).
fof(f278,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_52) ).
fof(f279,plain,
( ssList(sk7)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f278]) ).
fof(f280,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_53) ).
fof(f281,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk12) ),
inference(reorient_equations,[],[f280]) ).
fof(f282,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssList(sk13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_54) ).
fof(f283,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssList(sk13) ),
inference(reorient_equations,[],[f282]) ).
fof(f284,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_55) ).
fof(f285,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f284]) ).
fof(f286,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_56) ).
fof(f287,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f286]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f223,f204]) ).
fof(f292,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f225,f205]) ).
fof(f293,plain,
! [X2,X0,X1] :
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(definition_unfolding,[],[f233,f204]) ).
fof(f295,plain,
( ssItem(sk5)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f243,f204]) ).
fof(f296,plain,
( ssItem(sk5)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f245,f205]) ).
fof(f303,plain,
( ssItem(sk6)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f268,f204]) ).
fof(f304,plain,
( ssItem(sk6)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f270,f205]) ).
fof(f305,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk11) ),
inference(definition_unfolding,[],[f273,f204]) ).
fof(f306,plain,
( ssList(sk7)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f277,f204]) ).
fof(f307,plain,
( ssList(sk7)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f279,f205]) ).
fof(f308,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk12) ),
inference(definition_unfolding,[],[f281,f204]) ).
fof(f309,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssList(sk13) ),
inference(definition_unfolding,[],[f283,f204]) ).
fof(f310,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f285,f204,f204]) ).
fof(f311,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f287,f204,f205]) ).
fof(f428,definition,
( spl0_1
<=> sk3 = app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f430,plain,
( sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| spl0_1 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f432,definition,
( spl0_2
<=> sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f434,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f435,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f311,f432,f428]) ).
fof(f437,definition,
( spl0_3
<=> sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f439,plain,
( sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f440,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f310,f432,f437]) ).
fof(f442,definition,
( spl0_4
<=> ssList(sk13) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f444,plain,
( ssList(sk13)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f445,plain,
( spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f309,f432,f442]) ).
fof(f447,definition,
( spl0_5
<=> ssItem(sk12) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f449,plain,
( ssItem(sk12)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f450,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f308,f432,f447]) ).
fof(f452,definition,
( spl0_6
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f454,plain,
( ssList(sk7)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f455,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f307,f452,f428]) ).
fof(f456,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f306,f452,f437]) ).
fof(f457,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f275,f452,f442]) ).
fof(f458,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f274,f452,f447]) ).
fof(f460,definition,
( spl0_7
<=> ssItem(sk11) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f462,plain,
( ssItem(sk11)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f463,plain,
( spl0_7
| spl0_2 ),
inference(avatar_split_clause,[],[f305,f432,f460]) ).
fof(f464,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f271,f452,f460]) ).
fof(f466,definition,
( spl0_8
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f468,plain,
( ssItem(sk6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f469,plain,
( ~ spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f304,f466,f428]) ).
fof(f470,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f303,f466,f437]) ).
fof(f471,plain,
( spl0_4
| spl0_8 ),
inference(avatar_split_clause,[],[f266,f466,f442]) ).
fof(f472,plain,
( spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f265,f466,f447]) ).
fof(f473,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f264,f466,f460]) ).
fof(f503,definition,
( spl0_13
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f505,plain,
( ssItem(sk5)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f506,plain,
( ~ spl0_1
| spl0_13 ),
inference(avatar_split_clause,[],[f296,f503,f428]) ).
fof(f507,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f295,f503,f437]) ).
fof(f508,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f241,f503,f442]) ).
fof(f509,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f240,f503,f447]) ).
fof(f510,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f239,f503,f460]) ).
fof(f516,definition,
( spl0_14
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f517,plain,
( ! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),X2),cons(X1,nil))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil)) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f518,plain,
( spl0_14
| spl0_2 ),
inference(avatar_split_clause,[],[f293,f432,f516]) ).
fof(f519,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f231,f452,f516]) ).
fof(f520,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f229,f466,f516]) ).
fof(f521,plain,
( spl0_14
| spl0_13 ),
inference(avatar_split_clause,[],[f227,f503,f516]) ).
fof(f523,definition,
( spl0_15
<=> ! [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_15])],[avatar_definition]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f525,plain,
( ~ spl0_1
| spl0_15 ),
inference(avatar_split_clause,[],[f292,f523,f428]) ).
fof(f526,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f291,f523,f437]) ).
fof(f527,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f221,f523,f442]) ).
fof(f528,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f219,f523,f447]) ).
fof(f529,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f217,f523,f460]) ).
fof(f534,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f207,f523,f516]) ).
fof(f584,plain,
( sk4 != sk4
| ~ ssItem(sk11)
| ~ ssList(sk13)
| ~ ssItem(sk12)
| sk3 = app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ~ spl0_3
| ~ spl0_14 ),
inference(superposition,[],[f517,f439]) ).
fof(f585,plain,
( ~ ssItem(sk11)
| ~ ssList(sk13)
| ~ ssItem(sk12)
| sk3 = app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ~ spl0_3
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f584]) ).
fof(f586,plain,
( ~ ssList(sk13)
| ~ ssItem(sk12)
| sk3 = app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f585,f462]) ).
fof(f587,plain,
( ~ ssItem(sk12)
| sk3 = app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f586,f444]) ).
fof(f588,plain,
( sk3 = app(app(cons(sk12,nil),sk13),cons(sk11,nil))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f587,f449]) ).
fof(f589,plain,
( $false
| spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f588,f430]) ).
fof(f590,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f589]) ).
fof(f592,plain,
( sk4 != sk4
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f524,f434]) ).
fof(f593,plain,
( ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ spl0_2
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f592]) ).
fof(f595,plain,
( ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ spl0_2
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f593,f505]) ).
fof(f597,plain,
( ~ ssItem(sk6)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f595,f454]) ).
fof(f599,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f597,f468]) ).
fof(f600,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f599]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f435]) ).
cnf(s2,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f440]) ).
cnf(s3,plain,
( spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f445]) ).
cnf(s4,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f450]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f455]) ).
cnf(s6,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f456]) ).
cnf(s7,plain,
( spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f457]) ).
cnf(s8,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f458]) ).
cnf(s9,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f463]) ).
cnf(s10,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f464]) ).
cnf(s11,plain,
( ~ spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f469]) ).
cnf(s12,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f470]) ).
cnf(s13,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f471]) ).
cnf(s14,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f472]) ).
cnf(s15,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f473]) ).
cnf(s28,plain,
( ~ spl0_1
| spl0_13 ),
inference(sat_conversion,[],[f506]) ).
cnf(s29,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f507]) ).
cnf(s30,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f508]) ).
cnf(s31,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f509]) ).
cnf(s32,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f510]) ).
cnf(s37,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f518]) ).
cnf(s38,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f519]) ).
cnf(s39,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f520]) ).
cnf(s40,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f521]) ).
cnf(s41,plain,
( ~ spl0_1
| spl0_15 ),
inference(sat_conversion,[],[f525]) ).
cnf(s42,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f526]) ).
cnf(s43,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f527]) ).
cnf(s44,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f528]) ).
cnf(s45,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f529]) ).
cnf(s50,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f534]) ).
cnf(s62,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14 ),
inference(sat_conversion,[],[f590]) ).
cnf(s63,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f600]) ).
cnf(s69,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s62,s2,s3,s4,s9,s37]) ).
cnf(s70,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s63,s38,s39,s40,s50]) ).
cnf(s71,plain,
( spl0_7
| ~ spl0_2 ),
inference(rat,[],[s63,s10,s15,s32,s45]) ).
cnf(s72,plain,
( spl0_5
| ~ spl0_2 ),
inference(rat,[],[s63,s8,s14,s31,s44]) ).
cnf(s73,plain,
( spl0_4
| ~ spl0_2 ),
inference(rat,[],[s63,s7,s13,s30,s43]) ).
cnf(s74,plain,
spl0_1,
inference(rat,[],[s63,s6,s12,s29,s42,s62,s73,s72,s71,s70,s69]) ).
cnf(s75,plain,
spl0_15,
inference(rat,[],[s41,s74]) ).
cnf(s76,plain,
spl0_13,
inference(rat,[],[s28,s74]) ).
cnf(s77,plain,
spl0_8,
inference(rat,[],[s11,s74]) ).
cnf(s78,plain,
spl0_6,
inference(rat,[],[s5,s74]) ).
cnf(s79,plain,
spl0_2,
inference(rat,[],[s1,s74]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s63,s75,s76,s79,s77,s78]) ).
fof(f603,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC412-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n013.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 09:31:36 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.19/0.27 % (1048243)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (1048248)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2548435636_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (1048249)% WARNING: option uhcvi not known.
% 0.19/0.27 % (1048249)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=529174260:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (1048252)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2646146462:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (1048250)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2002425240:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (1048251)dis+10_1_sil=32000:sp=arity:random_seed=1810832479:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % TRYING [1]
% 0.19/0.27 % TRYING [2]
% 0.19/0.27 % (1048251) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1048243-1048251"...
% 0.19/0.27 % (1048249) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1048243-1048249"...
% 0.19/0.27 % (1048254)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1179752835:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % TRYING [3]
% 0.19/0.27 % (1048251)...printing done.
% 0.19/0.27 % (1048249)...printing done.
% 0.19/0.27 % (1048249)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (1048249)------------------------------
% 0.19/0.27 % (1048249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1048249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1048249)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1048249)Termination reason: Refutation
% 0.19/0.27 % (1048249)Time elapsed: 0.008 s
% 0.19/0.27 % (1048249)Peak memory usage: 12 MB
% 0.19/0.27 % (1048249)Instructions burned: 12 (million)
% 0.19/0.27 % (1048243)Success in time 0.049 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------