TSTP Solution File: SWC364-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC364-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 16:21:12 EDT 2024

% Result   : Unsatisfiable 1.52s 0.58s
% Output   : Refutation 1.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   73
% Syntax   : Number of formulae    :  240 (  23 unt;   0 def)
%            Number of atoms       :  695 ( 105 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  817 ( 362   ~; 421   |;   0   &)
%                                         (  34 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   46 (  44 usr;  35 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   92 (  92   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7759,plain,
    $false,
    inference(avatar_sat_refutation,[],[f250,f1014,f1030,f1034,f1052,f1303,f1307,f1386,f1405,f1500,f1533,f1564,f1576,f1586,f1590,f1650,f1654,f1850,f3405,f3428,f3597,f5858,f5862,f7753,f7758]) ).

fof(f7758,plain,
    ( ~ spl0_7
    | ~ spl0_34 ),
    inference(avatar_contradiction_clause,[],[f7757]) ).

fof(f7757,plain,
    ( $false
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(subsumption_resolution,[],[f7756,f187]) ).

fof(f187,axiom,
    ssList(sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).

fof(f7756,plain,
    ( ~ ssList(sk2)
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(forward_demodulation,[],[f7755,f5876]) ).

fof(f5876,plain,
    ( sk2 = app(sk2,skaf45(sk2,sk2))
    | ~ spl0_34 ),
    inference(subsumption_resolution,[],[f5874,f187]) ).

fof(f5874,plain,
    ( ~ ssList(sk2)
    | sk2 = app(sk2,skaf45(sk2,sk2))
    | ~ spl0_34 ),
    inference(duplicate_literal_removal,[],[f5871]) ).

fof(f5871,plain,
    ( ~ ssList(sk2)
    | ~ ssList(sk2)
    | sk2 = app(sk2,skaf45(sk2,sk2))
    | ~ spl0_34 ),
    inference(resolution,[],[f5857,f132]) ).

fof(f132,axiom,
    ! [X0,X1] :
      ( ~ frontsegP(X0,X1)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | app(X1,skaf45(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).

fof(f5857,plain,
    ( frontsegP(sk2,sk2)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f5855]) ).

fof(f5855,plain,
    ( spl0_34
  <=> frontsegP(sk2,sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f7755,plain,
    ( ~ ssList(app(sk2,skaf45(sk2,sk2)))
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(subsumption_resolution,[],[f7754,f51]) ).

fof(f51,axiom,
    ! [X0,X1] : ssList(skaf45(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).

fof(f7754,plain,
    ( ~ ssList(app(sk2,skaf45(sk2,sk2)))
    | ~ ssList(skaf45(sk2,sk2))
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(subsumption_resolution,[],[f7742,f243]) ).

fof(f243,plain,
    ~ segmentP(sk2,sk1),
    inference(subsumption_resolution,[],[f242,f230]) ).

fof(f230,plain,
    neq(sk2,nil),
    inference(duplicate_literal_removal,[],[f192]) ).

fof(f192,axiom,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).

fof(f242,plain,
    ( ~ neq(sk2,nil)
    | ~ segmentP(sk2,sk1) ),
    inference(forward_demodulation,[],[f199,f190]) ).

fof(f190,axiom,
    sk2 = sk4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).

fof(f199,axiom,
    ( ~ segmentP(sk2,sk1)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).

fof(f7742,plain,
    ( segmentP(sk2,sk1)
    | ~ ssList(app(sk2,skaf45(sk2,sk2)))
    | ~ ssList(skaf45(sk2,sk2))
    | ~ spl0_7
    | ~ spl0_34 ),
    inference(superposition,[],[f7728,f5876]) ).

fof(f7728,plain,
    ( ! [X0] :
        ( segmentP(app(sk2,X0),sk1)
        | ~ ssList(app(sk2,X0))
        | ~ ssList(X0) )
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f7727,f356]) ).

fof(f356,plain,
    sk2 = app(cons(sk5,nil),sk1),
    inference(forward_demodulation,[],[f355,f190]) ).

fof(f355,plain,
    sk4 = app(cons(sk5,nil),sk1),
    inference(forward_demodulation,[],[f354,f191]) ).

fof(f191,axiom,
    sk1 = sk3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).

fof(f354,plain,
    sk4 = app(cons(sk5,nil),sk3),
    inference(subsumption_resolution,[],[f353,f230]) ).

fof(f353,plain,
    ( ~ neq(sk2,nil)
    | sk4 = app(cons(sk5,nil),sk3) ),
    inference(forward_demodulation,[],[f198,f190]) ).

fof(f198,axiom,
    ( ~ neq(sk4,nil)
    | sk4 = app(cons(sk5,nil),sk3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).

fof(f7727,plain,
    ( ! [X0] :
        ( segmentP(app(sk2,X0),sk1)
        | ~ ssList(app(app(cons(sk5,nil),sk1),X0))
        | ~ ssList(X0) )
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f7726,f1297]) ).

fof(f1297,plain,
    ( ssList(cons(sk5,nil))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f1296]) ).

fof(f1296,plain,
    ( spl0_7
  <=> ssList(cons(sk5,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f7726,plain,
    ! [X0] :
      ( segmentP(app(sk2,X0),sk1)
      | ~ ssList(app(app(cons(sk5,nil),sk1),X0))
      | ~ ssList(cons(sk5,nil))
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f7500,f186]) ).

fof(f186,axiom,
    ssList(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).

fof(f7500,plain,
    ! [X0] :
      ( segmentP(app(sk2,X0),sk1)
      | ~ ssList(app(app(cons(sk5,nil),sk1),X0))
      | ~ ssList(sk1)
      | ~ ssList(cons(sk5,nil))
      | ~ ssList(X0) ),
    inference(superposition,[],[f215,f356]) ).

fof(f215,plain,
    ! [X2,X0,X1] :
      ( segmentP(app(app(X0,X1),X2),X1)
      | ~ ssList(app(app(X0,X1),X2))
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(X2) ),
    inference(equality_resolution,[],[f173]) ).

fof(f173,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X2)
      | ~ ssList(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | segmentP(X3,X1)
      | app(app(X0,X1),X2) != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).

fof(f7753,plain,
    ~ spl0_7,
    inference(avatar_contradiction_clause,[],[f7752]) ).

fof(f7752,plain,
    ( $false
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f7751,f187]) ).

fof(f7751,plain,
    ( ~ ssList(sk2)
    | ~ spl0_7 ),
    inference(forward_demodulation,[],[f7750,f314]) ).

fof(f314,plain,
    sk2 = app(sk2,nil),
    inference(resolution,[],[f73,f187]) ).

fof(f73,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).

fof(f7750,plain,
    ( ~ ssList(app(sk2,nil))
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f7749,f8]) ).

fof(f8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).

fof(f7749,plain,
    ( ~ ssList(app(sk2,nil))
    | ~ ssList(nil)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f7741,f243]) ).

fof(f7741,plain,
    ( segmentP(sk2,sk1)
    | ~ ssList(app(sk2,nil))
    | ~ ssList(nil)
    | ~ spl0_7 ),
    inference(superposition,[],[f7728,f314]) ).

fof(f5862,plain,
    spl0_33,
    inference(avatar_contradiction_clause,[],[f5861]) ).

fof(f5861,plain,
    ( $false
    | spl0_33 ),
    inference(subsumption_resolution,[],[f5860,f186]) ).

fof(f5860,plain,
    ( ~ ssList(sk1)
    | spl0_33 ),
    inference(resolution,[],[f5853,f61]) ).

fof(f61,axiom,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).

fof(f5853,plain,
    ( ~ frontsegP(sk1,sk1)
    | spl0_33 ),
    inference(avatar_component_clause,[],[f5851]) ).

fof(f5851,plain,
    ( spl0_33
  <=> frontsegP(sk1,sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f5858,plain,
    ( ~ spl0_33
    | spl0_34 ),
    inference(avatar_split_clause,[],[f5849,f5855,f5851]) ).

fof(f5849,plain,
    ( frontsegP(sk2,sk2)
    | ~ frontsegP(sk1,sk1) ),
    inference(subsumption_resolution,[],[f5844,f186]) ).

fof(f5844,plain,
    ( frontsegP(sk2,sk2)
    | ~ ssList(sk1)
    | ~ frontsegP(sk1,sk1) ),
    inference(superposition,[],[f4969,f4950]) ).

fof(f4950,plain,
    sk2 = cons(sk5,sk1),
    inference(forward_demodulation,[],[f4946,f356]) ).

fof(f4946,plain,
    app(cons(sk5,nil),sk1) = cons(sk5,sk1),
    inference(resolution,[],[f1353,f186]) ).

fof(f1353,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | cons(sk5,X0) = app(cons(sk5,nil),X0) ),
    inference(resolution,[],[f120,f241]) ).

fof(f241,plain,
    ssItem(sk5),
    inference(subsumption_resolution,[],[f240,f230]) ).

fof(f240,plain,
    ( ~ neq(sk2,nil)
    | ssItem(sk5) ),
    inference(forward_demodulation,[],[f197,f190]) ).

fof(f197,axiom,
    ( ssItem(sk5)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).

fof(f120,axiom,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | cons(X0,X1) = app(cons(X0,nil),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).

fof(f4969,plain,
    ! [X0] :
      ( frontsegP(cons(sk5,X0),sk2)
      | ~ ssList(X0)
      | ~ frontsegP(X0,sk1) ),
    inference(subsumption_resolution,[],[f4968,f241]) ).

fof(f4968,plain,
    ! [X0] :
      ( frontsegP(cons(sk5,X0),sk2)
      | ~ ssList(X0)
      | ~ frontsegP(X0,sk1)
      | ~ ssItem(sk5) ),
    inference(subsumption_resolution,[],[f4964,f186]) ).

fof(f4964,plain,
    ! [X0] :
      ( frontsegP(cons(sk5,X0),sk2)
      | ~ ssList(sk1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,sk1)
      | ~ ssItem(sk5) ),
    inference(superposition,[],[f224,f4950]) ).

fof(f224,plain,
    ! [X3,X0,X1] :
      ( frontsegP(cons(X3,X0),cons(X3,X1))
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | ~ ssItem(X3) ),
    inference(duplicate_literal_removal,[],[f217]) ).

fof(f217,plain,
    ! [X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssItem(X3)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X3,X0),cons(X3,X1)) ),
    inference(equality_resolution,[],[f178]) ).

fof(f178,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | X2 != X3
      | ~ frontsegP(X0,X1)
      | frontsegP(cons(X2,X0),cons(X3,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause178) ).

fof(f3597,plain,
    ( spl0_31
    | ~ spl0_32
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f2112,f1296,f3594,f3590]) ).

fof(f3590,plain,
    ( spl0_31
  <=> sk2 = skaf46(sk2,sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f3594,plain,
    ( spl0_32
  <=> frontsegP(skaf46(sk2,sk1),sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f2112,plain,
    ( ~ frontsegP(skaf46(sk2,sk1),sk2)
    | sk2 = skaf46(sk2,sk1)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f2111,f187]) ).

fof(f2111,plain,
    ( ~ ssList(sk2)
    | ~ frontsegP(skaf46(sk2,sk1),sk2)
    | sk2 = skaf46(sk2,sk1)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f2110,f50]) ).

fof(f50,axiom,
    ! [X0,X1] : ssList(skaf46(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).

fof(f2110,plain,
    ( ~ ssList(skaf46(sk2,sk1))
    | ~ ssList(sk2)
    | ~ frontsegP(skaf46(sk2,sk1),sk2)
    | sk2 = skaf46(sk2,sk1)
    | ~ spl0_7 ),
    inference(resolution,[],[f2109,f129]) ).

fof(f129,axiom,
    ! [X0,X1] :
      ( ~ frontsegP(X1,X0)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ frontsegP(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).

fof(f2109,plain,
    ( frontsegP(sk2,skaf46(sk2,sk1))
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f2108,f186]) ).

fof(f2108,plain,
    ( frontsegP(sk2,skaf46(sk2,sk1))
    | ~ ssList(sk1)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f2102,f50]) ).

fof(f2102,plain,
    ( frontsegP(sk2,skaf46(sk2,sk1))
    | ~ ssList(skaf46(sk2,sk1))
    | ~ ssList(sk1)
    | ~ spl0_7 ),
    inference(superposition,[],[f1897,f2101]) ).

fof(f2101,plain,
    ( sk2 = app(skaf46(sk2,sk1),sk1)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f2100,f186]) ).

fof(f2100,plain,
    ( ~ ssList(sk1)
    | sk2 = app(skaf46(sk2,sk1),sk1)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f2091,f187]) ).

fof(f2091,plain,
    ( ~ ssList(sk2)
    | ~ ssList(sk1)
    | sk2 = app(skaf46(sk2,sk1),sk1)
    | ~ spl0_7 ),
    inference(resolution,[],[f131,f1838]) ).

fof(f1838,plain,
    ( rearsegP(sk2,sk1)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f1837,f1297]) ).

fof(f1837,plain,
    ( rearsegP(sk2,sk1)
    | ~ ssList(cons(sk5,nil)) ),
    inference(subsumption_resolution,[],[f1832,f186]) ).

fof(f1832,plain,
    ( rearsegP(sk2,sk1)
    | ~ ssList(sk1)
    | ~ ssList(cons(sk5,nil)) ),
    inference(superposition,[],[f1756,f356]) ).

fof(f1756,plain,
    ! [X0,X1] :
      ( rearsegP(app(X0,X1),X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f210,f85]) ).

fof(f85,axiom,
    ! [X0,X1] :
      ( ssList(app(X1,X0))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(app(X0,X1))
      | ~ ssList(X1)
      | rearsegP(app(X0,X1),X1) ),
    inference(equality_resolution,[],[f143]) ).

fof(f143,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | rearsegP(X2,X1)
      | app(X0,X1) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).

fof(f131,axiom,
    ! [X0,X1] :
      ( ~ rearsegP(X0,X1)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | app(skaf46(X0,X1),X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).

fof(f1897,plain,
    ! [X0,X1] :
      ( frontsegP(app(X0,X1),X0)
      | ~ ssList(X0)
      | ~ ssList(X1) ),
    inference(subsumption_resolution,[],[f211,f85]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(app(X0,X1))
      | ~ ssList(X0)
      | frontsegP(app(X0,X1),X0) ),
    inference(equality_resolution,[],[f144]) ).

fof(f144,axiom,
    ! [X2,X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | frontsegP(X2,X0)
      | app(X0,X1) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).

fof(f3428,plain,
    ( spl0_29
    | ~ spl0_30
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f3416,f1296,f3425,f3421]) ).

fof(f3421,plain,
    ( spl0_29
  <=> nil = cons(sk5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f3425,plain,
    ( spl0_30
  <=> frontsegP(nil,sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f3416,plain,
    ( ~ frontsegP(nil,sk2)
    | nil = cons(sk5,nil)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f3415,f1297]) ).

fof(f3415,plain,
    ( ~ frontsegP(nil,sk2)
    | ~ ssList(cons(sk5,nil))
    | nil = cons(sk5,nil)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f3406,f8]) ).

fof(f3406,plain,
    ( ~ frontsegP(nil,sk2)
    | ~ ssList(nil)
    | ~ ssList(cons(sk5,nil))
    | nil = cons(sk5,nil)
    | ~ spl0_7 ),
    inference(resolution,[],[f3379,f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ~ frontsegP(nil,X0)
      | ~ ssList(X0)
      | nil = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).

fof(f3379,plain,
    ( ! [X0] :
        ( frontsegP(X0,cons(sk5,nil))
        | ~ frontsegP(X0,sk2)
        | ~ ssList(X0) )
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f3378,f1297]) ).

fof(f3378,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | ~ ssList(cons(sk5,nil))
        | ~ frontsegP(X0,sk2)
        | frontsegP(X0,cons(sk5,nil)) )
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f3360,f187]) ).

fof(f3360,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | ~ ssList(sk2)
        | ~ ssList(cons(sk5,nil))
        | ~ frontsegP(X0,sk2)
        | frontsegP(X0,cons(sk5,nil)) )
    | ~ spl0_7 ),
    inference(resolution,[],[f154,f1977]) ).

fof(f1977,plain,
    ( frontsegP(sk2,cons(sk5,nil))
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f1976,f186]) ).

fof(f1976,plain,
    ( frontsegP(sk2,cons(sk5,nil))
    | ~ ssList(sk1)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f1971,f1297]) ).

fof(f1971,plain,
    ( frontsegP(sk2,cons(sk5,nil))
    | ~ ssList(cons(sk5,nil))
    | ~ ssList(sk1) ),
    inference(superposition,[],[f1897,f356]) ).

fof(f154,axiom,
    ! [X2,X0,X1] :
      ( ~ frontsegP(X1,X2)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ frontsegP(X0,X1)
      | frontsegP(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause154) ).

fof(f3405,plain,
    ( spl0_27
    | ~ spl0_28
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f1980,f1296,f3402,f3398]) ).

fof(f3398,plain,
    ( spl0_27
  <=> sk2 = cons(sk5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f3402,plain,
    ( spl0_28
  <=> frontsegP(cons(sk5,nil),sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1980,plain,
    ( ~ frontsegP(cons(sk5,nil),sk2)
    | sk2 = cons(sk5,nil)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f1979,f187]) ).

fof(f1979,plain,
    ( ~ ssList(sk2)
    | ~ frontsegP(cons(sk5,nil),sk2)
    | sk2 = cons(sk5,nil)
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f1978,f1297]) ).

fof(f1978,plain,
    ( ~ ssList(cons(sk5,nil))
    | ~ ssList(sk2)
    | ~ frontsegP(cons(sk5,nil),sk2)
    | sk2 = cons(sk5,nil)
    | ~ spl0_7 ),
    inference(resolution,[],[f1977,f129]) ).

fof(f1850,plain,
    ( spl0_25
    | ~ spl0_26
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f1841,f1296,f1847,f1843]) ).

fof(f1843,plain,
    ( spl0_25
  <=> sk1 = sk2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1847,plain,
    ( spl0_26
  <=> rearsegP(sk1,sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1841,plain,
    ( ~ rearsegP(sk1,sk2)
    | sk1 = sk2
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f1840,f187]) ).

fof(f1840,plain,
    ( ~ ssList(sk2)
    | ~ rearsegP(sk1,sk2)
    | sk1 = sk2
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f1839,f186]) ).

fof(f1839,plain,
    ( ~ ssList(sk1)
    | ~ ssList(sk2)
    | ~ rearsegP(sk1,sk2)
    | sk1 = sk2
    | ~ spl0_7 ),
    inference(resolution,[],[f1838,f128]) ).

fof(f128,axiom,
    ! [X0,X1] :
      ( ~ rearsegP(X1,X0)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ rearsegP(X0,X1)
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).

fof(f1654,plain,
    ( spl0_8
    | spl0_23 ),
    inference(avatar_contradiction_clause,[],[f1653]) ).

fof(f1653,plain,
    ( $false
    | spl0_8
    | spl0_23 ),
    inference(subsumption_resolution,[],[f1652,f187]) ).

fof(f1652,plain,
    ( ~ ssList(sk2)
    | spl0_8
    | spl0_23 ),
    inference(subsumption_resolution,[],[f1651,f1302]) ).

fof(f1302,plain,
    ( nil != sk2
    | spl0_8 ),
    inference(avatar_component_clause,[],[f1300]) ).

fof(f1300,plain,
    ( spl0_8
  <=> nil = sk2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f1651,plain,
    ( nil = sk2
    | ~ ssList(sk2)
    | spl0_23 ),
    inference(resolution,[],[f1645,f75]) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).

fof(f1645,plain,
    ( ~ ssList(tl(sk2))
    | spl0_23 ),
    inference(avatar_component_clause,[],[f1643]) ).

fof(f1643,plain,
    ( spl0_23
  <=> ssList(tl(sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f1650,plain,
    ( ~ spl0_23
    | spl0_24
    | spl0_8
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f1641,f1379,f1300,f1647,f1643]) ).

fof(f1647,plain,
    ( spl0_24
  <=> memberP(sk2,hd(sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f1379,plain,
    ( spl0_9
  <=> ssItem(hd(sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f1641,plain,
    ( memberP(sk2,hd(sk2))
    | ~ ssList(tl(sk2))
    | spl0_8
    | ~ spl0_9 ),
    inference(subsumption_resolution,[],[f1371,f1380]) ).

fof(f1380,plain,
    ( ssItem(hd(sk2))
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f1379]) ).

fof(f1371,plain,
    ( memberP(sk2,hd(sk2))
    | ~ ssList(tl(sk2))
    | ~ ssItem(hd(sk2))
    | spl0_8 ),
    inference(superposition,[],[f226,f1370]) ).

fof(f1370,plain,
    ( sk2 = cons(hd(sk2),tl(sk2))
    | spl0_8 ),
    inference(subsumption_resolution,[],[f998,f1302]) ).

fof(f998,plain,
    ( nil = sk2
    | sk2 = cons(hd(sk2),tl(sk2)) ),
    inference(resolution,[],[f104,f187]) ).

fof(f104,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(hd(X0),tl(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).

fof(f226,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f209]) ).

fof(f209,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(equality_resolution,[],[f138]) ).

fof(f138,axiom,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | X0 != X1
      | memberP(cons(X1,X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).

fof(f1590,plain,
    ( spl0_4
    | spl0_21 ),
    inference(avatar_contradiction_clause,[],[f1589]) ).

fof(f1589,plain,
    ( $false
    | spl0_4
    | spl0_21 ),
    inference(subsumption_resolution,[],[f1588,f186]) ).

fof(f1588,plain,
    ( ~ ssList(sk1)
    | spl0_4
    | spl0_21 ),
    inference(subsumption_resolution,[],[f1587,f1012]) ).

fof(f1012,plain,
    ( nil != sk1
    | spl0_4 ),
    inference(avatar_component_clause,[],[f1011]) ).

fof(f1011,plain,
    ( spl0_4
  <=> nil = sk1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f1587,plain,
    ( nil = sk1
    | ~ ssList(sk1)
    | spl0_21 ),
    inference(resolution,[],[f1581,f75]) ).

fof(f1581,plain,
    ( ~ ssList(tl(sk1))
    | spl0_21 ),
    inference(avatar_component_clause,[],[f1579]) ).

fof(f1579,plain,
    ( spl0_21
  <=> ssList(tl(sk1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f1586,plain,
    ( ~ spl0_21
    | spl0_22
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f1577,f1023,f1007,f1583,f1579]) ).

fof(f1583,plain,
    ( spl0_22
  <=> memberP(sk1,hd(sk1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1007,plain,
    ( spl0_3
  <=> sk1 = cons(hd(sk1),tl(sk1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1023,plain,
    ( spl0_5
  <=> ssItem(hd(sk1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f1577,plain,
    ( memberP(sk1,hd(sk1))
    | ~ ssList(tl(sk1))
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(subsumption_resolution,[],[f1015,f1024]) ).

fof(f1024,plain,
    ( ssItem(hd(sk1))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f1023]) ).

fof(f1015,plain,
    ( memberP(sk1,hd(sk1))
    | ~ ssList(tl(sk1))
    | ~ ssItem(hd(sk1))
    | ~ spl0_3 ),
    inference(superposition,[],[f226,f1009]) ).

fof(f1009,plain,
    ( sk1 = cons(hd(sk1),tl(sk1))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f1007]) ).

fof(f1576,plain,
    ( spl0_19
    | ~ spl0_20
    | spl0_8
    | spl0_16 ),
    inference(avatar_split_clause,[],[f1567,f1553,f1300,f1573,f1569]) ).

fof(f1569,plain,
    ( spl0_19
  <=> totalorderedP(skaf82(sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f1573,plain,
    ( spl0_20
  <=> totalorderedP(sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f1553,plain,
    ( spl0_16
  <=> nil = skaf82(sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f1567,plain,
    ( ~ totalorderedP(sk2)
    | totalorderedP(skaf82(sk2))
    | spl0_8
    | spl0_16 ),
    inference(subsumption_resolution,[],[f1549,f1554]) ).

fof(f1554,plain,
    ( nil != skaf82(sk2)
    | spl0_16 ),
    inference(avatar_component_clause,[],[f1553]) ).

fof(f1549,plain,
    ( ~ totalorderedP(sk2)
    | totalorderedP(skaf82(sk2))
    | nil = skaf82(sk2)
    | spl0_8 ),
    inference(subsumption_resolution,[],[f1548,f12]) ).

fof(f12,axiom,
    ! [X0] : ssItem(skaf83(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).

fof(f1548,plain,
    ( ~ totalorderedP(sk2)
    | totalorderedP(skaf82(sk2))
    | nil = skaf82(sk2)
    | ~ ssItem(skaf83(sk2))
    | spl0_8 ),
    inference(subsumption_resolution,[],[f1541,f13]) ).

fof(f13,axiom,
    ! [X0] : ssList(skaf82(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).

fof(f1541,plain,
    ( ~ totalorderedP(sk2)
    | ~ ssList(skaf82(sk2))
    | totalorderedP(skaf82(sk2))
    | nil = skaf82(sk2)
    | ~ ssItem(skaf83(sk2))
    | spl0_8 ),
    inference(superposition,[],[f125,f1536]) ).

fof(f1536,plain,
    ( sk2 = cons(skaf83(sk2),skaf82(sk2))
    | spl0_8 ),
    inference(subsumption_resolution,[],[f1088,f1302]) ).

fof(f1088,plain,
    ( nil = sk2
    | sk2 = cons(skaf83(sk2),skaf82(sk2)) ),
    inference(resolution,[],[f109,f187]) ).

fof(f109,axiom,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(skaf83(X0),skaf82(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).

fof(f125,axiom,
    ! [X0,X1] :
      ( ~ totalorderedP(cons(X0,X1))
      | ~ ssList(X1)
      | totalorderedP(X1)
      | nil = X1
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).

fof(f1564,plain,
    ( spl0_16
    | spl0_17
    | ~ spl0_18
    | spl0_8 ),
    inference(avatar_split_clause,[],[f1547,f1300,f1561,f1557,f1553]) ).

fof(f1557,plain,
    ( spl0_17
  <=> strictorderedP(skaf82(sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f1561,plain,
    ( spl0_18
  <=> strictorderedP(sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f1547,plain,
    ( ~ strictorderedP(sk2)
    | strictorderedP(skaf82(sk2))
    | nil = skaf82(sk2)
    | spl0_8 ),
    inference(subsumption_resolution,[],[f1546,f12]) ).

fof(f1546,plain,
    ( ~ strictorderedP(sk2)
    | strictorderedP(skaf82(sk2))
    | nil = skaf82(sk2)
    | ~ ssItem(skaf83(sk2))
    | spl0_8 ),
    inference(subsumption_resolution,[],[f1540,f13]) ).

fof(f1540,plain,
    ( ~ strictorderedP(sk2)
    | ~ ssList(skaf82(sk2))
    | strictorderedP(skaf82(sk2))
    | nil = skaf82(sk2)
    | ~ ssItem(skaf83(sk2))
    | spl0_8 ),
    inference(superposition,[],[f124,f1536]) ).

fof(f124,axiom,
    ! [X0,X1] :
      ( ~ strictorderedP(cons(X0,X1))
      | ~ ssList(X1)
      | strictorderedP(X1)
      | nil = X1
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).

fof(f1533,plain,
    ( spl0_14
    | ~ spl0_15
    | spl0_4
    | spl0_11 ),
    inference(avatar_split_clause,[],[f1524,f1489,f1011,f1530,f1526]) ).

fof(f1526,plain,
    ( spl0_14
  <=> totalorderedP(skaf82(sk1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f1530,plain,
    ( spl0_15
  <=> totalorderedP(sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f1489,plain,
    ( spl0_11
  <=> nil = skaf82(sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f1524,plain,
    ( ~ totalorderedP(sk1)
    | totalorderedP(skaf82(sk1))
    | spl0_4
    | spl0_11 ),
    inference(subsumption_resolution,[],[f1523,f12]) ).

fof(f1523,plain,
    ( ~ totalorderedP(sk1)
    | totalorderedP(skaf82(sk1))
    | ~ ssItem(skaf83(sk1))
    | spl0_4
    | spl0_11 ),
    inference(subsumption_resolution,[],[f1522,f1490]) ).

fof(f1490,plain,
    ( nil != skaf82(sk1)
    | spl0_11 ),
    inference(avatar_component_clause,[],[f1489]) ).

fof(f1522,plain,
    ( ~ totalorderedP(sk1)
    | totalorderedP(skaf82(sk1))
    | nil = skaf82(sk1)
    | ~ ssItem(skaf83(sk1))
    | spl0_4 ),
    inference(subsumption_resolution,[],[f1518,f13]) ).

fof(f1518,plain,
    ( ~ totalorderedP(sk1)
    | ~ ssList(skaf82(sk1))
    | totalorderedP(skaf82(sk1))
    | nil = skaf82(sk1)
    | ~ ssItem(skaf83(sk1))
    | spl0_4 ),
    inference(superposition,[],[f125,f1092]) ).

fof(f1092,plain,
    ( sk1 = cons(skaf83(sk1),skaf82(sk1))
    | spl0_4 ),
    inference(subsumption_resolution,[],[f1087,f1012]) ).

fof(f1087,plain,
    ( nil = sk1
    | sk1 = cons(skaf83(sk1),skaf82(sk1)) ),
    inference(resolution,[],[f109,f186]) ).

fof(f1500,plain,
    ( spl0_11
    | spl0_12
    | ~ spl0_13
    | spl0_4 ),
    inference(avatar_split_clause,[],[f1487,f1011,f1497,f1493,f1489]) ).

fof(f1493,plain,
    ( spl0_12
  <=> strictorderedP(skaf82(sk1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f1497,plain,
    ( spl0_13
  <=> strictorderedP(sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f1487,plain,
    ( ~ strictorderedP(sk1)
    | strictorderedP(skaf82(sk1))
    | nil = skaf82(sk1)
    | spl0_4 ),
    inference(subsumption_resolution,[],[f1486,f12]) ).

fof(f1486,plain,
    ( ~ strictorderedP(sk1)
    | strictorderedP(skaf82(sk1))
    | nil = skaf82(sk1)
    | ~ ssItem(skaf83(sk1))
    | spl0_4 ),
    inference(subsumption_resolution,[],[f1482,f13]) ).

fof(f1482,plain,
    ( ~ strictorderedP(sk1)
    | ~ ssList(skaf82(sk1))
    | strictorderedP(skaf82(sk1))
    | nil = skaf82(sk1)
    | ~ ssItem(skaf83(sk1))
    | spl0_4 ),
    inference(superposition,[],[f124,f1092]) ).

fof(f1405,plain,
    ( spl0_8
    | spl0_9 ),
    inference(avatar_contradiction_clause,[],[f1404]) ).

fof(f1404,plain,
    ( $false
    | spl0_8
    | spl0_9 ),
    inference(subsumption_resolution,[],[f1403,f187]) ).

fof(f1403,plain,
    ( ~ ssList(sk2)
    | spl0_8
    | spl0_9 ),
    inference(subsumption_resolution,[],[f1402,f1302]) ).

fof(f1402,plain,
    ( nil = sk2
    | ~ ssList(sk2)
    | spl0_9 ),
    inference(resolution,[],[f1381,f76]) ).

fof(f76,axiom,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).

fof(f1381,plain,
    ( ~ ssItem(hd(sk2))
    | spl0_9 ),
    inference(avatar_component_clause,[],[f1379]) ).

fof(f1386,plain,
    ( ~ spl0_9
    | ~ spl0_10
    | spl0_8 ),
    inference(avatar_split_clause,[],[f1377,f1300,f1383,f1379]) ).

fof(f1383,plain,
    ( spl0_10
  <=> sk2 = tl(sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f1377,plain,
    ( sk2 != tl(sk2)
    | ~ ssItem(hd(sk2))
    | spl0_8 ),
    inference(subsumption_resolution,[],[f1376,f187]) ).

fof(f1376,plain,
    ( sk2 != tl(sk2)
    | ~ ssList(sk2)
    | ~ ssItem(hd(sk2))
    | spl0_8 ),
    inference(inner_rewriting,[],[f1372]) ).

fof(f1372,plain,
    ( sk2 != tl(sk2)
    | ~ ssList(tl(sk2))
    | ~ ssItem(hd(sk2))
    | spl0_8 ),
    inference(superposition,[],[f99,f1370]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( cons(X0,X1) != X1
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).

fof(f1307,plain,
    spl0_7,
    inference(avatar_contradiction_clause,[],[f1306]) ).

fof(f1306,plain,
    ( $false
    | spl0_7 ),
    inference(subsumption_resolution,[],[f1305,f241]) ).

fof(f1305,plain,
    ( ~ ssItem(sk5)
    | spl0_7 ),
    inference(subsumption_resolution,[],[f1304,f8]) ).

fof(f1304,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sk5)
    | spl0_7 ),
    inference(resolution,[],[f1298,f86]) ).

fof(f86,axiom,
    ! [X0,X1] :
      ( ssList(cons(X0,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).

fof(f1298,plain,
    ( ~ ssList(cons(sk5,nil))
    | spl0_7 ),
    inference(avatar_component_clause,[],[f1296]) ).

fof(f1303,plain,
    ( ~ spl0_7
    | ~ spl0_8
    | spl0_4 ),
    inference(avatar_split_clause,[],[f1294,f1011,f1300,f1296]) ).

fof(f1294,plain,
    ( nil != sk2
    | ~ ssList(cons(sk5,nil))
    | spl0_4 ),
    inference(subsumption_resolution,[],[f1293,f186]) ).

fof(f1293,plain,
    ( nil != sk2
    | ~ ssList(cons(sk5,nil))
    | ~ ssList(sk1)
    | spl0_4 ),
    inference(subsumption_resolution,[],[f1291,f1012]) ).

fof(f1291,plain,
    ( nil != sk2
    | ~ ssList(cons(sk5,nil))
    | nil = sk1
    | ~ ssList(sk1) ),
    inference(superposition,[],[f119,f356]) ).

fof(f119,axiom,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | ~ ssList(X0)
      | nil = X1
      | ~ ssList(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).

fof(f1052,plain,
    ~ spl0_4,
    inference(avatar_contradiction_clause,[],[f1051]) ).

fof(f1051,plain,
    ( $false
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f1050,f187]) ).

fof(f1050,plain,
    ( ~ ssList(sk2)
    | ~ spl0_4 ),
    inference(resolution,[],[f1037,f56]) ).

fof(f56,axiom,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).

fof(f1037,plain,
    ( ~ segmentP(sk2,nil)
    | ~ spl0_4 ),
    inference(superposition,[],[f243,f1013]) ).

fof(f1013,plain,
    ( nil = sk1
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f1011]) ).

fof(f1034,plain,
    ( spl0_4
    | spl0_5 ),
    inference(avatar_contradiction_clause,[],[f1033]) ).

fof(f1033,plain,
    ( $false
    | spl0_4
    | spl0_5 ),
    inference(subsumption_resolution,[],[f1032,f186]) ).

fof(f1032,plain,
    ( ~ ssList(sk1)
    | spl0_4
    | spl0_5 ),
    inference(subsumption_resolution,[],[f1031,f1012]) ).

fof(f1031,plain,
    ( nil = sk1
    | ~ ssList(sk1)
    | spl0_5 ),
    inference(resolution,[],[f1025,f76]) ).

fof(f1025,plain,
    ( ~ ssItem(hd(sk1))
    | spl0_5 ),
    inference(avatar_component_clause,[],[f1023]) ).

fof(f1030,plain,
    ( ~ spl0_5
    | ~ spl0_6
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f1021,f1007,f1027,f1023]) ).

fof(f1027,plain,
    ( spl0_6
  <=> sk1 = tl(sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f1021,plain,
    ( sk1 != tl(sk1)
    | ~ ssItem(hd(sk1))
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f1020,f186]) ).

fof(f1020,plain,
    ( sk1 != tl(sk1)
    | ~ ssList(sk1)
    | ~ ssItem(hd(sk1))
    | ~ spl0_3 ),
    inference(inner_rewriting,[],[f1016]) ).

fof(f1016,plain,
    ( sk1 != tl(sk1)
    | ~ ssList(tl(sk1))
    | ~ ssItem(hd(sk1))
    | ~ spl0_3 ),
    inference(superposition,[],[f99,f1009]) ).

fof(f1014,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f997,f1011,f1007]) ).

fof(f997,plain,
    ( nil = sk1
    | sk1 = cons(hd(sk1),tl(sk1)) ),
    inference(resolution,[],[f104,f186]) ).

fof(f250,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f72,f248,f245]) ).

fof(f245,plain,
    ( spl0_1
  <=> ! [X1] : ssItem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f248,plain,
    ( spl0_2
  <=> ! [X0] :
        ( ~ ssList(X0)
        | duplicatefreeP(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f72,axiom,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | duplicatefreeP(X0)
      | ssItem(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC364-1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Apr 30 04:04:56 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (22511)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (22515)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (22514)WARNING: value z3 for option sas not known
% 0.20/0.38  % (22512)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38  % (22514)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.38  % (22516)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.38  % (22517)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.38  % (22518)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.38  % (22513)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.39  TRYING [3]
% 0.20/0.43  TRYING [4]
% 0.20/0.43  TRYING [1]
% 0.20/0.44  TRYING [2]
% 0.20/0.50  TRYING [3]
% 0.20/0.53  TRYING [5]
% 1.52/0.58  % (22514)First to succeed.
% 1.52/0.58  % (22514)Refutation found. Thanks to Tanya!
% 1.52/0.58  % SZS status Unsatisfiable for theBenchmark
% 1.52/0.58  % SZS output start Proof for theBenchmark
% See solution above
% 1.52/0.58  % (22514)------------------------------
% 1.52/0.58  % (22514)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.52/0.58  % (22514)Termination reason: Refutation
% 1.52/0.58  
% 1.52/0.58  % (22514)Memory used [KB]: 4569
% 1.52/0.58  % (22514)Time elapsed: 0.206 s
% 1.52/0.58  % (22514)Instructions burned: 609 (million)
% 1.52/0.58  % (22514)------------------------------
% 1.52/0.58  % (22514)------------------------------
% 1.52/0.58  % (22511)Success in time 0.218 s
%------------------------------------------------------------------------------