TSTP Solution File: SWC315+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC315+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n022.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 : Sun May  5 09:50:14 EDT 2024

% Result   : Theorem 0.57s 0.78s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   40
% Syntax   : Number of formulae    :  150 (   8 unt;   0 def)
%            Number of atoms       :  640 ( 256 equ)
%            Maximal formula atoms :   38 (   4 avg)
%            Number of connectives :  752 ( 262   ~; 252   |; 174   &)
%                                         (  26 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   27 (  25 usr;  23 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-2 aty)
%            Number of variables   :  139 (  75   !;  64   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1222,plain,
    $false,
    inference(avatar_sat_refutation,[],[f601,f606,f611,f616,f631,f636,f641,f650,f651,f652,f653,f654,f741,f750,f752,f754,f888,f897,f899,f1103,f1118,f1151,f1162,f1192,f1206,f1209]) ).

fof(f1209,plain,
    ( ~ spl55_9
    | ~ spl55_10
    | spl55_42
    | ~ spl55_53 ),
    inference(avatar_split_clause,[],[f1182,f1147,f1006,f638,f633]) ).

fof(f633,plain,
    ( spl55_9
  <=> ssList(sK54) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_9])]) ).

fof(f638,plain,
    ( spl55_10
  <=> ssItem(sK53) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_10])]) ).

fof(f1006,plain,
    ( spl55_42
  <=> sK53 = hd(sK50) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_42])]) ).

fof(f1147,plain,
    ( spl55_53
  <=> sK50 = cons(sK53,sK54) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_53])]) ).

fof(f1182,plain,
    ( sK53 = hd(sK50)
    | ~ ssItem(sK53)
    | ~ ssList(sK54)
    | ~ spl55_53 ),
    inference(superposition,[],[f432,f1149]) ).

fof(f1149,plain,
    ( sK50 = cons(sK53,sK54)
    | ~ spl55_53 ),
    inference(avatar_component_clause,[],[f1147]) ).

fof(f432,plain,
    ! [X0,X1] :
      ( hd(cons(X1,X0)) = X1
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(cons(X1,X0)) = X1
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax23) ).

fof(f1206,plain,
    ( spl55_11
    | ~ spl55_1
    | ~ spl55_50
    | ~ spl55_56 ),
    inference(avatar_split_clause,[],[f1205,f1189,f1115,f594,f643]) ).

fof(f643,plain,
    ( spl55_11
  <=> sK49 = app(sK54,cons(sK53,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_11])]) ).

fof(f594,plain,
    ( spl55_1
  <=> sK49 = app(sK52,cons(sK51,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_1])]) ).

fof(f1115,plain,
    ( spl55_50
  <=> sK51 = sK53 ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_50])]) ).

fof(f1189,plain,
    ( spl55_56
  <=> sK52 = sK54 ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_56])]) ).

fof(f1205,plain,
    ( sK49 = app(sK54,cons(sK53,nil))
    | ~ spl55_1
    | ~ spl55_50
    | ~ spl55_56 ),
    inference(forward_demodulation,[],[f1199,f1117]) ).

fof(f1117,plain,
    ( sK51 = sK53
    | ~ spl55_50 ),
    inference(avatar_component_clause,[],[f1115]) ).

fof(f1199,plain,
    ( sK49 = app(sK54,cons(sK51,nil))
    | ~ spl55_1
    | ~ spl55_56 ),
    inference(superposition,[],[f596,f1191]) ).

fof(f1191,plain,
    ( sK52 = sK54
    | ~ spl55_56 ),
    inference(avatar_component_clause,[],[f1189]) ).

fof(f596,plain,
    ( sK49 = app(sK52,cons(sK51,nil))
    | ~ spl55_1 ),
    inference(avatar_component_clause,[],[f594]) ).

fof(f1192,plain,
    ( ~ spl55_9
    | ~ spl55_10
    | spl55_56
    | ~ spl55_53
    | ~ spl55_54 ),
    inference(avatar_split_clause,[],[f1187,f1159,f1147,f1189,f638,f633]) ).

fof(f1159,plain,
    ( spl55_54
  <=> sK52 = tl(sK50) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_54])]) ).

fof(f1187,plain,
    ( sK52 = sK54
    | ~ ssItem(sK53)
    | ~ ssList(sK54)
    | ~ spl55_53
    | ~ spl55_54 ),
    inference(forward_demodulation,[],[f1181,f1161]) ).

fof(f1161,plain,
    ( sK52 = tl(sK50)
    | ~ spl55_54 ),
    inference(avatar_component_clause,[],[f1159]) ).

fof(f1181,plain,
    ( sK54 = tl(sK50)
    | ~ ssItem(sK53)
    | ~ ssList(sK54)
    | ~ spl55_53 ),
    inference(superposition,[],[f434,f1149]) ).

fof(f434,plain,
    ! [X0,X1] :
      ( tl(cons(X1,X0)) = X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(cons(X1,X0)) = X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => tl(cons(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax25) ).

fof(f1162,plain,
    ( ~ spl55_4
    | spl55_54
    | ~ spl55_10
    | ~ spl55_49
    | ~ spl55_50 ),
    inference(avatar_split_clause,[],[f1157,f1115,f1098,f638,f1159,f608]) ).

fof(f608,plain,
    ( spl55_4
  <=> ssList(sK52) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_4])]) ).

fof(f1098,plain,
    ( spl55_49
  <=> sK50 = cons(sK51,sK52) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_49])]) ).

fof(f1157,plain,
    ( ~ ssItem(sK53)
    | sK52 = tl(sK50)
    | ~ ssList(sK52)
    | ~ spl55_49
    | ~ spl55_50 ),
    inference(forward_demodulation,[],[f1105,f1117]) ).

fof(f1105,plain,
    ( sK52 = tl(sK50)
    | ~ ssItem(sK51)
    | ~ ssList(sK52)
    | ~ spl55_49 ),
    inference(superposition,[],[f434,f1100]) ).

fof(f1100,plain,
    ( sK50 = cons(sK51,sK52)
    | ~ spl55_49 ),
    inference(avatar_component_clause,[],[f1098]) ).

fof(f1151,plain,
    ( ~ spl55_9
    | ~ spl55_10
    | spl55_53
    | ~ spl55_8 ),
    inference(avatar_split_clause,[],[f1080,f628,f1147,f638,f633]) ).

fof(f628,plain,
    ( spl55_8
  <=> sK50 = app(cons(sK53,nil),sK54) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_8])]) ).

fof(f1080,plain,
    ( sK50 = cons(sK53,sK54)
    | ~ ssItem(sK53)
    | ~ ssList(sK54)
    | ~ spl55_8 ),
    inference(superposition,[],[f511,f630]) ).

fof(f630,plain,
    ( sK50 = app(cons(sK53,nil),sK54)
    | ~ spl55_8 ),
    inference(avatar_component_clause,[],[f628]) ).

fof(f511,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax81) ).

fof(f1118,plain,
    ( ~ spl55_4
    | ~ spl55_5
    | spl55_50
    | ~ spl55_42
    | ~ spl55_49 ),
    inference(avatar_split_clause,[],[f1113,f1098,f1006,f1115,f613,f608]) ).

fof(f613,plain,
    ( spl55_5
  <=> ssItem(sK51) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_5])]) ).

fof(f1113,plain,
    ( sK51 = sK53
    | ~ ssItem(sK51)
    | ~ ssList(sK52)
    | ~ spl55_42
    | ~ spl55_49 ),
    inference(forward_demodulation,[],[f1106,f1008]) ).

fof(f1008,plain,
    ( sK53 = hd(sK50)
    | ~ spl55_42 ),
    inference(avatar_component_clause,[],[f1006]) ).

fof(f1106,plain,
    ( sK51 = hd(sK50)
    | ~ ssItem(sK51)
    | ~ ssList(sK52)
    | ~ spl55_49 ),
    inference(superposition,[],[f432,f1100]) ).

fof(f1103,plain,
    ( ~ spl55_4
    | ~ spl55_5
    | spl55_49
    | ~ spl55_3 ),
    inference(avatar_split_clause,[],[f1082,f603,f1098,f613,f608]) ).

fof(f603,plain,
    ( spl55_3
  <=> sK50 = app(cons(sK51,nil),sK52) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_3])]) ).

fof(f1082,plain,
    ( sK50 = cons(sK51,sK52)
    | ~ ssItem(sK51)
    | ~ ssList(sK52)
    | ~ spl55_3 ),
    inference(superposition,[],[f605,f511]) ).

fof(f605,plain,
    ( sK50 = app(cons(sK51,nil),sK52)
    | ~ spl55_3 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f899,plain,
    ( ~ spl55_18
    | ~ spl55_10
    | spl55_15 ),
    inference(avatar_split_clause,[],[f898,f733,f638,f747]) ).

fof(f747,plain,
    ( spl55_18
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_18])]) ).

fof(f733,plain,
    ( spl55_15
  <=> ssList(cons(sK53,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_15])]) ).

fof(f898,plain,
    ( ~ ssItem(sK53)
    | ~ ssList(nil)
    | spl55_15 ),
    inference(resolution,[],[f735,f422]) ).

fof(f422,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax16) ).

fof(f735,plain,
    ( ~ ssList(cons(sK53,nil))
    | spl55_15 ),
    inference(avatar_component_clause,[],[f733]) ).

fof(f897,plain,
    ( ~ spl55_15
    | spl55_26
    | ~ spl55_8
    | ~ spl55_12
    | ~ spl55_16 ),
    inference(avatar_split_clause,[],[f893,f737,f647,f628,f839,f733]) ).

fof(f839,plain,
    ( spl55_26
  <=> nil = cons(sK53,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_26])]) ).

fof(f647,plain,
    ( spl55_12
  <=> nil = sK50 ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_12])]) ).

fof(f737,plain,
    ( spl55_16
  <=> nil = sK54 ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_16])]) ).

fof(f893,plain,
    ( nil = cons(sK53,nil)
    | ~ ssList(cons(sK53,nil))
    | ~ spl55_8
    | ~ spl55_12
    | ~ spl55_16 ),
    inference(superposition,[],[f516,f831]) ).

fof(f831,plain,
    ( nil = app(cons(sK53,nil),nil)
    | ~ spl55_8
    | ~ spl55_12
    | ~ spl55_16 ),
    inference(forward_demodulation,[],[f827,f649]) ).

fof(f649,plain,
    ( nil = sK50
    | ~ spl55_12 ),
    inference(avatar_component_clause,[],[f647]) ).

fof(f827,plain,
    ( sK50 = app(cons(sK53,nil),nil)
    | ~ spl55_8
    | ~ spl55_16 ),
    inference(superposition,[],[f630,f739]) ).

fof(f739,plain,
    ( nil = sK54
    | ~ spl55_16 ),
    inference(avatar_component_clause,[],[f737]) ).

fof(f516,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f202,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax84) ).

fof(f888,plain,
    ( ~ spl55_18
    | ~ spl55_10
    | ~ spl55_26 ),
    inference(avatar_split_clause,[],[f870,f839,f638,f747]) ).

fof(f870,plain,
    ( ~ ssItem(sK53)
    | ~ ssList(nil)
    | ~ spl55_26 ),
    inference(trivial_inequality_removal,[],[f868]) ).

fof(f868,plain,
    ( nil != nil
    | ~ ssItem(sK53)
    | ~ ssList(nil)
    | ~ spl55_26 ),
    inference(superposition,[],[f424,f840]) ).

fof(f840,plain,
    ( nil = cons(sK53,nil)
    | ~ spl55_26 ),
    inference(avatar_component_clause,[],[f839]) ).

fof(f424,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax18) ).

fof(f754,plain,
    spl55_18,
    inference(avatar_contradiction_clause,[],[f753]) ).

fof(f753,plain,
    ( $false
    | spl55_18 ),
    inference(resolution,[],[f749,f423]) ).

fof(f423,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax17) ).

fof(f749,plain,
    ( ~ ssList(nil)
    | spl55_18 ),
    inference(avatar_component_clause,[],[f747]) ).

fof(f752,plain,
    spl55_17,
    inference(avatar_contradiction_clause,[],[f751]) ).

fof(f751,plain,
    ( $false
    | spl55_17 ),
    inference(resolution,[],[f745,f533]) ).

fof(f533,plain,
    ssList(sK50),
    inference(cnf_transformation,[],[f339]) ).

fof(f339,plain,
    ( ( ~ neq(sK50,nil)
      | ( sK49 = app(sK52,cons(sK51,nil))
        & sK50 = app(cons(sK51,nil),sK52)
        & ssList(sK52)
        & ssItem(sK51) ) )
    & ( ( nil != sK47
        & nil = sK48 )
      | ( sK47 != app(sK54,cons(sK53,nil))
        & sK48 = app(cons(sK53,nil),sK54)
        & ssList(sK54)
        & ssItem(sK53) ) )
    & ( nil != sK50
      | nil = sK49 )
    & sK47 = sK49
    & sK48 = sK50
    & ssList(sK50)
    & ssList(sK49)
    & ssList(sK48)
    & ssList(sK47) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49,sK50,sK51,sK52,sK53,sK54])],[f222,f338,f337,f336,f335,f334,f333,f332,f331]) ).

fof(f331,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ neq(X3,nil)
                      | ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X2
                              & app(cons(X4,nil),X5) = X3
                              & ssList(X5) )
                          & ssItem(X4) ) )
                    & ( ( nil != X0
                        & nil = X1 )
                      | ? [X6] :
                          ( ? [X7] :
                              ( app(X7,cons(X6,nil)) != X0
                              & app(cons(X6,nil),X7) = X1
                              & ssList(X7) )
                          & ssItem(X6) ) )
                    & ( nil != X3
                      | nil = X2 )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X2
                            & app(cons(X4,nil),X5) = X3
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ( ( nil != sK47
                      & nil = X1 )
                    | ? [X6] :
                        ( ? [X7] :
                            ( app(X7,cons(X6,nil)) != sK47
                            & app(cons(X6,nil),X7) = X1
                            & ssList(X7) )
                        & ssItem(X6) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & sK47 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK47) ) ),
    introduced(choice_axiom,[]) ).

fof(f332,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ neq(X3,nil)
                  | ? [X4] :
                      ( ? [X5] :
                          ( app(X5,cons(X4,nil)) = X2
                          & app(cons(X4,nil),X5) = X3
                          & ssList(X5) )
                      & ssItem(X4) ) )
                & ( ( nil != sK47
                    & nil = X1 )
                  | ? [X6] :
                      ( ? [X7] :
                          ( app(X7,cons(X6,nil)) != sK47
                          & app(cons(X6,nil),X7) = X1
                          & ssList(X7) )
                      & ssItem(X6) ) )
                & ( nil != X3
                  | nil = X2 )
                & sK47 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ neq(X3,nil)
                | ? [X4] :
                    ( ? [X5] :
                        ( app(X5,cons(X4,nil)) = X2
                        & app(cons(X4,nil),X5) = X3
                        & ssList(X5) )
                    & ssItem(X4) ) )
              & ( ( nil != sK47
                  & nil = sK48 )
                | ? [X6] :
                    ( ? [X7] :
                        ( app(X7,cons(X6,nil)) != sK47
                        & app(cons(X6,nil),X7) = sK48
                        & ssList(X7) )
                    & ssItem(X6) ) )
              & ( nil != X3
                | nil = X2 )
              & sK47 = X2
              & sK48 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK48) ) ),
    introduced(choice_axiom,[]) ).

fof(f333,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ neq(X3,nil)
              | ? [X4] :
                  ( ? [X5] :
                      ( app(X5,cons(X4,nil)) = X2
                      & app(cons(X4,nil),X5) = X3
                      & ssList(X5) )
                  & ssItem(X4) ) )
            & ( ( nil != sK47
                & nil = sK48 )
              | ? [X6] :
                  ( ? [X7] :
                      ( app(X7,cons(X6,nil)) != sK47
                      & app(cons(X6,nil),X7) = sK48
                      & ssList(X7) )
                  & ssItem(X6) ) )
            & ( nil != X3
              | nil = X2 )
            & sK47 = X2
            & sK48 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ neq(X3,nil)
            | ? [X4] :
                ( ? [X5] :
                    ( app(X5,cons(X4,nil)) = sK49
                    & app(cons(X4,nil),X5) = X3
                    & ssList(X5) )
                & ssItem(X4) ) )
          & ( ( nil != sK47
              & nil = sK48 )
            | ? [X6] :
                ( ? [X7] :
                    ( app(X7,cons(X6,nil)) != sK47
                    & app(cons(X6,nil),X7) = sK48
                    & ssList(X7) )
                & ssItem(X6) ) )
          & ( nil != X3
            | nil = sK49 )
          & sK47 = sK49
          & sK48 = X3
          & ssList(X3) )
      & ssList(sK49) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ( ? [X3] :
        ( ( ~ neq(X3,nil)
          | ? [X4] :
              ( ? [X5] :
                  ( app(X5,cons(X4,nil)) = sK49
                  & app(cons(X4,nil),X5) = X3
                  & ssList(X5) )
              & ssItem(X4) ) )
        & ( ( nil != sK47
            & nil = sK48 )
          | ? [X6] :
              ( ? [X7] :
                  ( app(X7,cons(X6,nil)) != sK47
                  & app(cons(X6,nil),X7) = sK48
                  & ssList(X7) )
              & ssItem(X6) ) )
        & ( nil != X3
          | nil = sK49 )
        & sK47 = sK49
        & sK48 = X3
        & ssList(X3) )
   => ( ( ~ neq(sK50,nil)
        | ? [X4] :
            ( ? [X5] :
                ( app(X5,cons(X4,nil)) = sK49
                & app(cons(X4,nil),X5) = sK50
                & ssList(X5) )
            & ssItem(X4) ) )
      & ( ( nil != sK47
          & nil = sK48 )
        | ? [X6] :
            ( ? [X7] :
                ( app(X7,cons(X6,nil)) != sK47
                & app(cons(X6,nil),X7) = sK48
                & ssList(X7) )
            & ssItem(X6) ) )
      & ( nil != sK50
        | nil = sK49 )
      & sK47 = sK49
      & sK48 = sK50
      & ssList(sK50) ) ),
    introduced(choice_axiom,[]) ).

fof(f335,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( app(X5,cons(X4,nil)) = sK49
            & app(cons(X4,nil),X5) = sK50
            & ssList(X5) )
        & ssItem(X4) )
   => ( ? [X5] :
          ( sK49 = app(X5,cons(sK51,nil))
          & sK50 = app(cons(sK51,nil),X5)
          & ssList(X5) )
      & ssItem(sK51) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ( ? [X5] :
        ( sK49 = app(X5,cons(sK51,nil))
        & sK50 = app(cons(sK51,nil),X5)
        & ssList(X5) )
   => ( sK49 = app(sK52,cons(sK51,nil))
      & sK50 = app(cons(sK51,nil),sK52)
      & ssList(sK52) ) ),
    introduced(choice_axiom,[]) ).

fof(f337,plain,
    ( ? [X6] :
        ( ? [X7] :
            ( app(X7,cons(X6,nil)) != sK47
            & app(cons(X6,nil),X7) = sK48
            & ssList(X7) )
        & ssItem(X6) )
   => ( ? [X7] :
          ( sK47 != app(X7,cons(sK53,nil))
          & sK48 = app(cons(sK53,nil),X7)
          & ssList(X7) )
      & ssItem(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f338,plain,
    ( ? [X7] :
        ( sK47 != app(X7,cons(sK53,nil))
        & sK48 = app(cons(sK53,nil),X7)
        & ssList(X7) )
   => ( sK47 != app(sK54,cons(sK53,nil))
      & sK48 = app(cons(sK53,nil),sK54)
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) = X2
                            & app(cons(X4,nil),X5) = X3
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ( ( nil != X0
                      & nil = X1 )
                    | ? [X6] :
                        ( ? [X7] :
                            ( app(X7,cons(X6,nil)) != X0
                            & app(cons(X6,nil),X7) = X1
                            & ssList(X7) )
                        & ssItem(X6) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( neq(X3,nil)
                      & ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( app(X5,cons(X4,nil)) != X2
                              | app(cons(X4,nil),X5) != X3
                              | ~ ssList(X5) ) ) )
                    | ( ( nil = X0
                        | nil != X1 )
                      & ! [X6] :
                          ( ssItem(X6)
                         => ! [X7] :
                              ( app(X7,cons(X6,nil)) = X0
                              | app(cons(X6,nil),X7) != X1
                              | ~ ssList(X7) ) ) )
                    | ( nil = X3
                      & nil != X2 )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( neq(X3,nil)
                      & ! [X6] :
                          ( ssItem(X6)
                         => ! [X7] :
                              ( app(X7,cons(X6,nil)) != X2
                              | app(cons(X6,nil),X7) != X3
                              | ~ ssList(X7) ) ) )
                    | ( ( nil = X0
                        | nil != X1 )
                      & ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( app(X5,cons(X4,nil)) = X0
                              | app(cons(X4,nil),X5) != X1
                              | ~ ssList(X5) ) ) )
                    | ( nil = X3
                      & nil != X2 )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( neq(X3,nil)
                    & ! [X6] :
                        ( ssItem(X6)
                       => ! [X7] :
                            ( app(X7,cons(X6,nil)) != X2
                            | app(cons(X6,nil),X7) != X3
                            | ~ ssList(X7) ) ) )
                  | ( ( nil = X0
                      | nil != X1 )
                    & ! [X4] :
                        ( ssItem(X4)
                       => ! [X5] :
                            ( app(X5,cons(X4,nil)) = X0
                            | app(cons(X4,nil),X5) != X1
                            | ~ ssList(X5) ) ) )
                  | ( nil = X3
                    & nil != X2 )
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',co1) ).

fof(f745,plain,
    ( ~ ssList(sK50)
    | spl55_17 ),
    inference(avatar_component_clause,[],[f743]) ).

fof(f743,plain,
    ( spl55_17
  <=> ssList(sK50) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_17])]) ).

fof(f750,plain,
    ( ~ spl55_17
    | ~ spl55_18
    | spl55_12
    | spl55_2 ),
    inference(avatar_split_clause,[],[f691,f598,f647,f747,f743]) ).

fof(f598,plain,
    ( spl55_2
  <=> neq(sK50,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_2])]) ).

fof(f691,plain,
    ( nil = sK50
    | ~ ssList(nil)
    | ~ ssList(sK50)
    | spl55_2 ),
    inference(resolution,[],[f421,f600]) ).

fof(f600,plain,
    ( ~ neq(sK50,nil)
    | spl55_2 ),
    inference(avatar_component_clause,[],[f598]) ).

fof(f421,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f304,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax15) ).

fof(f741,plain,
    ( ~ spl55_15
    | ~ spl55_9
    | spl55_16
    | ~ spl55_12
    | ~ spl55_8 ),
    inference(avatar_split_clause,[],[f726,f628,f647,f737,f633,f733]) ).

fof(f726,plain,
    ( nil != sK50
    | nil = sK54
    | ~ ssList(sK54)
    | ~ ssList(cons(sK53,nil))
    | ~ spl55_8 ),
    inference(superposition,[],[f513,f630]) ).

fof(f513,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f328]) ).

fof(f328,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f327]) ).

fof(f327,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f201]) ).

fof(f201,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057',ax83) ).

fof(f654,plain,
    ( spl55_7
    | ~ spl55_12 ),
    inference(avatar_split_clause,[],[f536,f647,f623]) ).

fof(f623,plain,
    ( spl55_7
  <=> nil = sK49 ),
    introduced(avatar_definition,[new_symbols(naming,[spl55_7])]) ).

fof(f536,plain,
    ( nil != sK50
    | nil = sK49 ),
    inference(cnf_transformation,[],[f339]) ).

fof(f653,plain,
    ( spl55_10
    | spl55_12 ),
    inference(avatar_split_clause,[],[f556,f647,f638]) ).

fof(f556,plain,
    ( nil = sK50
    | ssItem(sK53) ),
    inference(definition_unfolding,[],[f537,f534]) ).

fof(f534,plain,
    sK48 = sK50,
    inference(cnf_transformation,[],[f339]) ).

fof(f537,plain,
    ( nil = sK48
    | ssItem(sK53) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f652,plain,
    ( spl55_9
    | spl55_12 ),
    inference(avatar_split_clause,[],[f555,f647,f633]) ).

fof(f555,plain,
    ( nil = sK50
    | ssList(sK54) ),
    inference(definition_unfolding,[],[f538,f534]) ).

fof(f538,plain,
    ( nil = sK48
    | ssList(sK54) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f651,plain,
    ( spl55_8
    | spl55_12 ),
    inference(avatar_split_clause,[],[f554,f647,f628]) ).

fof(f554,plain,
    ( nil = sK50
    | sK50 = app(cons(sK53,nil),sK54) ),
    inference(definition_unfolding,[],[f539,f534,f534]) ).

fof(f539,plain,
    ( nil = sK48
    | sK48 = app(cons(sK53,nil),sK54) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f650,plain,
    ( ~ spl55_11
    | spl55_12 ),
    inference(avatar_split_clause,[],[f553,f647,f643]) ).

fof(f553,plain,
    ( nil = sK50
    | sK49 != app(sK54,cons(sK53,nil)) ),
    inference(definition_unfolding,[],[f540,f534,f535]) ).

fof(f535,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f339]) ).

fof(f540,plain,
    ( nil = sK48
    | sK47 != app(sK54,cons(sK53,nil)) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f641,plain,
    ( spl55_10
    | ~ spl55_7 ),
    inference(avatar_split_clause,[],[f552,f623,f638]) ).

fof(f552,plain,
    ( nil != sK49
    | ssItem(sK53) ),
    inference(definition_unfolding,[],[f541,f535]) ).

fof(f541,plain,
    ( nil != sK47
    | ssItem(sK53) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f636,plain,
    ( spl55_9
    | ~ spl55_7 ),
    inference(avatar_split_clause,[],[f551,f623,f633]) ).

fof(f551,plain,
    ( nil != sK49
    | ssList(sK54) ),
    inference(definition_unfolding,[],[f542,f535]) ).

fof(f542,plain,
    ( nil != sK47
    | ssList(sK54) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f631,plain,
    ( spl55_8
    | ~ spl55_7 ),
    inference(avatar_split_clause,[],[f550,f623,f628]) ).

fof(f550,plain,
    ( nil != sK49
    | sK50 = app(cons(sK53,nil),sK54) ),
    inference(definition_unfolding,[],[f543,f535,f534]) ).

fof(f543,plain,
    ( nil != sK47
    | sK48 = app(cons(sK53,nil),sK54) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f616,plain,
    ( spl55_5
    | ~ spl55_2 ),
    inference(avatar_split_clause,[],[f545,f598,f613]) ).

fof(f545,plain,
    ( ~ neq(sK50,nil)
    | ssItem(sK51) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f611,plain,
    ( spl55_4
    | ~ spl55_2 ),
    inference(avatar_split_clause,[],[f546,f598,f608]) ).

fof(f546,plain,
    ( ~ neq(sK50,nil)
    | ssList(sK52) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f606,plain,
    ( spl55_3
    | ~ spl55_2 ),
    inference(avatar_split_clause,[],[f547,f598,f603]) ).

fof(f547,plain,
    ( ~ neq(sK50,nil)
    | sK50 = app(cons(sK51,nil),sK52) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f601,plain,
    ( spl55_1
    | ~ spl55_2 ),
    inference(avatar_split_clause,[],[f548,f598,f594]) ).

fof(f548,plain,
    ( ~ neq(sK50,nil)
    | sK49 = app(sK52,cons(sK51,nil)) ),
    inference(cnf_transformation,[],[f339]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC315+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n022.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 20:32:08 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.6dpImG9gmL/Vampire---4.8_18057
% 0.57/0.76  % (18316)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.76  % (18310)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.76  % (18312)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.76  % (18311)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.76  % (18314)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.76  % (18315)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.76  % (18313)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.76  % (18317)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.77  % (18313)Instruction limit reached!
% 0.57/0.77  % (18313)------------------------------
% 0.57/0.77  % (18313)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.77  % (18313)Termination reason: Unknown
% 0.57/0.77  % (18313)Termination phase: Saturation
% 0.57/0.77  
% 0.57/0.77  % (18313)Memory used [KB]: 1490
% 0.57/0.78  % (18313)Time elapsed: 0.020 s
% 0.57/0.78  % (18313)Instructions burned: 34 (million)
% 0.57/0.78  % (18313)------------------------------
% 0.57/0.78  % (18313)------------------------------
% 0.57/0.78  % (18311)First to succeed.
% 0.57/0.78  % (18310)Instruction limit reached!
% 0.57/0.78  % (18310)------------------------------
% 0.57/0.78  % (18310)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.78  % (18310)Termination reason: Unknown
% 0.57/0.78  % (18310)Termination phase: Saturation
% 0.57/0.78  
% 0.57/0.78  % (18310)Memory used [KB]: 1439
% 0.57/0.78  % (18310)Time elapsed: 0.021 s
% 0.57/0.78  % (18310)Instructions burned: 34 (million)
% 0.57/0.78  % (18310)------------------------------
% 0.57/0.78  % (18310)------------------------------
% 0.57/0.78  % (18316)Instruction limit reached!
% 0.57/0.78  % (18316)------------------------------
% 0.57/0.78  % (18316)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.78  % (18316)Termination reason: Unknown
% 0.57/0.78  % (18316)Termination phase: Saturation
% 0.57/0.78  
% 0.57/0.78  % (18316)Memory used [KB]: 2040
% 0.57/0.78  % (18316)Time elapsed: 0.023 s
% 0.57/0.78  % (18316)Instructions burned: 83 (million)
% 0.57/0.78  % (18316)------------------------------
% 0.57/0.78  % (18316)------------------------------
% 0.57/0.78  % (18311)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18306"
% 0.57/0.78  % (18311)Refutation found. Thanks to Tanya!
% 0.57/0.78  % SZS status Theorem for Vampire---4
% 0.57/0.78  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.78  % (18311)------------------------------
% 0.57/0.78  % (18311)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.78  % (18311)Termination reason: Refutation
% 0.57/0.78  
% 0.57/0.78  % (18311)Memory used [KB]: 1632
% 0.57/0.78  % (18311)Time elapsed: 0.023 s
% 0.57/0.78  % (18311)Instructions burned: 37 (million)
% 0.57/0.78  % (18306)Success in time 0.412 s
% 0.57/0.78  % Vampire---4.8 exiting
%------------------------------------------------------------------------------