TSTP Solution File: SWC001+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC001+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.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 May 21 04:39:37 EDT 2024

% Result   : Theorem 0.22s 0.40s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   95 (  42 unt;   0 def)
%            Number of atoms       :  408 (  36 equ)
%            Maximal formula atoms :   36 (   4 avg)
%            Number of connectives :  458 ( 145   ~; 131   |; 141   &)
%                                         (  19 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   32 (  30 usr;  20 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   8 con; 0-0 aty)
%            Number of variables   :   76 (  32   !;  44   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f741,plain,
    $false,
    inference(avatar_sat_refutation,[],[f648,f653,f658,f663,f667,f671,f680,f681,f687,f692,f697,f702,f707,f712,f713,f719,f724,f729,f734,f739,f740]) ).

fof(f740,plain,
    ( ~ spl70_4
    | spl70_7
    | ~ spl70_5
    | ~ spl70_8 ),
    inference(avatar_split_clause,[],[f714,f677,f665,f673,f660]) ).

fof(f660,plain,
    ( spl70_4
  <=> ssItem(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_4])]) ).

fof(f673,plain,
    ( spl70_7
  <=> memberP(sK21,sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_7])]) ).

fof(f665,plain,
    ( spl70_5
  <=> ! [X5] :
        ( ~ memberP(sK20,X5)
        | memberP(sK21,X5)
        | ~ ssItem(X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_5])]) ).

fof(f677,plain,
    ( spl70_8
  <=> memberP(sK20,sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_8])]) ).

fof(f714,plain,
    ( memberP(sK21,sK22)
    | ~ ssItem(sK22)
    | ~ spl70_5
    | ~ spl70_8 ),
    inference(resolution,[],[f678,f666]) ).

fof(f666,plain,
    ( ! [X5] :
        ( ~ memberP(sK20,X5)
        | memberP(sK21,X5)
        | ~ ssItem(X5) )
    | ~ spl70_5 ),
    inference(avatar_component_clause,[],[f665]) ).

fof(f678,plain,
    ( memberP(sK20,sK22)
    | ~ spl70_8 ),
    inference(avatar_component_clause,[],[f677]) ).

fof(f739,plain,
    spl70_19,
    inference(avatar_split_clause,[],[f603,f736]) ).

fof(f736,plain,
    ( spl70_19
  <=> ssItem(sK69) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_19])]) ).

fof(f603,plain,
    ssItem(sK69),
    inference(cnf_transformation,[],[f375]) ).

fof(f375,plain,
    ( sK68 != sK69
    & ssItem(sK69)
    & ssItem(sK68) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69])],[f2,f374,f373]) ).

fof(f373,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( X0 != X1
            & ssItem(X1) )
        & ssItem(X0) )
   => ( ? [X1] :
          ( sK68 != X1
          & ssItem(X1) )
      & ssItem(sK68) ) ),
    introduced(choice_axiom,[]) ).

fof(f374,plain,
    ( ? [X1] :
        ( sK68 != X1
        & ssItem(X1) )
   => ( sK68 != sK69
      & ssItem(sK69) ) ),
    introduced(choice_axiom,[]) ).

fof(f2,axiom,
    ? [X0] :
      ( ? [X1] :
          ( X0 != X1
          & ssItem(X1) )
      & ssItem(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

fof(f734,plain,
    spl70_18,
    inference(avatar_split_clause,[],[f602,f731]) ).

fof(f731,plain,
    ( spl70_18
  <=> ssItem(sK68) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_18])]) ).

fof(f602,plain,
    ssItem(sK68),
    inference(cnf_transformation,[],[f375]) ).

fof(f729,plain,
    spl70_17,
    inference(avatar_split_clause,[],[f396,f726]) ).

fof(f726,plain,
    ( spl70_17
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_17])]) ).

fof(f396,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f724,plain,
    spl70_16,
    inference(avatar_split_clause,[],[f395,f721]) ).

fof(f721,plain,
    ( spl70_16
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_16])]) ).

fof(f395,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

fof(f719,plain,
    spl70_15,
    inference(avatar_split_clause,[],[f394,f716]) ).

fof(f716,plain,
    ( spl70_15
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_15])]) ).

fof(f394,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).

fof(f713,plain,
    ( ~ spl70_4
    | spl70_8
    | ~ spl70_6
    | ~ spl70_7 ),
    inference(avatar_split_clause,[],[f682,f673,f669,f677,f660]) ).

fof(f669,plain,
    ( spl70_6
  <=> ! [X5] :
        ( ~ memberP(sK21,X5)
        | memberP(sK20,X5)
        | ~ ssItem(X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_6])]) ).

fof(f682,plain,
    ( memberP(sK20,sK22)
    | ~ ssItem(sK22)
    | ~ spl70_6
    | ~ spl70_7 ),
    inference(resolution,[],[f670,f674]) ).

fof(f674,plain,
    ( memberP(sK21,sK22)
    | ~ spl70_7 ),
    inference(avatar_component_clause,[],[f673]) ).

fof(f670,plain,
    ( ! [X5] :
        ( ~ memberP(sK21,X5)
        | memberP(sK20,X5)
        | ~ ssItem(X5) )
    | ~ spl70_6 ),
    inference(avatar_component_clause,[],[f669]) ).

fof(f712,plain,
    spl70_14,
    inference(avatar_split_clause,[],[f393,f709]) ).

fof(f709,plain,
    ( spl70_14
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_14])]) ).

fof(f393,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).

fof(f707,plain,
    spl70_13,
    inference(avatar_split_clause,[],[f392,f704]) ).

fof(f704,plain,
    ( spl70_13
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_13])]) ).

fof(f392,plain,
    equalelemsP(nil),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,axiom,
    equalelemsP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).

fof(f702,plain,
    spl70_12,
    inference(avatar_split_clause,[],[f391,f699]) ).

fof(f699,plain,
    ( spl70_12
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_12])]) ).

fof(f391,plain,
    strictorderP(nil),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    strictorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).

fof(f697,plain,
    spl70_11,
    inference(avatar_split_clause,[],[f390,f694]) ).

fof(f694,plain,
    ( spl70_11
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_11])]) ).

fof(f390,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).

fof(f692,plain,
    spl70_10,
    inference(avatar_split_clause,[],[f389,f689]) ).

fof(f689,plain,
    ( spl70_10
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_10])]) ).

fof(f389,plain,
    totalorderP(nil),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    totalorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).

fof(f687,plain,
    ~ spl70_9,
    inference(avatar_split_clause,[],[f388,f684]) ).

fof(f684,plain,
    ( spl70_9
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_9])]) ).

fof(f388,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f681,plain,
    ( spl70_7
    | spl70_8
    | ~ spl70_3 ),
    inference(avatar_split_clause,[],[f606,f655,f677,f673]) ).

fof(f655,plain,
    ( spl70_3
  <=> duplicatefreeP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_3])]) ).

fof(f606,plain,
    ( ~ duplicatefreeP(sK20)
    | memberP(sK20,sK22)
    | memberP(sK21,sK22) ),
    inference(definition_unfolding,[],[f386,f381,f381,f380]) ).

fof(f380,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f256]) ).

fof(f256,plain,
    ( ( ~ duplicatefreeP(sK18)
      | ( ( ~ memberP(sK18,sK22)
          | ~ memberP(sK19,sK22) )
        & ( memberP(sK18,sK22)
          | memberP(sK19,sK22) )
        & ssItem(sK22) ) )
    & ! [X5] :
        ( ( ( ~ memberP(sK21,X5)
            | memberP(sK20,X5) )
          & ( ~ memberP(sK20,X5)
            | memberP(sK21,X5) ) )
        | ~ ssItem(X5) )
    & duplicatefreeP(sK20)
    & sK18 = sK20
    & sK19 = sK21
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f100,f255,f254,f253,f252,f251]) ).

fof(f251,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ duplicatefreeP(X0)
                      | ? [X4] :
                          ( ( ~ memberP(X0,X4)
                            | ~ memberP(X1,X4) )
                          & ( memberP(X0,X4)
                            | memberP(X1,X4) )
                          & ssItem(X4) ) )
                    & ! [X5] :
                        ( ( ( ~ memberP(X3,X5)
                            | memberP(X2,X5) )
                          & ( ~ memberP(X2,X5)
                            | memberP(X3,X5) ) )
                        | ~ ssItem(X5) )
                    & duplicatefreeP(X2)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ duplicatefreeP(sK18)
                    | ? [X4] :
                        ( ( ~ memberP(sK18,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(sK18,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) )
                      | ~ ssItem(X5) )
                  & duplicatefreeP(X2)
                  & sK18 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ duplicatefreeP(sK18)
                  | ? [X4] :
                      ( ( ~ memberP(sK18,X4)
                        | ~ memberP(X1,X4) )
                      & ( memberP(sK18,X4)
                        | memberP(X1,X4) )
                      & ssItem(X4) ) )
                & ! [X5] :
                    ( ( ( ~ memberP(X3,X5)
                        | memberP(X2,X5) )
                      & ( ~ memberP(X2,X5)
                        | memberP(X3,X5) ) )
                    | ~ ssItem(X5) )
                & duplicatefreeP(X2)
                & sK18 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ duplicatefreeP(sK18)
                | ? [X4] :
                    ( ( ~ memberP(sK18,X4)
                      | ~ memberP(sK19,X4) )
                    & ( memberP(sK18,X4)
                      | memberP(sK19,X4) )
                    & ssItem(X4) ) )
              & ! [X5] :
                  ( ( ( ~ memberP(X3,X5)
                      | memberP(X2,X5) )
                    & ( ~ memberP(X2,X5)
                      | memberP(X3,X5) ) )
                  | ~ ssItem(X5) )
              & duplicatefreeP(X2)
              & sK18 = X2
              & sK19 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ duplicatefreeP(sK18)
              | ? [X4] :
                  ( ( ~ memberP(sK18,X4)
                    | ~ memberP(sK19,X4) )
                  & ( memberP(sK18,X4)
                    | memberP(sK19,X4) )
                  & ssItem(X4) ) )
            & ! [X5] :
                ( ( ( ~ memberP(X3,X5)
                    | memberP(X2,X5) )
                  & ( ~ memberP(X2,X5)
                    | memberP(X3,X5) ) )
                | ~ ssItem(X5) )
            & duplicatefreeP(X2)
            & sK18 = X2
            & sK19 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ duplicatefreeP(sK18)
            | ? [X4] :
                ( ( ~ memberP(sK18,X4)
                  | ~ memberP(sK19,X4) )
                & ( memberP(sK18,X4)
                  | memberP(sK19,X4) )
                & ssItem(X4) ) )
          & ! [X5] :
              ( ( ( ~ memberP(X3,X5)
                  | memberP(sK20,X5) )
                & ( ~ memberP(sK20,X5)
                  | memberP(X3,X5) ) )
              | ~ ssItem(X5) )
          & duplicatefreeP(sK20)
          & sK18 = sK20
          & sK19 = X3
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f254,plain,
    ( ? [X3] :
        ( ( ~ duplicatefreeP(sK18)
          | ? [X4] :
              ( ( ~ memberP(sK18,X4)
                | ~ memberP(sK19,X4) )
              & ( memberP(sK18,X4)
                | memberP(sK19,X4) )
              & ssItem(X4) ) )
        & ! [X5] :
            ( ( ( ~ memberP(X3,X5)
                | memberP(sK20,X5) )
              & ( ~ memberP(sK20,X5)
                | memberP(X3,X5) ) )
            | ~ ssItem(X5) )
        & duplicatefreeP(sK20)
        & sK18 = sK20
        & sK19 = X3
        & ssList(X3) )
   => ( ( ~ duplicatefreeP(sK18)
        | ? [X4] :
            ( ( ~ memberP(sK18,X4)
              | ~ memberP(sK19,X4) )
            & ( memberP(sK18,X4)
              | memberP(sK19,X4) )
            & ssItem(X4) ) )
      & ! [X5] :
          ( ( ( ~ memberP(sK21,X5)
              | memberP(sK20,X5) )
            & ( ~ memberP(sK20,X5)
              | memberP(sK21,X5) ) )
          | ~ ssItem(X5) )
      & duplicatefreeP(sK20)
      & sK18 = sK20
      & sK19 = sK21
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f255,plain,
    ( ? [X4] :
        ( ( ~ memberP(sK18,X4)
          | ~ memberP(sK19,X4) )
        & ( memberP(sK18,X4)
          | memberP(sK19,X4) )
        & ssItem(X4) )
   => ( ( ~ memberP(sK18,sK22)
        | ~ memberP(sK19,sK22) )
      & ( memberP(sK18,sK22)
        | memberP(sK19,sK22) )
      & ssItem(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ duplicatefreeP(X0)
                    | ? [X4] :
                        ( ( ~ memberP(X0,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(X0,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) )
                      | ~ ssItem(X5) )
                  & duplicatefreeP(X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ duplicatefreeP(X0)
                    | ? [X4] :
                        ( ( ~ memberP(X0,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(X0,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) )
                      | ~ ssItem(X5) )
                  & duplicatefreeP(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] :
                    ( ssList(X3)
                   => ( ( duplicatefreeP(X0)
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ( memberP(X0,X4)
                                & memberP(X1,X4) )
                              | ( ~ memberP(X0,X4)
                                & ~ memberP(X1,X4) ) ) ) )
                      | ? [X5] :
                          ( ( ( memberP(X3,X5)
                              & ~ memberP(X2,X5) )
                            | ( memberP(X2,X5)
                              & ~ memberP(X3,X5) ) )
                          & ssItem(X5) )
                      | ~ duplicatefreeP(X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( duplicatefreeP(X0)
                        & ! [X5] :
                            ( ssItem(X5)
                           => ( ( memberP(X0,X5)
                                & memberP(X1,X5) )
                              | ( ~ memberP(X0,X5)
                                & ~ memberP(X1,X5) ) ) ) )
                      | ? [X4] :
                          ( ( ( memberP(X3,X4)
                              & ~ memberP(X2,X4) )
                            | ( memberP(X2,X4)
                              & ~ memberP(X3,X4) ) )
                          & ssItem(X4) )
                      | ~ duplicatefreeP(X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( duplicatefreeP(X0)
                      & ! [X5] :
                          ( ssItem(X5)
                         => ( ( memberP(X0,X5)
                              & memberP(X1,X5) )
                            | ( ~ memberP(X0,X5)
                              & ~ memberP(X1,X5) ) ) ) )
                    | ? [X4] :
                        ( ( ( memberP(X3,X4)
                            & ~ memberP(X2,X4) )
                          | ( memberP(X2,X4)
                            & ~ memberP(X3,X4) ) )
                        & ssItem(X4) )
                    | ~ duplicatefreeP(X2)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f381,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f256]) ).

fof(f386,plain,
    ( ~ duplicatefreeP(sK18)
    | memberP(sK18,sK22)
    | memberP(sK19,sK22) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f680,plain,
    ( ~ spl70_7
    | ~ spl70_8
    | ~ spl70_3 ),
    inference(avatar_split_clause,[],[f605,f655,f677,f673]) ).

fof(f605,plain,
    ( ~ duplicatefreeP(sK20)
    | ~ memberP(sK20,sK22)
    | ~ memberP(sK21,sK22) ),
    inference(definition_unfolding,[],[f387,f381,f381,f380]) ).

fof(f387,plain,
    ( ~ duplicatefreeP(sK18)
    | ~ memberP(sK18,sK22)
    | ~ memberP(sK19,sK22) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f671,plain,
    spl70_6,
    inference(avatar_split_clause,[],[f384,f669]) ).

fof(f384,plain,
    ! [X5] :
      ( ~ memberP(sK21,X5)
      | memberP(sK20,X5)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f667,plain,
    spl70_5,
    inference(avatar_split_clause,[],[f383,f665]) ).

fof(f383,plain,
    ! [X5] :
      ( ~ memberP(sK20,X5)
      | memberP(sK21,X5)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f663,plain,
    ( spl70_4
    | ~ spl70_3 ),
    inference(avatar_split_clause,[],[f607,f655,f660]) ).

fof(f607,plain,
    ( ~ duplicatefreeP(sK20)
    | ssItem(sK22) ),
    inference(definition_unfolding,[],[f385,f381]) ).

fof(f385,plain,
    ( ~ duplicatefreeP(sK18)
    | ssItem(sK22) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f658,plain,
    spl70_3,
    inference(avatar_split_clause,[],[f382,f655]) ).

fof(f382,plain,
    duplicatefreeP(sK20),
    inference(cnf_transformation,[],[f256]) ).

fof(f653,plain,
    spl70_2,
    inference(avatar_split_clause,[],[f379,f650]) ).

fof(f650,plain,
    ( spl70_2
  <=> ssList(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_2])]) ).

fof(f379,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f256]) ).

fof(f648,plain,
    spl70_1,
    inference(avatar_split_clause,[],[f378,f645]) ).

fof(f645,plain,
    ( spl70_1
  <=> ssList(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl70_1])]) ).

fof(f378,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWC001+1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n026.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 19 03:13:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (9451)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (9454)WARNING: value z3 for option sas not known
% 0.22/0.38  % (9458)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)
% 0.22/0.38  % (9456)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)
% 0.22/0.38  % (9452)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  % (9453)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39  % (9455)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39  % (9454)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)
% 0.22/0.39  % (9457)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)
% 0.22/0.39  % (9456)First to succeed.
% 0.22/0.40  % (9456)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9451"
% 0.22/0.40  % (9456)Refutation found. Thanks to Tanya!
% 0.22/0.40  % SZS status Theorem for theBenchmark
% 0.22/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40  % (9456)------------------------------
% 0.22/0.40  % (9456)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40  % (9456)Termination reason: Refutation
% 0.22/0.40  
% 0.22/0.40  % (9456)Memory used [KB]: 1253
% 0.22/0.40  % (9456)Time elapsed: 0.012 s
% 0.22/0.40  % (9456)Instructions burned: 19 (million)
% 0.22/0.40  % (9451)Success in time 0.031 s
%------------------------------------------------------------------------------