TSTP Solution File: SWC100+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC100+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n024.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 : Sat Sep  2 12:42:36 EDT 2023

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   68 (  19 unt;   0 def)
%            Number of atoms       :  498 ( 201 equ)
%            Maximal formula atoms :   46 (   7 avg)
%            Number of connectives :  680 ( 250   ~; 230   |; 172   &)
%                                         (   6 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  151 (; 103   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2925,plain,
    $false,
    inference(resolution,[],[f2918,f398]) ).

fof(f398,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.uREUYp4fkK/Vampire---4.8_19096',ax17) ).

fof(f2918,plain,
    ~ ssList(nil),
    inference(resolution,[],[f2466,f948]) ).

fof(f948,plain,
    ! [X0] :
      ( ~ neq(X0,X0)
      | ~ ssList(X0) ),
    inference(duplicate_literal_removal,[],[f947]) ).

fof(f947,plain,
    ! [X0] :
      ( ~ neq(X0,X0)
      | ~ ssList(X0)
      | ~ ssList(X0) ),
    inference(equality_resolution,[],[f577]) ).

fof(f577,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f356,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f198]) ).

fof(f198,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/sandbox2/tmp/tmp.uREUYp4fkK/Vampire---4.8_19096',ax15) ).

fof(f2466,plain,
    neq(nil,nil),
    inference(backward_demodulation,[],[f2360,f2362]) ).

fof(f2362,plain,
    nil = sK19,
    inference(backward_demodulation,[],[f379,f2358]) ).

fof(f2358,plain,
    nil = sK21,
    inference(trivial_inequality_removal,[],[f2221]) ).

fof(f2221,plain,
    ( nil != nil
    | nil = sK21 ),
    inference(backward_demodulation,[],[f611,f2214]) ).

fof(f2214,plain,
    nil = sK18,
    inference(resolution,[],[f2213,f614]) ).

fof(f614,plain,
    ssList(sK18),
    inference(forward_demodulation,[],[f377,f380]) ).

fof(f380,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f255]) ).

fof(f255,plain,
    ( ( ( ( ~ frontsegP(sK19,sK18)
          | ~ neq(sK18,nil) )
        & neq(sK19,nil) )
      | ( nil != sK18
        & nil = sK19 ) )
    & ( nil != sK20
      | nil = sK21 )
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ lt(X7,X5)
                    | app(X8,cons(X7,nil)) != sK20
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | app(cons(X5,nil),X6) != sK22
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & strictorderedP(sK20)
    & sK21 = app(sK20,sK22)
    & ssList(sK22)
    & sK18 = sK20
    & sK19 = sK21
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f99,f254,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ( ~ frontsegP(X1,X0)
                          | ~ neq(X0,nil) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ! [X8] :
                                        ( ~ lt(X7,X5)
                                        | app(X8,cons(X7,nil)) != X2
                                        | ~ ssList(X8) )
                                    | ~ ssItem(X7) )
                                | app(cons(X5,nil),X6) != X4
                                | ~ ssList(X6) )
                            | ~ ssItem(X5) )
                        & strictorderedP(X2)
                        & app(X2,X4) = X3
                        & ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ( ~ frontsegP(X1,sK18)
                        | ~ neq(sK18,nil) )
                      & neq(X1,nil) )
                    | ( nil != sK18
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ lt(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & strictorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & sK18 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ( ~ frontsegP(X1,sK18)
                      | ~ neq(sK18,nil) )
                    & neq(X1,nil) )
                  | ( nil != sK18
                    & nil = X1 ) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ~ lt(X7,X5)
                                    | app(X8,cons(X7,nil)) != X2
                                    | ~ ssList(X8) )
                                | ~ ssItem(X7) )
                            | app(cons(X5,nil),X6) != X4
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) )
                    & strictorderedP(X2)
                    & app(X2,X4) = X3
                    & ssList(X4) )
                & sK18 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ( ~ frontsegP(sK19,sK18)
                    | ~ neq(sK18,nil) )
                  & neq(sK19,nil) )
                | ( nil != sK18
                  & nil = sK19 ) )
              & ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ~ lt(X7,X5)
                                  | app(X8,cons(X7,nil)) != X2
                                  | ~ ssList(X8) )
                              | ~ ssItem(X7) )
                          | app(cons(X5,nil),X6) != X4
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & strictorderedP(X2)
                  & app(X2,X4) = X3
                  & ssList(X4) )
              & sK18 = X2
              & sK19 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ( ~ frontsegP(sK19,sK18)
                  | ~ neq(sK18,nil) )
                & neq(sK19,nil) )
              | ( nil != sK18
                & nil = sK19 ) )
            & ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ~ lt(X7,X5)
                                | app(X8,cons(X7,nil)) != X2
                                | ~ ssList(X8) )
                            | ~ ssItem(X7) )
                        | app(cons(X5,nil),X6) != X4
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) )
                & strictorderedP(X2)
                & app(X2,X4) = X3
                & ssList(X4) )
            & sK18 = X2
            & sK19 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ( ~ frontsegP(sK19,sK18)
                | ~ neq(sK18,nil) )
              & neq(sK19,nil) )
            | ( nil != sK18
              & nil = sK19 ) )
          & ( nil != sK20
            | nil = X3 )
          & ? [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ~ lt(X7,X5)
                              | app(X8,cons(X7,nil)) != sK20
                              | ~ ssList(X8) )
                          | ~ ssItem(X7) )
                      | app(cons(X5,nil),X6) != X4
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) )
              & strictorderedP(sK20)
              & app(sK20,X4) = X3
              & ssList(X4) )
          & sK18 = sK20
          & sK19 = X3
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ( ( ( ~ frontsegP(sK19,sK18)
              | ~ neq(sK18,nil) )
            & neq(sK19,nil) )
          | ( nil != sK18
            & nil = sK19 ) )
        & ( nil != sK20
          | nil = X3 )
        & ? [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ~ lt(X7,X5)
                            | app(X8,cons(X7,nil)) != sK20
                            | ~ ssList(X8) )
                        | ~ ssItem(X7) )
                    | app(cons(X5,nil),X6) != X4
                    | ~ ssList(X6) )
                | ~ ssItem(X5) )
            & strictorderedP(sK20)
            & app(sK20,X4) = X3
            & ssList(X4) )
        & sK18 = sK20
        & sK19 = X3
        & ssList(X3) )
   => ( ( ( ( ~ frontsegP(sK19,sK18)
            | ~ neq(sK18,nil) )
          & neq(sK19,nil) )
        | ( nil != sK18
          & nil = sK19 ) )
      & ( nil != sK20
        | nil = sK21 )
      & ? [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ~ lt(X7,X5)
                          | app(X8,cons(X7,nil)) != sK20
                          | ~ ssList(X8) )
                      | ~ ssItem(X7) )
                  | app(cons(X5,nil),X6) != X4
                  | ~ ssList(X6) )
              | ~ ssItem(X5) )
          & strictorderedP(sK20)
          & app(sK20,X4) = sK21
          & ssList(X4) )
      & sK18 = sK20
      & sK19 = sK21
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f254,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ~ lt(X7,X5)
                        | app(X8,cons(X7,nil)) != sK20
                        | ~ ssList(X8) )
                    | ~ ssItem(X7) )
                | app(cons(X5,nil),X6) != X4
                | ~ ssList(X6) )
            | ~ ssItem(X5) )
        & strictorderedP(sK20)
        & app(sK20,X4) = sK21
        & ssList(X4) )
   => ( ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ lt(X7,X5)
                      | app(X8,cons(X7,nil)) != sK20
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | app(cons(X5,nil),X6) != sK22
              | ~ ssList(X6) )
          | ~ ssItem(X5) )
      & strictorderedP(sK20)
      & sK21 = app(sK20,sK22)
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ( ~ frontsegP(X1,X0)
                        | ~ neq(X0,nil) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ lt(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & strictorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ( ~ frontsegP(X1,X0)
                        | ~ neq(X0,nil) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ lt(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & strictorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( ( frontsegP(X1,X0)
                            & neq(X0,nil) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( lt(X7,X5)
                                            & app(X8,cons(X7,nil)) = X2
                                            & ssList(X8) )
                                        & ssItem(X7) )
                                    & app(cons(X5,nil),X6) = X4
                                    & ssList(X6) )
                                & ssItem(X5) )
                            | ~ strictorderedP(X2)
                            | app(X2,X4) != X3 ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ( frontsegP(X1,X0)
                          & neq(X0,nil) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( ? [X8] :
                                          ( lt(X7,X5)
                                          & app(X8,cons(X7,nil)) = X2
                                          & ssList(X8) )
                                      & ssItem(X7) )
                                  & app(cons(X5,nil),X6) = X4
                                  & ssList(X6) )
                              & ssItem(X5) )
                          | ~ strictorderedP(X2)
                          | app(X2,X4) != X3 ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uREUYp4fkK/Vampire---4.8_19096',co1) ).

fof(f377,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f255]) ).

fof(f2213,plain,
    ( ~ ssList(sK18)
    | nil = sK18 ),
    inference(resolution,[],[f2211,f381]) ).

fof(f381,plain,
    ssList(sK22),
    inference(cnf_transformation,[],[f255]) ).

fof(f2211,plain,
    ( ~ ssList(sK22)
    | nil = sK18
    | ~ ssList(sK18) ),
    inference(trivial_inequality_removal,[],[f2210]) ).

fof(f2210,plain,
    ( nil != nil
    | nil = sK18
    | ~ ssList(sK22)
    | ~ ssList(sK18) ),
    inference(duplicate_literal_removal,[],[f2167]) ).

fof(f2167,plain,
    ( nil != nil
    | nil = sK18
    | ~ ssList(sK22)
    | ~ ssList(sK18)
    | nil = sK18 ),
    inference(superposition,[],[f1267,f2135]) ).

fof(f2135,plain,
    ( nil = sK19
    | nil = sK18 ),
    inference(resolution,[],[f2133,f398]) ).

fof(f2133,plain,
    ( ~ ssList(nil)
    | nil = sK18
    | nil = sK19 ),
    inference(resolution,[],[f2132,f614]) ).

fof(f2132,plain,
    ( ~ ssList(sK18)
    | ~ ssList(nil)
    | nil = sK18
    | nil = sK19 ),
    inference(resolution,[],[f2131,f613]) ).

fof(f613,plain,
    ssList(sK19),
    inference(forward_demodulation,[],[f378,f379]) ).

fof(f378,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f255]) ).

fof(f2131,plain,
    ( ~ ssList(sK19)
    | ~ ssList(sK18)
    | ~ ssList(nil)
    | nil = sK18
    | nil = sK19 ),
    inference(resolution,[],[f1953,f381]) ).

fof(f1953,plain,
    ( ~ ssList(sK22)
    | ~ ssList(sK18)
    | ~ ssList(sK19)
    | ~ ssList(nil)
    | nil = sK18
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f1945]) ).

fof(f1945,plain,
    ( ~ ssList(sK22)
    | ~ ssList(sK18)
    | ~ ssList(sK19)
    | ~ ssList(nil)
    | ~ ssList(sK18)
    | nil = sK18
    | nil = sK19 ),
    inference(resolution,[],[f1944,f988]) ).

fof(f988,plain,
    ( ~ frontsegP(sK19,sK18)
    | ~ ssList(nil)
    | ~ ssList(sK18)
    | nil = sK18
    | nil = sK19 ),
    inference(resolution,[],[f578,f388]) ).

fof(f388,plain,
    ( ~ neq(sK18,nil)
    | ~ frontsegP(sK19,sK18)
    | nil = sK19 ),
    inference(cnf_transformation,[],[f255]) ).

fof(f578,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f1944,plain,
    ( frontsegP(sK19,sK18)
    | ~ ssList(sK22)
    | ~ ssList(sK18)
    | ~ ssList(sK19) ),
    inference(equality_resolution,[],[f1938]) ).

fof(f1938,plain,
    ! [X8] :
      ( sK19 != X8
      | frontsegP(X8,sK18)
      | ~ ssList(sK22)
      | ~ ssList(sK18)
      | ~ ssList(X8) ),
    inference(superposition,[],[f588,f612]) ).

fof(f612,plain,
    sK19 = app(sK18,sK22),
    inference(backward_demodulation,[],[f608,f379]) ).

fof(f608,plain,
    sK21 = app(sK18,sK22),
    inference(backward_demodulation,[],[f382,f380]) ).

fof(f382,plain,
    sK21 = app(sK20,sK22),
    inference(cnf_transformation,[],[f255]) ).

fof(f588,plain,
    ! [X2,X0,X1] :
      ( app(X1,X2) != X0
      | frontsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f369]) ).

fof(f369,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK67(X0,X1)) = X0
                & ssList(sK67(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f367,f368]) ).

fof(f368,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK67(X0,X1)) = X0
        & ssList(sK67(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f367,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X1,X3) = X0
                  & ssList(X3) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f366]) ).

fof(f366,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f201]) ).

fof(f201,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uREUYp4fkK/Vampire---4.8_19096',ax5) ).

fof(f1267,plain,
    ( nil != sK19
    | nil = sK18
    | ~ ssList(sK22)
    | ~ ssList(sK18) ),
    inference(superposition,[],[f590,f612]) ).

fof(f590,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f371]) ).

fof(f371,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,[],[f370]) ).

fof(f370,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,[],[f202]) ).

fof(f202,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/sandbox2/tmp/tmp.uREUYp4fkK/Vampire---4.8_19096',ax83) ).

fof(f611,plain,
    ( nil != sK18
    | nil = sK21 ),
    inference(backward_demodulation,[],[f385,f380]) ).

fof(f385,plain,
    ( nil != sK20
    | nil = sK21 ),
    inference(cnf_transformation,[],[f255]) ).

fof(f379,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f255]) ).

fof(f2360,plain,
    neq(sK19,nil),
    inference(trivial_inequality_removal,[],[f2216]) ).

fof(f2216,plain,
    ( nil != nil
    | neq(sK19,nil) ),
    inference(backward_demodulation,[],[f387,f2214]) ).

fof(f387,plain,
    ( nil != sK18
    | neq(sK19,nil) ),
    inference(cnf_transformation,[],[f255]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SWC100+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.36  % Computer : n024.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Wed Aug 30 17:19:07 EDT 2023
% 0.13/0.36  % CPUTime    : 
% 0.20/0.44  % (19240)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.45  % (19253)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 Vampire---4 for (497ds/0Mi)
% 0.20/0.45  % (19242)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.20/0.45  % (19250)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 Vampire---4 for (531ds/0Mi)
% 0.20/0.45  % (19241)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.20/0.45  % (19252)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 Vampire---4 for (522ds/0Mi)
% 0.20/0.45  % (19247)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.20/0.45  % (19244)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 Vampire---4 for (569ds/0Mi)
% 0.20/0.46  TRYING [1]
% 0.20/0.46  TRYING [1]
% 0.20/0.46  TRYING [2]
% 0.20/0.46  TRYING [2]
% 0.20/0.46  TRYING [3]
% 0.20/0.47  TRYING [3]
% 0.20/0.49  TRYING [4]
% 0.20/0.50  TRYING [1]
% 0.20/0.50  TRYING [2]
% 0.20/0.50  TRYING [4]
% 0.20/0.50  TRYING [3]
% 0.20/0.53  TRYING [4]
% 0.20/0.53  % (19252)First to succeed.
% 0.20/0.54  % (19252)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Theorem for Vampire---4
% 0.20/0.54  % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.54  % (19252)------------------------------
% 0.20/0.54  % (19252)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.54  % (19252)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.54  % (19252)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (19252)Memory used [KB]: 3837
% 0.20/0.54  % (19252)Time elapsed: 0.090 s
% 0.20/0.54  % (19252)------------------------------
% 0.20/0.54  % (19252)------------------------------
% 0.20/0.54  % (19240)Success in time 0.174 s
% 0.20/0.54  % Vampire---4.8 exiting
%------------------------------------------------------------------------------