TSTP Solution File: SWC310+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC310+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 : Thu Aug 31 20:42:26 EDT 2023

% Result   : Theorem 17.13s 3.13s
% Output   : CNFRefutation 17.13s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f607)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).

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

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).

fof(f25,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => tl(cons(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ( ? [X6] :
                          ( ? [X7] :
                              ( ? [X8] :
                                  ( neq(nil,X1)
                                  & ? [X9] :
                                      ( neq(nil,X1)
                                      & hd(X1) = X9
                                      & cons(X9,nil) = X8
                                      & ssItem(X9) )
                                  & app(X7,X8) = X6
                                  & tl(X1) = X7
                                  & ssList(X8) )
                              & ssList(X7) )
                          & X0 = X6
                          & ssList(X6) )
                      | ~ neq(X1,nil) )
                    & ( nil = X0
                      | nil != X1 ) )
                  | ( neq(X3,nil)
                    & ! [X4] :
                        ( ssItem(X4)
                       => ! [X5] :
                            ( app(X5,cons(X4,nil)) != X2
                            | app(cons(X4,nil),X5) != X3
                            | ~ ssList(X5) ) ) )
                  | ( nil = X3
                    & nil != X2 )
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( ( ? [X6] :
                            ( ? [X7] :
                                ( ? [X8] :
                                    ( neq(nil,X1)
                                    & ? [X9] :
                                        ( neq(nil,X1)
                                        & hd(X1) = X9
                                        & cons(X9,nil) = X8
                                        & ssItem(X9) )
                                    & app(X7,X8) = X6
                                    & tl(X1) = X7
                                    & ssList(X8) )
                                & ssList(X7) )
                            & X0 = X6
                            & ssList(X6) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ( neq(X3,nil)
                      & ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( app(X5,cons(X4,nil)) != X2
                              | app(cons(X4,nil),X5) != X3
                              | ~ ssList(X5) ) ) )
                    | ( nil = X3
                      & nil != X2 )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( ( ? [X4] :
                            ( ? [X5] :
                                ( ? [X6] :
                                    ( neq(nil,X1)
                                    & ? [X7] :
                                        ( neq(nil,X1)
                                        & hd(X1) = X7
                                        & cons(X7,nil) = X6
                                        & ssItem(X7) )
                                    & app(X5,X6) = X4
                                    & tl(X1) = X5
                                    & ssList(X6) )
                                & ssList(X5) )
                            & X0 = X4
                            & ssList(X4) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ( neq(X3,nil)
                      & ! [X8] :
                          ( ssItem(X8)
                         => ! [X9] :
                              ( app(X9,cons(X8,nil)) != X2
                              | app(cons(X8,nil),X9) != X3
                              | ~ ssList(X9) ) ) )
                    | ( nil = X3
                      & nil != X2 )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

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

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

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f187,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f188,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f187]) ).

fof(f189,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f190,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f189]) ).

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

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ! [X5] :
                              ( ! [X6] :
                                  ( ~ neq(nil,X1)
                                  | ! [X7] :
                                      ( ~ neq(nil,X1)
                                      | hd(X1) != X7
                                      | cons(X7,nil) != X6
                                      | ~ ssItem(X7) )
                                  | app(X5,X6) != X4
                                  | tl(X1) != X5
                                  | ~ ssList(X6) )
                              | ~ ssList(X5) )
                          | X0 != X4
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( ~ neq(X3,nil)
                    | ? [X8] :
                        ( ? [X9] :
                            ( app(X9,cons(X8,nil)) = X2
                            & app(cons(X8,nil),X9) = X3
                            & ssList(X9) )
                        & ssItem(X8) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f316,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f335,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X0] :
      ( ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f188,f335]) ).

fof(f337,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f338,plain,
    ! [X0] :
      ( ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f190,f337]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ! [X4] :
                            ( ! [X5] :
                                ( ! [X6] :
                                    ( ~ neq(nil,X1)
                                    | ! [X7] :
                                        ( ~ neq(nil,X1)
                                        | hd(X1) != X7
                                        | cons(X7,nil) != X6
                                        | ~ ssItem(X7) )
                                    | app(X5,X6) != X4
                                    | tl(X1) != X5
                                    | ~ ssList(X6) )
                                | ~ ssList(X5) )
                            | X0 != X4
                            | ~ ssList(X4) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) )
                    & ( ~ neq(X3,nil)
                      | ? [X8] :
                          ( ? [X9] :
                              ( app(X9,cons(X8,nil)) = X2
                              & app(cons(X8,nil),X9) = X3
                              & ssList(X9) )
                          & ssItem(X8) ) )
                    & ( nil != X3
                      | nil = X2 )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ! [X5] :
                              ( ! [X6] :
                                  ( ~ neq(nil,X1)
                                  | ! [X7] :
                                      ( ~ neq(nil,X1)
                                      | hd(X1) != X7
                                      | cons(X7,nil) != X6
                                      | ~ ssItem(X7) )
                                  | app(X5,X6) != X4
                                  | tl(X1) != X5
                                  | ~ ssList(X6) )
                              | ~ ssList(X5) )
                          | sK53 != X4
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != sK53
                      & nil = X1 ) )
                  & ( ~ neq(X3,nil)
                    | ? [X8] :
                        ( ? [X9] :
                            ( app(X9,cons(X8,nil)) = X2
                            & app(cons(X8,nil),X9) = X3
                            & ssList(X9) )
                        & ssItem(X8) ) )
                  & ( nil != X3
                    | nil = X2 )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ! [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ~ neq(nil,X1)
                                | ! [X7] :
                                    ( ~ neq(nil,X1)
                                    | hd(X1) != X7
                                    | cons(X7,nil) != X6
                                    | ~ ssItem(X7) )
                                | app(X5,X6) != X4
                                | tl(X1) != X5
                                | ~ ssList(X6) )
                            | ~ ssList(X5) )
                        | sK53 != X4
                        | ~ ssList(X4) )
                    & neq(X1,nil) )
                  | ( nil != sK53
                    & nil = X1 ) )
                & ( ~ neq(X3,nil)
                  | ? [X8] :
                      ( ? [X9] :
                          ( app(X9,cons(X8,nil)) = X2
                          & app(cons(X8,nil),X9) = X3
                          & ssList(X9) )
                      & ssItem(X8) ) )
                & ( nil != X3
                  | nil = X2 )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ~ neq(nil,sK54)
                              | ! [X7] :
                                  ( ~ neq(nil,sK54)
                                  | hd(sK54) != X7
                                  | cons(X7,nil) != X6
                                  | ~ ssItem(X7) )
                              | app(X5,X6) != X4
                              | tl(sK54) != X5
                              | ~ ssList(X6) )
                          | ~ ssList(X5) )
                      | sK53 != X4
                      | ~ ssList(X4) )
                  & neq(sK54,nil) )
                | ( nil != sK53
                  & nil = sK54 ) )
              & ( ~ neq(X3,nil)
                | ? [X8] :
                    ( ? [X9] :
                        ( app(X9,cons(X8,nil)) = X2
                        & app(cons(X8,nil),X9) = X3
                        & ssList(X9) )
                    & ssItem(X8) ) )
              & ( nil != X3
                | nil = X2 )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ! [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( ~ neq(nil,sK54)
                            | ! [X7] :
                                ( ~ neq(nil,sK54)
                                | hd(sK54) != X7
                                | cons(X7,nil) != X6
                                | ~ ssItem(X7) )
                            | app(X5,X6) != X4
                            | tl(sK54) != X5
                            | ~ ssList(X6) )
                        | ~ ssList(X5) )
                    | sK53 != X4
                    | ~ ssList(X4) )
                & neq(sK54,nil) )
              | ( nil != sK53
                & nil = sK54 ) )
            & ( ~ neq(X3,nil)
              | ? [X8] :
                  ( ? [X9] :
                      ( app(X9,cons(X8,nil)) = X2
                      & app(cons(X8,nil),X9) = X3
                      & ssList(X9) )
                  & ssItem(X8) ) )
            & ( nil != X3
              | nil = X2 )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ! [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ~ neq(nil,sK54)
                          | ! [X7] :
                              ( ~ neq(nil,sK54)
                              | hd(sK54) != X7
                              | cons(X7,nil) != X6
                              | ~ ssItem(X7) )
                          | app(X5,X6) != X4
                          | tl(sK54) != X5
                          | ~ ssList(X6) )
                      | ~ ssList(X5) )
                  | sK53 != X4
                  | ~ ssList(X4) )
              & neq(sK54,nil) )
            | ( nil != sK53
              & nil = sK54 ) )
          & ( ~ neq(X3,nil)
            | ? [X8] :
                ( ? [X9] :
                    ( app(X9,cons(X8,nil)) = sK55
                    & app(cons(X8,nil),X9) = X3
                    & ssList(X9) )
                & ssItem(X8) ) )
          & ( nil != X3
            | nil = sK55 )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ( ! [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( ~ neq(nil,sK54)
                        | ! [X7] :
                            ( ~ neq(nil,sK54)
                            | hd(sK54) != X7
                            | cons(X7,nil) != X6
                            | ~ ssItem(X7) )
                        | app(X5,X6) != X4
                        | tl(sK54) != X5
                        | ~ ssList(X6) )
                    | ~ ssList(X5) )
                | sK53 != X4
                | ~ ssList(X4) )
            & neq(sK54,nil) )
          | ( nil != sK53
            & nil = sK54 ) )
        & ( ~ neq(X3,nil)
          | ? [X8] :
              ( ? [X9] :
                  ( app(X9,cons(X8,nil)) = sK55
                  & app(cons(X8,nil),X9) = X3
                  & ssList(X9) )
              & ssItem(X8) ) )
        & ( nil != X3
          | nil = sK55 )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( ! [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ~ neq(nil,sK54)
                      | ! [X7] :
                          ( ~ neq(nil,sK54)
                          | hd(sK54) != X7
                          | cons(X7,nil) != X6
                          | ~ ssItem(X7) )
                      | app(X5,X6) != X4
                      | tl(sK54) != X5
                      | ~ ssList(X6) )
                  | ~ ssList(X5) )
              | sK53 != X4
              | ~ ssList(X4) )
          & neq(sK54,nil) )
        | ( nil != sK53
          & nil = sK54 ) )
      & ( ~ neq(sK56,nil)
        | ? [X8] :
            ( ? [X9] :
                ( app(X9,cons(X8,nil)) = sK55
                & app(cons(X8,nil),X9) = sK56
                & ssList(X9) )
            & ssItem(X8) ) )
      & ( nil != sK56
        | nil = sK55 )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X8] :
        ( ? [X9] :
            ( app(X9,cons(X8,nil)) = sK55
            & app(cons(X8,nil),X9) = sK56
            & ssList(X9) )
        & ssItem(X8) )
   => ( ? [X9] :
          ( sK55 = app(X9,cons(sK57,nil))
          & sK56 = app(cons(sK57,nil),X9)
          & ssList(X9) )
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X9] :
        ( sK55 = app(X9,cons(sK57,nil))
        & sK56 = app(cons(sK57,nil),X9)
        & ssList(X9) )
   => ( sK55 = app(sK58,cons(sK57,nil))
      & sK56 = app(cons(sK57,nil),sK58)
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ( ( ! [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ~ neq(nil,sK54)
                    | ! [X7] :
                        ( ~ neq(nil,sK54)
                        | hd(sK54) != X7
                        | cons(X7,nil) != X6
                        | ~ ssItem(X7) )
                    | app(X5,X6) != X4
                    | tl(sK54) != X5
                    | ~ ssList(X6) )
                | ~ ssList(X5) )
            | sK53 != X4
            | ~ ssList(X4) )
        & neq(sK54,nil) )
      | ( nil != sK53
        & nil = sK54 ) )
    & ( ~ neq(sK56,nil)
      | ( sK55 = app(sK58,cons(sK57,nil))
        & sK56 = app(cons(sK57,nil),sK58)
        & ssList(sK58)
        & ssItem(sK57) ) )
    & ( nil != sK56
      | nil = sK55 )
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f222,f348,f347,f346,f345,f344,f343]) ).

fof(f440,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

fof(f441,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f442,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f451,plain,
    ! [X0,X1] :
      ( hd(cons(X1,X0)) = X1
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f453,plain,
    ! [X0,X1] :
      ( tl(cons(X1,X0)) = X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f454,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f523,plain,
    ! [X0] :
      ( hd(X0) = sK51(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f336]) ).

fof(f525,plain,
    ! [X0] :
      ( tl(X0) = sK52(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f530,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

fof(f550,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f349]) ).

fof(f553,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f349]) ).

fof(f554,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f349]) ).

fof(f555,plain,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f556,plain,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f557,plain,
    ( ~ neq(sK56,nil)
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f558,plain,
    ( ~ neq(sK56,nil)
    | sK56 = app(cons(sK57,nil),sK58) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f559,plain,
    ( ~ neq(sK56,nil)
    | sK55 = app(sK58,cons(sK57,nil)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f560,plain,
    ( neq(sK54,nil)
    | nil = sK54 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f561,plain,
    ( neq(sK54,nil)
    | nil != sK53 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f566,plain,
    ( neq(sK56,nil)
    | nil != sK55 ),
    inference(definition_unfolding,[],[f561,f553,f554]) ).

fof(f567,plain,
    ( neq(sK56,nil)
    | nil = sK56 ),
    inference(definition_unfolding,[],[f560,f553,f553]) ).

fof(f568,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f550,f553]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f607]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f442]) ).

cnf(c_150,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | hd(cons(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f451]) ).

cnf(c_152,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | tl(cons(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f453]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f454]) ).

cnf(c_219,plain,
    ( ~ ssList(X0)
    | hd(X0) = sK51(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f523]) ).

cnf(c_221,plain,
    ( ~ ssList(X0)
    | tl(X0) = sK52(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f525]) ).

cnf(c_227,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | app(cons(X0,nil),X1) = cons(X0,X1) ),
    inference(cnf_transformation,[],[f530]) ).

cnf(c_246,negated_conjecture,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | nil != sK55
    | ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
    | ~ ssList(cons(hd(sK56),nil))
    | ~ neq(nil,sK56)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56)) ),
    inference(cnf_transformation,[],[f612]) ).

cnf(c_247,negated_conjecture,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
    | ~ ssList(cons(hd(sK56),nil))
    | ~ neq(nil,sK56)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | nil = sK56 ),
    inference(cnf_transformation,[],[f613]) ).

cnf(c_248,negated_conjecture,
    ( nil != sK55
    | neq(sK56,nil) ),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_249,negated_conjecture,
    ( nil = sK56
    | neq(sK56,nil) ),
    inference(cnf_transformation,[],[f567]) ).

cnf(c_250,negated_conjecture,
    ( ~ neq(sK56,nil)
    | app(sK58,cons(sK57,nil)) = sK55 ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_251,negated_conjecture,
    ( ~ neq(sK56,nil)
    | app(cons(sK57,nil),sK58) = sK56 ),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_252,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_253,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_254,negated_conjecture,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_257,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_365,negated_conjecture,
    ssItem(sK57),
    inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_249,c_248,c_254]) ).

cnf(c_367,negated_conjecture,
    ssList(sK58),
    inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_249,c_248,c_254]) ).

cnf(c_375,negated_conjecture,
    neq(sK56,nil),
    inference(global_subsumption_just,[status(thm)],[c_249,c_249,c_248,c_254]) ).

cnf(c_377,negated_conjecture,
    neq(sK56,nil),
    inference(global_subsumption_just,[status(thm)],[c_248,c_375]) ).

cnf(c_385,negated_conjecture,
    app(cons(sK57,nil),sK58) = sK56,
    inference(global_subsumption_just,[status(thm)],[c_251,c_249,c_248,c_254,c_251]) ).

cnf(c_387,negated_conjecture,
    app(sK58,cons(sK57,nil)) = sK55,
    inference(global_subsumption_just,[status(thm)],[c_250,c_249,c_248,c_254,c_250]) ).

cnf(c_395,plain,
    ( ~ ssList(tl(sK56))
    | ~ ssItem(hd(sK56))
    | ~ neq(nil,sK56)
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
    | app(tl(sK56),cons(hd(sK56),nil)) != sK55 ),
    inference(global_subsumption_just,[status(thm)],[c_247,c_254,c_247,c_246]) ).

cnf(c_396,negated_conjecture,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
    | ~ ssList(cons(hd(sK56),nil))
    | ~ neq(nil,sK56)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56)) ),
    inference(renaming,[status(thm)],[c_395]) ).

cnf(c_833,plain,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | ~ ssList(cons(hd(sK56),nil))
    | ~ neq(nil,sK56)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_396,c_153]) ).

cnf(c_2611,plain,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | X0 != nil
    | X1 != sK56
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_833]) ).

cnf(c_2612,plain,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | ~ ssList(sK56)
    | nil = sK56 ),
    inference(unflattening,[status(thm)],[c_2611]) ).

cnf(c_2613,plain,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | nil = sK56 ),
    inference(global_subsumption_just,[status(thm)],[c_2612,c_257,c_141,c_2612]) ).

cnf(c_2634,plain,
    ( X0 != nil
    | X0 != sK56
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_139,c_377]) ).

cnf(c_2635,plain,
    ( nil != sK56
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_2634]) ).

cnf(c_2636,plain,
    nil != sK56,
    inference(global_subsumption_just,[status(thm)],[c_2635,c_141,c_2635]) ).

cnf(c_2641,plain,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_2613,c_2636]) ).

cnf(c_7645,plain,
    ( app(tl(sK56),cons(hd(sK56),nil)) != sK55
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56)) ),
    inference(subtyping,[status(esa)],[c_2641]) ).

cnf(c_7646,plain,
    nil != sK56,
    inference(subtyping,[status(esa)],[c_2636]) ).

cnf(c_7655,negated_conjecture,
    app(sK58,cons(sK57,nil)) = sK55,
    inference(subtyping,[status(esa)],[c_387]) ).

cnf(c_7656,negated_conjecture,
    app(cons(sK57,nil),sK58) = sK56,
    inference(subtyping,[status(esa)],[c_385]) ).

cnf(c_7661,negated_conjecture,
    ssList(sK58),
    inference(subtyping,[status(esa)],[c_367]) ).

cnf(c_7662,negated_conjecture,
    ssItem(sK57),
    inference(subtyping,[status(esa)],[c_365]) ).

cnf(c_7664,negated_conjecture,
    ssList(sK56),
    inference(subtyping,[status(esa)],[c_257]) ).

cnf(c_7680,plain,
    ( ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | app(cons(X0_14,nil),X0_13) = cons(X0_14,X0_13) ),
    inference(subtyping,[status(esa)],[c_227]) ).

cnf(c_7686,plain,
    ( ~ ssList(X0_13)
    | tl(X0_13) = sK52(X0_13)
    | X0_13 = nil ),
    inference(subtyping,[status(esa)],[c_221]) ).

cnf(c_7688,plain,
    ( ~ ssList(X0_13)
    | hd(X0_13) = sK51(X0_13)
    | X0_13 = nil ),
    inference(subtyping,[status(esa)],[c_219]) ).

cnf(c_7744,plain,
    ( ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | tl(cons(X0_14,X0_13)) = X0_13 ),
    inference(subtyping,[status(esa)],[c_152]) ).

cnf(c_7746,plain,
    ( ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | hd(cons(X0_14,X0_13)) = X0_14 ),
    inference(subtyping,[status(esa)],[c_150]) ).

cnf(c_7755,plain,
    ssList(nil),
    inference(subtyping,[status(esa)],[c_141]) ).

cnf(c_7756,plain,
    ( ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | ssList(cons(X0_14,X0_13)) ),
    inference(subtyping,[status(esa)],[c_140]) ).

cnf(c_10755,plain,
    ( ~ ssList(X0_13)
    | app(cons(sK57,nil),X0_13) = cons(sK57,X0_13) ),
    inference(superposition,[status(thm)],[c_7662,c_7680]) ).

cnf(c_10836,plain,
    ( tl(sK56) = sK52(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_7664,c_7686]) ).

cnf(c_10841,plain,
    tl(sK56) = sK52(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_10836,c_7646]) ).

cnf(c_10879,plain,
    ( ~ ssList(X0_13)
    | tl(cons(sK57,X0_13)) = X0_13 ),
    inference(superposition,[status(thm)],[c_7662,c_7744]) ).

cnf(c_11208,plain,
    app(cons(sK57,nil),sK58) = cons(sK57,sK58),
    inference(superposition,[status(thm)],[c_7661,c_10755]) ).

cnf(c_11216,plain,
    cons(sK57,sK58) = sK56,
    inference(demodulation,[status(thm)],[c_11208,c_7656]) ).

cnf(c_12586,plain,
    tl(cons(sK57,sK58)) = sK58,
    inference(superposition,[status(thm)],[c_7661,c_10879]) ).

cnf(c_12602,plain,
    sK52(sK56) = sK58,
    inference(demodulation,[status(thm)],[c_12586,c_10841,c_11216]) ).

cnf(c_18942,plain,
    ( ~ ssList(X0_13)
    | app(cons(sK57,nil),X0_13) = cons(sK57,X0_13) ),
    inference(superposition,[status(thm)],[c_7662,c_7680]) ).

cnf(c_19023,plain,
    ( tl(sK56) = sK52(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_7664,c_7686]) ).

cnf(c_19028,plain,
    tl(sK56) = sK52(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_19023,c_7646]) ).

cnf(c_19029,plain,
    tl(sK56) = sK58,
    inference(demodulation,[status(thm)],[c_19028,c_12602]) ).

cnf(c_19039,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_7664,c_7688]) ).

cnf(c_19044,plain,
    hd(sK56) = sK51(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_19039,c_7646]) ).

cnf(c_19085,plain,
    ( ~ ssList(X0_13)
    | hd(cons(sK57,X0_13)) = sK57 ),
    inference(superposition,[status(thm)],[c_7662,c_7746]) ).

cnf(c_19139,plain,
    ( app(sK58,cons(hd(sK56),nil)) != sK55
    | ~ ssList(cons(hd(sK56),nil))
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56)) ),
    inference(superposition,[status(thm)],[c_19029,c_7645]) ).

cnf(c_19141,plain,
    ( app(sK58,cons(sK51(sK56),nil)) != sK55
    | ~ ssList(cons(sK51(sK56),nil))
    | ~ ssItem(sK51(sK56))
    | ~ ssList(sK58) ),
    inference(demodulation,[status(thm)],[c_19139,c_19044,c_19029]) ).

cnf(c_19142,plain,
    ( app(sK58,cons(sK51(sK56),nil)) != sK55
    | ~ ssList(cons(sK51(sK56),nil))
    | ~ ssItem(sK51(sK56)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_19141,c_7661]) ).

cnf(c_19394,plain,
    app(cons(sK57,nil),sK58) = cons(sK57,sK58),
    inference(superposition,[status(thm)],[c_7661,c_18942]) ).

cnf(c_19402,plain,
    cons(sK57,sK58) = sK56,
    inference(demodulation,[status(thm)],[c_19394,c_7656]) ).

cnf(c_20764,plain,
    hd(cons(sK57,sK58)) = sK57,
    inference(superposition,[status(thm)],[c_7661,c_19085]) ).

cnf(c_20781,plain,
    sK51(sK56) = sK57,
    inference(demodulation,[status(thm)],[c_20764,c_19044,c_19402]) ).

cnf(c_21352,plain,
    ( sK55 != sK55
    | ~ ssList(cons(sK57,nil))
    | ~ ssItem(sK57) ),
    inference(demodulation,[status(thm)],[c_19142,c_7655,c_20781]) ).

cnf(c_21353,plain,
    ( ~ ssList(cons(sK57,nil))
    | ~ ssItem(sK57) ),
    inference(equality_resolution_simp,[status(thm)],[c_21352]) ).

cnf(c_21356,plain,
    ( ~ ssItem(sK57)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm)],[c_7756,c_21353]) ).

cnf(c_21357,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_21356,c_7755,c_7662]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWC310+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12  % Command  : run_iprover %s %d THM
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Aug 28 19:03:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.45  Running first-order theorem proving
% 0.20/0.45  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.13/3.13  % SZS status Started for theBenchmark.p
% 17.13/3.13  % SZS status Theorem for theBenchmark.p
% 17.13/3.13  
% 17.13/3.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.13/3.13  
% 17.13/3.13  ------  iProver source info
% 17.13/3.13  
% 17.13/3.13  git: date: 2023-05-31 18:12:56 +0000
% 17.13/3.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.13/3.13  git: non_committed_changes: false
% 17.13/3.13  git: last_make_outside_of_git: false
% 17.13/3.13  
% 17.13/3.13  ------ Parsing...
% 17.13/3.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.13/3.13  
% 17.13/3.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 17.13/3.13  
% 17.13/3.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.13/3.13  
% 17.13/3.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.13/3.13  ------ Proving...
% 17.13/3.13  ------ Problem Properties 
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  clauses                                 188
% 17.13/3.13  conjectures                             6
% 17.13/3.13  EPR                                     54
% 17.13/3.13  Horn                                    120
% 17.13/3.13  unary                                   23
% 17.13/3.13  binary                                  40
% 17.13/3.13  lits                                    629
% 17.13/3.13  lits eq                                 82
% 17.13/3.13  fd_pure                                 0
% 17.13/3.13  fd_pseudo                               0
% 17.13/3.13  fd_cond                                 21
% 17.13/3.13  fd_pseudo_cond                          14
% 17.13/3.13  AC symbols                              0
% 17.13/3.13  
% 17.13/3.13  ------ Input Options Time Limit: Unbounded
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  ------ 
% 17.13/3.13  Current options:
% 17.13/3.13  ------ 
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  ------ Proving...
% 17.13/3.13  
% 17.13/3.13  
% 17.13/3.13  % SZS status Theorem for theBenchmark.p
% 17.13/3.13  
% 17.13/3.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.13/3.13  
% 17.13/3.13  
%------------------------------------------------------------------------------