TSTP Solution File: SWC314+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC314+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.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 : Fri May  3 03:11:58 EDT 2024

% Result   : Theorem 20.27s 3.64s
% Output   : CNFRefutation 20.27s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f613)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

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

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

fof(f25,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => tl(cons(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ( nil = X0
                      | nil != X1 )
                    & ! [X8] :
                        ( ssItem(X8)
                       => ! [X9] :
                            ( app(X9,cons(X8,nil)) = X0
                            | app(cons(X8,nil),X9) != X1
                            | ~ ssList(X9) ) ) )
                  | ( neq(X3,nil)
                    & ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( neq(nil,X3)
                                & ? [X7] :
                                    ( neq(nil,X3)
                                    & hd(X3) = X7
                                    & cons(X7,nil) = X6
                                    & ssItem(X7) )
                                & app(X5,X6) = X4
                                & tl(X3) = X5
                                & ssList(X6) )
                            & ssList(X5) )
                        & X2 != X4
                        & ssList(X4) ) )
                  | ( nil = X3
                    & nil != X2 )
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

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

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f1]) ).

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(f126,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f127,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f128,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f127]) ).

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

fof(f130,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f131,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f130]) ).

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(f177,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

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

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

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

fof(f232,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f99]) ).

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

fof(f330,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f339,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f201]) ).

fof(f340,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,[],[f339]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil != X0
                        & nil = X1 )
                      | ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) != X0
                              & app(cons(X4,nil),X5) = X1
                              & ssList(X5) )
                          & ssItem(X4) ) )
                    & ( ~ neq(X3,nil)
                      | ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ~ neq(nil,X3)
                                  | ! [X9] :
                                      ( ~ neq(nil,X3)
                                      | hd(X3) != X9
                                      | cons(X9,nil) != X8
                                      | ~ ssItem(X9) )
                                  | app(X7,X8) != X6
                                  | tl(X3) != X7
                                  | ~ ssList(X8) )
                              | ~ ssList(X7) )
                          | X2 = X6
                          | ~ ssList(X6) ) )
                    & ( nil != X3
                      | nil = X2 )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil != sK53
                      & nil = X1 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(X5,cons(X4,nil)) != sK53
                            & app(cons(X4,nil),X5) = X1
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ( ~ neq(X3,nil)
                    | ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ~ neq(nil,X3)
                                | ! [X9] :
                                    ( ~ neq(nil,X3)
                                    | hd(X3) != X9
                                    | cons(X9,nil) != X8
                                    | ~ ssItem(X9) )
                                | app(X7,X8) != X6
                                | tl(X3) != X7
                                | ~ ssList(X8) )
                            | ~ ssList(X7) )
                        | X2 = X6
                        | ~ ssList(X6) ) )
                  & ( 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] :
                ( ( ( nil != sK53
                    & nil = X1 )
                  | ? [X4] :
                      ( ? [X5] :
                          ( app(X5,cons(X4,nil)) != sK53
                          & app(cons(X4,nil),X5) = X1
                          & ssList(X5) )
                      & ssItem(X4) ) )
                & ( ~ neq(X3,nil)
                  | ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ~ neq(nil,X3)
                              | ! [X9] :
                                  ( ~ neq(nil,X3)
                                  | hd(X3) != X9
                                  | cons(X9,nil) != X8
                                  | ~ ssItem(X9) )
                              | app(X7,X8) != X6
                              | tl(X3) != X7
                              | ~ ssList(X8) )
                          | ~ ssList(X7) )
                      | X2 = X6
                      | ~ ssList(X6) ) )
                & ( nil != X3
                  | nil = X2 )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil != sK53
                  & nil = sK54 )
                | ? [X4] :
                    ( ? [X5] :
                        ( app(X5,cons(X4,nil)) != sK53
                        & app(cons(X4,nil),X5) = sK54
                        & ssList(X5) )
                    & ssItem(X4) ) )
              & ( ~ neq(X3,nil)
                | ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ~ neq(nil,X3)
                            | ! [X9] :
                                ( ~ neq(nil,X3)
                                | hd(X3) != X9
                                | cons(X9,nil) != X8
                                | ~ ssItem(X9) )
                            | app(X7,X8) != X6
                            | tl(X3) != X7
                            | ~ ssList(X8) )
                        | ~ ssList(X7) )
                    | X2 = X6
                    | ~ ssList(X6) ) )
              & ( nil != X3
                | nil = X2 )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f347,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( app(X5,cons(X4,nil)) != sK53
            & app(cons(X4,nil),X5) = sK54
            & ssList(X5) )
        & ssItem(X4) )
   => ( ? [X5] :
          ( sK53 != app(X5,cons(sK57,nil))
          & sK54 = app(cons(sK57,nil),X5)
          & ssList(X5) )
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X5] :
        ( sK53 != app(X5,cons(sK57,nil))
        & sK54 = app(cons(sK57,nil),X5)
        & ssList(X5) )
   => ( sK53 != app(sK58,cons(sK57,nil))
      & sK54 = app(cons(sK57,nil),sK58)
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ( ( nil != sK53
        & nil = sK54 )
      | ( sK53 != app(sK58,cons(sK57,nil))
        & sK54 = app(cons(sK57,nil),sK58)
        & ssList(sK58)
        & ssItem(sK57) ) )
    & ( ~ neq(sK56,nil)
      | ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ~ neq(nil,sK56)
                  | ! [X9] :
                      ( ~ neq(nil,sK56)
                      | hd(sK56) != X9
                      | cons(X9,nil) != X8
                      | ~ ssItem(X9) )
                  | app(X7,X8) != X6
                  | tl(sK56) != X7
                  | ~ ssList(X8) )
              | ~ ssList(X7) )
          | sK55 = X6
          | ~ ssList(X6) ) )
    & ( 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(f351,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f232]) ).

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(f449,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f450,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f128]) ).

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

fof(f452,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f131]) ).

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(f496,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f497,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

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

fof(f533,plain,
    ! [X0,X1] :
      ( nil = X0
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f340]) ).

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(f557,plain,
    ( nil = sK54
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f558,plain,
    ( nil = sK54
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f559,plain,
    ( nil = sK54
    | sK54 = app(cons(sK57,nil),sK58) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f560,plain,
    ( nil = sK54
    | sK53 != app(sK58,cons(sK57,nil)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f561,plain,
    ( nil != sK53
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f562,plain,
    ( nil != sK53
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f563,plain,
    ( nil != sK53
    | sK54 = app(cons(sK57,nil),sK58) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f564,plain,
    ( nil != sK53
    | sK53 != app(sK58,cons(sK57,nil)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f565,plain,
    ( nil != sK55
    | sK55 != app(sK58,cons(sK57,nil)) ),
    inference(definition_unfolding,[],[f564,f554,f554]) ).

fof(f566,plain,
    ( nil != sK55
    | sK56 = app(cons(sK57,nil),sK58) ),
    inference(definition_unfolding,[],[f563,f554,f553]) ).

fof(f567,plain,
    ( nil != sK55
    | ssList(sK58) ),
    inference(definition_unfolding,[],[f562,f554]) ).

fof(f568,plain,
    ( nil != sK55
    | ssItem(sK57) ),
    inference(definition_unfolding,[],[f561,f554]) ).

fof(f569,plain,
    ( nil = sK56
    | sK55 != app(sK58,cons(sK57,nil)) ),
    inference(definition_unfolding,[],[f560,f553,f554]) ).

fof(f570,plain,
    ( nil = sK56
    | sK56 = app(cons(sK57,nil),sK58) ),
    inference(definition_unfolding,[],[f559,f553,f553]) ).

fof(f571,plain,
    ( nil = sK56
    | ssList(sK58) ),
    inference(definition_unfolding,[],[f558,f553]) ).

fof(f572,plain,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(definition_unfolding,[],[f557,f553]) ).

fof(f573,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f550,f553]) ).

fof(f594,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f497]) ).

cnf(c_49,plain,
    ( ~ ssItem(X0)
    | ~ ssItem(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

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

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_148,plain,
    ( cons(X0,X1) != nil
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f449]) ).

cnf(c_149,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(hd(X0)) ),
    inference(cnf_transformation,[],[f450]) ).

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

cnf(c_151,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(tl(X0)) ),
    inference(cnf_transformation,[],[f452]) ).

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_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f594]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f496]) ).

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

cnf(c_230,plain,
    ( app(X0,X1) != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = nil ),
    inference(cnf_transformation,[],[f533]) ).

cnf(c_246,negated_conjecture,
    ( app(sK58,cons(sK57,nil)) != sK55
    | nil != sK55 ),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_247,negated_conjecture,
    ( nil != sK55
    | app(cons(sK57,nil),sK58) = sK56 ),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_248,negated_conjecture,
    ( nil != sK55
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f567]) ).

cnf(c_249,negated_conjecture,
    ( nil != sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_250,negated_conjecture,
    ( app(sK58,cons(sK57,nil)) != sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_251,negated_conjecture,
    ( app(cons(sK57,nil),sK58) = sK56
    | nil = sK56 ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_252,negated_conjecture,
    ( nil = sK56
    | ssList(sK58) ),
    inference(cnf_transformation,[],[f571]) ).

cnf(c_253,negated_conjecture,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_254,negated_conjecture,
    ( ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
    | ~ ssList(cons(hd(sK56),nil))
    | ~ neq(nil,sK56)
    | ~ neq(sK56,nil)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
    inference(cnf_transformation,[],[f613]) ).

cnf(c_255,negated_conjecture,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_258,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f573]) ).

cnf(c_309,plain,
    ( ~ segmentP(nil,nil)
    | ~ ssList(nil)
    | nil = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_366,negated_conjecture,
    ssItem(sK57),
    inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_249,c_255]) ).

cnf(c_368,negated_conjecture,
    ssList(sK58),
    inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_248,c_255]) ).

cnf(c_376,negated_conjecture,
    ssItem(sK57),
    inference(global_subsumption_just,[status(thm)],[c_249,c_366]) ).

cnf(c_378,negated_conjecture,
    ssList(sK58),
    inference(global_subsumption_just,[status(thm)],[c_248,c_368]) ).

cnf(c_386,negated_conjecture,
    app(cons(sK57,nil),sK58) = sK56,
    inference(global_subsumption_just,[status(thm)],[c_251,c_255,c_251,c_247]) ).

cnf(c_388,negated_conjecture,
    app(sK58,cons(sK57,nil)) != sK55,
    inference(global_subsumption_just,[status(thm)],[c_250,c_255,c_250,c_246]) ).

cnf(c_390,negated_conjecture,
    app(cons(sK57,nil),sK58) = sK56,
    inference(global_subsumption_just,[status(thm)],[c_247,c_386]) ).

cnf(c_832,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ neq(nil,sK56)
    | ~ neq(sK56,nil)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_254,c_153]) ).

cnf(c_6388,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_9290,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | nil = sK56
    | neq(nil,sK56) ),
    inference(instantiation,[status(thm)],[c_138]) ).

cnf(c_9301,plain,
    ( nil != X0
    | sK56 != X0
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_6388]) ).

cnf(c_9302,plain,
    ( nil != nil
    | sK56 != nil
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_9301]) ).

cnf(c_9339,plain,
    ( cons(sK57,X0) != nil
    | ~ ssList(X0)
    | ~ ssItem(sK57) ),
    inference(instantiation,[status(thm)],[c_148]) ).

cnf(c_9343,plain,
    ( cons(sK57,nil) != nil
    | ~ ssItem(sK57)
    | ~ ssList(nil) ),
    inference(instantiation,[status(thm)],[c_9339]) ).

cnf(c_9422,plain,
    ( ~ ssList(X0)
    | ~ ssList(sK56)
    | sK56 = X0
    | neq(sK56,X0) ),
    inference(instantiation,[status(thm)],[c_138]) ).

cnf(c_9423,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | sK56 = nil
    | neq(sK56,nil) ),
    inference(instantiation,[status(thm)],[c_9422]) ).

cnf(c_10293,plain,
    ( ~ ssItem(sK57)
    | ~ ssList(nil)
    | ssList(cons(sK57,nil)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_11135,plain,
    ( ~ ssList(sK56)
    | sK56 = nil
    | ssItem(hd(sK56)) ),
    inference(instantiation,[status(thm)],[c_149]) ).

cnf(c_11136,plain,
    ( ~ ssList(sK56)
    | sK56 = nil
    | ssList(tl(sK56)) ),
    inference(instantiation,[status(thm)],[c_151]) ).

cnf(c_11702,plain,
    ( ~ neq(nil,sK56)
    | ~ neq(sK56,nil)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
    inference(superposition,[status(thm)],[c_140,c_832]) ).

cnf(c_11792,plain,
    ( ~ ssList(tl(sK56))
    | ~ ssItem(hd(sK56))
    | ~ neq(sK56,nil)
    | ~ neq(nil,sK56)
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
    inference(global_subsumption_just,[status(thm)],[c_11702,c_141,c_11702]) ).

cnf(c_11793,plain,
    ( ~ neq(nil,sK56)
    | ~ neq(sK56,nil)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
    inference(renaming,[status(thm)],[c_11792]) ).

cnf(c_12280,plain,
    ( ~ neq(nil,sK56)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssItem(nil)
    | ~ ssItem(sK56)
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_49,c_11793]) ).

cnf(c_12329,plain,
    ( app(tl(sK56),cons(hd(sK56),nil)) = sK55
    | nil = sK56 ),
    inference(global_subsumption_just,[status(thm)],[c_12280,c_258,c_141,c_195,c_309,c_9290,c_9302,c_9423,c_11136,c_11135,c_11702]) ).

cnf(c_22045,plain,
    ( nil != sK56
    | ~ ssList(cons(sK57,nil))
    | ~ ssList(sK58)
    | cons(sK57,nil) = nil ),
    inference(superposition,[status(thm)],[c_390,c_230]) ).

cnf(c_36267,plain,
    app(tl(sK56),cons(hd(sK56),nil)) = sK55,
    inference(global_subsumption_just,[status(thm)],[c_832,c_141,c_253,c_252,c_249,c_248,c_255,c_9343,c_10293,c_12329,c_22045]) ).

cnf(c_36449,plain,
    ( ~ ssList(X0)
    | hd(cons(sK57,X0)) = sK57 ),
    inference(superposition,[status(thm)],[c_376,c_150]) ).

cnf(c_36595,plain,
    hd(cons(sK57,sK58)) = sK57,
    inference(superposition,[status(thm)],[c_378,c_36449]) ).

cnf(c_36621,plain,
    ( ~ ssList(X0)
    | tl(cons(sK57,X0)) = X0 ),
    inference(superposition,[status(thm)],[c_376,c_152]) ).

cnf(c_36743,plain,
    tl(cons(sK57,sK58)) = sK58,
    inference(superposition,[status(thm)],[c_378,c_36621]) ).

cnf(c_36927,plain,
    ( ~ ssList(X0)
    | app(cons(sK57,nil),X0) = cons(sK57,X0) ),
    inference(superposition,[status(thm)],[c_376,c_227]) ).

cnf(c_37028,plain,
    app(cons(sK57,nil),sK58) = cons(sK57,sK58),
    inference(superposition,[status(thm)],[c_378,c_36927]) ).

cnf(c_37038,plain,
    cons(sK57,sK58) = sK56,
    inference(superposition,[status(thm)],[c_37028,c_390]) ).

cnf(c_37045,plain,
    tl(sK56) = sK58,
    inference(superposition,[status(thm)],[c_37038,c_36743]) ).

cnf(c_37046,plain,
    hd(sK56) = sK57,
    inference(superposition,[status(thm)],[c_37038,c_36595]) ).

cnf(c_37104,plain,
    app(sK58,cons(hd(sK56),nil)) = sK55,
    inference(superposition,[status(thm)],[c_37045,c_36267]) ).

cnf(c_37128,plain,
    app(sK58,cons(sK57,nil)) = sK55,
    inference(superposition,[status(thm)],[c_37046,c_37104]) ).

cnf(c_37134,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_37128,c_388]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SWC314+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.31  % Computer : n013.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May  2 23:24:04 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.27/3.64  % SZS status Started for theBenchmark.p
% 20.27/3.64  % SZS status Theorem for theBenchmark.p
% 20.27/3.64  
% 20.27/3.64  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.27/3.64  
% 20.27/3.64  ------  iProver source info
% 20.27/3.64  
% 20.27/3.64  git: date: 2024-05-02 19:28:25 +0000
% 20.27/3.64  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.27/3.64  git: non_committed_changes: false
% 20.27/3.64  
% 20.27/3.64  ------ Parsing...
% 20.27/3.64  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 20.27/3.64  
% 20.27/3.64  ------ 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: 4 0s  sf_e  pe_s  pe_e 
% 20.27/3.64  
% 20.27/3.64  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 20.27/3.64  
% 20.27/3.64  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 20.27/3.64  ------ Proving...
% 20.27/3.64  ------ Problem Properties 
% 20.27/3.64  
% 20.27/3.64  
% 20.27/3.64  clauses                                 192
% 20.27/3.64  conjectures                             7
% 20.27/3.64  EPR                                     58
% 20.27/3.64  Horn                                    122
% 20.27/3.64  unary                                   22
% 20.27/3.64  binary                                  43
% 20.27/3.64  lits                                    644
% 20.27/3.64  lits eq                                 85
% 20.27/3.64  fd_pure                                 0
% 20.27/3.64  fd_pseudo                               0
% 20.27/3.64  fd_cond                                 21
% 20.27/3.64  fd_pseudo_cond                          16
% 20.27/3.64  AC symbols                              0
% 20.27/3.64  
% 20.27/3.64  ------ Input Options Time Limit: Unbounded
% 20.27/3.64  
% 20.27/3.64  
% 20.27/3.64  ------ 
% 20.27/3.64  Current options:
% 20.27/3.64  ------ 
% 20.27/3.64  
% 20.27/3.64  
% 20.27/3.64  
% 20.27/3.64  
% 20.27/3.64  ------ Proving...
% 20.27/3.64  
% 20.27/3.64  
% 20.27/3.64  % SZS status Theorem for theBenchmark.p
% 20.27/3.64  
% 20.27/3.64  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.27/3.64  
% 20.27/3.65  
%------------------------------------------------------------------------------