TSTP Solution File: SWC308+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC308+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 03:11:56 EDT 2024

% Result   : Theorem 42.63s 6.54s
% Output   : CNFRefutation 42.63s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f595)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

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

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

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

fof(f41,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( frontsegP(X1,X0)
              & frontsegP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).

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(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).

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

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

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

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

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

fof(f152,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f153,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f152]) ).

fof(f193,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f194,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f193]) ).

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

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

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

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != X3
                          | app(X5,cons(X4,nil)) = X2
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & ! [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)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f246,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,[],[f102]) ).

fof(f247,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,[],[f246]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK11(X0,X1)) = X0
        & ssList(sK11(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f249,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK11(X0,X1)) = X0
                & ssList(sK11(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f247,f248]) ).

fof(f317,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X3
                      | nil = X2 )
                    & ! [X4] :
                        ( ! [X5] :
                            ( app(cons(X4,nil),X5) != X3
                            | app(X5,cons(X4,nil)) = X2
                            | ~ ssList(X5) )
                        | ~ ssItem(X4) )
                    & ! [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)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != X3
                          | app(X5,cons(X4,nil)) = X2
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & ! [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) )
                      | sK53 != X6
                      | ~ ssList(X6) )
                  & neq(X1,nil)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != X3
                  | nil = X2 )
                & ! [X4] :
                    ( ! [X5] :
                        ( app(cons(X4,nil),X5) != X3
                        | app(X5,cons(X4,nil)) = X2
                        | ~ ssList(X5) )
                    | ~ ssItem(X4) )
                & ! [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) )
                    | sK53 != X6
                    | ~ ssList(X6) )
                & neq(X1,nil)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X3
                | nil = X2 )
              & ! [X4] :
                  ( ! [X5] :
                      ( app(cons(X4,nil),X5) != X3
                      | app(X5,cons(X4,nil)) = X2
                      | ~ ssList(X5) )
                  | ~ ssItem(X4) )
              & ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ~ neq(nil,sK54)
                          | ! [X9] :
                              ( ~ neq(nil,sK54)
                              | hd(sK54) != X9
                              | cons(X9,nil) != X8
                              | ~ ssItem(X9) )
                          | app(X7,X8) != X6
                          | tl(sK54) != X7
                          | ~ ssList(X8) )
                      | ~ ssList(X7) )
                  | sK53 != X6
                  | ~ ssList(X6) )
              & neq(sK54,nil)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != X3
              | nil = X2 )
            & ! [X4] :
                ( ! [X5] :
                    ( app(cons(X4,nil),X5) != X3
                    | app(X5,cons(X4,nil)) = X2
                    | ~ ssList(X5) )
                | ~ ssItem(X4) )
            & ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ~ neq(nil,sK54)
                        | ! [X9] :
                            ( ~ neq(nil,sK54)
                            | hd(sK54) != X9
                            | cons(X9,nil) != X8
                            | ~ ssItem(X9) )
                        | app(X7,X8) != X6
                        | tl(sK54) != X7
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | sK53 != X6
                | ~ ssList(X6) )
            & neq(sK54,nil)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != X3
            | nil = sK55 )
          & ! [X4] :
              ( ! [X5] :
                  ( app(cons(X4,nil),X5) != X3
                  | app(X5,cons(X4,nil)) = sK55
                  | ~ ssList(X5) )
              | ~ ssItem(X4) )
          & ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ neq(nil,sK54)
                      | ! [X9] :
                          ( ~ neq(nil,sK54)
                          | hd(sK54) != X9
                          | cons(X9,nil) != X8
                          | ~ ssItem(X9) )
                      | app(X7,X8) != X6
                      | tl(sK54) != X7
                      | ~ ssList(X8) )
                  | ~ ssList(X7) )
              | sK53 != X6
              | ~ ssList(X6) )
          & neq(sK54,nil)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( nil != X3
          | nil = sK55 )
        & ! [X4] :
            ( ! [X5] :
                ( app(cons(X4,nil),X5) != X3
                | app(X5,cons(X4,nil)) = sK55
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ neq(nil,sK54)
                    | ! [X9] :
                        ( ~ neq(nil,sK54)
                        | hd(sK54) != X9
                        | cons(X9,nil) != X8
                        | ~ ssItem(X9) )
                    | app(X7,X8) != X6
                    | tl(sK54) != X7
                    | ~ ssList(X8) )
                | ~ ssList(X7) )
            | sK53 != X6
            | ~ ssList(X6) )
        & neq(sK54,nil)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( nil != sK56
        | nil = sK55 )
      & ! [X4] :
          ( ! [X5] :
              ( app(cons(X4,nil),X5) != sK56
              | app(X5,cons(X4,nil)) = sK55
              | ~ ssList(X5) )
          | ~ ssItem(X4) )
      & ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ~ neq(nil,sK54)
                  | ! [X9] :
                      ( ~ neq(nil,sK54)
                      | hd(sK54) != X9
                      | cons(X9,nil) != X8
                      | ~ ssItem(X9) )
                  | app(X7,X8) != X6
                  | tl(sK54) != X7
                  | ~ ssList(X8) )
              | ~ ssList(X7) )
          | sK53 != X6
          | ~ ssList(X6) )
      & neq(sK54,nil)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ( nil != sK56
      | nil = sK55 )
    & ! [X4] :
        ( ! [X5] :
            ( app(cons(X4,nil),X5) != sK56
            | app(X5,cons(X4,nil)) = sK55
            | ~ ssList(X5) )
        | ~ ssItem(X4) )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ~ neq(nil,sK54)
                | ! [X9] :
                    ( ~ neq(nil,sK54)
                    | hd(sK54) != X9
                    | cons(X9,nil) != X8
                    | ~ ssItem(X9) )
                | app(X7,X8) != X6
                | tl(sK54) != X7
                | ~ ssList(X8) )
            | ~ ssList(X7) )
        | sK53 != X6
        | ~ ssList(X6) )
    & neq(sK54,nil)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f223,f347,f346,f345,f344]) ).

fof(f363,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f439,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f317]) ).

fof(f440,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f441,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f449,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f451,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f453,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f474,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ frontsegP(X1,X0)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f526,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f529,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

fof(f534,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f549,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f348]) ).

fof(f552,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f348]) ).

fof(f554,plain,
    neq(sK54,nil),
    inference(cnf_transformation,[],[f348]) ).

fof(f556,plain,
    ! [X4,X5] :
      ( app(cons(X4,nil),X5) != sK56
      | app(X5,cons(X4,nil)) = sK55
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f559,plain,
    neq(sK56,nil),
    inference(definition_unfolding,[],[f554,f552]) ).

fof(f560,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f549,f552]) ).

fof(f565,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f363]) ).

cnf(c_61,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f439]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f595]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_149,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(hd(X0)) ),
    inference(cnf_transformation,[],[f449]) ).

cnf(c_151,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(tl(X0)) ),
    inference(cnf_transformation,[],[f451]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f453]) ).

cnf(c_174,plain,
    ( ~ frontsegP(X0,X1)
    | ~ frontsegP(X1,X0)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f474]) ).

cnf(c_224,plain,
    ( ~ ssList(X0)
    | cons(hd(X0),tl(X0)) = X0
    | X0 = nil ),
    inference(cnf_transformation,[],[f526]) ).

cnf(c_227,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | app(cons(X0,nil),X1) = cons(X0,X1) ),
    inference(cnf_transformation,[],[f529]) ).

cnf(c_232,plain,
    ( ~ ssList(X0)
    | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f534]) ).

cnf(c_247,negated_conjecture,
    ( app(cons(X0,nil),X1) != sK56
    | ~ ssItem(X0)
    | ~ ssList(X1)
    | app(X1,cons(X0,nil)) = sK55 ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_248,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(cnf_transformation,[],[f600]) ).

cnf(c_249,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_252,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_376,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).

cnf(c_805,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_248,c_153]) ).

cnf(c_1951,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_805]) ).

cnf(c_1952,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_1951]) ).

cnf(c_1953,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_1952,c_252,c_141,c_1952]) ).

cnf(c_1974,plain,
    ( X0 != nil
    | X0 != sK56
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_139,c_249]) ).

cnf(c_1975,plain,
    ( nil != sK56
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_1974]) ).

cnf(c_1976,plain,
    nil != sK56,
    inference(global_subsumption_just,[status(thm)],[c_1975,c_141,c_1975]) ).

cnf(c_1981,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_1953,c_1976]) ).

cnf(c_6381,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_1981]) ).

cnf(c_6382,plain,
    nil != sK56,
    inference(subtyping,[status(esa)],[c_1976]) ).

cnf(c_6389,plain,
    ( ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | frontsegP(app(X0_13,X1_13),X0_13) ),
    inference(subtyping,[status(esa)],[c_376]) ).

cnf(c_6396,negated_conjecture,
    ssList(sK56),
    inference(subtyping,[status(esa)],[c_252]) ).

cnf(c_6397,negated_conjecture,
    ( app(cons(X0_14,nil),X0_13) != sK56
    | ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | app(X0_13,cons(X0_14,nil)) = sK55 ),
    inference(subtyping,[status(esa)],[c_247]) ).

cnf(c_6409,plain,
    ( ~ ssList(X0_13)
    | app(X0_13,nil) = X0_13 ),
    inference(subtyping,[status(esa)],[c_232]) ).

cnf(c_6413,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_6416,plain,
    ( ~ ssList(X0_13)
    | cons(hd(X0_13),tl(X0_13)) = X0_13
    | X0_13 = nil ),
    inference(subtyping,[status(esa)],[c_224]) ).

cnf(c_6455,plain,
    ( ~ frontsegP(X0_13,X1_13)
    | ~ frontsegP(X1_13,X0_13)
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | X0_13 = X1_13 ),
    inference(subtyping,[status(esa)],[c_174]) ).

cnf(c_6478,plain,
    ( ~ ssList(X0_13)
    | X0_13 = nil
    | ssList(tl(X0_13)) ),
    inference(subtyping,[status(esa)],[c_151]) ).

cnf(c_6480,plain,
    ( ~ ssList(X0_13)
    | X0_13 = nil
    | ssItem(hd(X0_13)) ),
    inference(subtyping,[status(esa)],[c_149]) ).

cnf(c_6489,plain,
    ( ~ ssItem(X0_14)
    | ~ ssList(X0_13)
    | ssList(cons(X0_14,X0_13)) ),
    inference(subtyping,[status(esa)],[c_140]) ).

cnf(c_6567,plain,
    X0_13 = X0_13,
    theory(equality) ).

cnf(c_6569,plain,
    ( X0_13 != X1_13
    | X2_13 != X1_13
    | X2_13 = X0_13 ),
    theory(equality) ).

cnf(c_6596,plain,
    nil = nil,
    inference(instantiation,[status(thm)],[c_6567]) ).

cnf(c_9512,plain,
    ( nil != X0_13
    | sK56 != X0_13
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_6569]) ).

cnf(c_9513,plain,
    ( nil != nil
    | sK56 != nil
    | nil = sK56 ),
    inference(instantiation,[status(thm)],[c_9512]) ).

cnf(c_9650,plain,
    ( ~ frontsegP(X0_13,sK56)
    | ~ frontsegP(sK56,X0_13)
    | ~ ssList(X0_13)
    | ~ ssList(sK56)
    | sK56 = X0_13 ),
    inference(instantiation,[status(thm)],[c_6455]) ).

cnf(c_10415,plain,
    ( ~ ssList(sK56)
    | cons(hd(sK56),tl(sK56)) = sK56
    | sK56 = nil ),
    inference(instantiation,[status(thm)],[c_6416]) ).

cnf(c_10421,plain,
    ( ~ ssList(sK56)
    | sK56 = nil
    | ssItem(hd(sK56)) ),
    inference(instantiation,[status(thm)],[c_6480]) ).

cnf(c_10422,plain,
    ( ~ ssList(sK56)
    | sK56 = nil
    | ssList(tl(sK56)) ),
    inference(instantiation,[status(thm)],[c_6478]) ).

cnf(c_10446,plain,
    ( ~ frontsegP(sK56,sK56)
    | ~ ssList(sK56)
    | sK56 = sK56 ),
    inference(instantiation,[status(thm)],[c_9650]) ).

cnf(c_10955,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(nil)
    | ssList(cons(hd(sK56),nil)) ),
    inference(instantiation,[status(thm)],[c_6489]) ).

cnf(c_11072,plain,
    app(sK56,nil) = sK56,
    inference(superposition,[status(thm)],[c_6396,c_6409]) ).

cnf(c_11818,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK56)
    | frontsegP(sK56,sK56) ),
    inference(superposition,[status(thm)],[c_11072,c_6389]) ).

cnf(c_12293,plain,
    ( app(cons(X0_14,nil),X0_13) != X1_13
    | sK56 != X1_13
    | app(cons(X0_14,nil),X0_13) = sK56 ),
    inference(instantiation,[status(thm)],[c_6569]) ).

cnf(c_12404,plain,
    ( X0_13 != X1_13
    | sK56 != X1_13
    | sK56 = X0_13 ),
    inference(instantiation,[status(thm)],[c_6569]) ).

cnf(c_13085,plain,
    ( X0_13 != sK56
    | sK56 != sK56
    | sK56 = X0_13 ),
    inference(instantiation,[status(thm)],[c_12404]) ).

cnf(c_16682,plain,
    ( cons(hd(sK56),tl(sK56)) != sK56
    | sK56 != sK56
    | sK56 = cons(hd(sK56),tl(sK56)) ),
    inference(instantiation,[status(thm)],[c_13085]) ).

cnf(c_21283,plain,
    ( app(cons(X0_14,nil),X0_13) != cons(hd(sK56),tl(sK56))
    | sK56 != cons(hd(sK56),tl(sK56))
    | app(cons(X0_14,nil),X0_13) = sK56 ),
    inference(instantiation,[status(thm)],[c_12293]) ).

cnf(c_26613,plain,
    ( app(cons(hd(sK56),nil),tl(sK56)) != cons(hd(sK56),tl(sK56))
    | sK56 != cons(hd(sK56),tl(sK56))
    | app(cons(hd(sK56),nil),tl(sK56)) = sK56 ),
    inference(instantiation,[status(thm)],[c_21283]) ).

cnf(c_31393,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)) ),
    inference(instantiation,[status(thm)],[c_6413]) ).

cnf(c_51053,plain,
    ( app(cons(hd(sK56),nil),tl(sK56)) != sK56
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
    inference(instantiation,[status(thm)],[c_6397]) ).

cnf(c_51054,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_51053,c_31393,c_26613,c_16682,c_11818,c_10955,c_10446,c_10415,c_10421,c_10422,c_9513,c_6382,c_6381,c_6596,c_141,c_252]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem  : SWC308+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.07  % Command  : run_iprover %s %d THM
% 0.07/0.25  % Computer : n014.cluster.edu
% 0.07/0.25  % Model    : x86_64 x86_64
% 0.07/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25  % Memory   : 8042.1875MB
% 0.07/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25  % CPULimit : 300
% 0.07/0.25  % WCLimit  : 300
% 0.07/0.25  % DateTime : Thu May  2 23:20:17 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.10/0.33  Running first-order theorem proving
% 0.10/0.33  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 42.63/6.54  % SZS status Started for theBenchmark.p
% 42.63/6.54  % SZS status Theorem for theBenchmark.p
% 42.63/6.54  
% 42.63/6.54  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 42.63/6.54  
% 42.63/6.54  ------  iProver source info
% 42.63/6.54  
% 42.63/6.54  git: date: 2024-05-02 19:28:25 +0000
% 42.63/6.54  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 42.63/6.54  git: non_committed_changes: false
% 42.63/6.54  
% 42.63/6.54  ------ Parsing...
% 42.63/6.54  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 42.63/6.54  
% 42.63/6.54  ------ 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 
% 42.63/6.54  
% 42.63/6.54  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 42.63/6.54  
% 42.63/6.54  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 42.63/6.54  ------ Proving...
% 42.63/6.54  ------ Problem Properties 
% 42.63/6.54  
% 42.63/6.54  
% 42.63/6.54  clauses                                 185
% 42.63/6.54  conjectures                             3
% 42.63/6.54  EPR                                     52
% 42.63/6.54  Horn                                    117
% 42.63/6.54  unary                                   19
% 42.63/6.54  binary                                  40
% 42.63/6.54  lits                                    629
% 42.63/6.54  lits eq                                 82
% 42.63/6.54  fd_pure                                 0
% 42.63/6.54  fd_pseudo                               0
% 42.63/6.54  fd_cond                                 21
% 42.63/6.54  fd_pseudo_cond                          14
% 42.63/6.54  AC symbols                              0
% 42.63/6.54  
% 42.63/6.54  ------ Input Options Time Limit: Unbounded
% 42.63/6.54  
% 42.63/6.54  
% 42.63/6.54  ------ 
% 42.63/6.54  Current options:
% 42.63/6.54  ------ 
% 42.63/6.54  
% 42.63/6.54  
% 42.63/6.54  
% 42.63/6.54  
% 42.63/6.54  ------ Proving...
% 42.63/6.54  
% 42.63/6.54  
% 42.63/6.54  % SZS status Theorem for theBenchmark.p
% 42.63/6.54  
% 42.63/6.54  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 42.63/6.55  
% 42.63/6.55  
%------------------------------------------------------------------------------