TSTP Solution File: SWC384+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC384+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 03:12:16 EDT 2024

% Result   : Theorem 8.07s 1.68s
% Output   : CNFRefutation 8.07s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f606)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).

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

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

fof(f101,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f104,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ segmentP(X1,X0)
                    | ~ singletonP(X0) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ~ lt(X7,X4)
                                    | ~ memberP(X6,X7)
                                    | ~ ssItem(X7) )
                                & ! [X8] :
                                    ( ~ lt(X4,X8)
                                    | ~ memberP(X5,X8)
                                    | ~ ssItem(X8) )
                                & app(app(X5,X2),X6) = X3
                                & cons(X4,nil) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & 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] :
                  ( ( ~ segmentP(X1,X0)
                    | ~ singletonP(X0) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ~ lt(X7,X4)
                                    | ~ memberP(X6,X7)
                                    | ~ ssItem(X7) )
                                & ! [X8] :
                                    ( ~ lt(X4,X8)
                                    | ~ memberP(X5,X8)
                                    | ~ ssItem(X8) )
                                & app(app(X5,X2),X6) = X3
                                & cons(X4,nil) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f233,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ! [X7] :
                      ( ~ lt(X7,X4)
                      | ~ memberP(X6,X7)
                      | ~ ssItem(X7) )
                  & ! [X8] :
                      ( ~ lt(X4,X8)
                      | ~ memberP(X5,X8)
                      | ~ ssItem(X8) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ssList(X6) )
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP6(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f234,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ segmentP(X1,X0)
                    | ~ singletonP(X0) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP6(X3,X2) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f223,f233]) ).

fof(f244,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f101]) ).

fof(f245,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f244]) ).

fof(f246,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK11(X0),nil) = X0
        & ssItem(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f247,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK11(X0),nil) = X0
            & ssItem(sK11(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f245,f246]) ).

fof(f256,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f104]) ).

fof(f257,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f256]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK14(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK14(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK14(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
        & ssList(sK15(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f260,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
                & ssList(sK15(X0,X1))
                & ssList(sK14(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f257,f259,f258]) ).

fof(f346,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ! [X7] :
                      ( ~ lt(X7,X4)
                      | ~ memberP(X6,X7)
                      | ~ ssItem(X7) )
                  & ! [X8] :
                      ( ~ lt(X4,X8)
                      | ~ memberP(X5,X8)
                      | ~ ssItem(X8) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ssList(X6) )
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP6(X3,X2) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f347,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ lt(X2,X6)
                      | ~ memberP(X3,X6)
                      | ~ ssItem(X6) )
                  & app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP6(X0,X1) ),
    inference(rectify,[],[f346]) ).

fof(f348,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ lt(X2,X6)
                      | ~ memberP(X3,X6)
                      | ~ ssItem(X6) )
                  & app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ! [X5] :
                    ( ~ lt(X5,sK54(X0,X1))
                    | ~ memberP(X4,X5)
                    | ~ ssItem(X5) )
                & ! [X6] :
                    ( ~ lt(sK54(X0,X1),X6)
                    | ~ memberP(X3,X6)
                    | ~ ssItem(X6) )
                & app(app(X3,X1),X4) = X0
                & cons(sK54(X0,X1),nil) = X1
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK54(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ? [X4] :
              ( ! [X5] :
                  ( ~ lt(X5,sK54(X0,X1))
                  | ~ memberP(X4,X5)
                  | ~ ssItem(X5) )
              & ! [X6] :
                  ( ~ lt(sK54(X0,X1),X6)
                  | ~ memberP(X3,X6)
                  | ~ ssItem(X6) )
              & app(app(X3,X1),X4) = X0
              & cons(sK54(X0,X1),nil) = X1
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ! [X5] :
                ( ~ lt(X5,sK54(X0,X1))
                | ~ memberP(X4,X5)
                | ~ ssItem(X5) )
            & ! [X6] :
                ( ~ lt(sK54(X0,X1),X6)
                | ~ memberP(sK55(X0,X1),X6)
                | ~ ssItem(X6) )
            & app(app(sK55(X0,X1),X1),X4) = X0
            & cons(sK54(X0,X1),nil) = X1
            & ssList(X4) )
        & ssList(sK55(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ! [X5] :
              ( ~ lt(X5,sK54(X0,X1))
              | ~ memberP(X4,X5)
              | ~ ssItem(X5) )
          & ! [X6] :
              ( ~ lt(sK54(X0,X1),X6)
              | ~ memberP(sK55(X0,X1),X6)
              | ~ ssItem(X6) )
          & app(app(sK55(X0,X1),X1),X4) = X0
          & cons(sK54(X0,X1),nil) = X1
          & ssList(X4) )
     => ( ! [X5] :
            ( ~ lt(X5,sK54(X0,X1))
            | ~ memberP(sK56(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(sK54(X0,X1),X6)
            | ~ memberP(sK55(X0,X1),X6)
            | ~ ssItem(X6) )
        & app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
        & cons(sK54(X0,X1),nil) = X1
        & ssList(sK56(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f351,plain,
    ! [X0,X1] :
      ( ( ! [X5] :
            ( ~ lt(X5,sK54(X0,X1))
            | ~ memberP(sK56(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(sK54(X0,X1),X6)
            | ~ memberP(sK55(X0,X1),X6)
            | ~ ssItem(X6) )
        & app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
        & cons(sK54(X0,X1),nil) = X1
        & ssList(sK56(X0,X1))
        & ssList(sK55(X0,X1))
        & ssItem(sK54(X0,X1)) )
      | ~ sP6(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56])],[f347,f350,f349,f348]) ).

fof(f352,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ segmentP(X1,X0)
                      | ~ singletonP(X0) )
                    & ( ( nil = X2
                        & nil = X3 )
                      | sP6(X3,X2) )
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ segmentP(X1,sK57)
                    | ~ singletonP(sK57) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP6(X3,X2) )
                  & neq(X1,nil)
                  & sK57 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f353,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ segmentP(X1,sK57)
                  | ~ singletonP(sK57) )
                & ( ( nil = X2
                    & nil = X3 )
                  | sP6(X3,X2) )
                & neq(X1,nil)
                & sK57 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ segmentP(sK58,sK57)
                | ~ singletonP(sK57) )
              & ( ( nil = X2
                  & nil = X3 )
                | sP6(X3,X2) )
              & neq(sK58,nil)
              & sK57 = X2
              & sK58 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f354,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ segmentP(sK58,sK57)
              | ~ singletonP(sK57) )
            & ( ( nil = X2
                & nil = X3 )
              | sP6(X3,X2) )
            & neq(sK58,nil)
            & sK57 = X2
            & sK58 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ segmentP(sK58,sK57)
            | ~ singletonP(sK57) )
          & ( ( nil = sK59
              & nil = X3 )
            | sP6(X3,sK59) )
          & neq(sK58,nil)
          & sK57 = sK59
          & sK58 = X3
          & ssList(X3) )
      & ssList(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f355,plain,
    ( ? [X3] :
        ( ( ~ segmentP(sK58,sK57)
          | ~ singletonP(sK57) )
        & ( ( nil = sK59
            & nil = X3 )
          | sP6(X3,sK59) )
        & neq(sK58,nil)
        & sK57 = sK59
        & sK58 = X3
        & ssList(X3) )
   => ( ( ~ segmentP(sK58,sK57)
        | ~ singletonP(sK57) )
      & ( ( nil = sK59
          & nil = sK60 )
        | sP6(sK60,sK59) )
      & neq(sK58,nil)
      & sK57 = sK59
      & sK58 = sK60
      & ssList(sK60) ) ),
    introduced(choice_axiom,[]) ).

fof(f356,plain,
    ( ( ~ segmentP(sK58,sK57)
      | ~ singletonP(sK57) )
    & ( ( nil = sK59
        & nil = sK60 )
      | sP6(sK60,sK59) )
    & neq(sK58,nil)
    & sK57 = sK59
    & sK58 = sK60
    & ssList(sK60)
    & ssList(sK59)
    & ssList(sK58)
    & ssList(sK57) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60])],[f234,f355,f354,f353,f352]) ).

fof(f368,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f247]) ).

fof(f378,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(X0,X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f260]) ).

fof(f449,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f556,plain,
    ! [X0,X1] :
      ( ssItem(sK54(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f557,plain,
    ! [X0,X1] :
      ( ssList(sK55(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f558,plain,
    ! [X0,X1] :
      ( ssList(sK56(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f559,plain,
    ! [X0,X1] :
      ( cons(sK54(X0,X1),nil) = X1
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f560,plain,
    ! [X0,X1] :
      ( app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f563,plain,
    ssList(sK57),
    inference(cnf_transformation,[],[f356]) ).

fof(f564,plain,
    ssList(sK58),
    inference(cnf_transformation,[],[f356]) ).

fof(f567,plain,
    sK58 = sK60,
    inference(cnf_transformation,[],[f356]) ).

fof(f568,plain,
    sK57 = sK59,
    inference(cnf_transformation,[],[f356]) ).

fof(f569,plain,
    neq(sK58,nil),
    inference(cnf_transformation,[],[f356]) ).

fof(f570,plain,
    ( nil = sK60
    | sP6(sK60,sK59) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f572,plain,
    ( ~ segmentP(sK58,sK57)
    | ~ singletonP(sK57) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f573,plain,
    ( ~ segmentP(sK60,sK59)
    | ~ singletonP(sK59) ),
    inference(definition_unfolding,[],[f572,f567,f568,f568]) ).

fof(f574,plain,
    neq(sK60,nil),
    inference(definition_unfolding,[],[f569,f567]) ).

fof(f575,plain,
    ssList(sK60),
    inference(definition_unfolding,[],[f564,f567]) ).

fof(f576,plain,
    ssList(sK59),
    inference(definition_unfolding,[],[f563,f568]) ).

fof(f579,plain,
    ! [X1] :
      ( singletonP(cons(X1,nil))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,nil)) ),
    inference(equality_resolution,[],[f368]) ).

fof(f582,plain,
    ! [X2,X3,X1] :
      ( segmentP(app(app(X2,X1),X3),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(app(X2,X1),X3)) ),
    inference(equality_resolution,[],[f378]) ).

cnf(c_58,plain,
    ( ~ ssList(cons(X0,nil))
    | ~ ssItem(X0)
    | singletonP(cons(X0,nil)) ),
    inference(cnf_transformation,[],[f579]) ).

cnf(c_67,plain,
    ( ~ ssList(app(app(X0,X1),X2))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(app(app(X0,X1),X2),X1) ),
    inference(cnf_transformation,[],[f582]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f606]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f449]) ).

cnf(c_248,plain,
    ( ~ sP6(X0,X1)
    | app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_249,plain,
    ( ~ sP6(X0,X1)
    | cons(sK54(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_250,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK56(X0,X1)) ),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_251,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK55(X0,X1)) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_252,plain,
    ( ~ sP6(X0,X1)
    | ssItem(sK54(X0,X1)) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_253,negated_conjecture,
    ( ~ segmentP(sK60,sK59)
    | ~ singletonP(sK59) ),
    inference(cnf_transformation,[],[f573]) ).

cnf(c_255,negated_conjecture,
    ( nil = sK60
    | sP6(sK60,sK59) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_256,negated_conjecture,
    neq(sK60,nil),
    inference(cnf_transformation,[],[f574]) ).

cnf(c_259,negated_conjecture,
    ssList(sK60),
    inference(cnf_transformation,[],[f575]) ).

cnf(c_260,negated_conjecture,
    ssList(sK59),
    inference(cnf_transformation,[],[f576]) ).

cnf(c_418,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(prop_impl_just,[status(thm)],[c_139]) ).

cnf(c_510,plain,
    ( ~ sP6(X0,X1)
    | app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0 ),
    inference(prop_impl_just,[status(thm)],[c_248]) ).

cnf(c_512,plain,
    ( ~ sP6(X0,X1)
    | cons(sK54(X0,X1),nil) = X1 ),
    inference(prop_impl_just,[status(thm)],[c_249]) ).

cnf(c_514,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK56(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_250]) ).

cnf(c_516,plain,
    ( ~ sP6(X0,X1)
    | ssList(sK55(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_251]) ).

cnf(c_518,plain,
    ( ~ sP6(X0,X1)
    | ssItem(sK54(X0,X1)) ),
    inference(prop_impl_just,[status(thm)],[c_252]) ).

cnf(c_570,plain,
    ( nil = sK60
    | sP6(sK60,sK59) ),
    inference(prop_impl_just,[status(thm)],[c_255]) ).

cnf(c_848,plain,
    ( X0 != nil
    | X0 != sK60
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_418,c_256]) ).

cnf(c_849,plain,
    ( nil != sK60
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_848]) ).

cnf(c_850,plain,
    nil != sK60,
    inference(global_subsumption_just,[status(thm)],[c_849,c_141,c_849]) ).

cnf(c_858,plain,
    sP6(sK60,sK59),
    inference(backward_subsumption_resolution,[status(thm)],[c_570,c_850]) ).

cnf(c_859,plain,
    ( X0 != sK60
    | X1 != sK59
    | ssItem(sK54(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_518,c_858]) ).

cnf(c_860,plain,
    ssItem(sK54(sK60,sK59)),
    inference(unflattening,[status(thm)],[c_859]) ).

cnf(c_866,plain,
    ( X0 != sK60
    | X1 != sK59
    | ssList(sK55(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_516,c_858]) ).

cnf(c_867,plain,
    ssList(sK55(sK60,sK59)),
    inference(unflattening,[status(thm)],[c_866]) ).

cnf(c_873,plain,
    ( X0 != sK60
    | X1 != sK59
    | ssList(sK56(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_514,c_858]) ).

cnf(c_874,plain,
    ssList(sK56(sK60,sK59)),
    inference(unflattening,[status(thm)],[c_873]) ).

cnf(c_880,plain,
    ( X0 != sK60
    | X1 != sK59
    | cons(sK54(X0,X1),nil) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_512,c_858]) ).

cnf(c_881,plain,
    cons(sK54(sK60,sK59),nil) = sK59,
    inference(unflattening,[status(thm)],[c_880]) ).

cnf(c_887,plain,
    ( X0 != sK60
    | X1 != sK59
    | app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0 ),
    inference(resolution_lifted,[status(thm)],[c_510,c_858]) ).

cnf(c_888,plain,
    app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60,
    inference(unflattening,[status(thm)],[c_887]) ).

cnf(c_4226,plain,
    app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60,
    inference(subtyping,[status(esa)],[c_888]) ).

cnf(c_4227,plain,
    cons(sK54(sK60,sK59),nil) = sK59,
    inference(subtyping,[status(esa)],[c_881]) ).

cnf(c_4400,plain,
    ( ~ ssList(app(app(X0_13,X1_13),X2_13))
    | ~ ssList(X0_13)
    | ~ ssList(X1_13)
    | ~ ssList(X2_13)
    | segmentP(app(app(X0_13,X1_13),X2_13),X1_13) ),
    inference(subtyping,[status(esa)],[c_67]) ).

cnf(c_4407,plain,
    ( ~ ssList(cons(X0_14,nil))
    | ~ ssItem(X0_14)
    | singletonP(cons(X0_14,nil)) ),
    inference(subtyping,[status(esa)],[c_58]) ).

cnf(c_5927,plain,
    ( ~ ssItem(sK54(sK60,sK59))
    | ~ ssList(sK59)
    | singletonP(cons(sK54(sK60,sK59),nil)) ),
    inference(superposition,[status(thm)],[c_4227,c_4407]) ).

cnf(c_5940,plain,
    ( ~ ssItem(sK54(sK60,sK59))
    | ~ ssList(sK59)
    | singletonP(sK59) ),
    inference(demodulation,[status(thm)],[c_5927,c_4227]) ).

cnf(c_13484,plain,
    ( ~ ssList(app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)))
    | ~ ssList(sK56(sK60,sK59))
    | ~ ssList(sK55(sK60,sK59))
    | ~ ssList(sK59)
    | segmentP(sK60,sK59) ),
    inference(superposition,[status(thm)],[c_4226,c_4400]) ).

cnf(c_13514,plain,
    ( ~ ssList(sK56(sK60,sK59))
    | ~ ssList(sK55(sK60,sK59))
    | ~ ssList(sK60)
    | ~ ssList(sK59)
    | segmentP(sK60,sK59) ),
    inference(demodulation,[status(thm)],[c_13484,c_4226]) ).

cnf(c_13574,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_13514,c_5940,c_874,c_867,c_860,c_253,c_259,c_260]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWC384+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n031.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri May  3 00:07:31 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  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
% 8.07/1.68  % SZS status Started for theBenchmark.p
% 8.07/1.68  % SZS status Theorem for theBenchmark.p
% 8.07/1.68  
% 8.07/1.68  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.07/1.68  
% 8.07/1.68  ------  iProver source info
% 8.07/1.68  
% 8.07/1.68  git: date: 2024-05-02 19:28:25 +0000
% 8.07/1.68  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 8.07/1.68  git: non_committed_changes: false
% 8.07/1.68  
% 8.07/1.68  ------ Parsing...
% 8.07/1.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 8.07/1.68  
% 8.07/1.68  ------ Preprocessing... sup_sim: 0  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  pe_s  pe_e 
% 8.07/1.68  
% 8.07/1.68  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  scvd_s sp: 0 0s scvd_e  snvd_s sp: 0 0s snvd_e 
% 8.07/1.68  
% 8.07/1.68  ------ Preprocessing...
% 8.07/1.68  ------ Proving...
% 8.07/1.68  ------ Problem Properties 
% 8.07/1.68  
% 8.07/1.68  
% 8.07/1.68  clauses                                 191
% 8.07/1.68  conjectures                             3
% 8.07/1.68  EPR                                     53
% 8.07/1.68  Horn                                    123
% 8.07/1.68  unary                                   24
% 8.07/1.68  binary                                  41
% 8.07/1.68  lits                                    634
% 8.07/1.68  lits eq                                 81
% 8.07/1.68  fd_pure                                 0
% 8.07/1.68  fd_pseudo                               0
% 8.07/1.68  fd_cond                                 21
% 8.07/1.68  fd_pseudo_cond                          14
% 8.07/1.68  AC symbols                              0
% 8.07/1.68  
% 8.07/1.68  ------ Input Options Time Limit: Unbounded
% 8.07/1.68  
% 8.07/1.68  
% 8.07/1.68  ------ 
% 8.07/1.68  Current options:
% 8.07/1.68  ------ 
% 8.07/1.68  
% 8.07/1.68  
% 8.07/1.68  
% 8.07/1.68  
% 8.07/1.68  ------ Proving...
% 8.07/1.68  
% 8.07/1.68  
% 8.07/1.68  % SZS status Theorem for theBenchmark.p
% 8.07/1.68  
% 8.07/1.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.07/1.69  
% 8.07/1.69  
%------------------------------------------------------------------------------