TSTP Solution File: SWC112+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC112+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:41:04 EDT 2023

% Result   : Theorem 7.84s 1.68s
% Output   : CNFRefutation 7.84s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f602)

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

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

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

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ( segmentP(X1,X0)
                          & neq(X0,nil) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( ? [X10] :
                                  ( ? [X11] :
                                      ( ? [X12] :
                                          ( ? [X13] :
                                              ( lt(X12,X10)
                                              & app(X13,cons(X12,nil)) = X2
                                              & ssList(X13) )
                                          & ssItem(X12) )
                                      & app(cons(X10,nil),X11) = X5
                                      & ssList(X11) )
                                  & ssItem(X10) )
                              | ? [X6] :
                                  ( ? [X7] :
                                      ( ? [X8] :
                                          ( ? [X9] :
                                              ( lt(X6,X8)
                                              & app(cons(X8,nil),X9) = X2
                                              & ssList(X9) )
                                          & ssItem(X8) )
                                      & app(X7,cons(X6,nil)) = X4
                                      & ssList(X7) )
                                  & ssItem(X6) )
                              | ~ strictorderedP(X2)
                              | app(app(X4,X2),X5) != X3 ) ) )
                    | 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)
                            & neq(X0,nil) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ? [X10] :
                                    ( ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( lt(X12,X10)
                                                & app(X13,cons(X12,nil)) = X2
                                                & ssList(X13) )
                                            & ssItem(X12) )
                                        & app(cons(X10,nil),X11) = X5
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( lt(X6,X8)
                                                & app(cons(X8,nil),X9) = X2
                                                & ssList(X9) )
                                            & ssItem(X8) )
                                        & app(X7,cons(X6,nil)) = X4
                                        & ssList(X7) )
                                    & ssItem(X6) )
                                | ~ strictorderedP(X2)
                                | app(app(X4,X2),X5) != X3 ) ) )
                      | 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)
                            & neq(X0,nil) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( lt(X8,X6)
                                                & app(X9,cons(X8,nil)) = X2
                                                & ssList(X9) )
                                            & ssItem(X8) )
                                        & app(cons(X6,nil),X7) = X5
                                        & ssList(X7) )
                                    & ssItem(X6) )
                                | ? [X10] :
                                    ( ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( lt(X10,X12)
                                                & app(cons(X12,nil),X13) = X2
                                                & ssList(X13) )
                                            & ssItem(X12) )
                                        & app(X11,cons(X10,nil)) = X4
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | ~ strictorderedP(X2)
                                | app(app(X4,X2),X5) != X3 ) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ( ~ segmentP(X1,X0)
                        | ~ neq(X0,nil) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & strictorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & 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)
                        | ~ neq(X0,nil) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & strictorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f254,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(f255,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,[],[f254]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK13(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK13(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
        & ssList(sK14(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f258,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
                & ssList(sK14(X0,X1))
                & ssList(sK13(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f255,f257,f256]) ).

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

fof(f331,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ( ~ segmentP(X1,X0)
                          | ~ neq(X0,nil) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ? [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ! [X8] :
                                        ( ! [X9] :
                                            ( ~ lt(X8,X6)
                                            | app(X9,cons(X8,nil)) != X2
                                            | ~ ssList(X9) )
                                        | ~ ssItem(X8) )
                                    | app(cons(X6,nil),X7) != X5
                                    | ~ ssList(X7) )
                                | ~ ssItem(X6) )
                            & ! [X10] :
                                ( ! [X11] :
                                    ( ! [X12] :
                                        ( ! [X13] :
                                            ( ~ lt(X10,X12)
                                            | app(cons(X12,nil),X13) != X2
                                            | ~ ssList(X13) )
                                        | ~ ssItem(X12) )
                                    | app(X11,cons(X10,nil)) != X4
                                    | ~ ssList(X11) )
                                | ~ ssItem(X10) )
                            & strictorderedP(X2)
                            & app(app(X4,X2),X5) = X3
                            & ssList(X5) )
                        & ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ( ~ segmentP(X1,sK53)
                        | ~ neq(sK53,nil) )
                      & neq(X1,nil) )
                    | ( nil != sK53
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & strictorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ( ~ segmentP(X1,sK53)
                      | ~ neq(sK53,nil) )
                    & neq(X1,nil) )
                  | ( nil != sK53
                    & nil = X1 ) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ? [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ! [X9] :
                                        ( ~ lt(X8,X6)
                                        | app(X9,cons(X8,nil)) != X2
                                        | ~ ssList(X9) )
                                    | ~ ssItem(X8) )
                                | app(cons(X6,nil),X7) != X5
                                | ~ ssList(X7) )
                            | ~ ssItem(X6) )
                        & ! [X10] :
                            ( ! [X11] :
                                ( ! [X12] :
                                    ( ! [X13] :
                                        ( ~ lt(X10,X12)
                                        | app(cons(X12,nil),X13) != X2
                                        | ~ ssList(X13) )
                                    | ~ ssItem(X12) )
                                | app(X11,cons(X10,nil)) != X4
                                | ~ ssList(X11) )
                            | ~ ssItem(X10) )
                        & strictorderedP(X2)
                        & app(app(X4,X2),X5) = X3
                        & ssList(X5) )
                    & ssList(X4) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ( ~ segmentP(sK54,sK53)
                    | ~ neq(sK53,nil) )
                  & neq(sK54,nil) )
                | ( nil != sK53
                  & nil = sK54 ) )
              & ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ! [X9] :
                                      ( ~ lt(X8,X6)
                                      | app(X9,cons(X8,nil)) != X2
                                      | ~ ssList(X9) )
                                  | ~ ssItem(X8) )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & ! [X10] :
                          ( ! [X11] :
                              ( ! [X12] :
                                  ( ! [X13] :
                                      ( ~ lt(X10,X12)
                                      | app(cons(X12,nil),X13) != X2
                                      | ~ ssList(X13) )
                                  | ~ ssItem(X12) )
                              | app(X11,cons(X10,nil)) != X4
                              | ~ ssList(X11) )
                          | ~ ssItem(X10) )
                      & strictorderedP(X2)
                      & app(app(X4,X2),X5) = X3
                      & ssList(X5) )
                  & ssList(X4) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ( ~ segmentP(sK54,sK53)
                  | ~ neq(sK53,nil) )
                & neq(sK54,nil) )
              | ( nil != sK53
                & nil = sK54 ) )
            & ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ? [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ! [X9] :
                                    ( ~ lt(X8,X6)
                                    | app(X9,cons(X8,nil)) != X2
                                    | ~ ssList(X9) )
                                | ~ ssItem(X8) )
                            | app(cons(X6,nil),X7) != X5
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & ! [X10] :
                        ( ! [X11] :
                            ( ! [X12] :
                                ( ! [X13] :
                                    ( ~ lt(X10,X12)
                                    | app(cons(X12,nil),X13) != X2
                                    | ~ ssList(X13) )
                                | ~ ssItem(X12) )
                            | app(X11,cons(X10,nil)) != X4
                            | ~ ssList(X11) )
                        | ~ ssItem(X10) )
                    & strictorderedP(X2)
                    & app(app(X4,X2),X5) = X3
                    & ssList(X5) )
                & ssList(X4) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ( ~ segmentP(sK54,sK53)
                | ~ neq(sK53,nil) )
              & neq(sK54,nil) )
            | ( nil != sK53
              & nil = sK54 ) )
          & ( nil != sK55
            | nil = X3 )
          & ? [X4] :
              ( ? [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ! [X9] :
                                  ( ~ lt(X8,X6)
                                  | app(X9,cons(X8,nil)) != sK55
                                  | ~ ssList(X9) )
                              | ~ ssItem(X8) )
                          | app(cons(X6,nil),X7) != X5
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & ! [X10] :
                      ( ! [X11] :
                          ( ! [X12] :
                              ( ! [X13] :
                                  ( ~ lt(X10,X12)
                                  | app(cons(X12,nil),X13) != sK55
                                  | ~ ssList(X13) )
                              | ~ ssItem(X12) )
                          | app(X11,cons(X10,nil)) != X4
                          | ~ ssList(X11) )
                      | ~ ssItem(X10) )
                  & strictorderedP(sK55)
                  & app(app(X4,sK55),X5) = X3
                  & ssList(X5) )
              & ssList(X4) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( ( ( ~ segmentP(sK54,sK53)
              | ~ neq(sK53,nil) )
            & neq(sK54,nil) )
          | ( nil != sK53
            & nil = sK54 ) )
        & ( nil != sK55
          | nil = X3 )
        & ? [X4] :
            ( ? [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ! [X9] :
                                ( ~ lt(X8,X6)
                                | app(X9,cons(X8,nil)) != sK55
                                | ~ ssList(X9) )
                            | ~ ssItem(X8) )
                        | app(cons(X6,nil),X7) != X5
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & ! [X10] :
                    ( ! [X11] :
                        ( ! [X12] :
                            ( ! [X13] :
                                ( ~ lt(X10,X12)
                                | app(cons(X12,nil),X13) != sK55
                                | ~ ssList(X13) )
                            | ~ ssItem(X12) )
                        | app(X11,cons(X10,nil)) != X4
                        | ~ ssList(X11) )
                    | ~ ssItem(X10) )
                & strictorderedP(sK55)
                & app(app(X4,sK55),X5) = X3
                & ssList(X5) )
            & ssList(X4) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( ( ~ segmentP(sK54,sK53)
            | ~ neq(sK53,nil) )
          & neq(sK54,nil) )
        | ( nil != sK53
          & nil = sK54 ) )
      & ( nil != sK55
        | nil = sK56 )
      & ? [X4] :
          ( ? [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ! [X9] :
                              ( ~ lt(X8,X6)
                              | app(X9,cons(X8,nil)) != sK55
                              | ~ ssList(X9) )
                          | ~ ssItem(X8) )
                      | app(cons(X6,nil),X7) != X5
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & ! [X10] :
                  ( ! [X11] :
                      ( ! [X12] :
                          ( ! [X13] :
                              ( ~ lt(X10,X12)
                              | app(cons(X12,nil),X13) != sK55
                              | ~ ssList(X13) )
                          | ~ ssItem(X12) )
                      | app(X11,cons(X10,nil)) != X4
                      | ~ ssList(X11) )
                  | ~ ssItem(X10) )
              & strictorderedP(sK55)
              & app(app(X4,sK55),X5) = sK56
              & ssList(X5) )
          & ssList(X4) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ! [X9] :
                            ( ~ lt(X8,X6)
                            | app(X9,cons(X8,nil)) != sK55
                            | ~ ssList(X9) )
                        | ~ ssItem(X8) )
                    | app(cons(X6,nil),X7) != X5
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & ! [X10] :
                ( ! [X11] :
                    ( ! [X12] :
                        ( ! [X13] :
                            ( ~ lt(X10,X12)
                            | app(cons(X12,nil),X13) != sK55
                            | ~ ssList(X13) )
                        | ~ ssItem(X12) )
                    | app(X11,cons(X10,nil)) != X4
                    | ~ ssList(X11) )
                | ~ ssItem(X10) )
            & strictorderedP(sK55)
            & app(app(X4,sK55),X5) = sK56
            & ssList(X5) )
        & ssList(X4) )
   => ( ? [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ~ lt(X8,X6)
                          | app(X9,cons(X8,nil)) != sK55
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  | app(cons(X6,nil),X7) != X5
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & ! [X10] :
              ( ! [X11] :
                  ( ! [X12] :
                      ( ! [X13] :
                          ( ~ lt(X10,X12)
                          | app(cons(X12,nil),X13) != sK55
                          | ~ ssList(X13) )
                      | ~ ssItem(X12) )
                  | app(X11,cons(X10,nil)) != sK57
                  | ~ ssList(X11) )
              | ~ ssItem(X10) )
          & strictorderedP(sK55)
          & sK56 = app(app(sK57,sK55),X5)
          & ssList(X5) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ~ lt(X8,X6)
                        | app(X9,cons(X8,nil)) != sK55
                        | ~ ssList(X9) )
                    | ~ ssItem(X8) )
                | app(cons(X6,nil),X7) != X5
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & ! [X10] :
            ( ! [X11] :
                ( ! [X12] :
                    ( ! [X13] :
                        ( ~ lt(X10,X12)
                        | app(cons(X12,nil),X13) != sK55
                        | ~ ssList(X13) )
                    | ~ ssItem(X12) )
                | app(X11,cons(X10,nil)) != sK57
                | ~ ssList(X11) )
            | ~ ssItem(X10) )
        & strictorderedP(sK55)
        & sK56 = app(app(sK57,sK55),X5)
        & ssList(X5) )
   => ( ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ! [X9] :
                      ( ~ lt(X8,X6)
                      | app(X9,cons(X8,nil)) != sK55
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              | app(cons(X6,nil),X7) != sK58
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & ! [X10] :
          ( ! [X11] :
              ( ! [X12] :
                  ( ! [X13] :
                      ( ~ lt(X10,X12)
                      | app(cons(X12,nil),X13) != sK55
                      | ~ ssList(X13) )
                  | ~ ssItem(X12) )
              | app(X11,cons(X10,nil)) != sK57
              | ~ ssList(X11) )
          | ~ ssItem(X10) )
      & strictorderedP(sK55)
      & sK56 = app(app(sK57,sK55),sK58)
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ( ( ( ~ segmentP(sK54,sK53)
          | ~ neq(sK53,nil) )
        & neq(sK54,nil) )
      | ( nil != sK53
        & nil = sK54 ) )
    & ( nil != sK55
      | nil = sK56 )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( ~ lt(X8,X6)
                    | app(X9,cons(X8,nil)) != sK55
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            | app(cons(X6,nil),X7) != sK58
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & ! [X10] :
        ( ! [X11] :
            ( ! [X12] :
                ( ! [X13] :
                    ( ~ lt(X10,X12)
                    | app(cons(X12,nil),X13) != sK55
                    | ~ ssList(X13) )
                | ~ ssItem(X12) )
            | app(X11,cons(X10,nil)) != sK57
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & strictorderedP(sK55)
    & sK56 = app(app(sK57,sK55),sK58)
    & ssList(sK58)
    & ssList(sK57)
    & 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])],[f223,f349,f348,f347,f346,f345,f344]) ).

fof(f372,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,[],[f258]) ).

fof(f441,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f317]) ).

fof(f443,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f497,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f550,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f350]) ).

fof(f551,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f350]) ).

fof(f554,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f350]) ).

fof(f555,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f350]) ).

fof(f556,plain,
    ssList(sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    ssList(sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f558,plain,
    sK56 = app(app(sK57,sK55),sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f562,plain,
    ( nil != sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f350]) ).

fof(f564,plain,
    ( neq(sK54,nil)
    | nil != sK53 ),
    inference(cnf_transformation,[],[f350]) ).

fof(f565,plain,
    ( ~ segmentP(sK54,sK53)
    | ~ neq(sK53,nil)
    | nil = sK54 ),
    inference(cnf_transformation,[],[f350]) ).

fof(f568,plain,
    ( ~ segmentP(sK56,sK55)
    | ~ neq(sK55,nil)
    | nil = sK56 ),
    inference(definition_unfolding,[],[f565,f554,f555,f555,f554]) ).

fof(f569,plain,
    ( neq(sK56,nil)
    | nil != sK55 ),
    inference(definition_unfolding,[],[f564,f554,f555]) ).

fof(f571,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f551,f554]) ).

fof(f572,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f550,f555]) ).

fof(f578,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,[],[f372]) ).

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,[],[f578]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f602]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f443]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f497]) ).

cnf(c_247,negated_conjecture,
    ( ~ neq(sK55,nil)
    | ~ segmentP(sK56,sK55)
    | nil = sK56 ),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_248,negated_conjecture,
    ( nil != sK55
    | neq(sK56,nil) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_250,negated_conjecture,
    ( nil != sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_254,negated_conjecture,
    app(app(sK57,sK55),sK58) = sK56,
    inference(cnf_transformation,[],[f558]) ).

cnf(c_255,negated_conjecture,
    ssList(sK58),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_256,negated_conjecture,
    ssList(sK57),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_259,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f571]) ).

cnf(c_260,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_3312,plain,
    ( X0 != sK55
    | X1 != nil
    | ~ segmentP(sK56,sK55)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | nil = sK56 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).

cnf(c_3313,plain,
    ( ~ segmentP(sK56,sK55)
    | ~ ssList(nil)
    | ~ ssList(sK55)
    | nil = sK56
    | sK55 = nil ),
    inference(unflattening,[status(thm)],[c_3312]) ).

cnf(c_3314,plain,
    ( ~ segmentP(sK56,sK55)
    | nil = sK56
    | sK55 = nil ),
    inference(global_subsumption_just,[status(thm)],[c_3313,c_260,c_141,c_3313]) ).

cnf(c_3348,plain,
    ( X0 != nil
    | X0 != sK56
    | nil != sK55
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_139,c_248]) ).

cnf(c_3349,plain,
    ( nil != sK56
    | nil != sK55
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_3348]) ).

cnf(c_3350,plain,
    nil != sK55,
    inference(global_subsumption_just,[status(thm)],[c_3349,c_141,c_250,c_3349]) ).

cnf(c_26925,plain,
    ( ~ ssList(app(app(sK57,sK55),sK58))
    | ~ ssList(sK55)
    | ~ ssList(sK58)
    | ~ ssList(sK57)
    | segmentP(sK56,sK55) ),
    inference(superposition,[status(thm)],[c_254,c_67]) ).

cnf(c_26976,plain,
    ( ~ ssList(sK56)
    | ~ ssList(sK55)
    | ~ ssList(sK58)
    | ~ ssList(sK57)
    | segmentP(sK56,sK55) ),
    inference(light_normalisation,[status(thm)],[c_26925,c_254]) ).

cnf(c_26977,plain,
    segmentP(sK56,sK55),
    inference(forward_subsumption_resolution,[status(thm)],[c_26976,c_256,c_255,c_260,c_259]) ).

cnf(c_27207,plain,
    ( nil = sK56
    | nil = sK55 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_3314,c_26977]) ).

cnf(c_27210,plain,
    nil = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_27207,c_3350]) ).

cnf(c_27686,plain,
    segmentP(nil,sK55),
    inference(light_normalisation,[status(thm)],[c_26977,c_27210]) ).

cnf(c_27690,plain,
    ( ~ ssList(sK55)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_27686,c_196]) ).

cnf(c_27691,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_27690,c_3350,c_260]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC112+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Aug 28 17:44:47 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.84/1.68  % SZS status Started for theBenchmark.p
% 7.84/1.68  % SZS status Theorem for theBenchmark.p
% 7.84/1.68  
% 7.84/1.68  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.84/1.68  
% 7.84/1.68  ------  iProver source info
% 7.84/1.68  
% 7.84/1.68  git: date: 2023-05-31 18:12:56 +0000
% 7.84/1.68  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.84/1.68  git: non_committed_changes: false
% 7.84/1.68  git: last_make_outside_of_git: false
% 7.84/1.68  
% 7.84/1.68  ------ Parsing...
% 7.84/1.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.84/1.68  
% 7.84/1.68  ------ 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 
% 7.84/1.68  
% 7.84/1.68  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.84/1.68  
% 7.84/1.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.84/1.68  ------ Proving...
% 7.84/1.68  ------ Problem Properties 
% 7.84/1.68  
% 7.84/1.68  
% 7.84/1.68  clauses                                 191
% 7.84/1.68  conjectures                             8
% 7.84/1.68  EPR                                     57
% 7.84/1.68  Horn                                    122
% 7.84/1.68  unary                                   23
% 7.84/1.68  binary                                  40
% 7.84/1.68  lits                                    645
% 7.84/1.68  lits eq                                 88
% 7.84/1.68  fd_pure                                 0
% 7.84/1.68  fd_pseudo                               0
% 7.84/1.68  fd_cond                                 21
% 7.84/1.68  fd_pseudo_cond                          14
% 7.84/1.68  AC symbols                              0
% 7.84/1.68  
% 7.84/1.68  ------ Schedule dynamic 5 is on 
% 7.84/1.68  
% 7.84/1.68  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.84/1.68  
% 7.84/1.68  
% 7.84/1.68  ------ 
% 7.84/1.68  Current options:
% 7.84/1.68  ------ 
% 7.84/1.68  
% 7.84/1.68  
% 7.84/1.68  
% 7.84/1.68  
% 7.84/1.68  ------ Proving...
% 7.84/1.68  
% 7.84/1.68  
% 7.84/1.68  % SZS status Theorem for theBenchmark.p
% 7.84/1.68  
% 7.84/1.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.84/1.68  
% 7.84/1.69  
%------------------------------------------------------------------------------