TSTP Solution File: SWC339+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC339+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 03:12:04 EDT 2024

% Result   : Theorem 0.49s 1.17s
% Output   : CNFRefutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   42 (  14 unt;   0 def)
%            Number of atoms       :  522 ( 150 equ)
%            Maximal formula atoms :   56 (  12 avg)
%            Number of connectives :  779 ( 299   ~; 259   |; 191   &)
%                                         (   0 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   9 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :  237 (   0 sgn 157   !;  72   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).

fof(f56,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( segmentP(X0,X1)
                   => segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).

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

fof(f173,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f174,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f175,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f174]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ totalorderedP(X0)
                    | ~ segmentP(X1,X0) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ leq(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] :
                                          ( ~ leq(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & totalorderedP(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] :
                  ( ( ~ totalorderedP(X0)
                    | ~ segmentP(X1,X0) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ leq(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] :
                                          ( ~ leq(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & totalorderedP(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(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ totalorderedP(X0)
                      | ~ segmentP(X1,X0) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ? [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ! [X8] :
                                        ( ! [X9] :
                                            ( ~ leq(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] :
                                            ( ~ leq(X10,X12)
                                            | app(cons(X12,nil),X13) != X2
                                            | ~ ssList(X13) )
                                        | ~ ssItem(X12) )
                                    | app(X11,cons(X10,nil)) != X4
                                    | ~ ssList(X11) )
                                | ~ ssItem(X10) )
                            & totalorderedP(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] :
                  ( ( ~ totalorderedP(sK53)
                    | ~ segmentP(X1,sK53) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ leq(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] :
                                          ( ~ leq(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & totalorderedP(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] :
                ( ( ~ totalorderedP(sK53)
                  | ~ segmentP(X1,sK53) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ? [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ! [X9] :
                                        ( ~ leq(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] :
                                        ( ~ leq(X10,X12)
                                        | app(cons(X12,nil),X13) != X2
                                        | ~ ssList(X13) )
                                    | ~ ssItem(X12) )
                                | app(X11,cons(X10,nil)) != X4
                                | ~ ssList(X11) )
                            | ~ ssItem(X10) )
                        & totalorderedP(X2)
                        & app(app(X4,X2),X5) = X3
                        & ssList(X5) )
                    & ssList(X4) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ totalorderedP(sK53)
                | ~ segmentP(sK54,sK53) )
              & ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ! [X9] :
                                      ( ~ leq(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] :
                                      ( ~ leq(X10,X12)
                                      | app(cons(X12,nil),X13) != X2
                                      | ~ ssList(X13) )
                                  | ~ ssItem(X12) )
                              | app(X11,cons(X10,nil)) != X4
                              | ~ ssList(X11) )
                          | ~ ssItem(X10) )
                      & totalorderedP(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] :
            ( ( ~ totalorderedP(sK53)
              | ~ segmentP(sK54,sK53) )
            & ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ? [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ! [X9] :
                                    ( ~ leq(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] :
                                    ( ~ leq(X10,X12)
                                    | app(cons(X12,nil),X13) != X2
                                    | ~ ssList(X13) )
                                | ~ ssItem(X12) )
                            | app(X11,cons(X10,nil)) != X4
                            | ~ ssList(X11) )
                        | ~ ssItem(X10) )
                    & totalorderedP(X2)
                    & app(app(X4,X2),X5) = X3
                    & ssList(X5) )
                & ssList(X4) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ totalorderedP(sK53)
            | ~ segmentP(sK54,sK53) )
          & ( nil != sK55
            | nil = X3 )
          & ? [X4] :
              ( ? [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ! [X9] :
                                  ( ~ leq(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] :
                                  ( ~ leq(X10,X12)
                                  | app(cons(X12,nil),X13) != sK55
                                  | ~ ssList(X13) )
                              | ~ ssItem(X12) )
                          | app(X11,cons(X10,nil)) != X4
                          | ~ ssList(X11) )
                      | ~ ssItem(X10) )
                  & totalorderedP(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] :
        ( ( ~ totalorderedP(sK53)
          | ~ segmentP(sK54,sK53) )
        & ( nil != sK55
          | nil = X3 )
        & ? [X4] :
            ( ? [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ! [X9] :
                                ( ~ leq(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] :
                                ( ~ leq(X10,X12)
                                | app(cons(X12,nil),X13) != sK55
                                | ~ ssList(X13) )
                            | ~ ssItem(X12) )
                        | app(X11,cons(X10,nil)) != X4
                        | ~ ssList(X11) )
                    | ~ ssItem(X10) )
                & totalorderedP(sK55)
                & app(app(X4,sK55),X5) = X3
                & ssList(X5) )
            & ssList(X4) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ~ totalorderedP(sK53)
        | ~ segmentP(sK54,sK53) )
      & ( nil != sK55
        | nil = sK56 )
      & ? [X4] :
          ( ? [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ! [X9] :
                              ( ~ leq(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] :
                              ( ~ leq(X10,X12)
                              | app(cons(X12,nil),X13) != sK55
                              | ~ ssList(X13) )
                          | ~ ssItem(X12) )
                      | app(X11,cons(X10,nil)) != X4
                      | ~ ssList(X11) )
                  | ~ ssItem(X10) )
              & totalorderedP(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] :
                            ( ~ leq(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] :
                            ( ~ leq(X10,X12)
                            | app(cons(X12,nil),X13) != sK55
                            | ~ ssList(X13) )
                        | ~ ssItem(X12) )
                    | app(X11,cons(X10,nil)) != X4
                    | ~ ssList(X11) )
                | ~ ssItem(X10) )
            & totalorderedP(sK55)
            & app(app(X4,sK55),X5) = sK56
            & ssList(X5) )
        & ssList(X4) )
   => ( ? [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ~ leq(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] :
                          ( ~ leq(X10,X12)
                          | app(cons(X12,nil),X13) != sK55
                          | ~ ssList(X13) )
                      | ~ ssItem(X12) )
                  | app(X11,cons(X10,nil)) != sK57
                  | ~ ssList(X11) )
              | ~ ssItem(X10) )
          & totalorderedP(sK55)
          & sK56 = app(app(sK57,sK55),X5)
          & ssList(X5) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f350,plain,
    ( ( ~ totalorderedP(sK53)
      | ~ segmentP(sK54,sK53) )
    & ( nil != sK55
      | nil = sK56 )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( ~ leq(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] :
                    ( ~ leq(X10,X12)
                    | app(cons(X12,nil),X13) != sK55
                    | ~ ssList(X13) )
                | ~ ssItem(X12) )
            | app(X11,cons(X10,nil)) != sK57
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & totalorderedP(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(f494,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f173]) ).

fof(f495,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(app(app(X2,X0),X3),X1)
      | ~ segmentP(X0,X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f550,plain,
    ssList(sK53),
    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(f559,plain,
    totalorderedP(sK55),
    inference(cnf_transformation,[],[f350]) ).

fof(f563,plain,
    ( ~ totalorderedP(sK53)
    | ~ segmentP(sK54,sK53) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f564,plain,
    ( ~ totalorderedP(sK55)
    | ~ segmentP(sK56,sK55) ),
    inference(definition_unfolding,[],[f563,f555,f554,f555]) ).

fof(f566,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f550,f555]) ).

cnf(c_192,plain,
    ( ~ ssList(X0)
    | segmentP(X0,X0) ),
    inference(cnf_transformation,[],[f494]) ).

cnf(c_193,plain,
    ( ~ segmentP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | segmentP(app(app(X2,X0),X3),X1) ),
    inference(cnf_transformation,[],[f495]) ).

cnf(c_246,negated_conjecture,
    ( ~ segmentP(sK56,sK55)
    | ~ totalorderedP(sK55) ),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_250,negated_conjecture,
    totalorderedP(sK55),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_251,negated_conjecture,
    app(app(sK57,sK55),sK58) = sK56,
    inference(cnf_transformation,[],[f558]) ).

cnf(c_252,negated_conjecture,
    ssList(sK58),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_253,negated_conjecture,
    ssList(sK57),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_257,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_12042,plain,
    ( ~ segmentP(sK55,X0)
    | ~ ssList(X0)
    | ~ ssList(sK55)
    | ~ ssList(sK58)
    | ~ ssList(sK57)
    | segmentP(sK56,X0) ),
    inference(superposition,[status(thm)],[c_251,c_193]) ).

cnf(c_12870,plain,
    ( ~ ssList(X0)
    | ~ segmentP(sK55,X0)
    | segmentP(sK56,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_12042,c_257,c_253,c_252,c_12042]) ).

cnf(c_12871,plain,
    ( ~ segmentP(sK55,X0)
    | ~ ssList(X0)
    | segmentP(sK56,X0) ),
    inference(renaming,[status(thm)],[c_12870]) ).

cnf(c_12879,plain,
    ( ~ ssList(sK55)
    | segmentP(sK56,sK55) ),
    inference(superposition,[status(thm)],[c_192,c_12871]) ).

cnf(c_12881,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_12879,c_246,c_250,c_257]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC339+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n013.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 23:20:49 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  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
% 0.49/1.17  % SZS status Started for theBenchmark.p
% 0.49/1.17  % SZS status Theorem for theBenchmark.p
% 0.49/1.17  
% 0.49/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.49/1.17  
% 0.49/1.17  ------  iProver source info
% 0.49/1.17  
% 0.49/1.17  git: date: 2024-05-02 19:28:25 +0000
% 0.49/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.49/1.17  git: non_committed_changes: false
% 0.49/1.17  
% 0.49/1.17  ------ Parsing...
% 0.49/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.49/1.17  
% 0.49/1.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 0.49/1.17  
% 0.49/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.49/1.17  
% 0.49/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.49/1.17  ------ Proving...
% 0.49/1.17  ------ Problem Properties 
% 0.49/1.17  
% 0.49/1.17  
% 0.49/1.17  clauses                                 190
% 0.49/1.17  conjectures                             10
% 0.49/1.17  EPR                                     56
% 0.49/1.17  Horn                                    122
% 0.49/1.17  unary                                   23
% 0.49/1.17  binary                                  41
% 0.49/1.17  lits                                    641
% 0.49/1.17  lits eq                                 85
% 0.49/1.17  fd_pure                                 0
% 0.49/1.17  fd_pseudo                               0
% 0.49/1.17  fd_cond                                 21
% 0.49/1.17  fd_pseudo_cond                          14
% 0.49/1.17  AC symbols                              0
% 0.49/1.17  
% 0.49/1.17  ------ Input Options Time Limit: Unbounded
% 0.49/1.17  
% 0.49/1.17  
% 0.49/1.17  ------ 
% 0.49/1.17  Current options:
% 0.49/1.17  ------ 
% 0.49/1.17  
% 0.49/1.17  
% 0.49/1.17  
% 0.49/1.17  
% 0.49/1.17  ------ Proving...
% 0.49/1.17  
% 0.49/1.17  
% 0.49/1.17  % SZS status Theorem for theBenchmark.p
% 0.49/1.17  
% 0.49/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.49/1.17  
% 0.49/1.18  
%------------------------------------------------------------------------------