TSTP Solution File: SWC340+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC340+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n019.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 20:42:39 EDT 2023

% Result   : Theorem 10.31s 2.18s
% Output   : CNFRefutation 10.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   81 (  13 unt;   0 def)
%            Number of atoms       :  539 (  77 equ)
%            Maximal formula atoms :   20 (   6 avg)
%            Number of connectives :  684 ( 226   ~; 206   |; 206   &)
%                                         (   8 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   4 con; 0-2 aty)
%            Number of variables   :  226 (   0 sgn; 118   !;  94   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( totalorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => leq(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).

fof(f12,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => lt(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).

fof(f93,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( totalorderedP(X0)
                      & segmentP(X1,X0) )
                    | ~ strictorderedP(X2)
                    | ~ segmentP(X3,X2)
                    | 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) )
                      | ~ strictorderedP(X2)
                      | ~ segmentP(X3,X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f110,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f111,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f110]) ).

fof(f112,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f113,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f112]) ).

fof(f216,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ totalorderedP(X0)
                    | ~ segmentP(X1,X0) )
                  & strictorderedP(X2)
                  & segmentP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ totalorderedP(X0)
                    | ~ segmentP(X1,X0) )
                  & strictorderedP(X2)
                  & segmentP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f285,plain,
    ! [X0] :
      ( ( ( totalorderedP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ~ leq(X1,X2)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X1] :
              ( ! [X2] :
                  ( ! [X3] :
                      ( ! [X4] :
                          ( ! [X5] :
                              ( leq(X1,X2)
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | ~ ssList(X5) )
                          | ~ ssList(X4) )
                      | ~ ssList(X3) )
                  | ~ ssItem(X2) )
              | ~ ssItem(X1) )
          | ~ totalorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f111]) ).

fof(f286,plain,
    ! [X0] :
      ( ( ( totalorderedP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ~ leq(X1,X2)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( leq(X6,X7)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ totalorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f285]) ).

fof(f287,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ leq(sK30(X0),X2)
                        & app(app(X3,cons(sK30(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK30(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f288,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ leq(sK30(X0),X2)
                      & app(app(X3,cons(sK30(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ leq(sK30(X0),sK31(X0))
                    & app(app(X3,cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK31(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f289,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ leq(sK30(X0),sK31(X0))
                  & app(app(X3,cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ leq(sK30(X0),sK31(X0))
                & app(app(sK32(X0),cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK32(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f290,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ leq(sK30(X0),sK31(X0))
              & app(app(sK32(X0),cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ leq(sK30(X0),sK31(X0))
            & app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK33(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f291,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ leq(sK30(X0),sK31(X0))
          & app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ leq(sK30(X0),sK31(X0))
        & app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),sK34(X0))) = X0
        & ssList(sK34(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f292,plain,
    ! [X0] :
      ( ( ( totalorderedP(X0)
          | ( ~ leq(sK30(X0),sK31(X0))
            & app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),sK34(X0))) = X0
            & ssList(sK34(X0))
            & ssList(sK33(X0))
            & ssList(sK32(X0))
            & ssItem(sK31(X0))
            & ssItem(sK30(X0)) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( leq(X6,X7)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ totalorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33,sK34])],[f286,f291,f290,f289,f288,f287]) ).

fof(f293,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ~ lt(X1,X2)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X1] :
              ( ! [X2] :
                  ( ! [X3] :
                      ( ! [X4] :
                          ( ! [X5] :
                              ( lt(X1,X2)
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | ~ ssList(X5) )
                          | ~ ssList(X4) )
                      | ~ ssList(X3) )
                  | ~ ssItem(X2) )
              | ~ ssItem(X1) )
          | ~ strictorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f113]) ).

fof(f294,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( ? [X3] :
                      ( ? [X4] :
                          ( ? [X5] :
                              ( ~ lt(X1,X2)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ssList(X5) )
                          & ssList(X4) )
                      & ssList(X3) )
                  & ssItem(X2) )
              & ssItem(X1) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( lt(X6,X7)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ strictorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f293]) ).

fof(f295,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ lt(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ lt(sK35(X0),X2)
                        & app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK35(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f296,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(sK35(X0),X2)
                      & app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK35(X0),sK36(X0))
                    & app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK36(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f297,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK35(X0),sK36(X0))
                  & app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK35(X0),sK36(X0))
                & app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK37(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f298,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK35(X0),sK36(X0))
              & app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK35(X0),sK36(X0))
            & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK38(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f299,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK35(X0),sK36(X0))
          & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK35(X0),sK36(X0))
        & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
        & ssList(sK39(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f300,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ( ~ lt(sK35(X0),sK36(X0))
            & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
            & ssList(sK39(X0))
            & ssList(sK38(X0))
            & ssList(sK37(X0))
            & ssItem(sK36(X0))
            & ssItem(sK35(X0)) ) )
        & ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ! [X10] :
                              ( lt(X6,X7)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | ~ ssList(X10) )
                          | ~ ssList(X9) )
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | ~ ssItem(X6) )
          | ~ strictorderedP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37,sK38,sK39])],[f294,f299,f298,f297,f296,f295]) ).

fof(f341,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f216]) ).

fof(f342,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f341]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ totalorderedP(X0)
                      | ~ segmentP(X1,X0) )
                    & strictorderedP(X2)
                    & segmentP(X3,X2)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ totalorderedP(sK53)
                    | ~ segmentP(X1,sK53) )
                  & strictorderedP(X2)
                  & segmentP(X3,X2)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ totalorderedP(sK53)
                  | ~ segmentP(X1,sK53) )
                & strictorderedP(X2)
                & segmentP(X3,X2)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ totalorderedP(sK53)
                | ~ segmentP(sK54,sK53) )
              & strictorderedP(X2)
              & segmentP(X3,X2)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ totalorderedP(sK53)
              | ~ segmentP(sK54,sK53) )
            & strictorderedP(X2)
            & segmentP(X3,X2)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ totalorderedP(sK53)
            | ~ segmentP(sK54,sK53) )
          & strictorderedP(sK55)
          & segmentP(X3,sK55)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ~ totalorderedP(sK53)
          | ~ segmentP(sK54,sK53) )
        & strictorderedP(sK55)
        & segmentP(X3,sK55)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ~ totalorderedP(sK53)
        | ~ segmentP(sK54,sK53) )
      & strictorderedP(sK55)
      & segmentP(sK56,sK55)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ( ~ totalorderedP(sK53)
      | ~ segmentP(sK54,sK53) )
    & strictorderedP(sK55)
    & segmentP(sK56,sK55)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f222,f346,f345,f344,f343]) ).

fof(f407,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | ssItem(sK30(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f408,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | ssItem(sK31(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f409,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | ssList(sK32(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f410,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | ssList(sK33(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f411,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | ssList(sK34(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f412,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),sK34(X0))) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f413,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | ~ leq(sK30(X0),sK31(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f292]) ).

fof(f414,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f300]) ).

fof(f543,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f342]) ).

fof(f547,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f551,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f347]) ).

fof(f552,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f347]) ).

fof(f553,plain,
    segmentP(sK56,sK55),
    inference(cnf_transformation,[],[f347]) ).

fof(f554,plain,
    strictorderedP(sK55),
    inference(cnf_transformation,[],[f347]) ).

fof(f555,plain,
    ( ~ totalorderedP(sK53)
    | ~ segmentP(sK54,sK53) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f556,plain,
    ( ~ totalorderedP(sK55)
    | ~ segmentP(sK56,sK55) ),
    inference(definition_unfolding,[],[f555,f552,f551,f552]) ).

fof(f558,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f547,f552]) ).

fof(f569,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ strictorderedP(app(app(X8,cons(X6,X9)),cons(X7,X10)))
      | ~ ssList(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f414]) ).

cnf(c_107,plain,
    ( ~ leq(sK30(X0),sK31(X0))
    | ~ ssList(X0)
    | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f413]) ).

cnf(c_108,plain,
    ( ~ ssList(X0)
    | app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),sK34(X0))) = X0
    | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f412]) ).

cnf(c_109,plain,
    ( ~ ssList(X0)
    | ssList(sK34(X0))
    | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f411]) ).

cnf(c_110,plain,
    ( ~ ssList(X0)
    | ssList(sK33(X0))
    | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f410]) ).

cnf(c_111,plain,
    ( ~ ssList(X0)
    | ssList(sK32(X0))
    | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f409]) ).

cnf(c_112,plain,
    ( ~ ssList(X0)
    | ssItem(sK31(X0))
    | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f408]) ).

cnf(c_113,plain,
    ( ~ ssList(X0)
    | ssItem(sK30(X0))
    | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f407]) ).

cnf(c_122,plain,
    ( ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
    | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
    | ~ ssItem(X1)
    | ~ ssItem(X3)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ~ ssList(X4)
    | lt(X1,X3) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_242,plain,
    ( ~ lt(X0,X1)
    | ~ ssItem(X0)
    | ~ ssItem(X1)
    | leq(X0,X1) ),
    inference(cnf_transformation,[],[f543]) ).

cnf(c_246,negated_conjecture,
    ( ~ segmentP(sK56,sK55)
    | ~ totalorderedP(sK55) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_247,negated_conjecture,
    strictorderedP(sK55),
    inference(cnf_transformation,[],[f554]) ).

cnf(c_248,negated_conjecture,
    segmentP(sK56,sK55),
    inference(cnf_transformation,[],[f553]) ).

cnf(c_252,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_365,negated_conjecture,
    ~ totalorderedP(sK55),
    inference(global_subsumption_just,[status(thm)],[c_246,c_248,c_246]) ).

cnf(c_13025,plain,
    ( ~ ssList(sK55)
    | ssList(sK34(sK55))
    | totalorderedP(sK55) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_13026,plain,
    ( ~ ssList(sK55)
    | ssList(sK33(sK55))
    | totalorderedP(sK55) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_13027,plain,
    ( ~ ssList(sK55)
    | ssList(sK32(sK55))
    | totalorderedP(sK55) ),
    inference(instantiation,[status(thm)],[c_111]) ).

cnf(c_13028,plain,
    ( ~ ssList(sK55)
    | ssItem(sK31(sK55))
    | totalorderedP(sK55) ),
    inference(instantiation,[status(thm)],[c_112]) ).

cnf(c_13029,plain,
    ( ~ ssList(sK55)
    | ssItem(sK30(sK55))
    | totalorderedP(sK55) ),
    inference(instantiation,[status(thm)],[c_113]) ).

cnf(c_13036,plain,
    ( ~ leq(sK30(sK55),sK31(sK55))
    | ~ ssList(sK55)
    | totalorderedP(sK55) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_21206,plain,
    ( app(app(sK32(sK55),cons(sK30(sK55),sK33(sK55))),cons(sK31(sK55),sK34(sK55))) = sK55
    | totalorderedP(sK55) ),
    inference(superposition,[status(thm)],[c_252,c_108]) ).

cnf(c_21209,plain,
    app(app(sK32(sK55),cons(sK30(sK55),sK33(sK55))),cons(sK31(sK55),sK34(sK55))) = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_21206,c_365]) ).

cnf(c_29604,plain,
    ( ~ strictorderedP(app(app(sK32(sK55),cons(sK30(sK55),sK33(sK55))),cons(sK31(sK55),sK34(sK55))))
    | ~ ssItem(sK30(sK55))
    | ~ ssItem(sK31(sK55))
    | ~ ssList(sK32(sK55))
    | ~ ssList(sK33(sK55))
    | ~ ssList(sK34(sK55))
    | ~ ssList(sK55)
    | lt(sK30(sK55),sK31(sK55)) ),
    inference(superposition,[status(thm)],[c_21209,c_122]) ).

cnf(c_29631,plain,
    ( ~ ssItem(sK30(sK55))
    | ~ ssItem(sK31(sK55))
    | ~ ssList(sK32(sK55))
    | ~ ssList(sK33(sK55))
    | ~ ssList(sK34(sK55))
    | ~ ssList(sK55)
    | ~ strictorderedP(sK55)
    | lt(sK30(sK55),sK31(sK55)) ),
    inference(light_normalisation,[status(thm)],[c_29604,c_21209]) ).

cnf(c_29632,plain,
    ( ~ ssItem(sK30(sK55))
    | ~ ssItem(sK31(sK55))
    | ~ ssList(sK32(sK55))
    | ~ ssList(sK33(sK55))
    | ~ ssList(sK34(sK55))
    | lt(sK30(sK55),sK31(sK55)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29631,c_247,c_252]) ).

cnf(c_51812,plain,
    lt(sK30(sK55),sK31(sK55)),
    inference(global_subsumption_just,[status(thm)],[c_29632,c_252,c_248,c_246,c_13025,c_13026,c_13027,c_13028,c_13029,c_29632]) ).

cnf(c_51816,plain,
    ( ~ ssItem(sK30(sK55))
    | ~ ssItem(sK31(sK55))
    | leq(sK30(sK55),sK31(sK55)) ),
    inference(superposition,[status(thm)],[c_51812,c_242]) ).

cnf(c_51832,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_51816,c_13036,c_13029,c_13028,c_246,c_248,c_252]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC340+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon Aug 28 17:32:58 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.31/2.18  % SZS status Started for theBenchmark.p
% 10.31/2.18  % SZS status Theorem for theBenchmark.p
% 10.31/2.18  
% 10.31/2.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.31/2.18  
% 10.31/2.18  ------  iProver source info
% 10.31/2.18  
% 10.31/2.18  git: date: 2023-05-31 18:12:56 +0000
% 10.31/2.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.31/2.18  git: non_committed_changes: false
% 10.31/2.18  git: last_make_outside_of_git: false
% 10.31/2.18  
% 10.31/2.18  ------ Parsing...
% 10.31/2.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.31/2.18  
% 10.31/2.18  ------ 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 
% 10.31/2.18  
% 10.31/2.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.31/2.18  
% 10.31/2.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.31/2.18  ------ Proving...
% 10.31/2.18  ------ Problem Properties 
% 10.31/2.18  
% 10.31/2.18  
% 10.31/2.18  clauses                                 185
% 10.31/2.18  conjectures                             5
% 10.31/2.18  EPR                                     54
% 10.31/2.18  Horn                                    117
% 10.31/2.18  unary                                   21
% 10.31/2.18  binary                                  40
% 10.31/2.18  lits                                    623
% 10.31/2.18  lits eq                                 78
% 10.31/2.18  fd_pure                                 0
% 10.31/2.18  fd_pseudo                               0
% 10.31/2.18  fd_cond                                 21
% 10.31/2.18  fd_pseudo_cond                          14
% 10.31/2.18  AC symbols                              0
% 10.31/2.18  
% 10.31/2.18  ------ Schedule dynamic 5 is on 
% 10.31/2.18  
% 10.31/2.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.31/2.18  
% 10.31/2.18  
% 10.31/2.18  ------ 
% 10.31/2.18  Current options:
% 10.31/2.18  ------ 
% 10.31/2.18  
% 10.31/2.18  
% 10.31/2.18  
% 10.31/2.18  
% 10.31/2.18  ------ Proving...
% 10.31/2.18  
% 10.31/2.18  
% 10.31/2.18  % SZS status Theorem for theBenchmark.p
% 10.31/2.18  
% 10.31/2.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.31/2.18  
% 10.31/2.19  
%------------------------------------------------------------------------------