TSTP Solution File: NUM730_8 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM730_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 : Tue May 21 01:15:51 EDT 2024

% Result   : Theorem 0.21s 0.52s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   75 (   9 unt;  14 typ;   0 def)
%            Number of atoms       :  938 (  36 equ)
%            Maximal formula atoms :  117 (  15 avg)
%            Number of connectives :  669 ( 242   ~; 346   |;  77   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   5 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of FOOLs       :  450 ( 450 fml;   0 var)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   13 (   8   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   5 usr;   4 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   27 (   0 sgn  27   !;   0   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    frac: $tType ).

tff(decl_sort2,type,
    nat: $tType ).

tff(decl_22,type,
    x: frac ).

tff(decl_23,type,
    y: frac ).

tff(decl_24,type,
    orec3: ( $o * $o * $o ) > $o ).

tff(decl_25,type,
    ts: ( nat * nat ) > nat ).

tff(decl_26,type,
    c1x: frac > nat ).

tff(decl_27,type,
    c2y: frac > nat ).

tff(decl_28,type,
    c1y: frac > nat ).

tff(decl_29,type,
    c2x: frac > nat ).

tff(decl_30,type,
    more: ( nat * nat ) > $o ).

tff(decl_31,type,
    less: ( nat * nat ) > $o ).

tff(decl_32,type,
    epred1_0: $o ).

tff(decl_33,type,
    epred2_0: $o ).

tff(satz41,conjecture,
    orec3(ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)),more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))),less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41) ).

tff(satz10,axiom,
    ! [X1: nat,X2: nat] : orec3(X1 = X2,more(X1,X2),less(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10) ).

tff(c_0_2,plain,
    ( epred1_0
  <=> ( ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
      | ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$true,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$true,$false) ) ) )
        & ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$false,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$false,$false) ) ) ) ) ) ),
    introduced(definition) ).

tff(c_0_3,plain,
    ( epred2_0
  <=> ( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
      | ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$true,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$true,$false) ) ) )
        & ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$false,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$false,$false) ) ) ) ) ) ),
    introduced(definition) ).

fof(c_0_4,negated_conjecture,
    ~ ( epred1_0
      & epred2_0 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[satz41])]),c_0_2]),c_0_3]) ).

tff(c_0_5,plain,
    ( ( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
      | ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$true,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$true,$false) ) ) )
        & ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$false,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($false,$false,$false) ) ) ) ) )
   => epred2_0 ),
    inference(split_equiv,[status(thm)],[c_0_3]) ).

fof(c_0_6,negated_conjecture,
    ( ~ epred1_0
    | ~ epred2_0 ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

tff(c_0_7,plain,
    ( ( ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
      | epred2_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$false,$true)
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | ~ orec3($false,$false,$true)
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | ~ orec3($false,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$false,$true)
      | ~ orec3($false,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | ~ orec3($false,$false,$true)
      | ~ orec3($false,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred2_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | ~ orec3($false,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$false)
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$false)
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$true,$false)
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($false,$false,$true)
      | ~ orec3($false,$true,$false)
      | ~ orec3($false,$true,$true)
      | epred2_0 )
    & ( ~ orec3($false,$false,$false)
      | ~ orec3($false,$false,$true)
      | ~ orec3($false,$true,$false)
      | ~ orec3($false,$true,$true)
      | epred2_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

tff(c_0_8,plain,
    ( ( ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
      | ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$true,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$true,$false) ) ) )
        & ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
          | ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$false,$true) )
            & ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
              | orec3($true,$false,$false) ) ) ) ) )
   => epred1_0 ),
    inference(split_equiv,[status(thm)],[c_0_2]) ).

tff(c_0_9,axiom,
    ! [X1: nat,X2: nat] :
      ( ( ( X1 != X2 )
        | ( ( ~ more(X1,X2)
            | ( ( ~ less(X1,X2)
                | orec3($true,$true,$true) )
              & ( less(X1,X2)
                | orec3($true,$true,$false) ) ) )
          & ( more(X1,X2)
            | ( ( ~ less(X1,X2)
                | orec3($true,$false,$true) )
              & ( less(X1,X2)
                | orec3($true,$false,$false) ) ) ) ) )
      & ( ( X1 = X2 )
        | ( ( ~ more(X1,X2)
            | ( ( ~ less(X1,X2)
                | orec3($false,$true,$true) )
              & ( less(X1,X2)
                | orec3($false,$true,$false) ) ) )
          & ( more(X1,X2)
            | ( ( ~ less(X1,X2)
                | orec3($false,$false,$true) )
              & ( less(X1,X2)
                | orec3($false,$false,$false) ) ) ) ) ) ),
    inference(fool_unroll,[status(thm)],[satz10]) ).

cnf(c_0_10,negated_conjecture,
    ( ~ epred1_0
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

tcf(c_0_11,plain,
    ( epred2_0
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($false,$true,$true) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tff(c_0_12,plain,
    ( ( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
      | epred1_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$false,$true)
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | ~ orec3($true,$false,$true)
      | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | ~ orec3($true,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$false,$true)
      | ~ orec3($true,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | ~ orec3($true,$false,$true)
      | ~ orec3($true,$true,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | epred1_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | ~ orec3($true,$false,$true)
      | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$false)
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$false)
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$true,$false)
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
      | ~ orec3($true,$false,$true)
      | ~ orec3($true,$true,$false)
      | ~ orec3($true,$true,$true)
      | epred1_0 )
    & ( ~ orec3($true,$false,$false)
      | ~ orec3($true,$false,$true)
      | ~ orec3($true,$true,$false)
      | ~ orec3($true,$true,$true)
      | epred1_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

tff(c_0_13,plain,
    ! [X3: nat,X4: nat] :
      ( ( ~ less(X3,X4)
        | orec3($true,$true,$true)
        | ~ more(X3,X4)
        | ( X3 != X4 ) )
      & ( less(X3,X4)
        | orec3($true,$true,$false)
        | ~ more(X3,X4)
        | ( X3 != X4 ) )
      & ( ~ less(X3,X4)
        | orec3($true,$false,$true)
        | more(X3,X4)
        | ( X3 != X4 ) )
      & ( less(X3,X4)
        | orec3($true,$false,$false)
        | more(X3,X4)
        | ( X3 != X4 ) )
      & ( ~ less(X3,X4)
        | orec3($false,$true,$true)
        | ~ more(X3,X4)
        | ( X3 = X4 ) )
      & ( less(X3,X4)
        | orec3($false,$true,$false)
        | ~ more(X3,X4)
        | ( X3 = X4 ) )
      & ( ~ less(X3,X4)
        | orec3($false,$false,$true)
        | more(X3,X4)
        | ( X3 = X4 ) )
      & ( less(X3,X4)
        | orec3($false,$false,$false)
        | more(X3,X4)
        | ( X3 = X4 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).

tcf(c_0_14,plain,
    ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | epred2_0
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($false,$true,$false) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_15,negated_conjecture,
    ( ~ epred1_0
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($false,$true,$true) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

tcf(c_0_16,plain,
    ( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

tcf(c_0_17,plain,
    ! [X1: nat,X2: nat] :
      ( orec3($false,$true,$true)
      | ( X1 = X2 )
      | ~ less(X1,X2)
      | ~ more(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_18,plain,
    ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | epred2_0
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($false,$false,$true) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_19,negated_conjecture,
    ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ epred1_0
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($false,$true,$false) ),
    inference(spm,[status(thm)],[c_0_10,c_0_14]) ).

tcf(c_0_20,plain,
    ! [X1: nat,X2: nat] :
      ( less(X1,X2)
      | orec3($false,$true,$false)
      | ( X1 = X2 )
      | ~ more(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_21,plain,
    ( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

tcf(c_0_22,plain,
    ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | epred2_0
    | ~ orec3($false,$false,$false) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_23,negated_conjecture,
    ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ epred1_0
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($false,$false,$true) ),
    inference(spm,[status(thm)],[c_0_10,c_0_18]) ).

tcf(c_0_24,plain,
    ! [X1: nat,X2: nat] :
      ( orec3($false,$false,$true)
      | more(X1,X2)
      | ( X1 = X2 )
      | ~ less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_25,plain,
    ( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_20]),c_0_21]) ).

tcf(c_0_26,plain,
    ( epred2_0
    | ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

tcf(c_0_27,negated_conjecture,
    ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ epred1_0
    | ~ orec3($false,$false,$false) ),
    inference(spm,[status(thm)],[c_0_10,c_0_22]) ).

tcf(c_0_28,plain,
    ! [X1: nat,X2: nat] :
      ( less(X1,X2)
      | orec3($false,$false,$false)
      | more(X1,X2)
      | ( X1 = X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_29,plain,
    ( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_24]),c_0_25]) ).

tcf(c_0_30,negated_conjecture,
    ( ( ts(c1y(y),c2x(x)) != ts(c1x(x),c2y(y)) )
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_10,c_0_26]) ).

tcf(c_0_31,plain,
    ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_28]),c_0_25]),c_0_29]) ).

tcf(c_0_32,plain,
    ! [X1: nat,X2: nat] :
      ( orec3($true,$true,$true)
      | ~ less(X1,X2)
      | ~ more(X1,X2)
      | ( X1 != X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_33,plain,
    ( epred1_0
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($true,$true,$true) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_34,negated_conjecture,
    ~ epred1_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).

tcf(c_0_35,plain,
    ! [X1: nat] :
      ( orec3($true,$true,$true)
      | ~ less(X1,X1)
      | ~ more(X1,X1) ),
    inference(er,[status(thm)],[c_0_32]) ).

tcf(c_0_36,plain,
    ! [X1: nat,X2: nat] :
      ( orec3($true,$false,$true)
      | more(X1,X2)
      | ~ less(X1,X2)
      | ( X1 != X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_37,plain,
    ! [X1: nat,X2: nat] :
      ( less(X1,X2)
      | orec3($true,$true,$false)
      | ~ more(X1,X2)
      | ( X1 != X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_38,plain,
    ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | epred1_0
    | ~ orec3($true,$false,$false)
    | ~ orec3($true,$false,$true) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

tcf(c_0_39,plain,
    ( ~ less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
    | ~ more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_31]),c_0_31]),c_0_34]),c_0_35]) ).

tcf(c_0_40,plain,
    ! [X1: nat] :
      ( more(X1,X1)
      | orec3($true,$false,$true)
      | ~ less(X1,X1) ),
    inference(er,[status(thm)],[c_0_36]) ).

tcf(c_0_41,plain,
    ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | epred1_0
    | ~ orec3($true,$false,$false) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

tcf(c_0_42,plain,
    ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | epred1_0
    | ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($true,$true,$false) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

tcf(c_0_43,plain,
    ! [X1: nat] :
      ( less(X1,X1)
      | orec3($true,$true,$false)
      | ~ more(X1,X1) ),
    inference(er,[status(thm)],[c_0_37]) ).

tcf(c_0_44,plain,
    ( more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
    | ~ orec3($true,$false,$true)
    | ~ orec3($true,$false,$false) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_31]),c_0_34]) ).

tcf(c_0_45,plain,
    ( orec3($true,$false,$true)
    | ~ less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

tcf(c_0_46,plain,
    ! [X1: nat,X2: nat] :
      ( less(X1,X2)
      | orec3($true,$false,$false)
      | more(X1,X2)
      | ( X1 != X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

tcf(c_0_47,negated_conjecture,
    ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ( ts(c1y(y),c2x(x)) != ts(c1x(x),c2y(y)) )
    | ~ orec3($true,$false,$false) ),
    inference(spm,[status(thm)],[c_0_30,c_0_41]) ).

tcf(c_0_48,plain,
    ~ more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_31]),c_0_31]),c_0_34]),c_0_43]),c_0_39]) ).

tcf(c_0_49,plain,
    ( ~ less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
    | ~ orec3($true,$false,$false) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_44]),c_0_45]) ).

tcf(c_0_50,plain,
    ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | epred1_0
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($true,$false,$true) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

tcf(c_0_51,plain,
    ! [X1: nat] :
      ( less(X1,X1)
      | more(X1,X1)
      | orec3($true,$false,$false) ),
    inference(er,[status(thm)],[c_0_46]) ).

cnf(c_0_52,negated_conjecture,
    ~ orec3($true,$false,$false),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_31]),c_0_31]),c_0_31])]),c_0_48]),c_0_49]) ).

tcf(c_0_53,plain,
    ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($false,$false,$true)
    | ~ orec3($true,$false,$true) ),
    inference(spm,[status(thm)],[c_0_23,c_0_50]) ).

tcf(c_0_54,plain,
    ( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
    | orec3($false,$false,$true)
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
    inference(spm,[status(thm)],[c_0_21,c_0_24]) ).

tcf(c_0_55,plain,
    ! [X1: nat] :
      ( less(X1,X1)
      | more(X1,X1) ),
    inference(sr,[status(thm)],[c_0_51,c_0_52]) ).

tcf(c_0_56,plain,
    ( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($true,$false,$true) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_53]),c_0_54]) ).

tcf(c_0_57,plain,
    less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))),
    inference(spm,[status(thm)],[c_0_48,c_0_55]) ).

tcf(c_0_58,negated_conjecture,
    ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
    | ~ orec3($true,$false,$true) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_50]),c_0_56]) ).

cnf(c_0_59,plain,
    orec3($true,$false,$true),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_57])]) ).

cnf(c_0_60,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_31]),c_0_31]),c_0_57]),c_0_59])]),c_0_48]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM730_8 : TPTP v8.2.0. Released v8.0.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n021.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   : Mon May 20 04:52:23 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.52  # Version: 3.1.0
% 0.21/0.52  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.52  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.52  # Starting sh5l with 300s (1) cores
% 0.21/0.52  # new_bool_3 with pid 19593 completed with status 0
% 0.21/0.52  # Result found by new_bool_3
% 0.21/0.52  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.52  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52  # Search class: FGHSF-FFMF21-SFFFFFNN
% 0.21/0.52  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52  # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 181s (1) cores
% 0.21/0.52  # 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 19601 completed with status 0
% 0.21/0.52  # Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 0.21/0.52  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.52  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52  # Search class: FGHSF-FFMF21-SFFFFFNN
% 0.21/0.52  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52  # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 181s (1) cores
% 0.21/0.52  # Preprocessing time       : 0.002 s
% 0.21/0.52  # Presaturation interreduction done
% 0.21/0.52  
% 0.21/0.52  # Proof found!
% 0.21/0.52  # SZS status Theorem
% 0.21/0.52  # SZS output start CNFRefutation
% See solution above
% 0.21/0.52  # Parsed axioms                        : 14
% 0.21/0.52  # Removed by relevancy pruning/SinE    : 12
% 0.21/0.52  # Initial clauses                      : 61
% 0.21/0.52  # Removed in clause preprocessing      : 24
% 0.21/0.52  # Initial clauses in saturation        : 37
% 0.21/0.52  # Processed clauses                    : 358
% 0.21/0.52  # ...of these trivial                  : 5
% 0.21/0.52  # ...subsumed                          : 162
% 0.21/0.52  # ...remaining for further processing  : 190
% 0.21/0.52  # Other redundant clauses eliminated   : 4
% 0.21/0.52  # Clauses deleted for lack of memory   : 0
% 0.21/0.52  # Backward-subsumed                    : 78
% 0.21/0.52  # Backward-rewritten                   : 56
% 0.21/0.52  # Generated clauses                    : 432
% 0.21/0.52  # ...of the previous two non-redundant : 324
% 0.21/0.52  # ...aggressively subsumed             : 0
% 0.21/0.52  # Contextual simplify-reflections      : 30
% 0.21/0.52  # Paramodulations                      : 425
% 0.21/0.52  # Factorizations                       : 0
% 0.21/0.52  # NegExts                              : 0
% 0.21/0.52  # Equation resolutions                 : 4
% 0.21/0.52  # Disequality decompositions           : 0
% 0.21/0.52  # Total rewrite steps                  : 95
% 0.21/0.52  # ...of those cached                   : 91
% 0.21/0.52  # Propositional unsat checks           : 0
% 0.21/0.52  #    Propositional check models        : 0
% 0.21/0.52  #    Propositional check unsatisfiable : 0
% 0.21/0.52  #    Propositional clauses             : 0
% 0.21/0.52  #    Propositional clauses after purity: 0
% 0.21/0.52  #    Propositional unsat core size     : 0
% 0.21/0.52  #    Propositional preprocessing time  : 0.000
% 0.21/0.52  #    Propositional encoding time       : 0.000
% 0.21/0.52  #    Propositional solver time         : 0.000
% 0.21/0.52  #    Success case prop preproc time    : 0.000
% 0.21/0.52  #    Success case prop encoding time   : 0.000
% 0.21/0.52  #    Success case prop solver time     : 0.000
% 0.21/0.52  # Current number of processed clauses  : 20
% 0.21/0.52  #    Positive orientable unit clauses  : 4
% 0.21/0.52  #    Positive unorientable unit clauses: 0
% 0.21/0.52  #    Negative unit clauses             : 4
% 0.21/0.52  #    Non-unit-clauses                  : 12
% 0.21/0.52  # Current number of unprocessed clauses: 13
% 0.21/0.52  # ...number of literals in the above   : 55
% 0.21/0.52  # Current number of archived formulas  : 0
% 0.21/0.52  # Current number of archived clauses   : 166
% 0.21/0.52  # Clause-clause subsumption calls (NU) : 4270
% 0.21/0.52  # Rec. Clause-clause subsumption calls : 1234
% 0.21/0.52  # Non-unit clause-clause subsumptions  : 249
% 0.21/0.52  # Unit Clause-clause subsumption calls : 54
% 0.21/0.52  # Rewrite failures with RHS unbound    : 0
% 0.21/0.52  # BW rewrite match attempts            : 5
% 0.21/0.52  # BW rewrite match successes           : 4
% 0.21/0.52  # Condensation attempts                : 0
% 0.21/0.52  # Condensation successes               : 0
% 0.21/0.52  # Termbank termtop insertions          : 14306
% 0.21/0.52  # Search garbage collected termcells   : 428
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.027 s
% 0.21/0.52  # System time              : 0.002 s
% 0.21/0.52  # Total time               : 0.028 s
% 0.21/0.52  # Maximum resident set size: 1760 pages
% 0.21/0.52  
% 0.21/0.52  # -------------------------------------------------
% 0.21/0.52  # User time                : 0.029 s
% 0.21/0.52  # System time              : 0.003 s
% 0.21/0.52  # Total time               : 0.032 s
% 0.21/0.52  # Maximum resident set size: 1712 pages
% 0.21/0.52  % E---3.1 exiting
% 0.21/0.53  % E exiting
%------------------------------------------------------------------------------