TSTP Solution File: SYO040_8 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SYO040_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 08:50:49 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   73 (   8 unt;   9 typ;   0 def)
%            Number of atoms       : 1005 (  29 equ)
%            Maximal formula atoms :  118 (  15 avg)
%            Number of connectives : 1348 ( 407   ~; 726   |; 203   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   8 usr;   9 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 1-1 aty)
%            Number of variables   :    0 (   0 sgn   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    f: $o > $o ).

tff(decl_23,type,
    h: $o > $i ).

tff(decl_24,type,
    x: $o ).

tff(decl_25,type,
    epred1_0: $o ).

tff(decl_26,type,
    epred2_0: $o ).

tff(decl_27,type,
    epred3_0: $o ).

tff(decl_28,type,
    epred4_0: $o ).

tff(decl_29,type,
    epred5_0: $o ).

tff(decl_30,type,
    epred6_0: $o ).

fof(2,conjecture,
    h(f(f(f(x)))) = h(f(x)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',2) ).

fof(c_0_1,plain,
    ( epred3_0
  <=> ( ( ( ( ( ( ( ~ x
                  | ~ f($true) )
                & ( x
                  | ~ f($false) ) )
              | ~ f($true) )
            & ( ( ( ~ x
                  | f($true) )
                & ( x
                  | f($false) ) )
              | ~ f($false) ) )
          | ~ f($true) )
        & ( ( ( ( ( ~ x
                  | ~ f($true) )
                & ( x
                  | ~ f($false) ) )
              | f($true) )
            & ( ( ( ~ x
                  | f($true) )
                & ( x
                  | f($false) ) )
              | f($false) ) )
          | ~ f($false) ) )
      | ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | h($true) = h($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | h($true) = h($false) ) ) ) ),
    introduced(definition) ).

fof(c_0_2,plain,
    ( epred1_0
  <=> ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | ~ f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | ~ f($false) ) )
      | ~ f($true) ) ),
    introduced(definition) ).

fof(c_0_3,plain,
    ( epred2_0
  <=> ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | f($false) ) )
      | ~ f($false) ) ),
    introduced(definition) ).

fof(c_0_4,plain,
    ( ( ( epred1_0
        & epred2_0 )
      | ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | h($true) = h($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | h($true) = h($false) ) ) )
   => epred3_0 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_1]),c_0_2]),c_0_3]) ).

fof(c_0_5,plain,
    ( ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | f($false) ) )
      | ~ f($false) )
   => epred2_0 ),
    inference(split_equiv,[status(thm)],[c_0_3]) ).

fof(c_0_6,plain,
    ( ( ~ epred1_0
      | ~ epred2_0
      | epred3_0 )
    & ( ~ x
      | x
      | ~ x
      | x
      | epred3_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | x
      | epred3_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | x
      | epred3_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | x
      | epred3_0 )
    & ( h($true) != h($false)
      | ~ x
      | x
      | epred3_0 )
    & ( ~ x
      | x
      | f($false)
      | x
      | epred3_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | x
      | epred3_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | x
      | epred3_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | x
      | epred3_0 )
    & ( h($true) != h($false)
      | f($false)
      | x
      | epred3_0 )
    & ( ~ x
      | x
      | ~ x
      | f($true)
      | epred3_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | f($true)
      | epred3_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | f($true)
      | epred3_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | f($true)
      | epred3_0 )
    & ( h($true) != h($false)
      | ~ x
      | f($true)
      | epred3_0 )
    & ( ~ x
      | x
      | f($false)
      | f($true)
      | epred3_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | f($true)
      | epred3_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | f($true)
      | epred3_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | f($true)
      | epred3_0 )
    & ( h($true) != h($false)
      | f($false)
      | f($true)
      | epred3_0 )
    & ( ~ x
      | x
      | h($true) != h($true)
      | epred3_0 )
    & ( ~ f($false)
      | x
      | h($true) != h($true)
      | epred3_0 )
    & ( ~ x
      | ~ f($true)
      | h($true) != h($true)
      | epred3_0 )
    & ( ~ f($false)
      | ~ f($true)
      | h($true) != h($true)
      | epred3_0 )
    & ( h($true) != h($false)
      | h($true) != h($true)
      | epred3_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_7,plain,
    ( ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | ~ f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | ~ f($false) ) )
      | ~ f($true) )
   => epred1_0 ),
    inference(split_equiv,[status(thm)],[c_0_2]) ).

fof(c_0_8,plain,
    ( ( ~ x
      | x
      | ~ x
      | x
      | epred2_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | x
      | epred2_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | x
      | epred2_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | x
      | epred2_0 )
    & ( ~ f($false)
      | ~ x
      | x
      | epred2_0 )
    & ( ~ x
      | x
      | f($false)
      | x
      | epred2_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | x
      | epred2_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | x
      | epred2_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | x
      | epred2_0 )
    & ( ~ f($false)
      | f($false)
      | x
      | epred2_0 )
    & ( ~ x
      | x
      | ~ x
      | f($true)
      | epred2_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | f($true)
      | epred2_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | f($true)
      | epred2_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | f($true)
      | epred2_0 )
    & ( ~ f($false)
      | ~ x
      | f($true)
      | epred2_0 )
    & ( ~ x
      | x
      | f($false)
      | f($true)
      | epred2_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | f($true)
      | epred2_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | f($true)
      | epred2_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | f($true)
      | epred2_0 )
    & ( ~ f($false)
      | f($false)
      | f($true)
      | epred2_0 )
    & ( ~ x
      | x
      | ~ f($true)
      | epred2_0 )
    & ( ~ f($false)
      | x
      | ~ f($true)
      | epred2_0 )
    & ( ~ x
      | ~ f($true)
      | ~ f($true)
      | epred2_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ f($true)
      | epred2_0 )
    & ( ~ f($false)
      | ~ f($true)
      | epred2_0 )
    & ( f($false)
      | epred2_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_9,plain,
    ( epred4_0
  <=> ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | ~ f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | ~ f($false) ) )
      | f($true) ) ),
    introduced(definition) ).

fof(c_0_10,plain,
    ( epred5_0
  <=> ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | f($false) ) )
      | f($false) ) ),
    introduced(definition) ).

fof(c_0_11,plain,
    ( epred6_0
  <=> ( ( ( ( ( ( ( ~ x
                  | ~ f($true) )
                & ( x
                  | ~ f($false) ) )
              | ~ f($true) )
            & ( ( ( ~ x
                  | f($true) )
                & ( x
                  | f($false) ) )
              | ~ f($false) ) )
          | f($true) )
        & ( ( ( ( ( ~ x
                  | ~ f($true) )
                & ( x
                  | ~ f($false) ) )
              | f($true) )
            & ( ( ( ~ x
                  | f($true) )
                & ( x
                  | f($false) ) )
              | f($false) ) )
          | f($false) ) )
      | ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | h($false) = h($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | h($false) = h($false) ) ) ) ),
    introduced(definition) ).

cnf(c_0_12,plain,
    ( epred3_0
    | ~ x
    | ~ f($true)
    | $false ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_13,plain,
    ( ( ~ x
      | x
      | ~ x
      | x
      | epred1_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | x
      | epred1_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | x
      | epred1_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | x
      | epred1_0 )
    & ( f($false)
      | ~ x
      | x
      | epred1_0 )
    & ( ~ x
      | x
      | f($false)
      | x
      | epred1_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | x
      | epred1_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | x
      | epred1_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | x
      | epred1_0 )
    & ( f($false)
      | f($false)
      | x
      | epred1_0 )
    & ( ~ x
      | x
      | ~ x
      | f($true)
      | epred1_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | f($true)
      | epred1_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | f($true)
      | epred1_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | f($true)
      | epred1_0 )
    & ( f($false)
      | ~ x
      | f($true)
      | epred1_0 )
    & ( ~ x
      | x
      | f($false)
      | f($true)
      | epred1_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | f($true)
      | epred1_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | f($true)
      | epred1_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | f($true)
      | epred1_0 )
    & ( f($false)
      | f($false)
      | f($true)
      | epred1_0 )
    & ( ~ x
      | x
      | f($true)
      | epred1_0 )
    & ( ~ f($false)
      | x
      | f($true)
      | epred1_0 )
    & ( ~ x
      | ~ f($true)
      | f($true)
      | epred1_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($true)
      | epred1_0 )
    & ( f($false)
      | f($true)
      | epred1_0 )
    & ( f($true)
      | epred1_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_14,plain,
    ( epred2_0
    | ~ f($false)
    | ~ f($true) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( f($false)
    | epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_16,plain,
    ( ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | ~ f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | ~ f($false) ) )
      | f($true) )
   => epred4_0 ),
    inference(split_equiv,[status(thm)],[c_0_9]) ).

fof(c_0_17,plain,
    ( ( ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | f($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | f($false) ) )
      | f($false) )
   => epred5_0 ),
    inference(split_equiv,[status(thm)],[c_0_10]) ).

fof(c_0_18,plain,
    ( ( ( epred4_0
        & epred5_0 )
      | ( ( ( ( ~ x
              | ~ f($true) )
            & ( x
              | ~ f($false) ) )
          | h($false) = h($true) )
        & ( ( ( ~ x
              | f($true) )
            & ( x
              | f($false) ) )
          | h($false) = h($false) ) ) )
   => epred6_0 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_11]),c_0_9]),c_0_10]) ).

fof(c_0_19,negated_conjecture,
    ~ ( epred3_0
      & epred6_0 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[2])]),c_0_1]),c_0_11]) ).

cnf(c_0_20,plain,
    ( epred3_0
    | ~ x
    | ~ f($true) ),
    inference(cn,[status(thm)],[c_0_12]) ).

cnf(c_0_21,plain,
    ( f($true)
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,plain,
    ( f($true)
    | epred2_0
    | ~ f($false)
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_23,plain,
    ( epred2_0
    | ~ f($true) ),
    inference(csr,[status(thm)],[c_0_14,c_0_15]) ).

fof(c_0_24,plain,
    ( ( ~ x
      | x
      | ~ x
      | x
      | epred4_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | x
      | epred4_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | x
      | epred4_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | x
      | epred4_0 )
    & ( f($false)
      | ~ x
      | x
      | epred4_0 )
    & ( ~ x
      | x
      | f($false)
      | x
      | epred4_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | x
      | epred4_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | x
      | epred4_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | x
      | epred4_0 )
    & ( f($false)
      | f($false)
      | x
      | epred4_0 )
    & ( ~ x
      | x
      | ~ x
      | f($true)
      | epred4_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | f($true)
      | epred4_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | f($true)
      | epred4_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | f($true)
      | epred4_0 )
    & ( f($false)
      | ~ x
      | f($true)
      | epred4_0 )
    & ( ~ x
      | x
      | f($false)
      | f($true)
      | epred4_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | f($true)
      | epred4_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | f($true)
      | epred4_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | f($true)
      | epred4_0 )
    & ( f($false)
      | f($false)
      | f($true)
      | epred4_0 )
    & ( ~ x
      | x
      | f($true)
      | epred4_0 )
    & ( ~ f($false)
      | x
      | f($true)
      | epred4_0 )
    & ( ~ x
      | ~ f($true)
      | f($true)
      | epred4_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($true)
      | epred4_0 )
    & ( f($false)
      | f($true)
      | epred4_0 )
    & ( ~ f($true)
      | epred4_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

fof(c_0_25,plain,
    ( ( ~ x
      | x
      | ~ x
      | x
      | epred5_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | x
      | epred5_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | x
      | epred5_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | x
      | epred5_0 )
    & ( ~ f($false)
      | ~ x
      | x
      | epred5_0 )
    & ( ~ x
      | x
      | f($false)
      | x
      | epred5_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | x
      | epred5_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | x
      | epred5_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | x
      | epred5_0 )
    & ( ~ f($false)
      | f($false)
      | x
      | epred5_0 )
    & ( ~ x
      | x
      | ~ x
      | f($true)
      | epred5_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | f($true)
      | epred5_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | f($true)
      | epred5_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | f($true)
      | epred5_0 )
    & ( ~ f($false)
      | ~ x
      | f($true)
      | epred5_0 )
    & ( ~ x
      | x
      | f($false)
      | f($true)
      | epred5_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | f($true)
      | epred5_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | f($true)
      | epred5_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | f($true)
      | epred5_0 )
    & ( ~ f($false)
      | f($false)
      | f($true)
      | epred5_0 )
    & ( ~ x
      | x
      | ~ f($true)
      | epred5_0 )
    & ( ~ f($false)
      | x
      | ~ f($true)
      | epred5_0 )
    & ( ~ x
      | ~ f($true)
      | ~ f($true)
      | epred5_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ f($true)
      | epred5_0 )
    & ( ~ f($false)
      | ~ f($true)
      | epred5_0 )
    & ( ~ f($false)
      | epred5_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).

fof(c_0_26,plain,
    ( ( ~ epred4_0
      | ~ epred5_0
      | epred6_0 )
    & ( ~ x
      | x
      | ~ x
      | x
      | epred6_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | x
      | epred6_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | x
      | epred6_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | x
      | epred6_0 )
    & ( h($false) != h($false)
      | ~ x
      | x
      | epred6_0 )
    & ( ~ x
      | x
      | f($false)
      | x
      | epred6_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | x
      | epred6_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | x
      | epred6_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | x
      | epred6_0 )
    & ( h($false) != h($false)
      | f($false)
      | x
      | epred6_0 )
    & ( ~ x
      | x
      | ~ x
      | f($true)
      | epred6_0 )
    & ( ~ f($false)
      | x
      | ~ x
      | f($true)
      | epred6_0 )
    & ( ~ x
      | ~ f($true)
      | ~ x
      | f($true)
      | epred6_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ x
      | f($true)
      | epred6_0 )
    & ( h($false) != h($false)
      | ~ x
      | f($true)
      | epred6_0 )
    & ( ~ x
      | x
      | f($false)
      | f($true)
      | epred6_0 )
    & ( ~ f($false)
      | x
      | f($false)
      | f($true)
      | epred6_0 )
    & ( ~ x
      | ~ f($true)
      | f($false)
      | f($true)
      | epred6_0 )
    & ( ~ f($false)
      | ~ f($true)
      | f($false)
      | f($true)
      | epred6_0 )
    & ( h($false) != h($false)
      | f($false)
      | f($true)
      | epred6_0 )
    & ( ~ x
      | x
      | h($false) != h($true)
      | epred6_0 )
    & ( ~ f($false)
      | x
      | h($false) != h($true)
      | epred6_0 )
    & ( ~ x
      | ~ f($true)
      | h($false) != h($true)
      | epred6_0 )
    & ( ~ f($false)
      | ~ f($true)
      | h($false) != h($true)
      | epred6_0 )
    & ( h($false) != h($false)
      | h($false) != h($true)
      | epred6_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).

fof(c_0_27,negated_conjecture,
    ( ~ epred3_0
    | ~ epred6_0 ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).

cnf(c_0_28,plain,
    ( epred3_0
    | ~ epred1_0
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_29,plain,
    ( epred3_0
    | epred1_0
    | ~ x ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_30,plain,
    ( epred2_0
    | ~ x ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_22,c_0_15]),c_0_23]) ).

cnf(c_0_31,plain,
    ( f($false)
    | f($false)
    | x
    | epred4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_32,plain,
    ( epred5_0
    | ~ x
    | ~ f($true)
    | ~ f($true) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_33,plain,
    ( f($true)
    | epred6_0
    | $false
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_34,negated_conjecture,
    ( ~ epred3_0
    | ~ epred6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,plain,
    ( epred3_0
    | ~ x ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

cnf(c_0_36,plain,
    ( x
    | f($true)
    | epred4_0
    | ~ f($false) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_37,plain,
    ( x
    | epred4_0
    | f($false) ),
    inference(cn,[status(thm)],[c_0_31]) ).

cnf(c_0_38,plain,
    ( epred4_0
    | ~ f($true) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_39,plain,
    ( epred5_0
    | ~ x
    | ~ f($true) ),
    inference(cn,[status(thm)],[c_0_32]) ).

cnf(c_0_40,plain,
    ( epred6_0
    | f($true)
    | ~ x ),
    inference(cn,[status(thm)],[c_0_33]) ).

cnf(c_0_41,negated_conjecture,
    ( ~ epred6_0
    | ~ x ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_42,plain,
    ( epred4_0
    | x ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

cnf(c_0_43,plain,
    ( f($false)
    | f($false)
    | x
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_44,plain,
    ( epred6_0
    | ~ epred4_0
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_45,plain,
    ( epred5_0
    | ~ x ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).

cnf(c_0_46,plain,
    ( epred6_0
    | epred4_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_40]),c_0_42]) ).

cnf(c_0_47,plain,
    ( x
    | epred3_0
    | ~ f($false)
    | $false ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_48,plain,
    ( x
    | epred1_0
    | f($false) ),
    inference(cn,[status(thm)],[c_0_43]) ).

cnf(c_0_49,plain,
    ~ x,
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_41]) ).

cnf(c_0_50,plain,
    ( x
    | epred3_0
    | ~ f($false) ),
    inference(cn,[status(thm)],[c_0_47]) ).

cnf(c_0_51,plain,
    ( epred1_0
    | f($false) ),
    inference(sr,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_52,plain,
    ( epred3_0
    | epred1_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_49]) ).

cnf(c_0_53,plain,
    ( epred3_0
    | epred2_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_15]),c_0_49]) ).

cnf(c_0_54,plain,
    ( f($false)
    | x
    | epred6_0
    | $false ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_55,plain,
    epred3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_52]),c_0_53]) ).

cnf(c_0_56,plain,
    ( x
    | epred6_0
    | f($false) ),
    inference(cn,[status(thm)],[c_0_54]) ).

cnf(c_0_57,negated_conjecture,
    ~ epred6_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_55])]) ).

cnf(c_0_58,plain,
    epred4_0,
    inference(sr,[status(thm)],[c_0_42,c_0_49]) ).

cnf(c_0_59,plain,
    ( epred5_0
    | ~ f($false) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_60,plain,
    f($false),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_56,c_0_49]),c_0_57]) ).

cnf(c_0_61,plain,
    ( epred6_0
    | ~ epred5_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_58])]) ).

cnf(c_0_62,plain,
    epred5_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).

cnf(c_0_63,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),c_0_57]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SYO040_8 : TPTP v8.2.0. Released v8.0.0.
% 0.13/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 10:38:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  Running first-order model finding
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51  # Version: 3.1.0
% 0.21/0.51  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.51  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51  # Starting sh5l with 300s (1) cores
% 0.21/0.51  # new_bool_3 with pid 4842 completed with status 0
% 0.21/0.51  # Result found by new_bool_3
% 0.21/0.51  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.51  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.51  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51  # Search class: FGHSF-FFMM11-SFFFFFNN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.51  # SAT001_MinMin_p005000_rr_RG with pid 4845 completed with status 0
% 0.21/0.51  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.21/0.51  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.51  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.51  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.51  # Search class: FGHSF-FFMM11-SFFFFFNN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.21/0.51  # Preprocessing time       : 0.001 s
% 0.21/0.51  # Presaturation interreduction done
% 0.21/0.51  
% 0.21/0.51  # Proof found!
% 0.21/0.51  # SZS status Theorem
% 0.21/0.51  # SZS output start CNFRefutation
% See solution above
% 0.21/0.51  # Parsed axioms                        : 4
% 0.21/0.51  # Removed by relevancy pruning/SinE    : 3
% 0.21/0.51  # Initial clauses                      : 157
% 0.21/0.51  # Removed in clause preprocessing      : 116
% 0.21/0.51  # Initial clauses in saturation        : 41
% 0.21/0.51  # Processed clauses                    : 91
% 0.21/0.51  # ...of these trivial                  : 0
% 0.21/0.51  # ...subsumed                          : 21
% 0.21/0.51  # ...remaining for further processing  : 70
% 0.21/0.51  # Other redundant clauses eliminated   : 0
% 0.21/0.51  # Clauses deleted for lack of memory   : 0
% 0.21/0.51  # Backward-subsumed                    : 15
% 0.21/0.51  # Backward-rewritten                   : 20
% 0.21/0.51  # Generated clauses                    : 43
% 0.21/0.51  # ...of the previous two non-redundant : 41
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 14
% 0.21/0.51  # Paramodulations                      : 38
% 0.21/0.51  # Factorizations                       : 0
% 0.21/0.51  # NegExts                              : 0
% 0.21/0.51  # Equation resolutions                 : 0
% 0.21/0.51  # Disequality decompositions           : 0
% 0.21/0.51  # Total rewrite steps                  : 20
% 0.21/0.51  # ...of those cached                   : 14
% 0.21/0.51  # Propositional unsat checks           : 0
% 0.21/0.51  #    Propositional check models        : 0
% 0.21/0.51  #    Propositional check unsatisfiable : 0
% 0.21/0.51  #    Propositional clauses             : 0
% 0.21/0.51  #    Propositional clauses after purity: 0
% 0.21/0.51  #    Propositional unsat core size     : 0
% 0.21/0.51  #    Propositional preprocessing time  : 0.000
% 0.21/0.51  #    Propositional encoding time       : 0.000
% 0.21/0.51  #    Propositional solver time         : 0.000
% 0.21/0.51  #    Success case prop preproc time    : 0.000
% 0.21/0.51  #    Success case prop encoding time   : 0.000
% 0.21/0.51  #    Success case prop solver time     : 0.000
% 0.21/0.51  # Current number of processed clauses  : 9
% 0.21/0.51  #    Positive orientable unit clauses  : 6
% 0.21/0.51  #    Positive unorientable unit clauses: 0
% 0.21/0.51  #    Negative unit clauses             : 2
% 0.21/0.51  #    Non-unit-clauses                  : 1
% 0.21/0.51  # Current number of unprocessed clauses: 3
% 0.21/0.51  # ...number of literals in the above   : 9
% 0.21/0.51  # Current number of archived formulas  : 0
% 0.21/0.51  # Current number of archived clauses   : 61
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 138
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 121
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 42
% 0.21/0.51  # Unit Clause-clause subsumption calls : 13
% 0.21/0.51  # Rewrite failures with RHS unbound    : 0
% 0.21/0.51  # BW rewrite match attempts            : 6
% 0.21/0.51  # BW rewrite match successes           : 6
% 0.21/0.51  # Condensation attempts                : 0
% 0.21/0.51  # Condensation successes               : 0
% 0.21/0.51  # Termbank termtop insertions          : 4807
% 0.21/0.51  # Search garbage collected termcells   : 1024
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.010 s
% 0.21/0.51  # System time              : 0.002 s
% 0.21/0.51  # Total time               : 0.012 s
% 0.21/0.51  # Maximum resident set size: 1916 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.011 s
% 0.21/0.51  # System time              : 0.005 s
% 0.21/0.51  # Total time               : 0.016 s
% 0.21/0.51  # Maximum resident set size: 1684 pages
% 0.21/0.51  % E---3.1 exiting
%------------------------------------------------------------------------------