TSTP Solution File: SYO041_8 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SYO041_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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      :   19
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   80 (   9 unt;   7 typ;   0 def)
%            Number of atoms       :  679 (   0 equ)
%            Maximal formula atoms :  131 (   9 avg)
%            Number of connectives :  906 ( 300   ~; 474   |; 121   &)
%                                         (  10 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   33 (   5 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-1 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0 sgn   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_23,type,
    f: $o > $o ).

tff(decl_24,type,
    g: $o > $o ).

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

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

tff(decl_27,type,
    epred1_0: $o ).

tff(decl_28,type,
    epred2_0: $o ).

tff(decl_29,type,
    epred3_0: $o ).

fof(3,conjecture,
    ~ ( ( x
      <~> y )
      & ( g(x)
      <=> y )
      & ( g(y)
      <=> x )
      & ( f(f(f(x)))
      <=> g(f(x)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',3) ).

fof(c_0_1,plain,
    ( epred1_0
  <=> ( ( ( ( ~ x
            | ~ f($true) )
          & ( x
            | ~ f($false) ) )
        | ~ f($true) )
      & ( ( ( ~ x
            | f($true) )
          & ( x
            | f($false) ) )
        | ~ f($false) ) ) ),
    introduced(definition) ).

fof(c_0_2,plain,
    ( epred2_0
  <=> ( ( ( ( ~ x
            | ~ f($true) )
          & ( x
            | ~ f($false) ) )
        | f($true) )
      & ( ( ( ~ x
            | f($true) )
          & ( x
            | f($false) ) )
        | f($false) ) ) ),
    introduced(definition) ).

fof(c_0_3,plain,
    ( epred3_0
  <=> ( ( ( ( ~ x
            | ~ f($true) )
          & ( x
            | ~ f($false) ) )
        | g($true) )
      & ( ( ( ~ x
            | f($true) )
          & ( x
            | f($false) ) )
        | g($false) ) ) ),
    introduced(definition) ).

fof(c_0_4,negated_conjecture,
    ~ ~ ( ~ ( x
          <=> y )
        & ( ( ( ~ x
              | g($true) )
            & ( x
              | g($false) ) )
        <=> y )
        & ( ( ( ~ y
              | g($true) )
            & ( y
              | g($false) ) )
        <=> x )
        & ( ( ( epred1_0
              | f($true) )
            & ( epred2_0
              | f($false) ) )
        <=> epred3_0 ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[3])])]),c_0_1]),c_0_2]),c_0_3]) ).

fof(c_0_5,negated_conjecture,
    ( ( ~ x
      | ~ y )
    & ( x
      | y )
    & ( ~ x
      | x
      | y )
    & ( ~ g($false)
      | x
      | y )
    & ( ~ x
      | ~ g($true)
      | y )
    & ( ~ g($false)
      | ~ g($true)
      | y )
    & ( ~ x
      | g($true)
      | ~ y )
    & ( x
      | g($false)
      | ~ y )
    & ( ~ y
      | y
      | x )
    & ( ~ g($false)
      | y
      | x )
    & ( ~ y
      | ~ g($true)
      | x )
    & ( ~ g($false)
      | ~ g($true)
      | x )
    & ( ~ y
      | g($true)
      | ~ x )
    & ( y
      | g($false)
      | ~ x )
    & ( ~ epred2_0
      | ~ epred1_0
      | epred3_0 )
    & ( ~ f($false)
      | ~ epred1_0
      | epred3_0 )
    & ( ~ epred2_0
      | ~ f($true)
      | epred3_0 )
    & ( ~ f($false)
      | ~ f($true)
      | epred3_0 )
    & ( epred1_0
      | f($true)
      | ~ epred3_0 )
    & ( epred2_0
      | f($false)
      | ~ epred3_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_6,plain,
    ( ( ~ x
      | ~ f($true)
      | g($true)
      | ~ epred3_0 )
    & ( x
      | ~ f($false)
      | g($true)
      | ~ epred3_0 )
    & ( ~ x
      | f($true)
      | g($false)
      | ~ epred3_0 )
    & ( x
      | f($false)
      | g($false)
      | ~ 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 )
    & ( ~ g($false)
      | ~ x
      | x
      | epred3_0 )
    & ( ~ x
      | x
      | f($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($false)
      | x
      | epred3_0 )
    & ( ~ g($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($true)
      | epred3_0 )
    & ( ~ g($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($true)
      | epred3_0 )
    & ( ~ g($false)
      | f($false)
      | f($true)
      | epred3_0 )
    & ( ~ x
      | x
      | ~ g($true)
      | epred3_0 )
    & ( ~ f($false)
      | x
      | ~ g($true)
      | epred3_0 )
    & ( ~ x
      | ~ f($true)
      | ~ g($true)
      | epred3_0 )
    & ( ~ f($false)
      | ~ f($true)
      | ~ g($true)
      | epred3_0 )
    & ( ~ g($false)
      | ~ g($true)
      | epred3_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,negated_conjecture,
    ( x
    | g($false)
    | ~ y ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( x
    | y ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( f($false)
    | x
    | epred3_0
    | ~ g($false) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( x
    | g($false) ),
    inference(csr,[status(thm)],[c_0_7,c_0_8]) ).

fof(c_0_11,plain,
    ( ( ~ x
      | ~ f($true)
      | ~ f($true)
      | ~ epred1_0 )
    & ( x
      | ~ f($false)
      | ~ f($true)
      | ~ epred1_0 )
    & ( ~ x
      | f($true)
      | ~ f($false)
      | ~ epred1_0 )
    & ( x
      | f($false)
      | ~ f($false)
      | ~ epred1_0 )
    & ( ~ 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 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).

cnf(c_0_12,negated_conjecture,
    ( epred3_0
    | ~ f($false)
    | ~ f($true) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,plain,
    ( epred3_0
    | x
    | f($false) ),
    inference(csr,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    ( x
    | f($true)
    | epred1_0
    | ~ f($false) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ( f($false)
    | f($true)
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    ( epred3_0
    | ~ f($false)
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_17,plain,
    ( ( ~ x
      | ~ f($true)
      | f($true)
      | ~ epred2_0 )
    & ( x
      | ~ f($false)
      | f($true)
      | ~ epred2_0 )
    & ( ~ x
      | f($true)
      | f($false)
      | ~ epred2_0 )
    & ( x
      | f($false)
      | f($false)
      | ~ epred2_0 )
    & ( ~ 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 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

cnf(c_0_18,negated_conjecture,
    ( x
    | ~ y
    | ~ g($true) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_19,negated_conjecture,
    ( epred3_0
    | x
    | ~ f($true) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_20,plain,
    ( epred1_0
    | x
    | f($true) ),
    inference(csr,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    ( epred3_0
    | x
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_16,c_0_13]) ).

cnf(c_0_22,plain,
    ( x
    | f($false)
    | f($false)
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    ( x
    | g($true)
    | ~ f($false)
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_24,negated_conjecture,
    ( x
    | ~ g($true) ),
    inference(csr,[status(thm)],[c_0_18,c_0_8]) ).

cnf(c_0_25,negated_conjecture,
    ( epred2_0
    | f($false)
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_26,plain,
    ( epred3_0
    | x ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_27,plain,
    ( x
    | f($false)
    | ~ epred2_0 ),
    inference(cn,[status(thm)],[c_0_22]) ).

cnf(c_0_28,plain,
    ( x
    | ~ epred3_0
    | ~ f($false) ),
    inference(csr,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    ( x
    | f($false) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    ( y
    | g($false)
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_31,negated_conjecture,
    ( ~ x
    | ~ y ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_32,plain,
    x,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    ( y
    | g($false) ),
    inference(csr,[status(thm)],[c_0_30,c_0_10]) ).

cnf(c_0_34,negated_conjecture,
    ~ y,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).

cnf(c_0_35,plain,
    ( epred2_0
    | ~ x
    | ~ f($true)
    | ~ f($true) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_36,plain,
    ( f($true)
    | epred3_0
    | ~ g($false)
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_37,negated_conjecture,
    g($false),
    inference(sr,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_38,plain,
    ( epred2_0
    | ~ x
    | ~ f($true) ),
    inference(cn,[status(thm)],[c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    ( epred3_0
    | ~ epred2_0
    | ~ f($true) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_40,plain,
    ( epred3_0
    | f($true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_32])]),c_0_37])]) ).

cnf(c_0_41,plain,
    ( ~ x
    | ~ f($true)
    | ~ f($true)
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_42,plain,
    ( g($true)
    | ~ x
    | ~ f($true)
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_43,plain,
    ( epred2_0
    | ~ f($true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_32])]) ).

cnf(c_0_44,negated_conjecture,
    ( epred3_0
    | ~ epred2_0 ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_45,plain,
    ( x
    | ~ f($false)
    | ~ f($true)
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_46,plain,
    ( ~ x
    | ~ epred1_0
    | ~ f($true) ),
    inference(cn,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    ( g($true)
    | ~ epred3_0
    | ~ f($true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_32])]) ).

cnf(c_0_48,plain,
    epred3_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_44]) ).

cnf(c_0_49,negated_conjecture,
    ( epred1_0
    | f($true)
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_50,plain,
    ( f($true)
    | epred2_0
    | ~ f($false)
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_51,plain,
    ( epred2_0
    | ~ f($false)
    | ~ f($true) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_52,plain,
    ( f($true)
    | ~ x
    | ~ f($false)
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_53,plain,
    ( ~ epred1_0
    | ~ f($true)
    | ~ f($false) ),
    inference(csr,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_54,negated_conjecture,
    ( y
    | ~ x
    | ~ g($true) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_55,plain,
    ( g($true)
    | ~ f($true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).

cnf(c_0_56,negated_conjecture,
    ( epred1_0
    | f($true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_48])]) ).

cnf(c_0_57,plain,
    ( x
    | f($true)
    | ~ f($false)
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_58,plain,
    ( epred2_0
    | ~ x
    | ~ f($false) ),
    inference(csr,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_59,plain,
    ( ~ epred1_0
    | ~ x
    | ~ f($false) ),
    inference(csr,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_60,negated_conjecture,
    ( y
    | ~ g($true) ),
    inference(csr,[status(thm)],[c_0_54,c_0_24]) ).

cnf(c_0_61,plain,
    ( epred1_0
    | g($true) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_62,plain,
    ( f($true)
    | f($false)
    | ~ x
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_63,plain,
    ( x
    | f($true)
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[c_0_57,c_0_27]) ).

cnf(c_0_64,plain,
    ( epred2_0
    | ~ f($false) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_32])]) ).

cnf(c_0_65,plain,
    ( ~ epred1_0
    | ~ f($false) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_32])]) ).

cnf(c_0_66,negated_conjecture,
    epred1_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_34]) ).

cnf(c_0_67,plain,
    ( ~ epred1_0
    | ~ f($true) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_32])]) ).

cnf(c_0_68,plain,
    ( f($false)
    | f($true)
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_69,negated_conjecture,
    epred2_0,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_48])]),c_0_64]) ).

cnf(c_0_70,plain,
    ~ f($false),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).

cnf(c_0_71,plain,
    ~ f($true),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_66])]) ).

cnf(c_0_72,plain,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]),c_0_70]),c_0_71]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : SYO041_8 : TPTP v8.2.0. Released v8.0.0.
% 0.06/0.15  % Command    : run_E %s %d THM
% 0.14/0.36  % Computer : n010.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 May 20 10:54:23 EDT 2024
% 0.14/0.36  % 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: FSSSSLSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting SAT001_MinMin_p005000_rr_RG 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 13957 completed with status 0
% 0.21/0.51  # Result found by new_bool_3
% 0.21/0.51  # Preprocessing class: FSSSSLSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting SAT001_MinMin_p005000_rr_RG 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: FGHNF-FFMS00-SFFFFFNN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 181s (1) cores
% 0.21/0.51  # G-E--_208_C18_F1_AE_CS_SP_PI_S0a with pid 13960 completed with status 0
% 0.21/0.51  # Result found by G-E--_208_C18_F1_AE_CS_SP_PI_S0a
% 0.21/0.51  # Preprocessing class: FSSSSLSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting SAT001_MinMin_p005000_rr_RG 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: FGHNF-FFMS00-SFFFFFNN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting G-E--_208_C18_F1_AE_CS_SP_PI_S0a with 181s (1) cores
% 0.21/0.51  # Preprocessing time       : 0.001 s
% 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                        : 6
% 0.21/0.51  # Removed by relevancy pruning/SinE    : 5
% 0.21/0.51  # Initial clauses                      : 107
% 0.21/0.51  # Removed in clause preprocessing      : 62
% 0.21/0.51  # Initial clauses in saturation        : 45
% 0.21/0.51  # Processed clauses                    : 82
% 0.21/0.51  # ...of these trivial                  : 0
% 0.21/0.51  # ...subsumed                          : 19
% 0.21/0.51  # ...remaining for further processing  : 62
% 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                    : 19
% 0.21/0.51  # Backward-rewritten                   : 33
% 0.21/0.51  # Generated clauses                    : 71
% 0.21/0.51  # ...of the previous two non-redundant : 59
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 23
% 0.21/0.51  # Paramodulations                      : 70
% 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                  : 34
% 0.21/0.51  # ...of those cached                   : 29
% 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  : 5
% 0.21/0.51  #    Positive unorientable unit clauses: 0
% 0.21/0.51  #    Negative unit clauses             : 3
% 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   : 53
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 172
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 126
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 59
% 0.21/0.51  # Unit Clause-clause subsumption calls : 16
% 0.21/0.51  # Rewrite failures with RHS unbound    : 0
% 0.21/0.51  # BW rewrite match attempts            : 5
% 0.21/0.51  # BW rewrite match successes           : 5
% 0.21/0.51  # Condensation attempts                : 0
% 0.21/0.51  # Condensation successes               : 0
% 0.21/0.51  # Termbank termtop insertions          : 3948
% 0.21/0.51  # Search garbage collected termcells   : 696
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.007 s
% 0.21/0.51  # System time              : 0.004 s
% 0.21/0.51  # Total time               : 0.011 s
% 0.21/0.51  # Maximum resident set size: 1912 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.007 s
% 0.21/0.51  # System time              : 0.007 s
% 0.21/0.51  # Total time               : 0.014 s
% 0.21/0.51  # Maximum resident set size: 1680 pages
% 0.21/0.51  % E---3.1 exiting
%------------------------------------------------------------------------------