TSTP Solution File: SEU425+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU425+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% 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 Aug 22 10:58:43 EDT 2023

% Result   : Theorem 8.12s 2.94s
% Output   : CNFRefutation 8.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  104 (  35 unt;  32 typ;   0 def)
%            Number of atoms       :  141 (  31 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives :  122 (  53   ~;  41   |;   8   &)
%                                         (   4 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  25   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   22 (  22 usr;   7 con; 0-3 aty)
%            Number of variables   :   84 (;  83   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ v1_funct_2 > m2_relset_1 > m1_relset_1 > r2_hidden > r1_tarski > m1_subset_1 > v3_relat_1 > v1_xboole_0 > v1_relat_1 > v1_funct_1 > k4_relset_1 > k9_relat_1 > k5_relset_2 > k2_zfmisc_1 > k1_funct_1 > #nlpp > k2_relat_1 > k1_zfmisc_1 > k1_relat_1 > k1_xboole_0 > #skF_9 > #skF_11 > #skF_4 > #skF_13 > #skF_2 > #skF_10 > #skF_3 > #skF_1 > #skF_8 > #skF_12 > #skF_7 > #skF_5 > #skF_6

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

tff(m2_relset_1,type,
    m2_relset_1: ( $i * $i * $i ) > $o ).

tff(v1_funct_1,type,
    v1_funct_1: $i > $o ).

tff(r2_hidden,type,
    r2_hidden: ( $i * $i ) > $o ).

tff('#skF_11',type,
    '#skF_11': $i ).

tff(k1_xboole_0,type,
    k1_xboole_0: $i ).

tff(v3_relat_1,type,
    v3_relat_1: $i > $o ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

tff(r1_tarski,type,
    r1_tarski: ( $i * $i ) > $o ).

tff(k4_relset_1,type,
    k4_relset_1: ( $i * $i * $i ) > $i ).

tff(k2_relat_1,type,
    k2_relat_1: $i > $i ).

tff(m1_relset_1,type,
    m1_relset_1: ( $i * $i * $i ) > $o ).

tff(v1_funct_2,type,
    v1_funct_2: ( $i * $i * $i ) > $o ).

tff('#skF_13',type,
    '#skF_13': $i ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff(k9_relat_1,type,
    k9_relat_1: ( $i * $i ) > $i ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': $i ).

tff('#skF_1',type,
    '#skF_1': $i ).

tff(k1_zfmisc_1,type,
    k1_zfmisc_1: $i > $i ).

tff(k1_funct_1,type,
    k1_funct_1: ( $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': $i ).

tff(v1_relat_1,type,
    v1_relat_1: $i > $o ).

tff(k2_zfmisc_1,type,
    k2_zfmisc_1: ( $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': $i > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff(v1_xboole_0,type,
    v1_xboole_0: $i > $o ).

tff(k5_relset_2,type,
    k5_relset_2: ( $i * $i ) > $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff(k1_relat_1,type,
    k1_relat_1: $i > $i ).

tff('#skF_6',type,
    '#skF_6': $i > $i ).

tff(m1_subset_1,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(f_163,axiom,
    ? [A] :
      ( v1_xboole_0(A)
      & v1_relat_1(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_203,axiom,
    ! [A,B] : r1_tarski(A,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_38,negated_conjecture,
    ~ ! [A,B,C] :
        ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
       => ( v1_funct_1(k5_relset_2(A,C))
          & v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
          & m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relset_2) ).

tff(f_51,axiom,
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

tff(f_96,axiom,
    ! [A,B] :
      ( v1_relat_1(B)
     => ( v1_relat_1(k5_relset_2(A,B))
        & v1_funct_1(k5_relset_2(A,B)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_2) ).

tff(f_219,axiom,
    ! [A,B,C] :
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relset_2) ).

tff(f_211,axiom,
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).

tff(f_85,axiom,
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( C = k5_relset_2(A,B) )
          <=> ( ( k1_relat_1(C) = k1_zfmisc_1(A) )
              & ! [D] :
                  ( r1_tarski(D,A)
                 => ( k1_funct_1(C,D) = k9_relat_1(B,D) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relset_2) ).

tff(f_201,axiom,
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

tff(f_197,axiom,
    ! [A,B,C] :
      ( m1_relset_1(C,A,B)
     => ( k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).

tff(f_246,axiom,
    ! [A] :
      ( v1_xboole_0(A)
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_69,axiom,
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
     => ( ( ( ( B = k1_xboole_0 )
           => ( A = k1_xboole_0 ) )
         => ( v1_funct_2(C,A,B)
          <=> ( A = k4_relset_1(A,B,C) ) ) )
        & ( ( B = k1_xboole_0 )
         => ( ( A = k1_xboole_0 )
            | ( v1_funct_2(C,A,B)
            <=> ( C = k1_xboole_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).

tff(f_100,axiom,
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

tff(f_117,axiom,
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

tff(c_94,plain,
    v1_xboole_0('#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_124,plain,
    ! [A_59] : r1_tarski(A_59,A_59),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_4,plain,
    m1_subset_1('#skF_3',k1_zfmisc_1(k2_zfmisc_1('#skF_1','#skF_2'))),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_942,plain,
    ! [C_208,A_209,B_210] :
      ( v1_relat_1(C_208)
      | ~ m1_subset_1(C_208,k1_zfmisc_1(k2_zfmisc_1(A_209,B_210))) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_967,plain,
    v1_relat_1('#skF_3'),
    inference(resolution,[status(thm)],[c_4,c_942]) ).

tff(c_305,plain,
    ! [A_115,B_116] :
      ( v1_funct_1(k5_relset_2(A_115,B_116))
      | ~ v1_relat_1(B_116) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_2,plain,
    ( ~ m2_relset_1(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3')))
    | ~ v1_funct_2(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3')))
    | ~ v1_funct_1(k5_relset_2('#skF_1','#skF_3')) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_172,plain,
    ~ v1_funct_1(k5_relset_2('#skF_1','#skF_3')),
    inference(splitLeft,[status(thm)],[c_2]) ).

tff(c_309,plain,
    ~ v1_relat_1('#skF_3'),
    inference(resolution,[status(thm)],[c_305,c_172]) ).

tff(c_552,plain,
    ! [C_153,A_154,B_155] :
      ( v1_relat_1(C_153)
      | ~ m1_subset_1(C_153,k1_zfmisc_1(k2_zfmisc_1(A_154,B_155))) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_571,plain,
    v1_relat_1('#skF_3'),
    inference(resolution,[status(thm)],[c_4,c_552]) ).

tff(c_580,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_309,c_571]) ).

tff(c_582,plain,
    v1_funct_1(k5_relset_2('#skF_1','#skF_3')),
    inference(splitRight,[status(thm)],[c_2]) ).

tff(c_48,plain,
    ! [A_24,B_25] :
      ( v1_relat_1(k5_relset_2(A_24,B_25))
      | ~ v1_relat_1(B_25) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_1488,plain,
    ! [A_334,C_335,B_336] :
      ( r1_tarski(k2_relat_1(k5_relset_2(A_334,C_335)),k1_zfmisc_1(k2_relat_1(C_335)))
      | ~ m1_subset_1(C_335,k1_zfmisc_1(k2_zfmisc_1(A_334,B_336))) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_1523,plain,
    r1_tarski(k2_relat_1(k5_relset_2('#skF_1','#skF_3')),k1_zfmisc_1(k2_relat_1('#skF_3'))),
    inference(resolution,[status(thm)],[c_4,c_1488]) ).

tff(c_126,plain,
    ! [C_63,A_61,B_62] :
      ( m2_relset_1(C_63,A_61,B_62)
      | ~ r1_tarski(k2_relat_1(C_63),B_62)
      | ~ r1_tarski(k1_relat_1(C_63),A_61)
      | ~ v1_relat_1(C_63) ),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_1530,plain,
    ! [A_61] :
      ( m2_relset_1(k5_relset_2('#skF_1','#skF_3'),A_61,k1_zfmisc_1(k2_relat_1('#skF_3')))
      | ~ r1_tarski(k1_relat_1(k5_relset_2('#skF_1','#skF_3')),A_61)
      | ~ v1_relat_1(k5_relset_2('#skF_1','#skF_3')) ),
    inference(resolution,[status(thm)],[c_1523,c_126]) ).

tff(c_1537,plain,
    ~ v1_relat_1(k5_relset_2('#skF_1','#skF_3')),
    inference(splitLeft,[status(thm)],[c_1530]) ).

tff(c_1540,plain,
    ~ v1_relat_1('#skF_3'),
    inference(resolution,[status(thm)],[c_48,c_1537]) ).

tff(c_1544,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_967,c_1540]) ).

tff(c_1546,plain,
    v1_relat_1(k5_relset_2('#skF_1','#skF_3')),
    inference(splitRight,[status(thm)],[c_1530]) ).

tff(c_1795,plain,
    ! [A_380,B_381] :
      ( ( k1_relat_1(k5_relset_2(A_380,B_381)) = k1_zfmisc_1(A_380) )
      | ~ v1_funct_1(k5_relset_2(A_380,B_381))
      | ~ v1_relat_1(k5_relset_2(A_380,B_381))
      | ~ v1_relat_1(B_381) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_1798,plain,
    ( ( k1_relat_1(k5_relset_2('#skF_1','#skF_3')) = k1_zfmisc_1('#skF_1') )
    | ~ v1_funct_1(k5_relset_2('#skF_1','#skF_3'))
    | ~ v1_relat_1('#skF_3') ),
    inference(resolution,[status(thm)],[c_1546,c_1795]) ).

tff(c_1804,plain,
    k1_relat_1(k5_relset_2('#skF_1','#skF_3')) = k1_zfmisc_1('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_967,c_582,c_1798]) ).

tff(c_1614,plain,
    ! [A_356] :
      ( m2_relset_1(k5_relset_2('#skF_1','#skF_3'),A_356,k1_zfmisc_1(k2_relat_1('#skF_3')))
      | ~ r1_tarski(k1_relat_1(k5_relset_2('#skF_1','#skF_3')),A_356) ),
    inference(splitRight,[status(thm)],[c_1530]) ).

tff(c_581,plain,
    ( ~ v1_funct_2(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3')))
    | ~ m2_relset_1(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3'))) ),
    inference(splitRight,[status(thm)],[c_2]) ).

tff(c_649,plain,
    ~ m2_relset_1(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3'))),
    inference(splitLeft,[status(thm)],[c_581]) ).

tff(c_1627,plain,
    ~ r1_tarski(k1_relat_1(k5_relset_2('#skF_1','#skF_3')),k1_zfmisc_1('#skF_1')),
    inference(resolution,[status(thm)],[c_1614,c_649]) ).

tff(c_1806,plain,
    ~ r1_tarski(k1_zfmisc_1('#skF_1'),k1_zfmisc_1('#skF_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_1804,c_1627]) ).

tff(c_1810,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_124,c_1806]) ).

tff(c_1812,plain,
    m2_relset_1(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3'))),
    inference(splitRight,[status(thm)],[c_581]) ).

tff(c_2169,plain,
    ! [C_433,A_434,B_435] :
      ( m1_relset_1(C_433,A_434,B_435)
      | ~ m2_relset_1(C_433,A_434,B_435) ),
    inference(cnfTransformation,[status(thm)],[f_201]) ).

tff(c_2181,plain,
    m1_relset_1(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3'))),
    inference(resolution,[status(thm)],[c_1812,c_2169]) ).

tff(c_118,plain,
    ! [A_53,B_54,C_55] :
      ( ( k4_relset_1(A_53,B_54,C_55) = k1_relat_1(C_55) )
      | ~ m1_relset_1(C_55,A_53,B_54) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_2274,plain,
    k4_relset_1(k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3')),k5_relset_2('#skF_1','#skF_3')) = k1_relat_1(k5_relset_2('#skF_1','#skF_3')),
    inference(resolution,[status(thm)],[c_2181,c_118]) ).

tff(c_583,plain,
    ! [A_156] :
      ( ( k1_xboole_0 = A_156 )
      | ~ v1_xboole_0(A_156) ),
    inference(cnfTransformation,[status(thm)],[f_246]) ).

tff(c_594,plain,
    k1_xboole_0 = '#skF_8',
    inference(resolution,[status(thm)],[c_94,c_583]) ).

tff(c_18,plain,
    ! [B_8,C_9,A_7] :
      ( ( k1_xboole_0 = B_8 )
      | v1_funct_2(C_9,A_7,B_8)
      | ( k4_relset_1(A_7,B_8,C_9) != A_7 )
      | ~ m2_relset_1(C_9,A_7,B_8) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_3825,plain,
    ! [B_604,C_605,A_606] :
      ( ( B_604 = '#skF_8' )
      | v1_funct_2(C_605,A_606,B_604)
      | ( k4_relset_1(A_606,B_604,C_605) != A_606 )
      | ~ m2_relset_1(C_605,A_606,B_604) ),
    inference(demodulation,[status(thm),theory(equality)],[c_594,c_18]) ).

tff(c_1811,plain,
    ~ v1_funct_2(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3'))),
    inference(splitRight,[status(thm)],[c_581]) ).

tff(c_3836,plain,
    ( ( k1_zfmisc_1(k2_relat_1('#skF_3')) = '#skF_8' )
    | ( k4_relset_1(k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3')),k5_relset_2('#skF_1','#skF_3')) != k1_zfmisc_1('#skF_1') )
    | ~ m2_relset_1(k5_relset_2('#skF_1','#skF_3'),k1_zfmisc_1('#skF_1'),k1_zfmisc_1(k2_relat_1('#skF_3'))) ),
    inference(resolution,[status(thm)],[c_3825,c_1811]) ).

tff(c_3842,plain,
    ( ( k1_zfmisc_1(k2_relat_1('#skF_3')) = '#skF_8' )
    | ( k1_relat_1(k5_relset_2('#skF_1','#skF_3')) != k1_zfmisc_1('#skF_1') ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1812,c_2274,c_3836]) ).

tff(c_3843,plain,
    k1_relat_1(k5_relset_2('#skF_1','#skF_3')) != k1_zfmisc_1('#skF_1'),
    inference(splitLeft,[status(thm)],[c_3842]) ).

tff(c_2100,plain,
    ! [C_420,A_421,B_422] :
      ( v1_relat_1(C_420)
      | ~ m1_subset_1(C_420,k1_zfmisc_1(k2_zfmisc_1(A_421,B_422))) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_2125,plain,
    v1_relat_1('#skF_3'),
    inference(resolution,[status(thm)],[c_4,c_2100]) ).

tff(c_2319,plain,
    ! [C_468,A_469,B_470] :
      ( m1_subset_1(C_468,k1_zfmisc_1(k2_zfmisc_1(A_469,B_470)))
      | ~ m2_relset_1(C_468,A_469,B_470) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_10,plain,
    ! [C_6,A_4,B_5] :
      ( v1_relat_1(C_6)
      | ~ m1_subset_1(C_6,k1_zfmisc_1(k2_zfmisc_1(A_4,B_5))) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_2331,plain,
    ! [C_471,A_472,B_473] :
      ( v1_relat_1(C_471)
      | ~ m2_relset_1(C_471,A_472,B_473) ),
    inference(resolution,[status(thm)],[c_2319,c_10]) ).

tff(c_2343,plain,
    v1_relat_1(k5_relset_2('#skF_1','#skF_3')),
    inference(resolution,[status(thm)],[c_1812,c_2331]) ).

tff(c_5097,plain,
    ! [A_636,B_637] :
      ( ( k1_relat_1(k5_relset_2(A_636,B_637)) = k1_zfmisc_1(A_636) )
      | ~ v1_funct_1(k5_relset_2(A_636,B_637))
      | ~ v1_relat_1(k5_relset_2(A_636,B_637))
      | ~ v1_relat_1(B_637) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_5100,plain,
    ( ( k1_relat_1(k5_relset_2('#skF_1','#skF_3')) = k1_zfmisc_1('#skF_1') )
    | ~ v1_funct_1(k5_relset_2('#skF_1','#skF_3'))
    | ~ v1_relat_1('#skF_3') ),
    inference(resolution,[status(thm)],[c_2343,c_5097]) ).

tff(c_5106,plain,
    k1_relat_1(k5_relset_2('#skF_1','#skF_3')) = k1_zfmisc_1('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_2125,c_582,c_5100]) ).

tff(c_5108,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3843,c_5106]) ).

tff(c_5109,plain,
    k1_zfmisc_1(k2_relat_1('#skF_3')) = '#skF_8',
    inference(splitRight,[status(thm)],[c_3842]) ).

tff(c_70,plain,
    ! [A_37] : ~ v1_xboole_0(k1_zfmisc_1(A_37)),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_5169,plain,
    ~ v1_xboole_0('#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_5109,c_70]) ).

tff(c_5176,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_5169]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU425+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.36  % Computer : n010.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 11:41:28 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 8.12/2.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.12/2.95  
% 8.12/2.95  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.12/2.98  
% 8.12/2.98  Inference rules
% 8.12/2.98  ----------------------
% 8.12/2.98  #Ref     : 0
% 8.12/2.98  #Sup     : 1282
% 8.12/2.98  #Fact    : 0
% 8.12/2.98  #Define  : 0
% 8.12/2.98  #Split   : 12
% 8.12/2.98  #Chain   : 0
% 8.12/2.98  #Close   : 0
% 8.12/2.98  
% 8.12/2.98  Ordering : KBO
% 8.12/2.98  
% 8.12/2.98  Simplification rules
% 8.12/2.98  ----------------------
% 8.12/2.98  #Subsume      : 308
% 8.12/2.98  #Demod        : 437
% 8.12/2.98  #Tautology    : 287
% 8.12/2.98  #SimpNegUnit  : 33
% 8.12/2.98  #BackRed      : 22
% 8.12/2.98  
% 8.12/2.98  #Partial instantiations: 0
% 8.12/2.98  #Strategies tried      : 1
% 8.12/2.98  
% 8.12/2.98  Timing (in seconds)
% 8.12/2.98  ----------------------
% 8.12/2.99  Preprocessing        : 0.63
% 8.12/2.99  Parsing              : 0.32
% 8.12/2.99  CNF conversion       : 0.05
% 8.12/2.99  Main loop            : 1.28
% 8.12/2.99  Inferencing          : 0.45
% 8.12/2.99  Reduction            : 0.38
% 8.12/2.99  Demodulation         : 0.27
% 8.12/2.99  BG Simplification    : 0.05
% 8.12/2.99  Subsumption          : 0.30
% 8.12/2.99  Abstraction          : 0.05
% 8.12/2.99  MUC search           : 0.00
% 8.12/2.99  Cooper               : 0.00
% 8.12/2.99  Total                : 1.97
% 8.12/2.99  Index Insertion      : 0.00
% 8.12/2.99  Index Deletion       : 0.00
% 8.12/2.99  Index Matching       : 0.00
% 8.12/2.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------