TSTP Solution File: GRP628+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP628+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n007.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 10:41:42 EDT 2023

% Result   : Theorem 15.15s 5.38s
% Output   : CNFRefutation 15.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  144 (  39 unt;  63 typ;   0 def)
%            Number of atoms       :  278 (  21 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  341 ( 144   ~; 146   |;  31   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   74 (  46   >;  28   *;   0   +;   0  <<)
%            Number of predicates  :   25 (  23 usr;   1 prp; 0-4 aty)
%            Number of functors    :   40 (  40 usr;  17 con; 0-3 aty)
%            Number of variables   :   35 (;  35   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ m2_fraenkel > v1_partfun1 > v1_funct_2 > m2_relset_1 > m1_relset_1 > m1_fraenkel > v1_group_3 > r2_hidden > r1_tarski > m1_subset_1 > m1_group_2 > v4_group_1 > v3_struct_0 > v3_group_1 > v2_group_1 > v2_funct_1 > v1_xboole_0 > v1_relat_1 > v1_group_1 > v1_funct_1 > v1_fraenkel > l1_struct_0 > l1_group_1 > k3_group_1 > k2_zfmisc_1 > g1_group_1 > #nlpp > u1_struct_0 > u1_group_1 > k5_autgroup > k4_autgroup > k3_autgroup > k2_funct_1 > k2_autgroup > k1_zfmisc_1 > k1_autgroup > k1_xboole_0 > #skF_9 > #skF_7 > #skF_11 > #skF_22 > #skF_16 > #skF_6 > #skF_20 > #skF_18 > #skF_15 > #skF_25 > #skF_19 > #skF_14 > #skF_26 > #skF_5 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_21 > #skF_4 > #skF_17 > #skF_24 > #skF_23 > #skF_27 > #skF_12 > #skF_10

%Foreground sorts:

%Background operators:

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

tff(v2_group_1,type,
    v2_group_1: $i > $o ).

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

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

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

tff('#skF_22',type,
    '#skF_22': ( $i * $i ) > $i ).

tff('#skF_16',type,
    '#skF_16': $i > $i ).

tff(v3_group_1,type,
    v3_group_1: $i > $o ).

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

tff(u1_group_1,type,
    u1_group_1: $i > $i ).

tff('#skF_20',type,
    '#skF_20': $i ).

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

tff(k2_funct_1,type,
    k2_funct_1: $i > $i ).

tff(v2_funct_1,type,
    v2_funct_1: $i > $o ).

tff(k1_autgroup,type,
    k1_autgroup: $i > $i ).

tff('#skF_18',type,
    '#skF_18': $i ).

tff(k4_autgroup,type,
    k4_autgroup: $i > $i ).

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

tff('#skF_15',type,
    '#skF_15': $i ).

tff(v1_partfun1,type,
    v1_partfun1: ( $i * $i * $i ) > $o ).

tff('#skF_25',type,
    '#skF_25': $i ).

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

tff('#skF_19',type,
    '#skF_19': $i ).

tff(k3_group_1,type,
    k3_group_1: ( $i * $i ) > $i ).

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

tff(k3_autgroup,type,
    k3_autgroup: $i > $i ).

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

tff(m1_fraenkel,type,
    m1_fraenkel: ( $i * $i * $i ) > $o ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i ) > $i ).

tff(v1_group_3,type,
    v1_group_3: ( $i * $i ) > $o ).

tff('#skF_26',type,
    '#skF_26': $i ).

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

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

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

tff(v1_group_1,type,
    v1_group_1: $i > $o ).

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

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

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

tff(k2_autgroup,type,
    k2_autgroup: $i > $i ).

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

tff('#skF_21',type,
    '#skF_21': $i ).

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

tff(l1_struct_0,type,
    l1_struct_0: $i > $o ).

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

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

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

tff('#skF_17',type,
    '#skF_17': $i > $i ).

tff(m1_group_2,type,
    m1_group_2: ( $i * $i ) > $o ).

tff(m2_fraenkel,type,
    m2_fraenkel: ( $i * $i * $i * $i ) > $o ).

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

tff(v4_group_1,type,
    v4_group_1: $i > $o ).

tff(v1_fraenkel,type,
    v1_fraenkel: $i > $o ).

tff(k5_autgroup,type,
    k5_autgroup: $i > $i ).

tff('#skF_27',type,
    '#skF_27': $i > $i ).

tff(g1_group_1,type,
    g1_group_1: ( $i * $i ) > $i ).

tff(u1_struct_0,type,
    u1_struct_0: $i > $i ).

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

tff(l1_group_1,type,
    l1_group_1: $i > $o ).

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

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

tff(v3_struct_0,type,
    v3_struct_0: $i > $o ).

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

tff(f_51,negated_conjecture,
    ~ ! [A] :
        ( ( ~ v3_struct_0(A)
          & v1_group_1(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & l1_group_1(A) )
       => ! [B] :
            ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
               => ( ( B = C )
                 => ( k2_funct_1(B) = k3_group_1(k5_autgroup(A),C) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_autgroup) ).

tff(f_249,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ~ v3_struct_0(k3_autgroup(A))
        & v1_group_1(k3_autgroup(A))
        & v3_group_1(k3_autgroup(A))
        & v4_group_1(k3_autgroup(A))
        & l1_group_1(k3_autgroup(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_autgroup) ).

tff(f_292,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_1(k5_autgroup(A))
        & v1_group_3(k5_autgroup(A),k3_autgroup(A))
        & m1_group_2(k5_autgroup(A),k3_autgroup(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_autgroup) ).

tff(f_642,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_group_2) ).

tff(f_664,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( ( D = B )
                   => ( k3_group_1(C,D) = k3_group_1(A,B) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_group_2) ).

tff(f_607,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
         => m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_autgroup) ).

tff(f_591,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k3_autgroup(A)))
             => ( ( B = C )
               => ( k2_funct_1(B) = k3_group_1(k3_autgroup(A),C) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_autgroup) ).

tff(c_18,plain,
    ~ v3_struct_0('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_16,plain,
    v1_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_14,plain,
    v3_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_12,plain,
    v4_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_10,plain,
    l1_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_86,plain,
    ! [A_37] :
      ( l1_group_1(k3_autgroup(A_37))
      | ~ l1_group_1(A_37)
      | ~ v4_group_1(A_37)
      | ~ v3_group_1(A_37)
      | ~ v1_group_1(A_37)
      | v3_struct_0(A_37) ),
    inference(cnfTransformation,[status(thm)],[f_249]) ).

tff(c_88,plain,
    ! [A_37] :
      ( v4_group_1(k3_autgroup(A_37))
      | ~ l1_group_1(A_37)
      | ~ v4_group_1(A_37)
      | ~ v3_group_1(A_37)
      | ~ v1_group_1(A_37)
      | v3_struct_0(A_37) ),
    inference(cnfTransformation,[status(thm)],[f_249]) ).

tff(c_90,plain,
    ! [A_37] :
      ( v3_group_1(k3_autgroup(A_37))
      | ~ l1_group_1(A_37)
      | ~ v4_group_1(A_37)
      | ~ v3_group_1(A_37)
      | ~ v1_group_1(A_37)
      | v3_struct_0(A_37) ),
    inference(cnfTransformation,[status(thm)],[f_249]) ).

tff(c_4,plain,
    '#skF_2' = '#skF_3',
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_2,plain,
    k3_group_1(k5_autgroup('#skF_1'),'#skF_3') != k2_funct_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_306,plain,
    k3_group_1(k5_autgroup('#skF_1'),'#skF_3') != k2_funct_1('#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2]) ).

tff(c_100,plain,
    ! [A_41] :
      ( m1_group_2(k5_autgroup(A_41),k3_autgroup(A_41))
      | ~ l1_group_1(A_41)
      | ~ v4_group_1(A_41)
      | ~ v3_group_1(A_41)
      | ~ v1_group_1(A_41)
      | v3_struct_0(A_41) ),
    inference(cnfTransformation,[status(thm)],[f_292]) ).

tff(c_6,plain,
    m1_subset_1('#skF_3',u1_struct_0(k5_autgroup('#skF_1'))),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_3177,plain,
    ! [C_693,A_694,B_695] :
      ( m1_subset_1(C_693,u1_struct_0(A_694))
      | ~ m1_subset_1(C_693,u1_struct_0(B_695))
      | ~ m1_group_2(B_695,A_694)
      | ~ l1_group_1(A_694)
      | ~ v3_group_1(A_694)
      | v3_struct_0(A_694) ),
    inference(cnfTransformation,[status(thm)],[f_642]) ).

tff(c_3192,plain,
    ! [A_694] :
      ( m1_subset_1('#skF_3',u1_struct_0(A_694))
      | ~ m1_group_2(k5_autgroup('#skF_1'),A_694)
      | ~ l1_group_1(A_694)
      | ~ v3_group_1(A_694)
      | v3_struct_0(A_694) ),
    inference(resolution,[status(thm)],[c_6,c_3177]) ).

tff(c_11867,plain,
    ! [C_1239,D_1240,A_1241] :
      ( ( k3_group_1(C_1239,D_1240) = k3_group_1(A_1241,D_1240) )
      | ~ m1_subset_1(D_1240,u1_struct_0(C_1239))
      | ~ m1_group_2(C_1239,A_1241)
      | ~ m1_subset_1(D_1240,u1_struct_0(A_1241))
      | ~ l1_group_1(A_1241)
      | ~ v4_group_1(A_1241)
      | ~ v3_group_1(A_1241)
      | v3_struct_0(A_1241) ),
    inference(cnfTransformation,[status(thm)],[f_664]) ).

tff(c_11900,plain,
    ! [A_1247] :
      ( ( k3_group_1(k5_autgroup('#skF_1'),'#skF_3') = k3_group_1(A_1247,'#skF_3') )
      | ~ m1_group_2(k5_autgroup('#skF_1'),A_1247)
      | ~ m1_subset_1('#skF_3',u1_struct_0(A_1247))
      | ~ l1_group_1(A_1247)
      | ~ v4_group_1(A_1247)
      | ~ v3_group_1(A_1247)
      | v3_struct_0(A_1247) ),
    inference(resolution,[status(thm)],[c_6,c_11867]) ).

tff(c_12045,plain,
    ! [A_1257] :
      ( ( k3_group_1(k5_autgroup('#skF_1'),'#skF_3') = k3_group_1(A_1257,'#skF_3') )
      | ~ v4_group_1(A_1257)
      | ~ m1_group_2(k5_autgroup('#skF_1'),A_1257)
      | ~ l1_group_1(A_1257)
      | ~ v3_group_1(A_1257)
      | v3_struct_0(A_1257) ),
    inference(resolution,[status(thm)],[c_3192,c_11900]) ).

tff(c_12049,plain,
    ( ( k3_group_1(k5_autgroup('#skF_1'),'#skF_3') = k3_group_1(k3_autgroup('#skF_1'),'#skF_3') )
    | ~ v4_group_1(k3_autgroup('#skF_1'))
    | ~ l1_group_1(k3_autgroup('#skF_1'))
    | ~ v3_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1'))
    | ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_100,c_12045]) ).

tff(c_12052,plain,
    ( ( k3_group_1(k5_autgroup('#skF_1'),'#skF_3') = k3_group_1(k3_autgroup('#skF_1'),'#skF_3') )
    | ~ v4_group_1(k3_autgroup('#skF_1'))
    | ~ l1_group_1(k3_autgroup('#skF_1'))
    | ~ v3_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1'))
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12049]) ).

tff(c_12053,plain,
    ( ( k3_group_1(k5_autgroup('#skF_1'),'#skF_3') = k3_group_1(k3_autgroup('#skF_1'),'#skF_3') )
    | ~ v4_group_1(k3_autgroup('#skF_1'))
    | ~ l1_group_1(k3_autgroup('#skF_1'))
    | ~ v3_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_12052]) ).

tff(c_12251,plain,
    ~ v3_group_1(k3_autgroup('#skF_1')),
    inference(splitLeft,[status(thm)],[c_12053]) ).

tff(c_12254,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_90,c_12251]) ).

tff(c_12257,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12254]) ).

tff(c_12259,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12257]) ).

tff(c_12261,plain,
    v3_group_1(k3_autgroup('#skF_1')),
    inference(splitRight,[status(thm)],[c_12053]) ).

tff(c_8,plain,
    m2_fraenkel('#skF_2',u1_struct_0('#skF_1'),u1_struct_0('#skF_1'),k4_autgroup('#skF_1')),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_305,plain,
    m2_fraenkel('#skF_3',u1_struct_0('#skF_1'),u1_struct_0('#skF_1'),k4_autgroup('#skF_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_8]) ).

tff(c_11926,plain,
    ! [B_1253,A_1254] :
      ( m2_fraenkel(B_1253,u1_struct_0(A_1254),u1_struct_0(A_1254),k1_autgroup(A_1254))
      | ~ m2_fraenkel(B_1253,u1_struct_0(A_1254),u1_struct_0(A_1254),k4_autgroup(A_1254))
      | ~ l1_group_1(A_1254)
      | ~ v4_group_1(A_1254)
      | ~ v3_group_1(A_1254)
      | ~ v1_group_1(A_1254)
      | v3_struct_0(A_1254) ),
    inference(cnfTransformation,[status(thm)],[f_607]) ).

tff(c_11937,plain,
    ( m2_fraenkel('#skF_3',u1_struct_0('#skF_1'),u1_struct_0('#skF_1'),k1_autgroup('#skF_1'))
    | ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_305,c_11926]) ).

tff(c_11942,plain,
    ( m2_fraenkel('#skF_3',u1_struct_0('#skF_1'),u1_struct_0('#skF_1'),k1_autgroup('#skF_1'))
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_11937]) ).

tff(c_11943,plain,
    m2_fraenkel('#skF_3',u1_struct_0('#skF_1'),u1_struct_0('#skF_1'),k1_autgroup('#skF_1')),
    inference(negUnitSimplification,[status(thm)],[c_18,c_11942]) ).

tff(c_12116,plain,
    ! [A_1258,C_1259] :
      ( ( k3_group_1(k3_autgroup(A_1258),C_1259) = k2_funct_1(C_1259) )
      | ~ m1_subset_1(C_1259,u1_struct_0(k3_autgroup(A_1258)))
      | ~ m2_fraenkel(C_1259,u1_struct_0(A_1258),u1_struct_0(A_1258),k1_autgroup(A_1258))
      | ~ l1_group_1(A_1258)
      | ~ v4_group_1(A_1258)
      | ~ v3_group_1(A_1258)
      | ~ v1_group_1(A_1258)
      | v3_struct_0(A_1258) ),
    inference(cnfTransformation,[status(thm)],[f_591]) ).

tff(c_12119,plain,
    ( ( k3_group_1(k3_autgroup('#skF_1'),'#skF_3') = k2_funct_1('#skF_3') )
    | ~ m1_subset_1('#skF_3',u1_struct_0(k3_autgroup('#skF_1')))
    | ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_11943,c_12116]) ).

tff(c_12130,plain,
    ( ( k3_group_1(k3_autgroup('#skF_1'),'#skF_3') = k2_funct_1('#skF_3') )
    | ~ m1_subset_1('#skF_3',u1_struct_0(k3_autgroup('#skF_1')))
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12119]) ).

tff(c_12131,plain,
    ( ( k3_group_1(k3_autgroup('#skF_1'),'#skF_3') = k2_funct_1('#skF_3') )
    | ~ m1_subset_1('#skF_3',u1_struct_0(k3_autgroup('#skF_1'))) ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_12130]) ).

tff(c_12134,plain,
    ~ m1_subset_1('#skF_3',u1_struct_0(k3_autgroup('#skF_1'))),
    inference(splitLeft,[status(thm)],[c_12131]) ).

tff(c_12138,plain,
    ( ~ m1_group_2(k5_autgroup('#skF_1'),k3_autgroup('#skF_1'))
    | ~ l1_group_1(k3_autgroup('#skF_1'))
    | ~ v3_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(resolution,[status(thm)],[c_3192,c_12134]) ).

tff(c_12302,plain,
    ( ~ m1_group_2(k5_autgroup('#skF_1'),k3_autgroup('#skF_1'))
    | ~ l1_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12261,c_12138]) ).

tff(c_12303,plain,
    ~ l1_group_1(k3_autgroup('#skF_1')),
    inference(splitLeft,[status(thm)],[c_12302]) ).

tff(c_12306,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_86,c_12303]) ).

tff(c_12309,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12306]) ).

tff(c_12311,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12309]) ).

tff(c_12312,plain,
    ( ~ m1_group_2(k5_autgroup('#skF_1'),k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(splitRight,[status(thm)],[c_12302]) ).

tff(c_12314,plain,
    ~ m1_group_2(k5_autgroup('#skF_1'),k3_autgroup('#skF_1')),
    inference(splitLeft,[status(thm)],[c_12312]) ).

tff(c_12317,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_100,c_12314]) ).

tff(c_12320,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12317]) ).

tff(c_12322,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12320]) ).

tff(c_12323,plain,
    v3_struct_0(k3_autgroup('#skF_1')),
    inference(splitRight,[status(thm)],[c_12312]) ).

tff(c_94,plain,
    ! [A_37] :
      ( ~ v3_struct_0(k3_autgroup(A_37))
      | ~ l1_group_1(A_37)
      | ~ v4_group_1(A_37)
      | ~ v3_group_1(A_37)
      | ~ v1_group_1(A_37)
      | v3_struct_0(A_37) ),
    inference(cnfTransformation,[status(thm)],[f_249]) ).

tff(c_12327,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_12323,c_94]) ).

tff(c_12330,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12327]) ).

tff(c_12332,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12330]) ).

tff(c_12333,plain,
    k3_group_1(k3_autgroup('#skF_1'),'#skF_3') = k2_funct_1('#skF_3'),
    inference(splitRight,[status(thm)],[c_12131]) ).

tff(c_12417,plain,
    ( ( k3_group_1(k5_autgroup('#skF_1'),'#skF_3') = k2_funct_1('#skF_3') )
    | ~ v4_group_1(k3_autgroup('#skF_1'))
    | ~ l1_group_1(k3_autgroup('#skF_1'))
    | ~ v3_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12333,c_12053]) ).

tff(c_12418,plain,
    ( ~ v4_group_1(k3_autgroup('#skF_1'))
    | ~ l1_group_1(k3_autgroup('#skF_1'))
    | ~ v3_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(negUnitSimplification,[status(thm)],[c_306,c_12417]) ).

tff(c_12419,plain,
    ~ v3_group_1(k3_autgroup('#skF_1')),
    inference(splitLeft,[status(thm)],[c_12418]) ).

tff(c_12422,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_90,c_12419]) ).

tff(c_12425,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12422]) ).

tff(c_12427,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12425]) ).

tff(c_12428,plain,
    ( ~ l1_group_1(k3_autgroup('#skF_1'))
    | ~ v4_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(splitRight,[status(thm)],[c_12418]) ).

tff(c_12431,plain,
    ~ v4_group_1(k3_autgroup('#skF_1')),
    inference(splitLeft,[status(thm)],[c_12428]) ).

tff(c_12434,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_88,c_12431]) ).

tff(c_12437,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12434]) ).

tff(c_12439,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12437]) ).

tff(c_12440,plain,
    ( ~ l1_group_1(k3_autgroup('#skF_1'))
    | v3_struct_0(k3_autgroup('#skF_1')) ),
    inference(splitRight,[status(thm)],[c_12428]) ).

tff(c_12442,plain,
    ~ l1_group_1(k3_autgroup('#skF_1')),
    inference(splitLeft,[status(thm)],[c_12440]) ).

tff(c_12445,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_86,c_12442]) ).

tff(c_12448,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12445]) ).

tff(c_12450,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12448]) ).

tff(c_12451,plain,
    v3_struct_0(k3_autgroup('#skF_1')),
    inference(splitRight,[status(thm)],[c_12440]) ).

tff(c_12468,plain,
    ( ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | ~ v1_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_12451,c_94]) ).

tff(c_12471,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_12468]) ).

tff(c_12473,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_12471]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP628+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 21:51:09 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 15.15/5.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.15/5.38  
% 15.15/5.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.15/5.42  
% 15.15/5.42  Inference rules
% 15.15/5.42  ----------------------
% 15.15/5.42  #Ref     : 6
% 15.15/5.42  #Sup     : 2744
% 15.15/5.42  #Fact    : 0
% 15.15/5.42  #Define  : 0
% 15.15/5.42  #Split   : 98
% 15.15/5.42  #Chain   : 0
% 15.15/5.42  #Close   : 0
% 15.15/5.42  
% 15.15/5.42  Ordering : KBO
% 15.15/5.42  
% 15.15/5.42  Simplification rules
% 15.15/5.42  ----------------------
% 15.15/5.42  #Subsume      : 840
% 15.15/5.42  #Demod        : 2186
% 15.15/5.42  #Tautology    : 666
% 15.15/5.42  #SimpNegUnit  : 256
% 15.15/5.42  #BackRed      : 137
% 15.15/5.42  
% 15.15/5.42  #Partial instantiations: 0
% 15.15/5.42  #Strategies tried      : 1
% 15.15/5.42  
% 15.15/5.42  Timing (in seconds)
% 15.15/5.42  ----------------------
% 15.15/5.42  Preprocessing        : 0.76
% 15.15/5.42  Parsing              : 0.39
% 15.15/5.42  CNF conversion       : 0.07
% 15.15/5.42  Main loop            : 3.53
% 15.15/5.42  Inferencing          : 1.22
% 15.15/5.42  Reduction            : 1.30
% 15.15/5.42  Demodulation         : 0.92
% 15.15/5.42  BG Simplification    : 0.08
% 15.15/5.42  Subsumption          : 0.69
% 15.15/5.42  Abstraction          : 0.07
% 15.15/5.42  MUC search           : 0.00
% 15.15/5.42  Cooper               : 0.00
% 15.15/5.42  Total                : 4.35
% 15.15/5.42  Index Insertion      : 0.00
% 15.15/5.42  Index Deletion       : 0.00
% 15.15/5.42  Index Matching       : 0.00
% 15.15/5.42  BG Taut test         : 0.00
%------------------------------------------------------------------------------