TSTP Solution File: ALG219+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG219+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 : n009.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 10:32:23 EDT 2023

% Result   : Theorem 28.79s 15.36s
% Output   : CNFRefutation 28.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   80
% Syntax   : Number of formulae    :  128 (  32 unt;  72 typ;   0 def)
%            Number of atoms       :  346 (  27 equ)
%            Maximal formula atoms :   26 (   6 avg)
%            Number of connectives :  470 ( 180   ~; 200   |;  73   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   84 (  57   >;  27   *;   0   +;   0  <<)
%            Number of predicates  :   35 (  33 usr;   1 prp; 0-3 aty)
%            Number of functors    :   39 (  39 usr;  15 con; 0-5 aty)
%            Number of variables   :   34 (;  34   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ v1_funct_2 > m2_relset_1 > m1_rmod_2 > m1_relset_1 > v5_vectsp_2 > v3_vectsp_2 > r2_hidden > r1_tarski > m1_subset_1 > l1_vectsp_2 > v8_vectsp_1 > v7_vectsp_1 > v7_group_1 > v6_vectsp_1 > v6_rlvect_1 > v5_rlvect_1 > v4_rlvect_1 > v4_group_1 > v3_struct_0 > v3_rlvect_1 > v2_vectsp_2 > v2_group_1 > v1_xboole_0 > v1_relat_1 > v1_funct_1 > v10_vectsp_1 > l3_vectsp_1 > l2_vectsp_1 > l2_struct_0 > l1_vectsp_1 > l1_struct_0 > l1_rlvect_1 > l1_group_1 > g1_vectsp_2 > k1_rmod_5 > u1_vectsp_2 > k2_zfmisc_1 > k2_rmod_2 > #nlpp > u2_struct_0 > u1_struct_0 > u1_rlvect_1 > k2_group_1 > k1_zfmisc_1 > k1_rlvect_1 > k1_xboole_0 > #skF_25 > #skF_21 > #skF_16 > #skF_20 > #skF_11 > #skF_19 > #skF_8 > #skF_7 > #skF_13 > #skF_10 > #skF_12 > #skF_18 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_26 > #skF_4 > #skF_17 > #skF_22 > #skF_14 > #skF_24 > #skF_23 > #skF_27 > #skF_15

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(v2_vectsp_2,type,
    v2_vectsp_2: $i > $o ).

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

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

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

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

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

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

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

tff(l3_vectsp_1,type,
    l3_vectsp_1: $i > $o ).

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

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

tff(g1_vectsp_2,type,
    g1_vectsp_2: ( $i * $i * $i * $i * $i ) > $i ).

tff(v4_rlvect_1,type,
    v4_rlvect_1: $i > $o ).

tff(v8_vectsp_1,type,
    v8_vectsp_1: $i > $o ).

tff(u2_struct_0,type,
    u2_struct_0: $i > $i ).

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

tff(k1_rlvect_1,type,
    k1_rlvect_1: $i > $i ).

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

tff(v5_vectsp_2,type,
    v5_vectsp_2: ( $i * $i ) > $o ).

tff(v6_rlvect_1,type,
    v6_rlvect_1: $i > $o ).

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

tff(l1_rlvect_1,type,
    l1_rlvect_1: $i > $o ).

tff(v7_group_1,type,
    v7_group_1: $i > $o ).

tff(k2_rmod_2,type,
    k2_rmod_2: ( $i * $i ) > $i ).

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

tff(u1_vectsp_2,type,
    u1_vectsp_2: ( $i * $i ) > $i ).

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

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

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

tff(v3_vectsp_2,type,
    v3_vectsp_2: ( $i * $i ) > $o ).

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

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

tff(k1_rmod_5,type,
    k1_rmod_5: ( $i * $i * $i ) > $i ).

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

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

tff(v10_vectsp_1,type,
    v10_vectsp_1: $i > $o ).

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

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

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

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

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

tff(k2_group_1,type,
    k2_group_1: $i > $i ).

tff(l1_vectsp_2,type,
    l1_vectsp_2: ( $i * $i ) > $o ).

tff(m1_rmod_2,type,
    m1_rmod_2: ( $i * $i * $i ) > $o ).

tff(l2_struct_0,type,
    l2_struct_0: $i > $o ).

tff(l2_vectsp_1,type,
    l2_vectsp_1: $i > $o ).

tff('#skF_9',type,
    '#skF_9': $i ).

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

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

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

tff(l1_vectsp_1,type,
    l1_vectsp_1: $i > $o ).

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

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

tff(v7_vectsp_1,type,
    v7_vectsp_1: $i > $o ).

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

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

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

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

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

tff(v5_rlvect_1,type,
    v5_rlvect_1: $i > $o ).

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

tff(v6_vectsp_1,type,
    v6_vectsp_1: $i > $o ).

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

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

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

tff(v3_rlvect_1,type,
    v3_rlvect_1: $i > $o ).

tff(u1_rlvect_1,type,
    u1_rlvect_1: $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_84,negated_conjecture,
    ~ ! [A] :
        ( ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & v6_vectsp_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A)
          & ~ v10_vectsp_1(A)
          & v2_vectsp_2(A)
          & l3_vectsp_1(A) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v3_rlvect_1(B)
              & v4_rlvect_1(B)
              & v5_rlvect_1(B)
              & v6_rlvect_1(B)
              & v3_vectsp_2(B,A)
              & v5_vectsp_2(B,A)
              & l1_vectsp_2(B,A) )
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
               => ( ( C = u1_struct_0(B) )
                 => ( ( k1_rlvect_1(A) = k2_group_1(A) )
                    | ( k1_rmod_5(A,B,C) = B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_rmod_5) ).

tff(f_332,axiom,
    ! [A] :
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).

tff(f_326,axiom,
    ! [A] :
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).

tff(f_320,axiom,
    ! [A] :
      ( l2_struct_0(A)
     => l1_struct_0(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).

tff(f_176,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ( k2_rmod_2(A,B) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_rmod_2) ).

tff(f_92,axiom,
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_vectsp_2(B,A) )
     => ( v3_vectsp_2(B,A)
       => ( B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).

tff(f_297,axiom,
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v5_vectsp_2(B,A)
        & l1_vectsp_2(B,A) )
     => ( v3_vectsp_2(k2_rmod_2(A,B),A)
        & m1_rmod_2(k2_rmod_2(A,B),A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_rmod_2) ).

tff(f_802,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v5_vectsp_2(B,A)
            & l1_vectsp_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] :
                  ( ( v3_vectsp_2(D,A)
                    & m1_rmod_2(D,A,B) )
                 => ( ( C = u1_struct_0(D) )
                   => ( ( k1_rlvect_1(A) = k2_group_1(A) )
                      | ( k1_rmod_5(A,B,C) = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_rmod_5) ).

tff(c_50,plain,
    ~ v3_struct_0('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_30,plain,
    ~ v10_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_24,plain,
    ~ v3_struct_0('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_4,plain,
    k2_group_1('#skF_1') != k1_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_2,plain,
    k1_rmod_5('#skF_1','#skF_2','#skF_3') != '#skF_2',
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_48,plain,
    v3_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_46,plain,
    v4_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_44,plain,
    v5_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_42,plain,
    v6_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_40,plain,
    v4_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_38,plain,
    v7_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_36,plain,
    v6_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_34,plain,
    v7_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_32,plain,
    v8_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_28,plain,
    v2_vectsp_2('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_26,plain,
    l3_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_22,plain,
    v3_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_20,plain,
    v4_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_18,plain,
    v5_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_16,plain,
    v6_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_12,plain,
    v5_vectsp_2('#skF_2','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_10,plain,
    l1_vectsp_2('#skF_2','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_6,plain,
    u1_struct_0('#skF_2') = '#skF_3',
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_8,plain,
    m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0('#skF_2'))),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_303,plain,
    m1_subset_1('#skF_3',k1_zfmisc_1('#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_8]) ).

tff(c_14,plain,
    v3_vectsp_2('#skF_2','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_334,plain,
    ! [A_146] :
      ( l2_vectsp_1(A_146)
      | ~ l3_vectsp_1(A_146) ),
    inference(cnfTransformation,[status(thm)],[f_332]) ).

tff(c_341,plain,
    l2_vectsp_1('#skF_1'),
    inference(resolution,[status(thm)],[c_26,c_334]) ).

tff(c_393,plain,
    ! [A_152] :
      ( l2_struct_0(A_152)
      | ~ l2_vectsp_1(A_152) ),
    inference(cnfTransformation,[status(thm)],[f_326]) ).

tff(c_404,plain,
    l2_struct_0('#skF_1'),
    inference(resolution,[status(thm)],[c_341,c_393]) ).

tff(c_108,plain,
    ! [A_35] :
      ( l1_struct_0(A_35)
      | ~ l2_struct_0(A_35) ),
    inference(cnfTransformation,[status(thm)],[f_320]) ).

tff(c_430,plain,
    l1_struct_0('#skF_1'),
    inference(resolution,[status(thm)],[c_404,c_108]) ).

tff(c_15510,plain,
    ! [A_964,B_965] :
      ( ( g1_vectsp_2(A_964,u1_struct_0(B_965),u1_rlvect_1(B_965),u2_struct_0(B_965),u1_vectsp_2(A_964,B_965)) = k2_rmod_2(A_964,B_965) )
      | ~ l1_vectsp_2(B_965,A_964)
      | ~ v5_vectsp_2(B_965,A_964)
      | ~ v6_rlvect_1(B_965)
      | ~ v5_rlvect_1(B_965)
      | ~ v4_rlvect_1(B_965)
      | ~ v3_rlvect_1(B_965)
      | v3_struct_0(B_965)
      | ~ l3_vectsp_1(A_964)
      | ~ v8_vectsp_1(A_964)
      | ~ v7_vectsp_1(A_964)
      | ~ v6_vectsp_1(A_964)
      | ~ v4_group_1(A_964)
      | ~ v6_rlvect_1(A_964)
      | ~ v5_rlvect_1(A_964)
      | ~ v4_rlvect_1(A_964)
      | ~ v3_rlvect_1(A_964)
      | v3_struct_0(A_964) ),
    inference(cnfTransformation,[status(thm)],[f_176]) ).

tff(c_52,plain,
    ! [A_5,B_6] :
      ( ( g1_vectsp_2(A_5,u1_struct_0(B_6),u1_rlvect_1(B_6),u2_struct_0(B_6),u1_vectsp_2(A_5,B_6)) = B_6 )
      | ~ v3_vectsp_2(B_6,A_5)
      | ~ l1_vectsp_2(B_6,A_5)
      | ~ l1_struct_0(A_5) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_45756,plain,
    ! [A_1233,B_1234] :
      ( ( k2_rmod_2(A_1233,B_1234) = B_1234 )
      | ~ v3_vectsp_2(B_1234,A_1233)
      | ~ l1_vectsp_2(B_1234,A_1233)
      | ~ l1_struct_0(A_1233)
      | ~ l1_vectsp_2(B_1234,A_1233)
      | ~ v5_vectsp_2(B_1234,A_1233)
      | ~ v6_rlvect_1(B_1234)
      | ~ v5_rlvect_1(B_1234)
      | ~ v4_rlvect_1(B_1234)
      | ~ v3_rlvect_1(B_1234)
      | v3_struct_0(B_1234)
      | ~ l3_vectsp_1(A_1233)
      | ~ v8_vectsp_1(A_1233)
      | ~ v7_vectsp_1(A_1233)
      | ~ v6_vectsp_1(A_1233)
      | ~ v4_group_1(A_1233)
      | ~ v6_rlvect_1(A_1233)
      | ~ v5_rlvect_1(A_1233)
      | ~ v4_rlvect_1(A_1233)
      | ~ v3_rlvect_1(A_1233)
      | v3_struct_0(A_1233) ),
    inference(superposition,[status(thm),theory(equality)],[c_15510,c_52]) ).

tff(c_45774,plain,
    ( ( k2_rmod_2('#skF_1','#skF_2') = '#skF_2' )
    | ~ v3_vectsp_2('#skF_2','#skF_1')
    | ~ l1_struct_0('#skF_1')
    | ~ l1_vectsp_2('#skF_2','#skF_1')
    | ~ v6_rlvect_1('#skF_2')
    | ~ v5_rlvect_1('#skF_2')
    | ~ v4_rlvect_1('#skF_2')
    | ~ v3_rlvect_1('#skF_2')
    | v3_struct_0('#skF_2')
    | ~ l3_vectsp_1('#skF_1')
    | ~ v8_vectsp_1('#skF_1')
    | ~ v7_vectsp_1('#skF_1')
    | ~ v6_vectsp_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v6_rlvect_1('#skF_1')
    | ~ v5_rlvect_1('#skF_1')
    | ~ v4_rlvect_1('#skF_1')
    | ~ v3_rlvect_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_12,c_45756]) ).

tff(c_45782,plain,
    ( ( k2_rmod_2('#skF_1','#skF_2') = '#skF_2' )
    | v3_struct_0('#skF_2')
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_48,c_46,c_44,c_42,c_40,c_36,c_34,c_32,c_26,c_22,c_20,c_18,c_16,c_10,c_430,c_14,c_45774]) ).

tff(c_45783,plain,
    k2_rmod_2('#skF_1','#skF_2') = '#skF_2',
    inference(negUnitSimplification,[status(thm)],[c_50,c_24,c_45782]) ).

tff(c_92,plain,
    ! [A_27,B_28] :
      ( m1_rmod_2(k2_rmod_2(A_27,B_28),A_27,B_28)
      | ~ l1_vectsp_2(B_28,A_27)
      | ~ v5_vectsp_2(B_28,A_27)
      | ~ v6_rlvect_1(B_28)
      | ~ v5_rlvect_1(B_28)
      | ~ v4_rlvect_1(B_28)
      | ~ v3_rlvect_1(B_28)
      | v3_struct_0(B_28)
      | ~ l3_vectsp_1(A_27)
      | ~ v8_vectsp_1(A_27)
      | ~ v7_vectsp_1(A_27)
      | ~ v6_vectsp_1(A_27)
      | ~ v4_group_1(A_27)
      | ~ v6_rlvect_1(A_27)
      | ~ v5_rlvect_1(A_27)
      | ~ v4_rlvect_1(A_27)
      | ~ v3_rlvect_1(A_27)
      | v3_struct_0(A_27) ),
    inference(cnfTransformation,[status(thm)],[f_297]) ).

tff(c_45808,plain,
    ( m1_rmod_2('#skF_2','#skF_1','#skF_2')
    | ~ l1_vectsp_2('#skF_2','#skF_1')
    | ~ v5_vectsp_2('#skF_2','#skF_1')
    | ~ v6_rlvect_1('#skF_2')
    | ~ v5_rlvect_1('#skF_2')
    | ~ v4_rlvect_1('#skF_2')
    | ~ v3_rlvect_1('#skF_2')
    | v3_struct_0('#skF_2')
    | ~ l3_vectsp_1('#skF_1')
    | ~ v8_vectsp_1('#skF_1')
    | ~ v7_vectsp_1('#skF_1')
    | ~ v6_vectsp_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v6_rlvect_1('#skF_1')
    | ~ v5_rlvect_1('#skF_1')
    | ~ v4_rlvect_1('#skF_1')
    | ~ v3_rlvect_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_45783,c_92]) ).

tff(c_45836,plain,
    ( m1_rmod_2('#skF_2','#skF_1','#skF_2')
    | v3_struct_0('#skF_2')
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_48,c_46,c_44,c_42,c_40,c_36,c_34,c_32,c_26,c_22,c_20,c_18,c_16,c_12,c_10,c_45808]) ).

tff(c_45837,plain,
    m1_rmod_2('#skF_2','#skF_1','#skF_2'),
    inference(negUnitSimplification,[status(thm)],[c_50,c_24,c_45836]) ).

tff(c_19557,plain,
    ! [A_1005,B_1006,D_1007] :
      ( ( k1_rmod_5(A_1005,B_1006,u1_struct_0(D_1007)) = D_1007 )
      | ( k2_group_1(A_1005) = k1_rlvect_1(A_1005) )
      | ~ m1_rmod_2(D_1007,A_1005,B_1006)
      | ~ v3_vectsp_2(D_1007,A_1005)
      | ~ m1_subset_1(u1_struct_0(D_1007),k1_zfmisc_1(u1_struct_0(B_1006)))
      | ~ l1_vectsp_2(B_1006,A_1005)
      | ~ v5_vectsp_2(B_1006,A_1005)
      | ~ v6_rlvect_1(B_1006)
      | ~ v5_rlvect_1(B_1006)
      | ~ v4_rlvect_1(B_1006)
      | ~ v3_rlvect_1(B_1006)
      | v3_struct_0(B_1006)
      | ~ l3_vectsp_1(A_1005)
      | ~ v2_vectsp_2(A_1005)
      | v10_vectsp_1(A_1005)
      | ~ v8_vectsp_1(A_1005)
      | ~ v7_vectsp_1(A_1005)
      | ~ v6_vectsp_1(A_1005)
      | ~ v7_group_1(A_1005)
      | ~ v4_group_1(A_1005)
      | ~ v6_rlvect_1(A_1005)
      | ~ v5_rlvect_1(A_1005)
      | ~ v4_rlvect_1(A_1005)
      | ~ v3_rlvect_1(A_1005)
      | v3_struct_0(A_1005) ),
    inference(cnfTransformation,[status(thm)],[f_802]) ).

tff(c_19562,plain,
    ! [A_1005,B_1006] :
      ( ( k1_rmod_5(A_1005,B_1006,u1_struct_0('#skF_2')) = '#skF_2' )
      | ( k2_group_1(A_1005) = k1_rlvect_1(A_1005) )
      | ~ m1_rmod_2('#skF_2',A_1005,B_1006)
      | ~ v3_vectsp_2('#skF_2',A_1005)
      | ~ m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0(B_1006)))
      | ~ l1_vectsp_2(B_1006,A_1005)
      | ~ v5_vectsp_2(B_1006,A_1005)
      | ~ v6_rlvect_1(B_1006)
      | ~ v5_rlvect_1(B_1006)
      | ~ v4_rlvect_1(B_1006)
      | ~ v3_rlvect_1(B_1006)
      | v3_struct_0(B_1006)
      | ~ l3_vectsp_1(A_1005)
      | ~ v2_vectsp_2(A_1005)
      | v10_vectsp_1(A_1005)
      | ~ v8_vectsp_1(A_1005)
      | ~ v7_vectsp_1(A_1005)
      | ~ v6_vectsp_1(A_1005)
      | ~ v7_group_1(A_1005)
      | ~ v4_group_1(A_1005)
      | ~ v6_rlvect_1(A_1005)
      | ~ v5_rlvect_1(A_1005)
      | ~ v4_rlvect_1(A_1005)
      | ~ v3_rlvect_1(A_1005)
      | v3_struct_0(A_1005) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_19557]) ).

tff(c_63794,plain,
    ! [A_1517,B_1518] :
      ( ( k1_rmod_5(A_1517,B_1518,'#skF_3') = '#skF_2' )
      | ( k2_group_1(A_1517) = k1_rlvect_1(A_1517) )
      | ~ m1_rmod_2('#skF_2',A_1517,B_1518)
      | ~ v3_vectsp_2('#skF_2',A_1517)
      | ~ m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0(B_1518)))
      | ~ l1_vectsp_2(B_1518,A_1517)
      | ~ v5_vectsp_2(B_1518,A_1517)
      | ~ v6_rlvect_1(B_1518)
      | ~ v5_rlvect_1(B_1518)
      | ~ v4_rlvect_1(B_1518)
      | ~ v3_rlvect_1(B_1518)
      | v3_struct_0(B_1518)
      | ~ l3_vectsp_1(A_1517)
      | ~ v2_vectsp_2(A_1517)
      | v10_vectsp_1(A_1517)
      | ~ v8_vectsp_1(A_1517)
      | ~ v7_vectsp_1(A_1517)
      | ~ v6_vectsp_1(A_1517)
      | ~ v7_group_1(A_1517)
      | ~ v4_group_1(A_1517)
      | ~ v6_rlvect_1(A_1517)
      | ~ v5_rlvect_1(A_1517)
      | ~ v4_rlvect_1(A_1517)
      | ~ v3_rlvect_1(A_1517)
      | v3_struct_0(A_1517) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_19562]) ).

tff(c_63796,plain,
    ( ( k1_rmod_5('#skF_1','#skF_2','#skF_3') = '#skF_2' )
    | ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
    | ~ v3_vectsp_2('#skF_2','#skF_1')
    | ~ m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0('#skF_2')))
    | ~ l1_vectsp_2('#skF_2','#skF_1')
    | ~ v5_vectsp_2('#skF_2','#skF_1')
    | ~ v6_rlvect_1('#skF_2')
    | ~ v5_rlvect_1('#skF_2')
    | ~ v4_rlvect_1('#skF_2')
    | ~ v3_rlvect_1('#skF_2')
    | v3_struct_0('#skF_2')
    | ~ l3_vectsp_1('#skF_1')
    | ~ v2_vectsp_2('#skF_1')
    | v10_vectsp_1('#skF_1')
    | ~ v8_vectsp_1('#skF_1')
    | ~ v7_vectsp_1('#skF_1')
    | ~ v6_vectsp_1('#skF_1')
    | ~ v7_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v6_rlvect_1('#skF_1')
    | ~ v5_rlvect_1('#skF_1')
    | ~ v4_rlvect_1('#skF_1')
    | ~ v3_rlvect_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_45837,c_63794]) ).

tff(c_63799,plain,
    ( ( k1_rmod_5('#skF_1','#skF_2','#skF_3') = '#skF_2' )
    | ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
    | v3_struct_0('#skF_2')
    | v10_vectsp_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_48,c_46,c_44,c_42,c_40,c_38,c_36,c_34,c_32,c_28,c_26,c_22,c_20,c_18,c_16,c_12,c_10,c_303,c_6,c_14,c_63796]) ).

tff(c_63801,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_50,c_30,c_24,c_4,c_2,c_63799]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG219+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
% 0.14/0.36  % Computer : n009.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 : Thu Aug  3 20:10:08 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 28.79/15.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.79/15.36  
% 28.79/15.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.79/15.40  
% 28.79/15.40  Inference rules
% 28.79/15.40  ----------------------
% 28.79/15.40  #Ref     : 10
% 28.79/15.40  #Sup     : 19180
% 28.79/15.40  #Fact    : 2
% 28.79/15.40  #Define  : 0
% 28.79/15.40  #Split   : 63
% 28.79/15.40  #Chain   : 0
% 28.79/15.40  #Close   : 0
% 28.79/15.40  
% 28.79/15.40  Ordering : KBO
% 28.79/15.40  
% 28.79/15.40  Simplification rules
% 28.79/15.40  ----------------------
% 28.79/15.40  #Subsume      : 17174
% 28.79/15.40  #Demod        : 1861
% 28.79/15.40  #Tautology    : 403
% 28.79/15.40  #SimpNegUnit  : 3293
% 28.79/15.40  #BackRed      : 1870
% 28.79/15.40  
% 28.79/15.40  #Partial instantiations: 0
% 28.79/15.40  #Strategies tried      : 1
% 28.79/15.40  
% 28.79/15.40  Timing (in seconds)
% 28.79/15.40  ----------------------
% 28.79/15.40  Preprocessing        : 0.82
% 28.79/15.40  Parsing              : 0.41
% 28.79/15.41  CNF conversion       : 0.07
% 28.79/15.41  Main loop            : 13.43
% 28.79/15.41  Inferencing          : 2.31
% 28.79/15.41  Reduction            : 5.79
% 28.79/15.41  Demodulation         : 4.67
% 28.79/15.41  BG Simplification    : 0.14
% 28.79/15.41  Subsumption          : 4.84
% 28.79/15.41  Abstraction          : 0.21
% 28.79/15.41  MUC search           : 0.00
% 28.79/15.41  Cooper               : 0.00
% 28.79/15.41  Total                : 14.32
% 28.79/15.41  Index Insertion      : 0.00
% 28.79/15.41  Index Deletion       : 0.00
% 28.79/15.41  Index Matching       : 0.00
% 28.79/15.41  BG Taut test         : 0.00
%------------------------------------------------------------------------------