TSTP Solution File: ALG216+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG216+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 10:32:22 EDT 2023

% Result   : Theorem 6.91s 2.57s
% Output   : CNFRefutation 7.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   64
% Syntax   : Number of formulae    :  149 (  52 unt;  52 typ;   0 def)
%            Number of atoms       :  260 (  24 equ)
%            Maximal formula atoms :   23 (   2 avg)
%            Number of connectives :  273 ( 110   ~; 100   |;  44   &)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  37   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :   26 (  24 usr;   1 prp; 0-3 aty)
%            Number of functors    :   28 (  28 usr;  15 con; 0-3 aty)
%            Number of variables   :   64 (;  64   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ v1_rmod_5 > v5_vectsp_2 > r2_hidden > r1_tarski > m1_subset_1 > l1_vectsp_2 > v8_vectsp_1 > v7_vectsp_1 > v6_vectsp_1 > v6_rlvect_1 > v5_rlvect_1 > v4_rlvect_1 > v4_group_1 > v3_struct_0 > v3_rlvect_1 > v1_xboole_0 > v1_finset_1 > l3_vectsp_1 > l2_vectsp_1 > l2_struct_0 > l1_vectsp_1 > l1_struct_0 > l1_rlvect_1 > l1_group_1 > k8_rlvect_2 > k2_tarski > #nlpp > u1_struct_0 > k2_group_1 > k1_zfmisc_1 > k1_rlvect_1 > k1_xboole_0 > #skF_7 > #skF_5 > #skF_21 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_8 > #skF_16 > #skF_14 > #skF_10 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_4 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff(k8_rlvect_2,type,
    k8_rlvect_2: ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

tff(k2_tarski,type,
    k2_tarski: ( $i * $i ) > $i ).

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

tff(v1_rmod_5,type,
    v1_rmod_5: ( $i * $i * $i ) > $o ).

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

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

tff('#skF_13',type,
    '#skF_13': $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(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(l1_vectsp_1,type,
    l1_vectsp_1: $i > $o ).

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

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

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

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(v1_finset_1,type,
    v1_finset_1: $i > $o ).

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

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

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

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

tff(f_78,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)
          & 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) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(B))
               => ( ( k1_rlvect_1(A) != k2_group_1(A) )
                 => ( ~ v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B)
                    & ~ v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_rmod_5) ).

tff(f_311,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_206,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_200,axiom,
    ! [A] :
      ( l2_struct_0(A)
     => l1_struct_0(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).

tff(f_305,axiom,
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_vectsp_2(B,A)
         => l1_rlvect_1(B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).

tff(f_196,axiom,
    ! [A] :
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).

tff(f_278,axiom,
    ! [A] :
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).

tff(f_298,axiom,
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_finset_1(k8_rlvect_2(A,B,C))
        & m1_subset_1(k8_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_rlvect_2) ).

tff(f_178,axiom,
    ! [A,B] : ( k2_tarski(A,B) = k2_tarski(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

tff(f_274,axiom,
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( k8_rlvect_2(A,B,C) = k2_tarski(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_rlvect_2) ).

tff(f_364,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) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( v1_rmod_5(k8_rlvect_2(B,C,D),A,B)
                   => ( ( k1_rlvect_1(A) = k2_group_1(A) )
                      | ( ( C != k1_rlvect_1(B) )
                        & ( D != k1_rlvect_1(B) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_rmod_5) ).

tff(f_253,axiom,
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( k8_rlvect_2(A,B,C) = k8_rlvect_2(A,C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k8_rlvect_2) ).

tff(c_22,plain,
    l3_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_174,plain,
    ! [A_84] :
      ( l2_vectsp_1(A_84)
      | ~ l3_vectsp_1(A_84) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_181,plain,
    l2_vectsp_1('#skF_1'),
    inference(resolution,[status(thm)],[c_22,c_174]) ).

tff(c_193,plain,
    ! [A_87] :
      ( l2_struct_0(A_87)
      | ~ l2_vectsp_1(A_87) ),
    inference(cnfTransformation,[status(thm)],[f_206]) ).

tff(c_204,plain,
    l2_struct_0('#skF_1'),
    inference(resolution,[status(thm)],[c_181,c_193]) ).

tff(c_207,plain,
    ! [A_89] :
      ( l1_struct_0(A_89)
      | ~ l2_struct_0(A_89) ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_226,plain,
    l1_struct_0('#skF_1'),
    inference(resolution,[status(thm)],[c_204,c_207]) ).

tff(c_8,plain,
    l1_vectsp_2('#skF_2','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_950,plain,
    ! [B_213,A_214] :
      ( l1_rlvect_1(B_213)
      | ~ l1_vectsp_2(B_213,A_214)
      | ~ l1_struct_0(A_214) ),
    inference(cnfTransformation,[status(thm)],[f_305]) ).

tff(c_959,plain,
    ( l1_rlvect_1('#skF_2')
    | ~ l1_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_8,c_950]) ).

tff(c_964,plain,
    l1_rlvect_1('#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_226,c_959]) ).

tff(c_108,plain,
    ! [A_36] :
      ( l2_struct_0(A_36)
      | ~ l1_rlvect_1(A_36) ),
    inference(cnfTransformation,[status(thm)],[f_196]) ).

tff(c_150,plain,
    ! [A_57] :
      ( m1_subset_1(k1_rlvect_1(A_57),u1_struct_0(A_57))
      | ~ l2_struct_0(A_57) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_229,plain,
    ! [A_36] :
      ( l1_struct_0(A_36)
      | ~ l1_rlvect_1(A_36) ),
    inference(resolution,[status(thm)],[c_108,c_207]) ).

tff(c_20,plain,
    ~ v3_struct_0('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_6,plain,
    m1_subset_1('#skF_3',u1_struct_0('#skF_2')),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1167,plain,
    ! [A_264,B_265,C_266] :
      ( v1_finset_1(k8_rlvect_2(A_264,B_265,C_266))
      | ~ m1_subset_1(C_266,u1_struct_0(A_264))
      | ~ m1_subset_1(B_265,u1_struct_0(A_264))
      | ~ l1_struct_0(A_264)
      | v3_struct_0(A_264) ),
    inference(cnfTransformation,[status(thm)],[f_298]) ).

tff(c_1176,plain,
    ! [B_265] :
      ( v1_finset_1(k8_rlvect_2('#skF_2',B_265,'#skF_3'))
      | ~ m1_subset_1(B_265,u1_struct_0('#skF_2'))
      | ~ l1_struct_0('#skF_2')
      | v3_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_6,c_1167]) ).

tff(c_1182,plain,
    ! [B_265] :
      ( v1_finset_1(k8_rlvect_2('#skF_2',B_265,'#skF_3'))
      | ~ m1_subset_1(B_265,u1_struct_0('#skF_2'))
      | ~ l1_struct_0('#skF_2') ),
    inference(negUnitSimplification,[status(thm)],[c_20,c_1176]) ).

tff(c_1186,plain,
    ~ l1_struct_0('#skF_2'),
    inference(splitLeft,[status(thm)],[c_1182]) ).

tff(c_1189,plain,
    ~ l1_rlvect_1('#skF_2'),
    inference(resolution,[status(thm)],[c_229,c_1186]) ).

tff(c_1196,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_964,c_1189]) ).

tff(c_1199,plain,
    ! [B_269] :
      ( v1_finset_1(k8_rlvect_2('#skF_2',B_269,'#skF_3'))
      | ~ m1_subset_1(B_269,u1_struct_0('#skF_2')) ),
    inference(splitRight,[status(thm)],[c_1182]) ).

tff(c_1218,plain,
    ( v1_finset_1(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'))
    | ~ l2_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_150,c_1199]) ).

tff(c_1238,plain,
    ~ l2_struct_0('#skF_2'),
    inference(splitLeft,[status(thm)],[c_1218]) ).

tff(c_1241,plain,
    ~ l1_rlvect_1('#skF_2'),
    inference(resolution,[status(thm)],[c_108,c_1238]) ).

tff(c_1245,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_964,c_1241]) ).

tff(c_1247,plain,
    l2_struct_0('#skF_2'),
    inference(splitRight,[status(thm)],[c_1218]) ).

tff(c_90,plain,
    ! [B_34,A_33] : ( k2_tarski(B_34,A_33) = k2_tarski(A_33,B_34) ),
    inference(cnfTransformation,[status(thm)],[f_178]) ).

tff(c_1198,plain,
    l1_struct_0('#skF_2'),
    inference(splitRight,[status(thm)],[c_1182]) ).

tff(c_1221,plain,
    ! [A_270,B_271,C_272] :
      ( ( k8_rlvect_2(A_270,B_271,C_272) = k2_tarski(B_271,C_272) )
      | ~ m1_subset_1(C_272,u1_struct_0(A_270))
      | ~ m1_subset_1(B_271,u1_struct_0(A_270))
      | ~ l1_struct_0(A_270)
      | v3_struct_0(A_270) ),
    inference(cnfTransformation,[status(thm)],[f_274]) ).

tff(c_1230,plain,
    ! [B_271] :
      ( ( k8_rlvect_2('#skF_2',B_271,'#skF_3') = k2_tarski(B_271,'#skF_3') )
      | ~ m1_subset_1(B_271,u1_struct_0('#skF_2'))
      | ~ l1_struct_0('#skF_2')
      | v3_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_6,c_1221]) ).

tff(c_1236,plain,
    ! [B_271] :
      ( ( k8_rlvect_2('#skF_2',B_271,'#skF_3') = k2_tarski(B_271,'#skF_3') )
      | ~ m1_subset_1(B_271,u1_struct_0('#skF_2'))
      | v3_struct_0('#skF_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_1198,c_1230]) ).

tff(c_1255,plain,
    ! [B_274] :
      ( ( k8_rlvect_2('#skF_2',B_274,'#skF_3') = k2_tarski(B_274,'#skF_3') )
      | ~ m1_subset_1(B_274,u1_struct_0('#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_20,c_1236]) ).

tff(c_1263,plain,
    ( ( k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3') = k2_tarski(k1_rlvect_1('#skF_2'),'#skF_3') )
    | ~ l2_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_150,c_1255]) ).

tff(c_1276,plain,
    k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3') = k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_1247,c_90,c_1263]) ).

tff(c_369,plain,
    ! [B_118,A_119] :
      ( l1_rlvect_1(B_118)
      | ~ l1_vectsp_2(B_118,A_119)
      | ~ l1_struct_0(A_119) ),
    inference(cnfTransformation,[status(thm)],[f_305]) ).

tff(c_378,plain,
    ( l1_rlvect_1('#skF_2')
    | ~ l1_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_8,c_369]) ).

tff(c_383,plain,
    l1_rlvect_1('#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_226,c_378]) ).

tff(c_548,plain,
    ! [A_163,B_164,C_165] :
      ( v1_finset_1(k8_rlvect_2(A_163,B_164,C_165))
      | ~ m1_subset_1(C_165,u1_struct_0(A_163))
      | ~ m1_subset_1(B_164,u1_struct_0(A_163))
      | ~ l1_struct_0(A_163)
      | v3_struct_0(A_163) ),
    inference(cnfTransformation,[status(thm)],[f_298]) ).

tff(c_557,plain,
    ! [B_164] :
      ( v1_finset_1(k8_rlvect_2('#skF_2',B_164,'#skF_3'))
      | ~ m1_subset_1(B_164,u1_struct_0('#skF_2'))
      | ~ l1_struct_0('#skF_2')
      | v3_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_6,c_548]) ).

tff(c_563,plain,
    ! [B_164] :
      ( v1_finset_1(k8_rlvect_2('#skF_2',B_164,'#skF_3'))
      | ~ m1_subset_1(B_164,u1_struct_0('#skF_2'))
      | ~ l1_struct_0('#skF_2') ),
    inference(negUnitSimplification,[status(thm)],[c_20,c_557]) ).

tff(c_571,plain,
    ~ l1_struct_0('#skF_2'),
    inference(splitLeft,[status(thm)],[c_563]) ).

tff(c_574,plain,
    ~ l1_rlvect_1('#skF_2'),
    inference(resolution,[status(thm)],[c_229,c_571]) ).

tff(c_581,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_383,c_574]) ).

tff(c_584,plain,
    ! [B_169] :
      ( v1_finset_1(k8_rlvect_2('#skF_2',B_169,'#skF_3'))
      | ~ m1_subset_1(B_169,u1_struct_0('#skF_2')) ),
    inference(splitRight,[status(thm)],[c_563]) ).

tff(c_603,plain,
    ( v1_finset_1(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'))
    | ~ l2_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_150,c_584]) ).

tff(c_651,plain,
    ~ l2_struct_0('#skF_2'),
    inference(splitLeft,[status(thm)],[c_603]) ).

tff(c_654,plain,
    ~ l1_rlvect_1('#skF_2'),
    inference(resolution,[status(thm)],[c_108,c_651]) ).

tff(c_658,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_383,c_654]) ).

tff(c_660,plain,
    l2_struct_0('#skF_2'),
    inference(splitRight,[status(thm)],[c_603]) ).

tff(c_40,plain,
    ~ v3_struct_0('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_4,plain,
    k2_group_1('#skF_1') != k1_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_38,plain,
    v3_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_36,plain,
    v4_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_34,plain,
    v5_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_32,plain,
    v6_rlvect_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_30,plain,
    v4_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_28,plain,
    v6_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_26,plain,
    v7_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_24,plain,
    v8_vectsp_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_18,plain,
    v3_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_16,plain,
    v4_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_14,plain,
    v5_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_12,plain,
    v6_rlvect_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_10,plain,
    v5_vectsp_2('#skF_2','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_2,plain,
    ( v1_rmod_5(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'),'#skF_1','#skF_2')
    | v1_rmod_5(k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_265,plain,
    v1_rmod_5(k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
    inference(splitLeft,[status(thm)],[c_2]) ).

tff(c_843,plain,
    ! [A_188,B_189,C_190] :
      ( ( k2_group_1(A_188) = k1_rlvect_1(A_188) )
      | ~ v1_rmod_5(k8_rlvect_2(B_189,C_190,k1_rlvect_1(B_189)),A_188,B_189)
      | ~ m1_subset_1(k1_rlvect_1(B_189),u1_struct_0(B_189))
      | ~ m1_subset_1(C_190,u1_struct_0(B_189))
      | ~ l1_vectsp_2(B_189,A_188)
      | ~ v5_vectsp_2(B_189,A_188)
      | ~ v6_rlvect_1(B_189)
      | ~ v5_rlvect_1(B_189)
      | ~ v4_rlvect_1(B_189)
      | ~ v3_rlvect_1(B_189)
      | v3_struct_0(B_189)
      | ~ l3_vectsp_1(A_188)
      | ~ v8_vectsp_1(A_188)
      | ~ v7_vectsp_1(A_188)
      | ~ v6_vectsp_1(A_188)
      | ~ v4_group_1(A_188)
      | ~ v6_rlvect_1(A_188)
      | ~ v5_rlvect_1(A_188)
      | ~ v4_rlvect_1(A_188)
      | ~ v3_rlvect_1(A_188)
      | v3_struct_0(A_188) ),
    inference(cnfTransformation,[status(thm)],[f_364]) ).

tff(c_846,plain,
    ( ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
    | ~ m1_subset_1(k1_rlvect_1('#skF_2'),u1_struct_0('#skF_2'))
    | ~ m1_subset_1('#skF_3',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')
    | ~ 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_265,c_843]) ).

tff(c_849,plain,
    ( ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
    | ~ m1_subset_1(k1_rlvect_1('#skF_2'),u1_struct_0('#skF_2'))
    | v3_struct_0('#skF_2')
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_36,c_34,c_32,c_30,c_28,c_26,c_24,c_22,c_18,c_16,c_14,c_12,c_10,c_8,c_6,c_846]) ).

tff(c_850,plain,
    ~ m1_subset_1(k1_rlvect_1('#skF_2'),u1_struct_0('#skF_2')),
    inference(negUnitSimplification,[status(thm)],[c_40,c_20,c_4,c_849]) ).

tff(c_853,plain,
    ~ l2_struct_0('#skF_2'),
    inference(resolution,[status(thm)],[c_150,c_850]) ).

tff(c_857,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_660,c_853]) ).

tff(c_858,plain,
    v1_rmod_5(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'),'#skF_1','#skF_2'),
    inference(splitRight,[status(thm)],[c_2]) ).

tff(c_1327,plain,
    v1_rmod_5(k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_1276,c_858]) ).

tff(c_1338,plain,
    ! [A_278,C_279,B_280] :
      ( ( k8_rlvect_2(A_278,C_279,B_280) = k8_rlvect_2(A_278,B_280,C_279) )
      | ~ m1_subset_1(C_279,u1_struct_0(A_278))
      | ~ m1_subset_1(B_280,u1_struct_0(A_278))
      | ~ l1_struct_0(A_278)
      | v3_struct_0(A_278) ),
    inference(cnfTransformation,[status(thm)],[f_253]) ).

tff(c_1347,plain,
    ! [B_280] :
      ( ( k8_rlvect_2('#skF_2',B_280,'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',B_280) )
      | ~ m1_subset_1(B_280,u1_struct_0('#skF_2'))
      | ~ l1_struct_0('#skF_2')
      | v3_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_6,c_1338]) ).

tff(c_1353,plain,
    ! [B_280] :
      ( ( k8_rlvect_2('#skF_2',B_280,'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',B_280) )
      | ~ m1_subset_1(B_280,u1_struct_0('#skF_2'))
      | v3_struct_0('#skF_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_1198,c_1347]) ).

tff(c_1363,plain,
    ! [B_282] :
      ( ( k8_rlvect_2('#skF_2',B_282,'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',B_282) )
      | ~ m1_subset_1(B_282,u1_struct_0('#skF_2')) ),
    inference(negUnitSimplification,[status(thm)],[c_20,c_1353]) ).

tff(c_1371,plain,
    ( ( k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')) )
    | ~ l2_struct_0('#skF_2') ),
    inference(resolution,[status(thm)],[c_150,c_1363]) ).

tff(c_1383,plain,
    k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')) = k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_1247,c_1276,c_1371]) ).

tff(c_859,plain,
    ~ v1_rmod_5(k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
    inference(splitRight,[status(thm)],[c_2]) ).

tff(c_1387,plain,
    ~ v1_rmod_5(k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_1383,c_859]) ).

tff(c_1390,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1327,c_1387]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : ALG216+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.15  % 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
% 0.16/0.36  % Computer : n009.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu Aug  3 20:24:53 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 6.91/2.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.91/2.58  
% 6.91/2.58  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.10/2.63  
% 7.10/2.63  Inference rules
% 7.10/2.63  ----------------------
% 7.10/2.63  #Ref     : 0
% 7.10/2.63  #Sup     : 255
% 7.10/2.63  #Fact    : 0
% 7.10/2.63  #Define  : 0
% 7.10/2.63  #Split   : 13
% 7.10/2.63  #Chain   : 0
% 7.10/2.63  #Close   : 0
% 7.10/2.63  
% 7.10/2.63  Ordering : KBO
% 7.10/2.63  
% 7.10/2.63  Simplification rules
% 7.10/2.63  ----------------------
% 7.10/2.63  #Subsume      : 28
% 7.10/2.63  #Demod        : 82
% 7.10/2.63  #Tautology    : 59
% 7.10/2.63  #SimpNegUnit  : 42
% 7.10/2.63  #BackRed      : 10
% 7.10/2.63  
% 7.10/2.63  #Partial instantiations: 0
% 7.10/2.63  #Strategies tried      : 1
% 7.10/2.63  
% 7.10/2.63  Timing (in seconds)
% 7.10/2.63  ----------------------
% 7.10/2.63  Preprocessing        : 0.65
% 7.10/2.63  Parsing              : 0.33
% 7.10/2.63  CNF conversion       : 0.05
% 7.10/2.63  Main loop            : 0.86
% 7.10/2.63  Inferencing          : 0.30
% 7.10/2.63  Reduction            : 0.28
% 7.10/2.63  Demodulation         : 0.18
% 7.10/2.63  BG Simplification    : 0.04
% 7.10/2.63  Subsumption          : 0.16
% 7.10/2.63  Abstraction          : 0.03
% 7.10/2.63  MUC search           : 0.00
% 7.10/2.63  Cooper               : 0.00
% 7.10/2.63  Total                : 1.58
% 7.10/2.63  Index Insertion      : 0.00
% 7.10/2.63  Index Deletion       : 0.00
% 7.10/2.63  Index Matching       : 0.00
% 7.10/2.63  BG Taut test         : 0.00
%------------------------------------------------------------------------------