TSTP Solution File: GRP645+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP645+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 : n011.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 10:41:47 EDT 2023

% Result   : Theorem 42.33s 27.38s
% Output   : CNFRefutation 42.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  103 (  23 unt;  47 typ;   0 def)
%            Number of atoms       :  233 (  32 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  296 ( 119   ~; 126   |;  37   &)
%                                         (   1 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   63 (  38   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-3 aty)
%            Number of functors    :   30 (  30 usr;   9 con; 0-3 aty)
%            Number of variables   :   58 (;  58   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ v1_partfun1 > v1_funct_2 > m2_relset_1 > m1_relset_1 > r2_hidden > r1_tarski > m1_subset_1 > m1_group_2 > v4_group_1 > v3_struct_0 > v3_group_1 > v1_xboole_0 > v1_relat_1 > v1_group_1 > v1_funct_1 > l1_struct_0 > l1_group_1 > k9_group_2 > k8_group_2 > k3_xboole_0 > k2_zfmisc_1 > k1_funct_1 > g1_group_1 > #nlpp > u1_struct_0 > u1_group_1 > k1_zfmisc_1 > k1_latsubgr > k1_group_3 > k1_xboole_0 > #skF_9 > #skF_7 > #skF_11 > #skF_18 > #skF_17 > #skF_16 > #skF_14 > #skF_15 > #skF_5 > #skF_6 > #skF_13 > #skF_2 > #skF_10 > #skF_3 > #skF_1 > #skF_8 > #skF_12 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff(k8_group_2,type,
    k8_group_2: ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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_10',type,
    '#skF_10': ( $i * $i ) > $i ).

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

tff(k1_group_3,type,
    k1_group_3: $i > $i ).

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

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

tff(k1_latsubgr,type,
    k1_latsubgr: $i > $i ).

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

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

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

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

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

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

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

tff(k3_xboole_0,type,
    k3_xboole_0: ( $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': $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(k9_group_2,type,
    k9_group_2: ( $i * $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': ( $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)
          & v3_group_1(A)
          & v4_group_1(A)
          & l1_group_1(A) )
       => ! [B] :
            ( ( v1_group_1(B)
              & m1_group_2(B,A) )
           => ! [C] :
                ( ( v1_group_1(C)
                  & m1_group_2(C,A) )
               => ( k1_funct_1(k1_latsubgr(A),k9_group_2(A,B,C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A),B),k1_funct_1(k1_latsubgr(A),C)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_latsubgr) ).

tff(f_386,axiom,
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => ( k9_group_2(A,B,C) = k8_group_2(A,B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_group_2) ).

tff(f_131,axiom,
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => ( k9_group_2(A,B,C) = k9_group_2(A,C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k9_group_2) ).

tff(f_216,axiom,
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => ( v1_group_1(k9_group_2(A,B,C))
        & m1_group_2(k9_group_2(A,B,C),A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_2) ).

tff(f_182,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_funct_1(k1_latsubgr(A))
        & v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
        & m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).

tff(f_156,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( B = k1_latsubgr(A) )
          <=> ! [C] :
                ( ( v1_group_1(C)
                  & m1_group_2(C,A) )
               => ( k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).

tff(f_417,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_1(C)
                & m1_group_2(C,A) )
             => ( u1_struct_0(k9_group_2(A,B,C)) = k3_xboole_0(k1_funct_1(k1_latsubgr(A),B),k1_funct_1(k1_latsubgr(A),C)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsubgr) ).

tff(f_116,axiom,
    ! [A,B] : ( k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

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

tff(c_16,plain,
    v3_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_14,plain,
    v4_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_12,plain,
    l1_group_1('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_4,plain,
    m1_group_2('#skF_3','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_8,plain,
    m1_group_2('#skF_2','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_1598,plain,
    ! [A_392,B_393,C_394] :
      ( ( k9_group_2(A_392,B_393,C_394) = k8_group_2(A_392,B_393,C_394) )
      | ~ m1_group_2(C_394,A_392)
      | ~ m1_group_2(B_393,A_392)
      | ~ l1_group_1(A_392)
      | ~ v4_group_1(A_392)
      | ~ v3_group_1(A_392)
      | v3_struct_0(A_392) ),
    inference(cnfTransformation,[status(thm)],[f_386]) ).

tff(c_1610,plain,
    ! [B_393] :
      ( ( k9_group_2('#skF_1',B_393,'#skF_2') = k8_group_2('#skF_1',B_393,'#skF_2') )
      | ~ m1_group_2(B_393,'#skF_1')
      | ~ l1_group_1('#skF_1')
      | ~ v4_group_1('#skF_1')
      | ~ v3_group_1('#skF_1')
      | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_8,c_1598]) ).

tff(c_1626,plain,
    ! [B_393] :
      ( ( k9_group_2('#skF_1',B_393,'#skF_2') = k8_group_2('#skF_1',B_393,'#skF_2') )
      | ~ m1_group_2(B_393,'#skF_1')
      | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_1610]) ).

tff(c_1632,plain,
    ! [B_395] :
      ( ( k9_group_2('#skF_1',B_395,'#skF_2') = k8_group_2('#skF_1',B_395,'#skF_2') )
      | ~ m1_group_2(B_395,'#skF_1') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_1626]) ).

tff(c_1672,plain,
    k9_group_2('#skF_1','#skF_3','#skF_2') = k8_group_2('#skF_1','#skF_3','#skF_2'),
    inference(resolution,[status(thm)],[c_4,c_1632]) ).

tff(c_1426,plain,
    ! [A_384,C_385,B_386] :
      ( ( k9_group_2(A_384,C_385,B_386) = k9_group_2(A_384,B_386,C_385) )
      | ~ m1_group_2(C_385,A_384)
      | ~ m1_group_2(B_386,A_384)
      | ~ l1_group_1(A_384)
      | ~ v4_group_1(A_384)
      | ~ v3_group_1(A_384)
      | v3_struct_0(A_384) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_1434,plain,
    ! [B_386] :
      ( ( k9_group_2('#skF_1',B_386,'#skF_2') = k9_group_2('#skF_1','#skF_2',B_386) )
      | ~ m1_group_2(B_386,'#skF_1')
      | ~ l1_group_1('#skF_1')
      | ~ v4_group_1('#skF_1')
      | ~ v3_group_1('#skF_1')
      | v3_struct_0('#skF_1') ),
    inference(resolution,[status(thm)],[c_8,c_1426]) ).

tff(c_1442,plain,
    ! [B_386] :
      ( ( k9_group_2('#skF_1',B_386,'#skF_2') = k9_group_2('#skF_1','#skF_2',B_386) )
      | ~ m1_group_2(B_386,'#skF_1')
      | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_1434]) ).

tff(c_1448,plain,
    ! [B_387] :
      ( ( k9_group_2('#skF_1',B_387,'#skF_2') = k9_group_2('#skF_1','#skF_2',B_387) )
      | ~ m1_group_2(B_387,'#skF_1') ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_1442]) ).

tff(c_1481,plain,
    k9_group_2('#skF_1','#skF_2','#skF_3') = k9_group_2('#skF_1','#skF_3','#skF_2'),
    inference(resolution,[status(thm)],[c_4,c_1448]) ).

tff(c_84,plain,
    ! [A_43,B_44,C_45] :
      ( v1_group_1(k9_group_2(A_43,B_44,C_45))
      | ~ m1_group_2(C_45,A_43)
      | ~ m1_group_2(B_44,A_43)
      | ~ l1_group_1(A_43)
      | ~ v4_group_1(A_43)
      | ~ v3_group_1(A_43)
      | v3_struct_0(A_43) ),
    inference(cnfTransformation,[status(thm)],[f_216]) ).

tff(c_1489,plain,
    ( v1_group_1(k9_group_2('#skF_1','#skF_3','#skF_2'))
    | ~ m1_group_2('#skF_3','#skF_1')
    | ~ m1_group_2('#skF_2','#skF_1')
    | ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_1481,c_84]) ).

tff(c_1496,plain,
    ( v1_group_1(k9_group_2('#skF_1','#skF_3','#skF_2'))
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_8,c_4,c_1489]) ).

tff(c_1497,plain,
    v1_group_1(k9_group_2('#skF_1','#skF_3','#skF_2')),
    inference(negUnitSimplification,[status(thm)],[c_18,c_1496]) ).

tff(c_1734,plain,
    v1_group_1(k8_group_2('#skF_1','#skF_3','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_1672,c_1497]) ).

tff(c_82,plain,
    ! [A_43,B_44,C_45] :
      ( m1_group_2(k9_group_2(A_43,B_44,C_45),A_43)
      | ~ m1_group_2(C_45,A_43)
      | ~ m1_group_2(B_44,A_43)
      | ~ l1_group_1(A_43)
      | ~ v4_group_1(A_43)
      | ~ v3_group_1(A_43)
      | v3_struct_0(A_43) ),
    inference(cnfTransformation,[status(thm)],[f_216]) ).

tff(c_1739,plain,
    ( m1_group_2(k8_group_2('#skF_1','#skF_3','#skF_2'),'#skF_1')
    | ~ m1_group_2('#skF_2','#skF_1')
    | ~ m1_group_2('#skF_3','#skF_1')
    | ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_1672,c_82]) ).

tff(c_1746,plain,
    ( m1_group_2(k8_group_2('#skF_1','#skF_3','#skF_2'),'#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_4,c_8,c_1739]) ).

tff(c_1747,plain,
    m1_group_2(k8_group_2('#skF_1','#skF_3','#skF_2'),'#skF_1'),
    inference(negUnitSimplification,[status(thm)],[c_18,c_1746]) ).

tff(c_68,plain,
    ! [A_39] :
      ( v1_funct_1(k1_latsubgr(A_39))
      | ~ l1_group_1(A_39)
      | ~ v4_group_1(A_39)
      | ~ v3_group_1(A_39)
      | v3_struct_0(A_39) ),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_64,plain,
    ! [A_39] :
      ( m2_relset_1(k1_latsubgr(A_39),k1_group_3(A_39),k1_zfmisc_1(u1_struct_0(A_39)))
      | ~ l1_group_1(A_39)
      | ~ v4_group_1(A_39)
      | ~ v3_group_1(A_39)
      | v3_struct_0(A_39) ),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_66,plain,
    ! [A_39] :
      ( v1_funct_2(k1_latsubgr(A_39),k1_group_3(A_39),k1_zfmisc_1(u1_struct_0(A_39)))
      | ~ l1_group_1(A_39)
      | ~ v4_group_1(A_39)
      | ~ v3_group_1(A_39)
      | v3_struct_0(A_39) ),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_2278,plain,
    ! [A_411,C_412] :
      ( ( k1_funct_1(k1_latsubgr(A_411),C_412) = u1_struct_0(C_412) )
      | ~ m1_group_2(C_412,A_411)
      | ~ v1_group_1(C_412)
      | ~ m2_relset_1(k1_latsubgr(A_411),k1_group_3(A_411),k1_zfmisc_1(u1_struct_0(A_411)))
      | ~ v1_funct_2(k1_latsubgr(A_411),k1_group_3(A_411),k1_zfmisc_1(u1_struct_0(A_411)))
      | ~ v1_funct_1(k1_latsubgr(A_411))
      | ~ l1_group_1(A_411)
      | ~ v4_group_1(A_411)
      | ~ v3_group_1(A_411)
      | v3_struct_0(A_411) ),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_5811,plain,
    ! [A_490,C_491] :
      ( ( k1_funct_1(k1_latsubgr(A_490),C_491) = u1_struct_0(C_491) )
      | ~ m1_group_2(C_491,A_490)
      | ~ v1_group_1(C_491)
      | ~ m2_relset_1(k1_latsubgr(A_490),k1_group_3(A_490),k1_zfmisc_1(u1_struct_0(A_490)))
      | ~ v1_funct_1(k1_latsubgr(A_490))
      | ~ l1_group_1(A_490)
      | ~ v4_group_1(A_490)
      | ~ v3_group_1(A_490)
      | v3_struct_0(A_490) ),
    inference(resolution,[status(thm)],[c_66,c_2278]) ).

tff(c_13654,plain,
    ! [A_571,C_572] :
      ( ( k1_funct_1(k1_latsubgr(A_571),C_572) = u1_struct_0(C_572) )
      | ~ m1_group_2(C_572,A_571)
      | ~ v1_group_1(C_572)
      | ~ v1_funct_1(k1_latsubgr(A_571))
      | ~ l1_group_1(A_571)
      | ~ v4_group_1(A_571)
      | ~ v3_group_1(A_571)
      | v3_struct_0(A_571) ),
    inference(resolution,[status(thm)],[c_64,c_5811]) ).

tff(c_73873,plain,
    ! [A_887,C_888] :
      ( ( k1_funct_1(k1_latsubgr(A_887),C_888) = u1_struct_0(C_888) )
      | ~ m1_group_2(C_888,A_887)
      | ~ v1_group_1(C_888)
      | ~ l1_group_1(A_887)
      | ~ v4_group_1(A_887)
      | ~ v3_group_1(A_887)
      | v3_struct_0(A_887) ),
    inference(resolution,[status(thm)],[c_68,c_13654]) ).

tff(c_10,plain,
    v1_group_1('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_6,plain,
    v1_group_1('#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_1735,plain,
    k9_group_2('#skF_1','#skF_2','#skF_3') = k8_group_2('#skF_1','#skF_3','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_1672,c_1481]) ).

tff(c_1911,plain,
    ! [A_402,B_403,C_404] :
      ( ( k3_xboole_0(k1_funct_1(k1_latsubgr(A_402),B_403),k1_funct_1(k1_latsubgr(A_402),C_404)) = u1_struct_0(k9_group_2(A_402,B_403,C_404)) )
      | ~ m1_group_2(C_404,A_402)
      | ~ v1_group_1(C_404)
      | ~ m1_group_2(B_403,A_402)
      | ~ v1_group_1(B_403)
      | ~ l1_group_1(A_402)
      | ~ v4_group_1(A_402)
      | ~ v3_group_1(A_402)
      | v3_struct_0(A_402) ),
    inference(cnfTransformation,[status(thm)],[f_417]) ).

tff(c_44,plain,
    ! [B_23,A_22] : ( k3_xboole_0(B_23,A_22) = k3_xboole_0(A_22,B_23) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_1917,plain,
    ! [A_402,C_404,B_403] :
      ( ( k3_xboole_0(k1_funct_1(k1_latsubgr(A_402),C_404),k1_funct_1(k1_latsubgr(A_402),B_403)) = u1_struct_0(k9_group_2(A_402,B_403,C_404)) )
      | ~ m1_group_2(C_404,A_402)
      | ~ v1_group_1(C_404)
      | ~ m1_group_2(B_403,A_402)
      | ~ v1_group_1(B_403)
      | ~ l1_group_1(A_402)
      | ~ v4_group_1(A_402)
      | ~ v3_group_1(A_402)
      | v3_struct_0(A_402) ),
    inference(superposition,[status(thm),theory(equality)],[c_1911,c_44]) ).

tff(c_2,plain,
    k3_xboole_0(k1_funct_1(k1_latsubgr('#skF_1'),'#skF_2'),k1_funct_1(k1_latsubgr('#skF_1'),'#skF_3')) != k1_funct_1(k1_latsubgr('#skF_1'),k9_group_2('#skF_1','#skF_2','#skF_3')),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_201,plain,
    k3_xboole_0(k1_funct_1(k1_latsubgr('#skF_1'),'#skF_3'),k1_funct_1(k1_latsubgr('#skF_1'),'#skF_2')) != k1_funct_1(k1_latsubgr('#skF_1'),k9_group_2('#skF_1','#skF_2','#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_44,c_2]) ).

tff(c_1482,plain,
    k3_xboole_0(k1_funct_1(k1_latsubgr('#skF_1'),'#skF_3'),k1_funct_1(k1_latsubgr('#skF_1'),'#skF_2')) != k1_funct_1(k1_latsubgr('#skF_1'),k9_group_2('#skF_1','#skF_3','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_1481,c_201]) ).

tff(c_10029,plain,
    k3_xboole_0(k1_funct_1(k1_latsubgr('#skF_1'),'#skF_3'),k1_funct_1(k1_latsubgr('#skF_1'),'#skF_2')) != k1_funct_1(k1_latsubgr('#skF_1'),k8_group_2('#skF_1','#skF_3','#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_1672,c_1482]) ).

tff(c_10032,plain,
    ( ( k1_funct_1(k1_latsubgr('#skF_1'),k8_group_2('#skF_1','#skF_3','#skF_2')) != u1_struct_0(k9_group_2('#skF_1','#skF_2','#skF_3')) )
    | ~ m1_group_2('#skF_3','#skF_1')
    | ~ v1_group_1('#skF_3')
    | ~ m1_group_2('#skF_2','#skF_1')
    | ~ v1_group_1('#skF_2')
    | ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_1917,c_10029]) ).

tff(c_10043,plain,
    ( ( k1_funct_1(k1_latsubgr('#skF_1'),k8_group_2('#skF_1','#skF_3','#skF_2')) != u1_struct_0(k8_group_2('#skF_1','#skF_3','#skF_2')) )
    | v3_struct_0('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_10,c_8,c_6,c_4,c_1735,c_10032]) ).

tff(c_10044,plain,
    k1_funct_1(k1_latsubgr('#skF_1'),k8_group_2('#skF_1','#skF_3','#skF_2')) != u1_struct_0(k8_group_2('#skF_1','#skF_3','#skF_2')),
    inference(negUnitSimplification,[status(thm)],[c_18,c_10043]) ).

tff(c_73980,plain,
    ( ~ m1_group_2(k8_group_2('#skF_1','#skF_3','#skF_2'),'#skF_1')
    | ~ v1_group_1(k8_group_2('#skF_1','#skF_3','#skF_2'))
    | ~ l1_group_1('#skF_1')
    | ~ v4_group_1('#skF_1')
    | ~ v3_group_1('#skF_1')
    | v3_struct_0('#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_73873,c_10044]) ).

tff(c_74056,plain,
    v3_struct_0('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_12,c_1734,c_1747,c_73980]) ).

tff(c_74058,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_74056]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : GRP645+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.15  % 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
% 0.15/0.37  % Computer : n011.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 22:12:36 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 42.33/27.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.33/27.39  
% 42.33/27.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.33/27.43  
% 42.33/27.43  Inference rules
% 42.33/27.43  ----------------------
% 42.33/27.43  #Ref     : 6
% 42.33/27.43  #Sup     : 14341
% 42.33/27.43  #Fact    : 0
% 42.33/27.43  #Define  : 0
% 42.33/27.43  #Split   : 14
% 42.33/27.43  #Chain   : 0
% 42.33/27.43  #Close   : 0
% 42.33/27.43  
% 42.33/27.43  Ordering : KBO
% 42.33/27.43  
% 42.33/27.43  Simplification rules
% 42.33/27.43  ----------------------
% 42.33/27.43  #Subsume      : 1373
% 42.33/27.43  #Demod        : 51892
% 42.33/27.43  #Tautology    : 2558
% 42.33/27.43  #SimpNegUnit  : 6473
% 42.33/27.43  #BackRed      : 202
% 42.33/27.43  
% 42.33/27.43  #Partial instantiations: 0
% 42.33/27.43  #Strategies tried      : 1
% 42.33/27.43  
% 42.33/27.43  Timing (in seconds)
% 42.33/27.43  ----------------------
% 42.33/27.43  Preprocessing        : 0.73
% 42.33/27.43  Parsing              : 0.37
% 42.33/27.43  CNF conversion       : 0.07
% 42.33/27.43  Main loop            : 25.58
% 42.33/27.43  Inferencing          : 3.47
% 42.33/27.43  Reduction            : 17.38
% 42.33/27.43  Demodulation         : 16.03
% 42.33/27.43  BG Simplification    : 0.36
% 42.33/27.43  Subsumption          : 3.74
% 42.33/27.43  Abstraction          : 0.57
% 42.33/27.43  MUC search           : 0.00
% 42.33/27.43  Cooper               : 0.00
% 42.33/27.43  Total                : 26.37
% 42.33/27.43  Index Insertion      : 0.00
% 42.33/27.43  Index Deletion       : 0.00
% 42.33/27.43  Index Matching       : 0.00
% 42.33/27.43  BG Taut test         : 0.00
%------------------------------------------------------------------------------