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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GRP640+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n031.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 May  5 04:26:39 PM UTC 2026

% Result   : Theorem 1.40s 1.77s
% Output   : CNFRefutation 1.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   46 (  17 unt;   0 def)
%            Number of atoms       :  271 (  27 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  342 ( 117   ~; 112   |;  79   &)
%                                         (   3 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-4 aty)
%            Number of variables   :   92 (   0 sgn  62   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t13_latsubgr,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( ( ~ v3_struct_0(X2)
            & v3_group_1(X2)
            & v4_group_1(X2)
            & l1_group_1(X2) )
         => ! [X3] :
              ( m1_group_2(X3,X1)
             => ! [X4] :
                  ( m1_group_2(X4,X1)
                 => ! [X5] :
                      ( ( v1_funct_1(X5)
                        & v1_funct_2(X5,u1_struct_0(X1),u1_struct_0(X2))
                        & m2_relset_1(X5,u1_struct_0(X1),u1_struct_0(X2)) )
                     => ! [X6] :
                          ( m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X1)))
                         => ( X6 = k2_xboole_0(u1_struct_0(X3),u1_struct_0(X4))
                           => k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X5,u1_struct_0(k8_group_4(X1,X3,X4))) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X5,u1_struct_0(k5_group_4(X1,X6))) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_latsubgr) ).

fof(redefinition_r1_group_2,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & v1_group_1(X2)
        & m1_group_2(X2,X1)
        & v1_group_1(X3)
        & m1_group_2(X3,X1) )
     => ( r1_group_2(X1,X2,X3)
      <=> X2 = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_group_2) ).

fof(t4_latsubgr,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_group_2(X2,X1)
         => ! [X3] :
              ( m1_group_2(X3,X1)
             => ! [X4] :
                  ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
                 => ( X4 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
                   => r1_group_2(X1,k8_group_4(X1,X2,X3),k5_group_4(X1,X4)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_latsubgr) ).

fof(dt_k5_group_4,axiom,
    ! [X1,X2] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
     => ( v1_group_1(k5_group_4(X1,X2))
        & m1_group_2(k5_group_4(X1,X2),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_group_4) ).

fof(dt_k8_group_4,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & m1_group_2(X2,X1)
        & m1_group_2(X3,X1) )
     => ( v1_group_1(k8_group_4(X1,X2,X3))
        & m1_group_2(k8_group_4(X1,X2,X3),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_group_4) ).

fof(redefinition_m2_relset_1,axiom,
    ! [X1,X2,X3] :
      ( m2_relset_1(X3,X1,X2)
    <=> m1_relset_1(X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

fof(redefinition_k2_funct_2,axiom,
    ! [X1,X2,X3,X4] :
      ( ( v1_funct_1(X3)
        & v1_funct_2(X3,X1,X2)
        & m1_relset_1(X3,X1,X2) )
     => k2_funct_2(X1,X2,X3,X4) = k9_relat_1(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v3_group_1(X1)
          & v4_group_1(X1)
          & l1_group_1(X1) )
       => ! [X2] :
            ( ( ~ v3_struct_0(X2)
              & v3_group_1(X2)
              & v4_group_1(X2)
              & l1_group_1(X2) )
           => ! [X3] :
                ( m1_group_2(X3,X1)
               => ! [X4] :
                    ( m1_group_2(X4,X1)
                   => ! [X5] :
                        ( ( v1_funct_1(X5)
                          & v1_funct_2(X5,u1_struct_0(X1),u1_struct_0(X2))
                          & m2_relset_1(X5,u1_struct_0(X1),u1_struct_0(X2)) )
                       => ! [X6] :
                            ( m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X1)))
                           => ( X6 = k2_xboole_0(u1_struct_0(X3),u1_struct_0(X4))
                             => k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X5,u1_struct_0(k8_group_4(X1,X3,X4))) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X5,u1_struct_0(k5_group_4(X1,X6))) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t13_latsubgr])]) ).

fof(c_0_8,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & v1_group_1(X2)
        & m1_group_2(X2,X1)
        & v1_group_1(X3)
        & m1_group_2(X3,X1) )
     => ( r1_group_2(X1,X2,X3)
      <=> X2 = X3 ) ),
    inference(fof_simplification,[status(thm)],[redefinition_r1_group_2]) ).

fof(c_0_9,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( m1_group_2(X2,X1)
         => ! [X3] :
              ( m1_group_2(X3,X1)
             => ! [X4] :
                  ( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
                 => ( X4 = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
                   => r1_group_2(X1,k8_group_4(X1,X2,X3),k5_group_4(X1,X4)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[t4_latsubgr]) ).

fof(c_0_10,plain,
    ! [X1,X2] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) )
     => ( v1_group_1(k5_group_4(X1,X2))
        & m1_group_2(k5_group_4(X1,X2),X1) ) ),
    inference(fof_simplification,[status(thm)],[dt_k5_group_4]) ).

fof(c_0_11,plain,
    ! [X1,X2,X3] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1)
        & m1_group_2(X2,X1)
        & m1_group_2(X3,X1) )
     => ( v1_group_1(k8_group_4(X1,X2,X3))
        & m1_group_2(k8_group_4(X1,X2,X3),X1) ) ),
    inference(fof_simplification,[status(thm)],[dt_k8_group_4]) ).

fof(c_0_12,plain,
    ! [X221,X222,X223] :
      ( ( ~ m2_relset_1(X223,X221,X222)
        | m1_relset_1(X223,X221,X222) )
      & ( ~ m1_relset_1(X223,X221,X222)
        | m2_relset_1(X223,X221,X222) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).

fof(c_0_13,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v3_group_1(esk1_0)
    & v4_group_1(esk1_0)
    & l1_group_1(esk1_0)
    & ~ v3_struct_0(esk2_0)
    & v3_group_1(esk2_0)
    & v4_group_1(esk2_0)
    & l1_group_1(esk2_0)
    & m1_group_2(esk3_0,esk1_0)
    & m1_group_2(esk4_0,esk1_0)
    & v1_funct_1(esk5_0)
    & v1_funct_2(esk5_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0))
    & m2_relset_1(esk5_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0))
    & m1_subset_1(esk6_0,k1_zfmisc_1(u1_struct_0(esk1_0)))
    & esk6_0 = k2_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0))
    & k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk5_0,u1_struct_0(k8_group_4(esk1_0,esk3_0,esk4_0))) != k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk5_0,u1_struct_0(k5_group_4(esk1_0,esk6_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_14,plain,
    ! [X224,X225,X226] :
      ( ( ~ r1_group_2(X224,X225,X226)
        | X225 = X226
        | v3_struct_0(X224)
        | ~ v3_group_1(X224)
        | ~ v4_group_1(X224)
        | ~ l1_group_1(X224)
        | ~ v1_group_1(X225)
        | ~ m1_group_2(X225,X224)
        | ~ v1_group_1(X226)
        | ~ m1_group_2(X226,X224) )
      & ( X225 != X226
        | r1_group_2(X224,X225,X226)
        | v3_struct_0(X224)
        | ~ v3_group_1(X224)
        | ~ v4_group_1(X224)
        | ~ l1_group_1(X224)
        | ~ v1_group_1(X225)
        | ~ m1_group_2(X225,X224)
        | ~ v1_group_1(X226)
        | ~ m1_group_2(X226,X224) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_15,plain,
    ! [X245,X246,X247,X248] :
      ( v3_struct_0(X245)
      | ~ v3_group_1(X245)
      | ~ v4_group_1(X245)
      | ~ l1_group_1(X245)
      | ~ m1_group_2(X246,X245)
      | ~ m1_group_2(X247,X245)
      | ~ m1_subset_1(X248,k1_zfmisc_1(u1_struct_0(X245)))
      | X248 != k2_xboole_0(u1_struct_0(X246),u1_struct_0(X247))
      | r1_group_2(X245,k8_group_4(X245,X246,X247),k5_group_4(X245,X248)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

fof(c_0_16,plain,
    ! [X231,X232] :
      ( ( v1_group_1(k5_group_4(X231,X232))
        | v3_struct_0(X231)
        | ~ v3_group_1(X231)
        | ~ v4_group_1(X231)
        | ~ l1_group_1(X231)
        | ~ m1_subset_1(X232,k1_zfmisc_1(u1_struct_0(X231))) )
      & ( m1_group_2(k5_group_4(X231,X232),X231)
        | v3_struct_0(X231)
        | ~ v3_group_1(X231)
        | ~ v4_group_1(X231)
        | ~ l1_group_1(X231)
        | ~ m1_subset_1(X232,k1_zfmisc_1(u1_struct_0(X231))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_17,plain,
    ! [X233,X234,X235] :
      ( ( v1_group_1(k8_group_4(X233,X234,X235))
        | v3_struct_0(X233)
        | ~ v3_group_1(X233)
        | ~ v4_group_1(X233)
        | ~ l1_group_1(X233)
        | ~ m1_group_2(X234,X233)
        | ~ m1_group_2(X235,X233) )
      & ( m1_group_2(k8_group_4(X233,X234,X235),X233)
        | v3_struct_0(X233)
        | ~ v3_group_1(X233)
        | ~ v4_group_1(X233)
        | ~ l1_group_1(X233)
        | ~ m1_group_2(X234,X233)
        | ~ m1_group_2(X235,X233) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_18,plain,
    ! [X217,X218,X219,X220] :
      ( ~ v1_funct_1(X219)
      | ~ v1_funct_2(X219,X217,X218)
      | ~ m1_relset_1(X219,X217,X218)
      | k2_funct_2(X217,X218,X219,X220) = k9_relat_1(X219,X220) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_funct_2])]) ).

cnf(c_0_19,plain,
    ( m1_relset_1(X1,X2,X3)
    | ~ m2_relset_1(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,negated_conjecture,
    m2_relset_1(esk5_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( X2 = X3
    | v3_struct_0(X1)
    | ~ r1_group_2(X1,X2,X3)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ v1_group_1(X2)
    | ~ m1_group_2(X2,X1)
    | ~ v1_group_1(X3)
    | ~ m1_group_2(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ( v3_struct_0(X1)
    | r1_group_2(X1,k8_group_4(X1,X2,X3),k5_group_4(X1,X4))
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_group_2(X2,X1)
    | ~ m1_group_2(X3,X1)
    | ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
    | X4 != k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,plain,
    ( m1_group_2(k5_group_4(X1,X2),X1)
    | v3_struct_0(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,plain,
    ( m1_group_2(k8_group_4(X1,X2,X3),X1)
    | v3_struct_0(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_group_2(X2,X1)
    | ~ m1_group_2(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    ( v1_group_1(k5_group_4(X1,X2))
    | v3_struct_0(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,plain,
    ( v1_group_1(k8_group_4(X1,X2,X3))
    | v3_struct_0(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1)
    | ~ m1_group_2(X2,X1)
    | ~ m1_group_2(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_27,negated_conjecture,
    k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk5_0,u1_struct_0(k8_group_4(esk1_0,esk3_0,esk4_0))) != k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk5_0,u1_struct_0(k5_group_4(esk1_0,esk6_0))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_28,plain,
    ( k2_funct_2(X2,X3,X1,X4) = k9_relat_1(X1,X4)
    | ~ v1_funct_1(X1)
    | ~ v1_funct_2(X1,X2,X3)
    | ~ m1_relset_1(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_29,negated_conjecture,
    v1_funct_2(esk5_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_30,negated_conjecture,
    v1_funct_1(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_31,negated_conjecture,
    m1_relset_1(esk5_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_32,plain,
    ( k8_group_4(X1,X2,X3) = k5_group_4(X1,X4)
    | v3_struct_0(X1)
    | X4 != k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
    | ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ m1_group_2(X3,X1)
    | ~ m1_group_2(X2,X1)
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    esk6_0 = k2_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_34,negated_conjecture,
    k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk5_0,u1_struct_0(k5_group_4(esk1_0,esk6_0))) != k9_relat_1(esk5_0,u1_struct_0(k8_group_4(esk1_0,esk3_0,esk4_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]),c_0_31])]) ).

cnf(c_0_35,negated_conjecture,
    ( k8_group_4(X1,esk3_0,esk4_0) = k5_group_4(X1,X2)
    | v3_struct_0(X1)
    | X2 != esk6_0
    | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ m1_group_2(esk4_0,X1)
    | ~ m1_group_2(esk3_0,X1)
    | ~ l1_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    m1_subset_1(esk6_0,k1_zfmisc_1(u1_struct_0(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_37,negated_conjecture,
    m1_group_2(esk4_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_38,negated_conjecture,
    m1_group_2(esk3_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_39,negated_conjecture,
    l1_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_40,negated_conjecture,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_41,negated_conjecture,
    v3_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_42,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_43,negated_conjecture,
    k9_relat_1(esk5_0,u1_struct_0(k8_group_4(esk1_0,esk3_0,esk4_0))) != k9_relat_1(esk5_0,u1_struct_0(k5_group_4(esk1_0,esk6_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_31]),c_0_29]),c_0_30])]) ).

cnf(c_0_44,negated_conjecture,
    k8_group_4(esk1_0,esk3_0,esk4_0) = k5_group_4(esk1_0,esk6_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP640+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.34  % Computer : n031.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Mon May  4 18:54:38 EDT 2026
% 0.15/0.34  % CPUTime    : 
% 0.15/0.35  % start to proof: theBenchmark
% 1.40/1.77  % Version  : CSE_E---1.7
% 1.40/1.77  % Problem  : theBenchmark.p
% 1.40/1.77  % SZS status Theorem for theBenchmark.p
% 1.40/1.77  % SZS output start CNFRefutation
% See solution above
% 1.40/1.77  % Total time : 1.373s
%------------------------------------------------------------------------------