TSTP Solution File: GRP645+3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : GRP645+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 17:49:49 EDT 2023

% Result   : Theorem 143.92s 20.57s
% Output   : CNFRefutation 143.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   46 (  20 unt;   0 def)
%            Number of atoms       :  247 (  30 equ)
%            Maximal formula atoms :   38 (   5 avg)
%            Number of connectives :  311 ( 110   ~; 113   |;  64   &)
%                                         (   2 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   62 (   0 sgn;  40   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d1_latsubgr,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( ( v1_funct_1(X2)
            & v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
            & m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
         => ( X2 = k1_latsubgr(X1)
          <=> ! [X3] :
                ( ( v1_group_1(X3)
                  & m1_group_2(X3,X1) )
               => k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VTl2s4umQC/E---3.1_26221.p',d1_latsubgr) ).

fof(dt_k1_latsubgr,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ( v1_funct_1(k1_latsubgr(X1))
        & v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
        & m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VTl2s4umQC/E---3.1_26221.p',dt_k1_latsubgr) ).

fof(dt_k9_group_2,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(k9_group_2(X1,X2,X3))
        & m1_group_2(k9_group_2(X1,X2,X3),X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VTl2s4umQC/E---3.1_26221.p',dt_k9_group_2) ).

fof(t24_latsubgr,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( ( v1_group_1(X2)
            & m1_group_2(X2,X1) )
         => ! [X3] :
              ( ( v1_group_1(X3)
                & m1_group_2(X3,X1) )
             => k1_funct_1(k1_latsubgr(X1),k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VTl2s4umQC/E---3.1_26221.p',t24_latsubgr) ).

fof(t1_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)
             => u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.VTl2s4umQC/E---3.1_26221.p',t1_latsubgr) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.VTl2s4umQC/E---3.1_26221.p',commutativity_k3_xboole_0) ).

fof(c_0_6,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ! [X2] :
          ( ( v1_funct_1(X2)
            & v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
            & m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
         => ( X2 = k1_latsubgr(X1)
          <=> ! [X3] :
                ( ( v1_group_1(X3)
                  & m1_group_2(X3,X1) )
               => k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
    inference(fof_simplification,[status(thm)],[d1_latsubgr]) ).

fof(c_0_7,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => ( v1_funct_1(k1_latsubgr(X1))
        & v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
        & m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
    inference(fof_simplification,[status(thm)],[dt_k1_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)
        & m1_group_2(X2,X1)
        & m1_group_2(X3,X1) )
     => ( v1_group_1(k9_group_2(X1,X2,X3))
        & m1_group_2(k9_group_2(X1,X2,X3),X1) ) ),
    inference(fof_simplification,[status(thm)],[dt_k9_group_2]) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v3_group_1(X1)
          & v4_group_1(X1)
          & l1_group_1(X1) )
       => ! [X2] :
            ( ( v1_group_1(X2)
              & m1_group_2(X2,X1) )
           => ! [X3] :
                ( ( v1_group_1(X3)
                  & m1_group_2(X3,X1) )
               => k1_funct_1(k1_latsubgr(X1),k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t24_latsubgr])]) ).

fof(c_0_10,plain,
    ! [X281,X282,X283] :
      ( ( X282 != k1_latsubgr(X281)
        | ~ v1_group_1(X283)
        | ~ m1_group_2(X283,X281)
        | k1_funct_1(X282,X283) = u1_struct_0(X283)
        | ~ v1_funct_1(X282)
        | ~ v1_funct_2(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | ~ m2_relset_1(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | v3_struct_0(X281)
        | ~ v3_group_1(X281)
        | ~ v4_group_1(X281)
        | ~ l1_group_1(X281) )
      & ( v1_group_1(esk32_2(X281,X282))
        | X282 = k1_latsubgr(X281)
        | ~ v1_funct_1(X282)
        | ~ v1_funct_2(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | ~ m2_relset_1(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | v3_struct_0(X281)
        | ~ v3_group_1(X281)
        | ~ v4_group_1(X281)
        | ~ l1_group_1(X281) )
      & ( m1_group_2(esk32_2(X281,X282),X281)
        | X282 = k1_latsubgr(X281)
        | ~ v1_funct_1(X282)
        | ~ v1_funct_2(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | ~ m2_relset_1(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | v3_struct_0(X281)
        | ~ v3_group_1(X281)
        | ~ v4_group_1(X281)
        | ~ l1_group_1(X281) )
      & ( k1_funct_1(X282,esk32_2(X281,X282)) != u1_struct_0(esk32_2(X281,X282))
        | X282 = k1_latsubgr(X281)
        | ~ v1_funct_1(X282)
        | ~ v1_funct_2(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | ~ m2_relset_1(X282,k1_group_3(X281),k1_zfmisc_1(u1_struct_0(X281)))
        | v3_struct_0(X281)
        | ~ v3_group_1(X281)
        | ~ v4_group_1(X281)
        | ~ l1_group_1(X281) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).

fof(c_0_11,plain,
    ! [X280] :
      ( ( v1_funct_1(k1_latsubgr(X280))
        | v3_struct_0(X280)
        | ~ v3_group_1(X280)
        | ~ v4_group_1(X280)
        | ~ l1_group_1(X280) )
      & ( v1_funct_2(k1_latsubgr(X280),k1_group_3(X280),k1_zfmisc_1(u1_struct_0(X280)))
        | v3_struct_0(X280)
        | ~ v3_group_1(X280)
        | ~ v4_group_1(X280)
        | ~ l1_group_1(X280) )
      & ( m2_relset_1(k1_latsubgr(X280),k1_group_3(X280),k1_zfmisc_1(u1_struct_0(X280)))
        | v3_struct_0(X280)
        | ~ v3_group_1(X280)
        | ~ v4_group_1(X280)
        | ~ l1_group_1(X280) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_12,plain,
    ! [X332,X333,X334] :
      ( ( v1_group_1(k9_group_2(X332,X333,X334))
        | v3_struct_0(X332)
        | ~ v3_group_1(X332)
        | ~ v4_group_1(X332)
        | ~ l1_group_1(X332)
        | ~ m1_group_2(X333,X332)
        | ~ m1_group_2(X334,X332) )
      & ( m1_group_2(k9_group_2(X332,X333,X334),X332)
        | v3_struct_0(X332)
        | ~ v3_group_1(X332)
        | ~ v4_group_1(X332)
        | ~ l1_group_1(X332)
        | ~ m1_group_2(X333,X332)
        | ~ m1_group_2(X334,X332) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

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)
    & v1_group_1(esk2_0)
    & m1_group_2(esk2_0,esk1_0)
    & v1_group_1(esk3_0)
    & m1_group_2(esk3_0,esk1_0)
    & k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(k1_funct_1(k1_latsubgr(esk1_0),esk2_0),k1_funct_1(k1_latsubgr(esk1_0),esk3_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_14,plain,
    ( k1_funct_1(X1,X3) = u1_struct_0(X3)
    | v3_struct_0(X2)
    | X1 != k1_latsubgr(X2)
    | ~ v1_group_1(X3)
    | ~ m1_group_2(X3,X2)
    | ~ v1_funct_1(X1)
    | ~ v1_funct_2(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
    | ~ m2_relset_1(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
    | ~ v3_group_1(X2)
    | ~ v4_group_1(X2)
    | ~ l1_group_1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ( v1_funct_1(k1_latsubgr(X1))
    | v3_struct_0(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
    | v3_struct_0(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
    | v3_struct_0(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    ( m1_group_2(k9_group_2(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_12]) ).

cnf(c_0_19,negated_conjecture,
    m1_group_2(esk3_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,negated_conjecture,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    v3_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,negated_conjecture,
    l1_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_24,plain,
    ( v1_group_1(k9_group_2(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_12]) ).

fof(c_0_25,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)
             => u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[t1_latsubgr]) ).

cnf(c_0_26,plain,
    ( k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2)
    | v3_struct_0(X1)
    | ~ m1_group_2(X2,X1)
    | ~ v4_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v1_group_1(X2)
    | ~ l1_group_1(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_15]),c_0_16]),c_0_17]) ).

cnf(c_0_27,negated_conjecture,
    v1_group_1(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_28,plain,
    ! [X35,X36] : k3_xboole_0(X35,X36) = k3_xboole_0(X36,X35),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_29,negated_conjecture,
    m1_group_2(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_30,negated_conjecture,
    v1_group_1(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_31,negated_conjecture,
    ( m1_group_2(k9_group_2(esk1_0,X1,esk3_0),esk1_0)
    | ~ m1_group_2(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).

cnf(c_0_32,negated_conjecture,
    ( v1_group_1(k9_group_2(esk1_0,X1,esk3_0))
    | ~ m1_group_2(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).

fof(c_0_33,plain,
    ! [X360,X361,X362] :
      ( v3_struct_0(X360)
      | ~ v3_group_1(X360)
      | ~ v4_group_1(X360)
      | ~ l1_group_1(X360)
      | ~ m1_group_2(X361,X360)
      | ~ m1_group_2(X362,X360)
      | u1_struct_0(k9_group_2(X360,X361,X362)) = k3_xboole_0(u1_struct_0(X361),u1_struct_0(X362)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).

cnf(c_0_34,negated_conjecture,
    k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(k1_funct_1(k1_latsubgr(esk1_0),esk2_0),k1_funct_1(k1_latsubgr(esk1_0),esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_35,negated_conjecture,
    k1_funct_1(k1_latsubgr(esk1_0),esk3_0) = u1_struct_0(esk3_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(spm,[status(thm)],[c_0_26,c_0_19]),c_0_20]),c_0_21]),c_0_27]),c_0_22])]),c_0_23]) ).

cnf(c_0_36,plain,
    k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,negated_conjecture,
    k1_funct_1(k1_latsubgr(esk1_0),esk2_0) = u1_struct_0(esk2_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(spm,[status(thm)],[c_0_26,c_0_29]),c_0_20]),c_0_21]),c_0_30]),c_0_22])]),c_0_23]) ).

cnf(c_0_38,negated_conjecture,
    m1_group_2(k9_group_2(esk1_0,esk2_0,esk3_0),esk1_0),
    inference(spm,[status(thm)],[c_0_31,c_0_29]) ).

cnf(c_0_39,negated_conjecture,
    v1_group_1(k9_group_2(esk1_0,esk2_0,esk3_0)),
    inference(spm,[status(thm)],[c_0_32,c_0_29]) ).

cnf(c_0_40,plain,
    ( v3_struct_0(X1)
    | u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3))
    | ~ 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_33]) ).

cnf(c_0_41,negated_conjecture,
    k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk3_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]),c_0_36]) ).

cnf(c_0_42,negated_conjecture,
    k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) = u1_struct_0(k9_group_2(esk1_0,esk2_0,esk3_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(spm,[status(thm)],[c_0_26,c_0_38]),c_0_20]),c_0_21]),c_0_39]),c_0_22])]),c_0_23]) ).

cnf(c_0_43,negated_conjecture,
    ( u1_struct_0(k9_group_2(esk1_0,X1,esk3_0)) = k3_xboole_0(u1_struct_0(X1),u1_struct_0(esk3_0))
    | ~ m1_group_2(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).

cnf(c_0_44,negated_conjecture,
    u1_struct_0(k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk3_0)),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_45,plain,
    $false,
    inference(cdclpropres,[status(thm)],[c_0_43,c_0_44,c_0_29]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : GRP645+3 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n027.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 2400
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Tue Oct  3 02:50:17 EDT 2023
% 0.11/0.33  % CPUTime    : 
% 1.72/1.93  Running first-order model finding
% 1.72/1.93  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.VTl2s4umQC/E---3.1_26221.p
% 143.92/20.57  # Version: 3.1pre001
% 143.92/20.57  # Preprocessing class: FMLLSMLLSSSNFFN.
% 143.92/20.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 143.92/20.57  # Starting new_bool_3 with 900s (3) cores
% 143.92/20.57  # Starting new_bool_1 with 900s (3) cores
% 143.92/20.57  # Starting sh5l with 300s (1) cores
% 143.92/20.57  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 143.92/20.57  # new_bool_1 with pid 26300 completed with status 0
% 143.92/20.57  # Result found by new_bool_1
% 143.92/20.57  # Preprocessing class: FMLLSMLLSSSNFFN.
% 143.92/20.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 143.92/20.57  # Starting new_bool_3 with 900s (3) cores
% 143.92/20.57  # Starting new_bool_1 with 900s (3) cores
% 143.92/20.57  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 143.92/20.57  # Search class: FGHSM-SMLM32-MFFFFFNN
% 143.92/20.57  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 143.92/20.57  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 143.92/20.57  # Starting new_bool_1 with 91s (1) cores
% 143.92/20.57  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 68s (1) cores
% 143.92/20.57  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 26304 completed with status 0
% 143.92/20.57  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 143.92/20.57  # Preprocessing class: FMLLSMLLSSSNFFN.
% 143.92/20.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 143.92/20.57  # Starting new_bool_3 with 900s (3) cores
% 143.92/20.57  # Starting new_bool_1 with 900s (3) cores
% 143.92/20.57  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 143.92/20.57  # Search class: FGHSM-SMLM32-MFFFFFNN
% 143.92/20.57  # Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 143.92/20.57  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 68s (1) cores
% 143.92/20.57  # Preprocessing time       : 0.055 s
% 143.92/20.57  # Presaturation interreduction done
% 143.92/20.57  # SatCheck found unsatisfiable ground set
% 143.92/20.57  
% 143.92/20.57  # Proof found!
% 143.92/20.57  # SZS status Theorem
% 143.92/20.57  # SZS output start CNFRefutation
% See solution above
% 143.92/20.57  # Parsed axioms                        : 13988
% 143.92/20.57  # Removed by relevancy pruning/SinE    : 12713
% 143.92/20.57  # Initial clauses                      : 2637
% 143.92/20.57  # Removed in clause preprocessing      : 116
% 143.92/20.57  # Initial clauses in saturation        : 2521
% 143.92/20.57  # Processed clauses                    : 27308
% 143.92/20.57  # ...of these trivial                  : 1591
% 143.92/20.57  # ...subsumed                          : 10717
% 143.92/20.57  # ...remaining for further processing  : 15000
% 143.92/20.57  # Other redundant clauses eliminated   : 434
% 143.92/20.57  # Clauses deleted for lack of memory   : 0
% 143.92/20.57  # Backward-subsumed                    : 57
% 143.92/20.57  # Backward-rewritten                   : 472
% 143.92/20.57  # Generated clauses                    : 392089
% 143.92/20.57  # ...of the previous two non-redundant : 379126
% 143.92/20.57  # ...aggressively subsumed             : 0
% 143.92/20.57  # Contextual simplify-reflections      : 165
% 143.92/20.57  # Paramodulations                      : 391571
% 143.92/20.57  # Factorizations                       : 24
% 143.92/20.57  # NegExts                              : 0
% 143.92/20.57  # Equation resolutions                 : 513
% 143.92/20.57  # Total rewrite steps                  : 949553
% 143.92/20.57  # Propositional unsat checks           : 3
% 143.92/20.57  #    Propositional check models        : 0
% 143.92/20.57  #    Propositional check unsatisfiable : 1
% 143.92/20.57  #    Propositional clauses             : 368409
% 143.92/20.57  #    Propositional clauses after purity: 18077
% 143.92/20.57  #    Propositional unsat core size     : 3
% 143.92/20.57  #    Propositional preprocessing time  : 0.000
% 143.92/20.57  #    Propositional encoding time       : 1.201
% 143.92/20.57  #    Propositional solver time         : 0.415
% 143.92/20.57  #    Success case prop preproc time    : 0.000
% 143.92/20.57  #    Success case prop encoding time   : 0.969
% 143.92/20.57  #    Success case prop solver time     : 0.100
% 143.92/20.57  # Current number of processed clauses  : 11928
% 143.92/20.57  #    Positive orientable unit clauses  : 5953
% 143.92/20.57  #    Positive unorientable unit clauses: 5
% 143.92/20.57  #    Negative unit clauses             : 2248
% 143.92/20.57  #    Non-unit-clauses                  : 3722
% 143.92/20.57  # Current number of unprocessed clauses: 356481
% 143.92/20.57  # ...number of literals in the above   : 962224
% 143.92/20.57  # Current number of archived formulas  : 0
% 143.92/20.57  # Current number of archived clauses   : 2864
% 143.92/20.57  # Clause-clause subsumption calls (NU) : 7987109
% 143.92/20.57  # Rec. Clause-clause subsumption calls : 597197
% 143.92/20.57  # Non-unit clause-clause subsumptions  : 887
% 143.92/20.57  # Unit Clause-clause subsumption calls : 1289736
% 143.92/20.57  # Rewrite failures with RHS unbound    : 0
% 143.92/20.57  # BW rewrite match attempts            : 401795
% 143.92/20.57  # BW rewrite match successes           : 392
% 143.92/20.57  # Condensation attempts                : 0
% 143.92/20.57  # Condensation successes               : 0
% 143.92/20.57  # Termbank termtop insertions          : 20170715
% 143.92/20.57  
% 143.92/20.57  # -------------------------------------------------
% 143.92/20.57  # User time                : 17.304 s
% 143.92/20.57  # System time              : 0.529 s
% 143.92/20.57  # Total time               : 17.833 s
% 143.92/20.57  # Maximum resident set size: 29404 pages
% 143.92/20.57  
% 143.92/20.57  # -------------------------------------------------
% 143.92/20.57  # User time                : 52.622 s
% 143.92/20.57  # System time              : 0.959 s
% 143.92/20.57  # Total time               : 53.581 s
% 143.92/20.57  # Maximum resident set size: 20644 pages
% 143.92/20.57  % E---3.1 exiting
%------------------------------------------------------------------------------