TSTP Solution File: GRP622+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : GRP622+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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 17:42:19 EDT 2023

% Result   : Theorem 0.21s 0.53s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   67 (  18 unt;   0 def)
%            Number of atoms       :  206 (   4 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  221 (  82   ~;  71   |;  43   &)
%                                         (   3 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :  103 (   2 sgn;  69   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fc1_struct_0,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',fc1_struct_0) ).

fof(t12_autgroup,conjecture,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',t12_autgroup) ).

fof(dt_k4_autgroup,axiom,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',dt_k4_autgroup) ).

fof(dt_l1_group_1,axiom,
    ! [X1] :
      ( l1_group_1(X1)
     => l1_struct_0(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',dt_l1_group_1) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( r1_tarski(X1,X2)
    <=> ! [X3] :
          ( r2_hidden(X3,X1)
         => r2_hidden(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',d3_tarski) ).

fof(redefinition_m2_fraenkel,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
        <=> m1_subset_1(X4,X3) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',redefinition_m2_fraenkel) ).

fof(t1_subset,axiom,
    ! [X1,X2] :
      ( r2_hidden(X1,X2)
     => m1_subset_1(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',t1_subset) ).

fof(redefinition_k1_fraenkel,axiom,
    ! [X1,X2] :
      ( ~ v1_xboole_0(X2)
     => k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',redefinition_k1_fraenkel) ).

fof(dt_m2_fraenkel,axiom,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
         => ( v1_funct_1(X4)
            & v1_funct_2(X4,X1,X2)
            & m2_relset_1(X4,X1,X2) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',dt_m2_fraenkel) ).

fof(dt_m1_fraenkel,axiom,
    ! [X1,X2,X3] :
      ( m1_fraenkel(X3,X1,X2)
     => ( ~ v1_xboole_0(X3)
        & v1_fraenkel(X3) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',dt_m1_fraenkel) ).

fof(cc1_fraenkel,axiom,
    ! [X1] :
      ( v1_fraenkel(X1)
     => ! [X2] :
          ( m1_subset_1(X2,X1)
         => ( v1_relat_1(X2)
            & v1_funct_1(X2) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',cc1_fraenkel) ).

fof(t12_funct_2,axiom,
    ! [X1,X2] :
      ( ( v1_funct_1(X2)
        & v1_funct_2(X2,X1,X1)
        & m2_relset_1(X2,X1,X1) )
     => r2_hidden(X2,k1_funct_2(X1,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p',t12_funct_2) ).

fof(c_0_12,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & l1_struct_0(X1) )
     => ~ v1_xboole_0(u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ v3_struct_0(X1)
          & v1_group_1(X1)
          & v3_group_1(X1)
          & v4_group_1(X1)
          & l1_group_1(X1) )
       => r1_tarski(k4_autgroup(X1),k1_fraenkel(u1_struct_0(X1),u1_struct_0(X1))) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t12_autgroup])]) ).

fof(c_0_14,plain,
    ! [X1] :
      ( ( ~ v3_struct_0(X1)
        & v1_group_1(X1)
        & v3_group_1(X1)
        & v4_group_1(X1)
        & l1_group_1(X1) )
     => m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
    inference(fof_simplification,[status(thm)],[dt_k4_autgroup]) ).

fof(c_0_15,plain,
    ! [X72] :
      ( v3_struct_0(X72)
      | ~ l1_struct_0(X72)
      | ~ v1_xboole_0(u1_struct_0(X72)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).

fof(c_0_16,plain,
    ! [X37] :
      ( ~ l1_group_1(X37)
      | l1_struct_0(X37) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).

fof(c_0_17,negated_conjecture,
    ( ~ v3_struct_0(esk1_0)
    & v1_group_1(esk1_0)
    & v3_group_1(esk1_0)
    & v4_group_1(esk1_0)
    & l1_group_1(esk1_0)
    & ~ r1_tarski(k4_autgroup(esk1_0),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

fof(c_0_18,plain,
    ! [X26,X27,X28,X29,X30] :
      ( ( ~ r1_tarski(X26,X27)
        | ~ r2_hidden(X28,X26)
        | r2_hidden(X28,X27) )
      & ( r2_hidden(esk2_2(X29,X30),X29)
        | r1_tarski(X29,X30) )
      & ( ~ r2_hidden(esk2_2(X29,X30),X30)
        | r1_tarski(X29,X30) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).

fof(c_0_19,plain,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
        <=> m1_subset_1(X4,X3) ) ),
    inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).

fof(c_0_20,plain,
    ! [X36] :
      ( v3_struct_0(X36)
      | ~ v1_group_1(X36)
      | ~ v3_group_1(X36)
      | ~ v4_group_1(X36)
      | ~ l1_group_1(X36)
      | m1_fraenkel(k4_autgroup(X36),u1_struct_0(X36),u1_struct_0(X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).

cnf(c_0_21,plain,
    ( v3_struct_0(X1)
    | ~ l1_struct_0(X1)
    | ~ v1_xboole_0(u1_struct_0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    ( l1_struct_0(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_23,plain,
    ! [X109,X110] :
      ( ~ r2_hidden(X109,X110)
      | m1_subset_1(X109,X110) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).

cnf(c_0_24,negated_conjecture,
    ~ r1_tarski(k4_autgroup(esk1_0),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    ( r2_hidden(esk2_2(X1,X2),X1)
    | r1_tarski(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_26,plain,
    ! [X1,X2] :
      ( ~ v1_xboole_0(X2)
     => k1_fraenkel(X1,X2) = k1_funct_2(X1,X2) ),
    inference(fof_simplification,[status(thm)],[redefinition_k1_fraenkel]) ).

fof(c_0_27,plain,
    ! [X1,X2,X3] :
      ( ( ~ v1_xboole_0(X2)
        & m1_fraenkel(X3,X1,X2) )
     => ! [X4] :
          ( m2_fraenkel(X4,X1,X2,X3)
         => ( v1_funct_1(X4)
            & v1_funct_2(X4,X1,X2)
            & m2_relset_1(X4,X1,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[dt_m2_fraenkel]) ).

fof(c_0_28,plain,
    ! [X99,X100,X101,X102] :
      ( ( ~ m2_fraenkel(X102,X99,X100,X101)
        | m1_subset_1(X102,X101)
        | v1_xboole_0(X100)
        | ~ m1_fraenkel(X101,X99,X100) )
      & ( ~ m1_subset_1(X102,X101)
        | m2_fraenkel(X102,X99,X100,X101)
        | v1_xboole_0(X100)
        | ~ m1_fraenkel(X101,X99,X100) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).

cnf(c_0_29,plain,
    ( v3_struct_0(X1)
    | m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
    | ~ v1_group_1(X1)
    | ~ v3_group_1(X1)
    | ~ v4_group_1(X1)
    | ~ l1_group_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_30,negated_conjecture,
    l1_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_31,negated_conjecture,
    v4_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_32,negated_conjecture,
    v3_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_33,negated_conjecture,
    v1_group_1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_34,negated_conjecture,
    ~ v3_struct_0(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_35,plain,
    ( v3_struct_0(X1)
    | ~ v1_xboole_0(u1_struct_0(X1))
    | ~ l1_group_1(X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_36,plain,
    ( m1_subset_1(X1,X2)
    | ~ r2_hidden(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_37,negated_conjecture,
    r2_hidden(esk2_2(k4_autgroup(esk1_0),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),k4_autgroup(esk1_0)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_38,plain,
    ! [X97,X98] :
      ( v1_xboole_0(X98)
      | k1_fraenkel(X97,X98) = k1_funct_2(X97,X98) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).

fof(c_0_39,plain,
    ! [X1,X2,X3] :
      ( m1_fraenkel(X3,X1,X2)
     => ( ~ v1_xboole_0(X3)
        & v1_fraenkel(X3) ) ),
    inference(fof_simplification,[status(thm)],[dt_m1_fraenkel]) ).

fof(c_0_40,plain,
    ! [X41,X42,X43,X44] :
      ( ( v1_funct_1(X44)
        | ~ m2_fraenkel(X44,X41,X42,X43)
        | v1_xboole_0(X42)
        | ~ m1_fraenkel(X43,X41,X42) )
      & ( v1_funct_2(X44,X41,X42)
        | ~ m2_fraenkel(X44,X41,X42,X43)
        | v1_xboole_0(X42)
        | ~ m1_fraenkel(X43,X41,X42) )
      & ( m2_relset_1(X44,X41,X42)
        | ~ m2_fraenkel(X44,X41,X42,X43)
        | v1_xboole_0(X42)
        | ~ m1_fraenkel(X43,X41,X42) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).

cnf(c_0_41,plain,
    ( m2_fraenkel(X1,X3,X4,X2)
    | v1_xboole_0(X4)
    | ~ m1_subset_1(X1,X2)
    | ~ m1_fraenkel(X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_42,negated_conjecture,
    m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(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_29,c_0_30]),c_0_31]),c_0_32]),c_0_33])]),c_0_34]) ).

cnf(c_0_43,negated_conjecture,
    ~ v1_xboole_0(u1_struct_0(esk1_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30])]) ).

fof(c_0_44,plain,
    ! [X9,X10] :
      ( ( v1_relat_1(X10)
        | ~ m1_subset_1(X10,X9)
        | ~ v1_fraenkel(X9) )
      & ( v1_funct_1(X10)
        | ~ m1_subset_1(X10,X9)
        | ~ v1_fraenkel(X9) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_fraenkel])])])]) ).

cnf(c_0_45,negated_conjecture,
    m1_subset_1(esk2_2(k4_autgroup(esk1_0),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),k4_autgroup(esk1_0)),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_46,plain,
    ( v1_xboole_0(X1)
    | k1_fraenkel(X2,X1) = k1_funct_2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

fof(c_0_47,plain,
    ! [X38,X39,X40] :
      ( ( ~ v1_xboole_0(X40)
        | ~ m1_fraenkel(X40,X38,X39) )
      & ( v1_fraenkel(X40)
        | ~ m1_fraenkel(X40,X38,X39) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).

cnf(c_0_48,plain,
    ( m2_relset_1(X1,X2,X3)
    | v1_xboole_0(X3)
    | ~ m2_fraenkel(X1,X2,X3,X4)
    | ~ m1_fraenkel(X4,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_49,negated_conjecture,
    ( m2_fraenkel(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
    | ~ m1_subset_1(X1,k4_autgroup(esk1_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_50,plain,
    ( v1_funct_2(X1,X2,X3)
    | v1_xboole_0(X3)
    | ~ m2_fraenkel(X1,X2,X3,X4)
    | ~ m1_fraenkel(X4,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_51,plain,
    ( v1_funct_1(X1)
    | ~ m1_subset_1(X1,X2)
    | ~ v1_fraenkel(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_52,negated_conjecture,
    m1_subset_1(esk2_2(k4_autgroup(esk1_0),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),k4_autgroup(esk1_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_43]) ).

cnf(c_0_53,plain,
    ( v1_fraenkel(X1)
    | ~ m1_fraenkel(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_54,plain,
    ( r1_tarski(X1,X2)
    | ~ r2_hidden(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_55,plain,
    ! [X107,X108] :
      ( ~ v1_funct_1(X108)
      | ~ v1_funct_2(X108,X107,X107)
      | ~ m2_relset_1(X108,X107,X107)
      | r2_hidden(X108,k1_funct_2(X107,X107)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_funct_2])]) ).

cnf(c_0_56,negated_conjecture,
    ( m2_relset_1(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
    | ~ m1_subset_1(X1,k4_autgroup(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_42])]),c_0_43]) ).

cnf(c_0_57,negated_conjecture,
    ( v1_funct_2(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
    | ~ m1_subset_1(X1,k4_autgroup(esk1_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_49]),c_0_42])]),c_0_43]) ).

cnf(c_0_58,negated_conjecture,
    ( v1_funct_1(esk2_2(k4_autgroup(esk1_0),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0))))
    | ~ v1_fraenkel(k4_autgroup(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_59,negated_conjecture,
    v1_fraenkel(k4_autgroup(esk1_0)),
    inference(spm,[status(thm)],[c_0_53,c_0_42]) ).

cnf(c_0_60,negated_conjecture,
    ~ r2_hidden(esk2_2(k4_autgroup(esk1_0),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),k1_fraenkel(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),
    inference(spm,[status(thm)],[c_0_24,c_0_54]) ).

cnf(c_0_61,plain,
    ( r2_hidden(X1,k1_funct_2(X2,X2))
    | ~ v1_funct_1(X1)
    | ~ v1_funct_2(X1,X2,X2)
    | ~ m2_relset_1(X1,X2,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_62,negated_conjecture,
    m2_relset_1(esk2_2(k4_autgroup(esk1_0),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
    inference(spm,[status(thm)],[c_0_56,c_0_52]) ).

cnf(c_0_63,negated_conjecture,
    v1_funct_2(esk2_2(k4_autgroup(esk1_0),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),u1_struct_0(esk1_0),u1_struct_0(esk1_0)),
    inference(spm,[status(thm)],[c_0_57,c_0_52]) ).

cnf(c_0_64,negated_conjecture,
    v1_funct_1(esk2_2(k4_autgroup(esk1_0),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).

cnf(c_0_65,negated_conjecture,
    ~ r2_hidden(esk2_2(k4_autgroup(esk1_0),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),k1_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_46]),c_0_43]) ).

cnf(c_0_66,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64])]),c_0_65]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP622+1 : TPTP v8.1.2. Released v3.4.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n024.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 2400
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Oct  3 02:49:27 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.f47ZkVft3W/E---3.1_21451.p
% 0.21/0.53  # Version: 3.1pre001
% 0.21/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.53  # Starting sh5l with 300s (1) cores
% 0.21/0.53  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 21562 completed with status 0
% 0.21/0.53  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.21/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.53  # No SInE strategy applied
% 0.21/0.53  # Search class: FGHSM-FFMM31-SFFFFFNN
% 0.21/0.53  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.53  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.21/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.21/0.53  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.21/0.53  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.21/0.53  # Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 136s (1) cores
% 0.21/0.53  # G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 21578 completed with status 0
% 0.21/0.53  # Result found by G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.21/0.53  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/0.53  # No SInE strategy applied
% 0.21/0.53  # Search class: FGHSM-FFMM31-SFFFFFNN
% 0.21/0.53  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.53  # Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.21/0.53  # Preprocessing time       : 0.002 s
% 0.21/0.53  # Presaturation interreduction done
% 0.21/0.53  
% 0.21/0.53  # Proof found!
% 0.21/0.53  # SZS status Theorem
% 0.21/0.53  # SZS output start CNFRefutation
% See solution above
% 0.21/0.53  # Parsed axioms                        : 69
% 0.21/0.53  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.53  # Initial clauses                      : 121
% 0.21/0.53  # Removed in clause preprocessing      : 16
% 0.21/0.53  # Initial clauses in saturation        : 105
% 0.21/0.53  # Processed clauses                    : 376
% 0.21/0.53  # ...of these trivial                  : 6
% 0.21/0.53  # ...subsumed                          : 26
% 0.21/0.53  # ...remaining for further processing  : 344
% 0.21/0.53  # Other redundant clauses eliminated   : 4
% 0.21/0.53  # Clauses deleted for lack of memory   : 0
% 0.21/0.53  # Backward-subsumed                    : 0
% 0.21/0.53  # Backward-rewritten                   : 13
% 0.21/0.53  # Generated clauses                    : 292
% 0.21/0.53  # ...of the previous two non-redundant : 255
% 0.21/0.53  # ...aggressively subsumed             : 0
% 0.21/0.53  # Contextual simplify-reflections      : 2
% 0.21/0.53  # Paramodulations                      : 286
% 0.21/0.53  # Factorizations                       : 0
% 0.21/0.53  # NegExts                              : 0
% 0.21/0.53  # Equation resolutions                 : 6
% 0.21/0.53  # Total rewrite steps                  : 102
% 0.21/0.53  # Propositional unsat checks           : 0
% 0.21/0.53  #    Propositional check models        : 0
% 0.21/0.53  #    Propositional check unsatisfiable : 0
% 0.21/0.53  #    Propositional clauses             : 0
% 0.21/0.53  #    Propositional clauses after purity: 0
% 0.21/0.53  #    Propositional unsat core size     : 0
% 0.21/0.53  #    Propositional preprocessing time  : 0.000
% 0.21/0.53  #    Propositional encoding time       : 0.000
% 0.21/0.53  #    Propositional solver time         : 0.000
% 0.21/0.53  #    Success case prop preproc time    : 0.000
% 0.21/0.53  #    Success case prop encoding time   : 0.000
% 0.21/0.53  #    Success case prop solver time     : 0.000
% 0.21/0.53  # Current number of processed clauses  : 228
% 0.21/0.53  #    Positive orientable unit clauses  : 92
% 0.21/0.53  #    Positive unorientable unit clauses: 0
% 0.21/0.53  #    Negative unit clauses             : 33
% 0.21/0.53  #    Non-unit-clauses                  : 103
% 0.21/0.53  # Current number of unprocessed clauses: 83
% 0.21/0.53  # ...number of literals in the above   : 232
% 0.21/0.53  # Current number of archived formulas  : 0
% 0.21/0.53  # Current number of archived clauses   : 116
% 0.21/0.53  # Clause-clause subsumption calls (NU) : 2272
% 0.21/0.53  # Rec. Clause-clause subsumption calls : 1281
% 0.21/0.53  # Non-unit clause-clause subsumptions  : 15
% 0.21/0.53  # Unit Clause-clause subsumption calls : 653
% 0.21/0.53  # Rewrite failures with RHS unbound    : 0
% 0.21/0.53  # BW rewrite match attempts            : 11
% 0.21/0.53  # BW rewrite match successes           : 4
% 0.21/0.53  # Condensation attempts                : 0
% 0.21/0.53  # Condensation successes               : 0
% 0.21/0.53  # Termbank termtop insertions          : 10032
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.024 s
% 0.21/0.53  # System time              : 0.007 s
% 0.21/0.53  # Total time               : 0.031 s
% 0.21/0.53  # Maximum resident set size: 2076 pages
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.108 s
% 0.21/0.53  # System time              : 0.022 s
% 0.21/0.53  # Total time               : 0.129 s
% 0.21/0.53  # Maximum resident set size: 1736 pages
% 0.21/0.53  % E---3.1 exiting
% 0.21/0.53  % E---3.1 exiting
%------------------------------------------------------------------------------