TSTP Solution File: NUM639+4 by E-SAT---3.1

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%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : NUM639+4 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.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 19:08:06 EDT 2023

% Result   : Theorem 117.63s 15.39s
% Output   : CNFRefutation 117.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   60 (  28 unt;   0 def)
%            Number of atoms       :  120 (  26 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  101 (  41   ~;  45   |;   7   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  12 con; 0-2 aty)
%            Number of variables   :   70 (   5 sgn;  36   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_ATP_Olambda__3,axiom,
    ! [X25] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X25))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X25),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X25))) ),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',fact_ATP_Olambda__3) ).

fof(fact_def__n__pl,axiom,
    ! [X4] : scratc1289955817d_n_pl(X4) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X4)),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',fact_def__n__pl) ).

fof(fact_def__e__is,axiom,
    ! [X4] : scratc1770836270d_e_is(X4) = fequal_TPTP_ind,
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',fact_def__e__is) ).

fof(fact_ATP_Olambda__7,axiom,
    ! [X25] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X25))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X25)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X25),scratc214542084nd_n_1))) ),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',fact_ATP_Olambda__7) ).

fof(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T,axiom,
    ! [X34,X35] :
      ( ( gg_TPTP_ind(X34)
        & gg_TPTP_ind(X35) )
     => ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X34),X35))
        | X34 = X35 ) ),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).

fof(fact_def__n__is,axiom,
    scratc1289496631d_n_is = scratc1770836270d_e_is(scratc1472361728nd_nat),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',fact_def__n__is) ).

fof(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind,axiom,
    ! [X1,X2] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).

fof(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T,axiom,
    ! [X34,X35] :
      ( X34 != X35
      | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X34),X35)) ),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) ).

fof(fact_def__all__of,axiom,
    ! [X4,X5] :
      ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X4),X5))
    <=> ! [X12] :
          ( gg_TPTP_ind(X12)
         => ( scratc1829621698_is_of(X12,X4)
           => pp(aa_TPTP_ind_bool(X5,X12)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',fact_def__all__of) ).

fof(help_fFalse_1_1_T,axiom,
    ! [X32] :
      ( gg_bool(X32)
     => ( X32 = fTrue
        | X32 = fFalse ) ),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',help_fFalse_1_1_T) ).

fof(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool,hypothesis,
    ! [X1,X2] : gg_bool(aa_fun171081125l_bool(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) ).

fof(fact_satz4a,axiom,
    pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',fact_satz4a) ).

fof(conj_0,conjecture,
    pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',conj_0) ).

fof(help_pp_2_1_U,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',help_pp_2_1_U) ).

fof(help_fFalse_1_1_U,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p',help_fFalse_1_1_U) ).

fof(c_0_15,plain,
    ! [X489] :
      ( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X489))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X489),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X489))) )
      & ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X489),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X489)))
        | pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X489)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__3])]) ).

fof(c_0_16,plain,
    ! [X68] : scratc1289955817d_n_pl(X68) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X68)),
    inference(variable_rename,[status(thm)],[fact_def__n__pl]) ).

fof(c_0_17,plain,
    ! [X228] : scratc1770836270d_e_is(X228) = fequal_TPTP_ind,
    inference(variable_rename,[status(thm)],[fact_def__e__is]) ).

fof(c_0_18,plain,
    ! [X493] :
      ( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X493))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X493)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X493),scratc214542084nd_n_1))) )
      & ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X493)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X493),scratc214542084nd_n_1)))
        | pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X493)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__7])]) ).

fof(c_0_19,plain,
    ! [X34,X35] :
      ( ( gg_TPTP_ind(X34)
        & gg_TPTP_ind(X35) )
     => ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X34),X35))
        | X34 = X35 ) ),
    inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T]) ).

cnf(c_0_20,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    scratc1289955817d_n_pl(X1) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    scratc1289496631d_n_is = scratc1770836270d_e_is(scratc1472361728nd_nat),
    inference(split_conjunct,[status(thm)],[fact_def__n__is]) ).

cnf(c_0_23,plain,
    scratc1770836270d_e_is(X1) = fequal_TPTP_ind,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1),scratc214542084nd_n_1))) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_25,plain,
    ! [X753,X754] :
      ( ~ gg_TPTP_ind(X753)
      | ~ gg_TPTP_ind(X754)
      | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X753),X754))
      | X753 = X754 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).

cnf(c_0_26,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
    inference(rw,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,plain,
    fequal_TPTP_ind = scratc1289496631d_n_is,
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_28,plain,
    ! [X59,X60] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X59,X60)),
    inference(variable_rename,[status(thm)],[gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind]) ).

fof(c_0_29,plain,
    ! [X751,X752] :
      ( X751 != X752
      | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X751),X752)) ),
    inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T]) ).

cnf(c_0_30,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1))) ),
    inference(rw,[status(thm)],[c_0_24,c_0_21]) ).

cnf(c_0_31,plain,
    ( X1 = X2
    | ~ gg_TPTP_ind(X1)
    | ~ gg_TPTP_ind(X2)
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
    inference(rw,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_33,plain,
    gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_34,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_35,plain,
    ! [X336,X337,X338,X339,X340] :
      ( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X336),X337))
        | ~ gg_TPTP_ind(X338)
        | ~ scratc1829621698_is_of(X338,X336)
        | pp(aa_TPTP_ind_bool(X337,X338)) )
      & ( gg_TPTP_ind(esk13_2(X339,X340))
        | pp(aa_fun171081125l_bool(scratc1153622423all_of(X339),X340)) )
      & ( scratc1829621698_is_of(esk13_2(X339,X340),X339)
        | pp(aa_fun171081125l_bool(scratc1153622423all_of(X339),X340)) )
      & ( ~ pp(aa_TPTP_ind_bool(X340,esk13_2(X339,X340)))
        | pp(aa_fun171081125l_bool(scratc1153622423all_of(X339),X340)) ) ),
    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)],[fact_def__all__of])])])])])]) ).

fof(c_0_36,plain,
    ! [X742] :
      ( ~ gg_bool(X742)
      | X742 = fTrue
      | X742 = fFalse ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).

fof(c_0_37,hypothesis,
    ! [X61,X62] : gg_bool(aa_fun171081125l_bool(X61,X62)),
    inference(variable_rename,[status(thm)],[gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool]) ).

cnf(c_0_38,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1))) ),
    inference(rw,[status(thm)],[c_0_30,c_0_27]) ).

cnf(c_0_39,plain,
    ( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1) = aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_33])]) ).

cnf(c_0_40,plain,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1),X1)),
    inference(er,[status(thm)],[c_0_34]) ).

cnf(c_0_41,plain,
    ( pp(aa_TPTP_ind_bool(X2,X3))
    | ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X2))
    | ~ gg_TPTP_ind(X3)
    | ~ scratc1829621698_is_of(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,plain,
    pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
    inference(split_conjunct,[status(thm)],[fact_satz4a]) ).

fof(c_0_43,negated_conjecture,
    ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

cnf(c_0_44,plain,
    ( X1 = fTrue
    | X1 = fFalse
    | ~ gg_bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_45,hypothesis,
    gg_bool(aa_fun171081125l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,plain,
    ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X2),X1))
    | ~ pp(aa_TPTP_ind_bool(X1,esk13_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_47,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).

cnf(c_0_48,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1))
    | ~ scratc1829621698_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_49,plain,
    ( scratc1829621698_is_of(esk13_2(X1,X2),X1)
    | pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_50,plain,
    ( gg_TPTP_ind(esk13_2(X1,X2))
    | pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_51,negated_conjecture,
    ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_52,hypothesis,
    ( aa_fun171081125l_bool(X1,X2) = fTrue
    | aa_fun171081125l_bool(X1,X2) = fFalse ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_53,plain,
    pp(fTrue),
    inference(split_conjunct,[status(thm)],[help_pp_2_1_U]) ).

fof(c_0_54,plain,
    ~ pp(fFalse),
    inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).

cnf(c_0_55,plain,
    ( pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),aTP_Lamm_aa))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,esk13_2(X1,aTP_Lamm_aa))) ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_56,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,esk13_2(aTP_Lamm_a,X1)))
    | pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),X1)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).

cnf(c_0_57,negated_conjecture,
    aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa) = fFalse,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).

cnf(c_0_58,plain,
    ~ pp(fFalse),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_59,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : NUM639+4 : TPTP v8.1.2. Released v7.3.0.
% 0.05/0.10  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n007.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 2400
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Mon Oct  2 13:07:54 EDT 2023
% 0.10/0.30  % CPUTime    : 
% 0.14/0.43  Running first-order model finding
% 0.14/0.43  Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.nWOEYhwf6G/E---3.1_11881.p
% 117.63/15.39  # Version: 3.1pre001
% 117.63/15.39  # Preprocessing class: FSLMSMSMSSSNFFN.
% 117.63/15.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.63/15.39  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 117.63/15.39  # Starting new_bool_3 with 600s (2) cores
% 117.63/15.39  # Starting new_bool_1 with 300s (1) cores
% 117.63/15.39  # Starting sh5l with 300s (1) cores
% 117.63/15.39  # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 11958 completed with status 0
% 117.63/15.39  # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 117.63/15.39  # Preprocessing class: FSLMSMSMSSSNFFN.
% 117.63/15.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.63/15.39  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 117.63/15.39  # No SInE strategy applied
% 117.63/15.39  # Search class: FGHSM-FSLM31-DFFFFFNN
% 117.63/15.39  # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 117.63/15.39  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 544s (1) cores
% 117.63/15.39  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 117.63/15.39  # Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 109s (1) cores
% 117.63/15.39  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 109s (1) cores
% 117.63/15.39  # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 11966 completed with status 0
% 117.63/15.39  # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 117.63/15.39  # Preprocessing class: FSLMSMSMSSSNFFN.
% 117.63/15.39  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 117.63/15.39  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 117.63/15.39  # No SInE strategy applied
% 117.63/15.39  # Search class: FGHSM-FSLM31-DFFFFFNN
% 117.63/15.39  # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 117.63/15.39  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 544s (1) cores
% 117.63/15.39  # Preprocessing time       : 0.007 s
% 117.63/15.39  # Presaturation interreduction done
% 117.63/15.39  
% 117.63/15.39  # Proof found!
% 117.63/15.39  # SZS status Theorem
% 117.63/15.39  # SZS output start CNFRefutation
% See solution above
% 117.63/15.39  # Parsed axioms                        : 317
% 117.63/15.39  # Removed by relevancy pruning/SinE    : 0
% 117.63/15.39  # Initial clauses                      : 524
% 117.63/15.39  # Removed in clause preprocessing      : 18
% 117.63/15.39  # Initial clauses in saturation        : 506
% 117.63/15.39  # Processed clauses                    : 58566
% 117.63/15.39  # ...of these trivial                  : 498
% 117.63/15.39  # ...subsumed                          : 48758
% 117.63/15.39  # ...remaining for further processing  : 9310
% 117.63/15.39  # Other redundant clauses eliminated   : 103
% 117.63/15.39  # Clauses deleted for lack of memory   : 0
% 117.63/15.39  # Backward-subsumed                    : 95
% 117.63/15.39  # Backward-rewritten                   : 713
% 117.63/15.39  # Generated clauses                    : 572801
% 117.63/15.39  # ...of the previous two non-redundant : 476343
% 117.63/15.39  # ...aggressively subsumed             : 0
% 117.63/15.39  # Contextual simplify-reflections      : 93
% 117.63/15.39  # Paramodulations                      : 572638
% 117.63/15.39  # Factorizations                       : 27
% 117.63/15.39  # NegExts                              : 0
% 117.63/15.39  # Equation resolutions                 : 136
% 117.63/15.39  # Total rewrite steps                  : 254445
% 117.63/15.39  # Propositional unsat checks           : 1
% 117.63/15.39  #    Propositional check models        : 0
% 117.63/15.39  #    Propositional check unsatisfiable : 0
% 117.63/15.39  #    Propositional clauses             : 0
% 117.63/15.39  #    Propositional clauses after purity: 0
% 117.63/15.39  #    Propositional unsat core size     : 0
% 117.63/15.39  #    Propositional preprocessing time  : 0.000
% 117.63/15.39  #    Propositional encoding time       : 0.273
% 117.63/15.39  #    Propositional solver time         : 0.151
% 117.63/15.39  #    Success case prop preproc time    : 0.000
% 117.63/15.39  #    Success case prop encoding time   : 0.000
% 117.63/15.39  #    Success case prop solver time     : 0.000
% 117.63/15.39  # Current number of processed clauses  : 8000
% 117.63/15.39  #    Positive orientable unit clauses  : 1263
% 117.63/15.39  #    Positive unorientable unit clauses: 30
% 117.63/15.39  #    Negative unit clauses             : 967
% 117.63/15.39  #    Non-unit-clauses                  : 5740
% 117.63/15.39  # Current number of unprocessed clauses: 415912
% 117.63/15.39  # ...number of literals in the above   : 1270347
% 117.63/15.39  # Current number of archived formulas  : 0
% 117.63/15.39  # Current number of archived clauses   : 1318
% 117.63/15.39  # Clause-clause subsumption calls (NU) : 6021520
% 117.63/15.39  # Rec. Clause-clause subsumption calls : 4163013
% 117.63/15.39  # Non-unit clause-clause subsumptions  : 4087
% 117.63/15.39  # Unit Clause-clause subsumption calls : 2817114
% 117.63/15.39  # Rewrite failures with RHS unbound    : 0
% 117.63/15.39  # BW rewrite match attempts            : 17690
% 117.63/15.39  # BW rewrite match successes           : 673
% 117.63/15.39  # Condensation attempts                : 0
% 117.63/15.39  # Condensation successes               : 0
% 117.63/15.39  # Termbank termtop insertions          : 11315055
% 117.63/15.39  
% 117.63/15.39  # -------------------------------------------------
% 117.63/15.39  # User time                : 14.141 s
% 117.63/15.39  # System time              : 0.444 s
% 117.63/15.39  # Total time               : 14.585 s
% 117.63/15.39  # Maximum resident set size: 3988 pages
% 117.63/15.39  
% 117.63/15.39  # -------------------------------------------------
% 117.63/15.39  # User time                : 56.231 s
% 117.63/15.39  # System time              : 1.761 s
% 117.63/15.39  # Total time               : 57.991 s
% 117.63/15.39  # Maximum resident set size: 2196 pages
% 117.63/15.39  % E---3.1 exiting
%------------------------------------------------------------------------------