TSTP Solution File: NUM694+4 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : NUM694+4 : TPTP v8.2.0. Released v7.3.0.
% 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 : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 01:27:41 EDT 2024

% Result   : Theorem 9.35s 1.65s
% Output   : CNFRefutation 9.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  143 (  65 unt;   0 def)
%            Number of atoms       :  285 (  29 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  229 (  87   ~; 104   |;  18   &)
%                                         (  12 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   29 (  29 usr;  19 con; 0-2 aty)
%            Number of variables   :  127 (  17 sgn  62   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_def__all__of,axiom,
    ! [X4,X5] :
      ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X4),X5))
    <=> ! [X12] :
          ( gg_TPTP_ind(X12)
         => ( scratc2135361906_is_of(X12,X4)
           => pp(aa_TPTP_ind_bool(X5,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__all__of) ).

fof(fact_satz10c,axiom,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gu)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz10c) ).

fof(fact_satz24,axiom,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz24) ).

fof(fact_ATP_Olambda__39,axiom,
    ! [X25] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X25))
    <=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__39) ).

fof(fact_n__1__p,axiom,
    scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__1__p) ).

fof(gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__n__1,hypothesis,
    gg_TPTP_ind(scratc2094053556nd_n_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__n__1) ).

fof(help_fimplies_1_1_U,axiom,
    ! [X32,X33] :
      ( pp(X32)
      | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X32),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

fof(fact_ATP_Olambda__15,axiom,
    ! [X25] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X25))
    <=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),scratc2094053556nd_n_1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__15) ).

fof(help_fFalse_1_1_U,axiom,
    ~ pp(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

fof(help_fFalse_1_1_T,axiom,
    ! [X32] :
      ( gg_bool(X32)
     => ( X32 = fTrue
        | X32 = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

fof(gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__d__not,axiom,
    ! [X1] : gg_bool(scratc1230282688_d_not(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__d__not) ).

fof(fact_def__d__not,axiom,
    ! [X4] :
      ( pp(scratc1230282688_d_not(X4))
    <=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X4),fFalse)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__d__not) ).

fof(fact_def__imp,axiom,
    scratc302099643nd_imp = fimplies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__imp) ).

fof(fact_satz10j,axiom,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gi)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz10j) ).

fof(fact_ATP_Olambda__107,axiom,
    ! [X25,X26] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X25),X26))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),X26))
       => pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X25),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__107) ).

fof(fact_l__et,axiom,
    ! [X17] :
      ( scratc417235917nd_wel(X17)
     => pp(X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_l__et) ).

fof(fact_def__wel,axiom,
    ! [X4] :
      ( scratc417235917nd_wel(X4)
    <=> pp(scratc1230282688_d_not(scratc1230282688_d_not(X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__wel) ).

fof(fact_def__r__ec,axiom,
    ! [X4,X5] :
      ( scratc2146893183d_r_ec(X4,X5)
    <=> ( pp(X4)
       => pp(scratc1230282688_d_not(X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__r__ec) ).

fof(fact_ATP_Olambda__45,axiom,
    ! [X25] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X25))
    <=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__45) ).

fof(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool,axiom,
    ! [X1,X2] : gg_bool(aa_TPTP_ind_bool(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) ).

fof(help_pp_2_1_U,axiom,
    pp(fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).

fof(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U,axiom,
    ! [X32,X34] :
      ( ~ pp(aa_TPTP_ind_bool(X32,X34))
      | pp(fEx_TPTP_ind(X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) ).

fof(fact_ATP_Olambda__11,axiom,
    ! [X25] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X25))
    <=> scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X25),aTP_Lamm_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__11) ).

fof(conj_0,conjecture,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

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/sandbox2/benchmark/theBenchmark.p',gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) ).

fof(fact_def__n__1,axiom,
    scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__n__1) ).

fof(fact_ATP_Olambda__116,axiom,
    ! [X25,X26] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X25),X26))
    <=> ( pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),X26)))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X25),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__116) ).

fof(fact_satz13,axiom,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_satz13) ).

fof(fact_ATP_Olambda__103,axiom,
    ! [X25,X26] :
      ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X25),X26))
    <=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),X26))
       => pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X26),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__103) ).

fof(fact_ATP_Olambda__37,axiom,
    ! [X25] :
      ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X25))
    <=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ATP_Olambda__37) ).

fof(c_0_30,plain,
    ! [X359,X360,X361,X362,X363] :
      ( ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X359),X360))
        | ~ gg_TPTP_ind(X361)
        | ~ scratc2135361906_is_of(X361,X359)
        | pp(aa_TPTP_ind_bool(X360,X361)) )
      & ( gg_TPTP_ind(esk13_2(X362,X363))
        | pp(aa_fun171081125l_bool(scratc2055738343all_of(X362),X363)) )
      & ( scratc2135361906_is_of(esk13_2(X362,X363),X362)
        | pp(aa_fun171081125l_bool(scratc2055738343all_of(X362),X363)) )
      & ( ~ pp(aa_TPTP_ind_bool(X363,esk13_2(X362,X363)))
        | pp(aa_fun171081125l_bool(scratc2055738343all_of(X362),X363)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).

cnf(c_0_31,plain,
    ( pp(aa_TPTP_ind_bool(X2,X3))
    | ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X1),X2))
    | ~ gg_TPTP_ind(X3)
    | ~ scratc2135361906_is_of(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_32,plain,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gu)),
    inference(split_conjunct,[status(thm)],[fact_satz10c]) ).

cnf(c_0_33,plain,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
    inference(split_conjunct,[status(thm)],[fact_satz24]) ).

fof(c_0_34,plain,
    ! [X548] :
      ( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X548))
        | pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X548))) )
      & ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X548)))
        | pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X548)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__39])])]) ).

cnf(c_0_35,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X1))
    | ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,plain,
    scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
    inference(split_conjunct,[status(thm)],[fact_n__1__p]) ).

cnf(c_0_37,hypothesis,
    gg_TPTP_ind(scratc2094053556nd_n_1),
    inference(split_conjunct,[status(thm)],[gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__n__1]) ).

fof(c_0_38,plain,
    ! [X1125,X1126] :
      ( pp(X1125)
      | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X1125),X1126)) ),
    inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).

fof(c_0_39,plain,
    ! [X524] :
      ( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X524))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X524),scratc2094053556nd_n_1)) )
      & ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X524),scratc2094053556nd_n_1))
        | pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X524)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__15])])]) ).

cnf(c_0_40,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X1))
    | ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_33]) ).

cnf(c_0_41,plain,
    ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X1)))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_42,plain,
    pp(aa_TPTP_ind_bool(aTP_Lamm_gu,scratc2094053556nd_n_1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).

fof(c_0_43,plain,
    ~ pp(fFalse),
    inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).

fof(c_0_44,plain,
    ! [X1120] :
      ( ~ gg_bool(X1120)
      | X1120 = fTrue
      | X1120 = fFalse ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])])]) ).

fof(c_0_45,plain,
    ! [X41] : gg_bool(scratc1230282688_d_not(X41)),
    inference(variable_rename,[status(thm)],[gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__d__not]) ).

fof(c_0_46,plain,
    ! [X280] :
      ( ( ~ pp(scratc1230282688_d_not(X280))
        | pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X280),fFalse)) )
      & ( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X280),fFalse))
        | pp(scratc1230282688_d_not(X280)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__d__not])])]) ).

cnf(c_0_47,plain,
    ( pp(X1)
    | pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_48,plain,
    scratc302099643nd_imp = fimplies,
    inference(split_conjunct,[status(thm)],[fact_def__imp]) ).

cnf(c_0_49,plain,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gi)),
    inference(split_conjunct,[status(thm)],[fact_satz10j]) ).

fof(c_0_50,plain,
    ! [X640,X641] :
      ( ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X640),X641))
        | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X640),X641))
        | pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X640),X641))) )
      & ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X640),X641))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X640),X641)) )
      & ( ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X640),X641)))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X640),X641)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__107])])])]) ).

cnf(c_0_51,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),scratc2094053556nd_n_1))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_52,plain,
    pp(aa_TPTP_ind_bool(aTP_Lamm_bo,scratc2094053556nd_n_1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_37])]) ).

cnf(c_0_53,plain,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1))),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

fof(c_0_54,plain,
    ~ pp(fFalse),
    inference(fof_nnf,[status(thm)],[c_0_43]) ).

fof(c_0_55,plain,
    ! [X403] :
      ( ~ scratc417235917nd_wel(X403)
      | pp(X403) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_l__et])])]) ).

fof(c_0_56,plain,
    ! [X279] :
      ( ( ~ scratc417235917nd_wel(X279)
        | pp(scratc1230282688_d_not(scratc1230282688_d_not(X279))) )
      & ( ~ pp(scratc1230282688_d_not(scratc1230282688_d_not(X279)))
        | scratc417235917nd_wel(X279) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__wel])])]) ).

cnf(c_0_57,plain,
    ( X1 = fTrue
    | X1 = fFalse
    | ~ gg_bool(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_58,plain,
    gg_bool(scratc1230282688_d_not(X1)),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

fof(c_0_59,plain,
    ! [X177,X178] :
      ( ( ~ scratc2146893183d_r_ec(X177,X178)
        | ~ pp(X177)
        | pp(scratc1230282688_d_not(X178)) )
      & ( pp(X177)
        | scratc2146893183d_r_ec(X177,X178) )
      & ( ~ pp(scratc1230282688_d_not(X178))
        | scratc2146893183d_r_ec(X177,X178) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__r__ec])])])]) ).

cnf(c_0_60,plain,
    ( pp(scratc1230282688_d_not(X1))
    | ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X1),fFalse)) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_61,plain,
    ( pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X1),X2))
    | pp(X1) ),
    inference(rw,[status(thm)],[c_0_47,c_0_48]) ).

fof(c_0_62,plain,
    ! [X554] :
      ( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X554))
        | pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X554))) )
      & ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X554)))
        | pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X554)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__45])])]) ).

cnf(c_0_63,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X1))
    | ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_49]) ).

cnf(c_0_64,plain,
    ( pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X1),X2)))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X1),X2))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_65,plain,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1)),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_66,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1),X1))
    | ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_53]) ).

fof(c_0_67,plain,
    ! [X57,X58] : gg_bool(aa_TPTP_ind_bool(X57,X58)),
    inference(variable_rename,[status(thm)],[gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool]) ).

cnf(c_0_68,plain,
    ~ pp(fFalse),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_69,plain,
    ( pp(X1)
    | ~ scratc417235917nd_wel(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_70,plain,
    ( scratc417235917nd_wel(X1)
    | ~ pp(scratc1230282688_d_not(scratc1230282688_d_not(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_71,plain,
    ( scratc1230282688_d_not(X1) = fFalse
    | scratc1230282688_d_not(X1) = fTrue ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_72,plain,
    pp(fTrue),
    inference(split_conjunct,[status(thm)],[help_pp_2_1_U]) ).

cnf(c_0_73,plain,
    ( scratc2146893183d_r_ec(X2,X1)
    | ~ pp(scratc1230282688_d_not(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_74,plain,
    ( pp(scratc1230282688_d_not(X1))
    | pp(X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

fof(c_0_75,plain,
    ! [X32,X34] :
      ( ~ pp(aa_TPTP_ind_bool(X32,X34))
      | pp(fEx_TPTP_ind(X32)) ),
    inference(fof_simplification,[status(thm)],[help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U]) ).

fof(c_0_76,plain,
    ! [X520] :
      ( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X520))
        | scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X520),aTP_Lamm_a) )
      & ( ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X520),aTP_Lamm_a)
        | pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X520)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__11])])]) ).

fof(c_0_77,negated_conjecture,
    ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(c_0_78,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_79,plain,
    ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X1)))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_80,plain,
    pp(aa_TPTP_ind_bool(aTP_Lamm_gi,scratc2094053556nd_n_1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_36]),c_0_37])]) ).

cnf(c_0_81,plain,
    ( pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1)))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1),scratc2094053556nd_n_1)) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_82,plain,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1),scratc2094053556nd_n_1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_36]),c_0_37])]) ).

cnf(c_0_83,plain,
    gg_bool(aa_TPTP_ind_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_84,plain,
    ~ scratc417235917nd_wel(fFalse),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_85,plain,
    ( scratc1230282688_d_not(scratc1230282688_d_not(X1)) = fFalse
    | scratc417235917nd_wel(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).

cnf(c_0_86,plain,
    ( scratc2146893183d_r_ec(X1,X2)
    | pp(X2) ),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

fof(c_0_87,plain,
    ! [X1127,X1128] :
      ( ~ pp(aa_TPTP_ind_bool(X1127,X1128))
      | pp(fEx_TPTP_ind(X1127)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_75])]) ).

cnf(c_0_88,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X1))
    | ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X1),aTP_Lamm_a) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_89,plain,
    scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),
    inference(split_conjunct,[status(thm)],[fact_def__n__1]) ).

fof(c_0_90,negated_conjecture,
    ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
    inference(fof_nnf,[status(thm)],[c_0_77]) ).

cnf(c_0_91,hypothesis,
    gg_bool(aa_fun171081125l_bool(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_92,plain,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,scratc2094053556nd_n_1))),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_93,plain,
    pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).

cnf(c_0_94,plain,
    ( aa_TPTP_ind_bool(X1,X2) = fFalse
    | aa_TPTP_ind_bool(X1,X2) = fTrue ),
    inference(spm,[status(thm)],[c_0_57,c_0_83]) ).

cnf(c_0_95,plain,
    scratc1230282688_d_not(scratc1230282688_d_not(fFalse)) = fFalse,
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_96,plain,
    ( pp(scratc1230282688_d_not(X2))
    | ~ scratc2146893183d_r_ec(X1,X2)
    | ~ pp(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_97,plain,
    scratc2146893183d_r_ec(X1,fFalse),
    inference(spm,[status(thm)],[c_0_68,c_0_86]) ).

cnf(c_0_98,plain,
    ( pp(fEx_TPTP_ind(X1))
    | ~ pp(aa_TPTP_ind_bool(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

cnf(c_0_99,plain,
    pp(aa_TPTP_ind_bool(aTP_Lamm_jf,scratc1150508294ptyset)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_36])]) ).

cnf(c_0_100,plain,
    ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X2),X1))
    | ~ pp(aa_TPTP_ind_bool(X1,esk13_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_101,plain,
    ( pp(X1)
    | scratc2146893183d_r_ec(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_102,negated_conjecture,
    ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
    inference(split_conjunct,[status(thm)],[c_0_90]) ).

cnf(c_0_103,hypothesis,
    ( aa_fun171081125l_bool(X1,X2) = fFalse
    | aa_fun171081125l_bool(X1,X2) = fTrue ),
    inference(spm,[status(thm)],[c_0_57,c_0_91]) ).

fof(c_0_104,plain,
    ! [X658,X659] :
      ( ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X658),X659))
        | ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X658),X659)))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X658),X659)) )
      & ( pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X658),X659)))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X658),X659)) )
      & ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X658),X659))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X658),X659)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__116])])])]) ).

cnf(c_0_105,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,scratc2094053556nd_n_1),X1))
    | ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_92]) ).

cnf(c_0_106,plain,
    ( aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1) = fFalse
    | pp(scratc1230282688_d_not(fTrue)) ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_107,plain,
    ( scratc1230282688_d_not(fFalse) = fFalse
    | scratc1230282688_d_not(fTrue) = fFalse ),
    inference(spm,[status(thm)],[c_0_95,c_0_71]) ).

cnf(c_0_108,plain,
    ( pp(scratc1230282688_d_not(fFalse))
    | ~ pp(X1) ),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_109,plain,
    pp(fEx_TPTP_ind(aTP_Lamm_jf)),
    inference(spm,[status(thm)],[c_0_98,c_0_99]) ).

cnf(c_0_110,plain,
    ( scratc2135361906_is_of(esk13_2(X1,X2),X1)
    | pp(aa_fun171081125l_bool(scratc2055738343all_of(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_111,plain,
    ( gg_TPTP_ind(esk13_2(X1,X2))
    | pp(aa_fun171081125l_bool(scratc2055738343all_of(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_112,plain,
    ( scratc2146893183d_r_ec(aa_TPTP_ind_bool(X1,esk13_2(X2,X1)),X3)
    | pp(aa_fun171081125l_bool(scratc2055738343all_of(X2),X1)) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_113,negated_conjecture,
    aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)) = fFalse,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_72])]) ).

cnf(c_0_114,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X1),X2))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X1),X2))
    | ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_115,plain,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,scratc2094053556nd_n_1),scratc2094053556nd_n_1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_36]),c_0_37])]) ).

cnf(c_0_116,plain,
    ( aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1) = fFalse
    | scratc1230282688_d_not(fFalse) = fFalse ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_68]) ).

cnf(c_0_117,plain,
    pp(scratc1230282688_d_not(fFalse)),
    inference(spm,[status(thm)],[c_0_108,c_0_109]) ).

cnf(c_0_118,negated_conjecture,
    scratc2135361906_is_of(esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)),aTP_Lamm_a),
    inference(spm,[status(thm)],[c_0_102,c_0_110]) ).

cnf(c_0_119,negated_conjecture,
    gg_TPTP_ind(esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
    inference(spm,[status(thm)],[c_0_102,c_0_111]) ).

cnf(c_0_120,negated_conjecture,
    scratc2146893183d_r_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),X1),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_68]) ).

cnf(c_0_121,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1))
    | ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1))) ),
    inference(spm,[status(thm)],[c_0_114,c_0_115]) ).

cnf(c_0_122,plain,
    aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1) = fFalse,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_116]),c_0_117])]),c_0_84]) ).

cnf(c_0_123,plain,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
    inference(split_conjunct,[status(thm)],[fact_satz13]) ).

fof(c_0_124,plain,
    ! [X632,X633] :
      ( ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X632),X633))
        | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X632),X633))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X633),X632)) )
      & ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X632),X633))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X632),X633)) )
      & ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X633),X632))
        | pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X632),X633)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__103])])])]) ).

cnf(c_0_125,negated_conjecture,
    pp(aa_TPTP_ind_bool(aTP_Lamm_bo,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_118]),c_0_119])]) ).

cnf(c_0_126,negated_conjecture,
    ( pp(scratc1230282688_d_not(X1))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))) ),
    inference(spm,[status(thm)],[c_0_96,c_0_120]) ).

cnf(c_0_127,plain,
    ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1))),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122]),c_0_68]) ).

fof(c_0_128,plain,
    ! [X546] :
      ( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X546))
        | pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X546))) )
      & ( ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X546)))
        | pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X546)) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__37])])]) ).

cnf(c_0_129,plain,
    ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X1))
    | ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_123]) ).

cnf(c_0_130,plain,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X2),X1))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X1),X2))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

cnf(c_0_131,negated_conjecture,
    pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1)),
    inference(spm,[status(thm)],[c_0_51,c_0_125]) ).

cnf(c_0_132,negated_conjecture,
    ( aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))) = fFalse
    | pp(scratc1230282688_d_not(X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_94]),c_0_72])]) ).

cnf(c_0_133,plain,
    scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1)) = fFalse,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_71]),c_0_72])]) ).

cnf(c_0_134,plain,
    ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X1)))
    | ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_128]) ).

cnf(c_0_135,negated_conjecture,
    pp(aa_TPTP_ind_bool(aTP_Lamm_gy,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_118]),c_0_119])]) ).

cnf(c_0_136,negated_conjecture,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))))
    | ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1)) ),
    inference(spm,[status(thm)],[c_0_130,c_0_131]) ).

cnf(c_0_137,negated_conjecture,
    aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))) = fFalse,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_68]) ).

cnf(c_0_138,negated_conjecture,
    pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))))),
    inference(spm,[status(thm)],[c_0_134,c_0_135]) ).

cnf(c_0_139,negated_conjecture,
    ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1)),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137]),c_0_68]) ).

cnf(c_0_140,negated_conjecture,
    ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),X1))
    | ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
    | ~ gg_TPTP_ind(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_138]) ).

cnf(c_0_141,negated_conjecture,
    aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1) = fFalse,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_94]),c_0_72])]) ).

cnf(c_0_142,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_140,c_0_36]),c_0_141]),c_0_37])]),c_0_68]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM694+4 : TPTP v8.2.0. Released v7.3.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 04:39:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.46  Running first-order model finding
% 0.19/0.46  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/benchmark/theBenchmark.p
% 9.35/1.65  # Version: 3.1.0
% 9.35/1.65  # Preprocessing class: FSLMSMSLSSSNFFN.
% 9.35/1.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.35/1.65  # Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 9.35/1.65  # Starting new_bool_3 with 600s (2) cores
% 9.35/1.65  # Starting new_bool_1 with 600s (2) cores
% 9.35/1.65  # Starting sh5l with 300s (1) cores
% 9.35/1.65  # G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 13514 completed with status 0
% 9.35/1.65  # Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 9.35/1.65  # Preprocessing class: FSLMSMSLSSSNFFN.
% 9.35/1.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.35/1.65  # Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 9.35/1.65  # No SInE strategy applied
% 9.35/1.65  # Search class: FGHSM-SSLM31-DFFFFFNN
% 9.35/1.65  # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 9.35/1.65  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 487s (1) cores
% 9.35/1.65  # Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 91s (1) cores
% 9.35/1.65  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 82s (1) cores
% 9.35/1.65  # G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 13526 completed with status 0
% 9.35/1.65  # Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 9.35/1.65  # Preprocessing class: FSLMSMSLSSSNFFN.
% 9.35/1.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.35/1.65  # Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 9.35/1.65  # No SInE strategy applied
% 9.35/1.65  # Search class: FGHSM-SSLM31-DFFFFFNN
% 9.35/1.65  # Scheduled 6 strats onto 3 cores with 900 seconds (900 total)
% 9.35/1.65  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 487s (1) cores
% 9.35/1.65  # Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 91s (1) cores
% 9.35/1.65  # Preprocessing time       : 0.013 s
% 9.35/1.65  
% 9.35/1.65  # Proof found!
% 9.35/1.65  # SZS status Theorem
% 9.35/1.65  # SZS output start CNFRefutation
% See solution above
% 9.35/1.65  # Parsed axioms                        : 573
% 9.35/1.65  # Removed by relevancy pruning/SinE    : 0
% 9.35/1.65  # Initial clauses                      : 1035
% 9.35/1.65  # Removed in clause preprocessing      : 18
% 9.35/1.65  # Initial clauses in saturation        : 1017
% 9.35/1.65  # Processed clauses                    : 6470
% 9.35/1.65  # ...of these trivial                  : 79
% 9.35/1.65  # ...subsumed                          : 612
% 9.35/1.65  # ...remaining for further processing  : 5779
% 9.35/1.65  # Other redundant clauses eliminated   : 8
% 9.35/1.65  # Clauses deleted for lack of memory   : 0
% 9.35/1.65  # Backward-subsumed                    : 26
% 9.35/1.65  # Backward-rewritten                   : 188
% 9.35/1.65  # Generated clauses                    : 56514
% 9.35/1.65  # ...of the previous two non-redundant : 49494
% 9.35/1.65  # ...aggressively subsumed             : 0
% 9.35/1.65  # Contextual simplify-reflections      : 1
% 9.35/1.65  # Paramodulations                      : 56491
% 9.35/1.65  # Factorizations                       : 13
% 9.35/1.65  # NegExts                              : 0
% 9.35/1.65  # Equation resolutions                 : 10
% 9.35/1.65  # Disequality decompositions           : 0
% 9.35/1.65  # Total rewrite steps                  : 15268
% 9.35/1.65  # ...of those cached                   : 12789
% 9.35/1.65  # Propositional unsat checks           : 0
% 9.35/1.65  #    Propositional check models        : 0
% 9.35/1.65  #    Propositional check unsatisfiable : 0
% 9.35/1.65  #    Propositional clauses             : 0
% 9.35/1.65  #    Propositional clauses after purity: 0
% 9.35/1.65  #    Propositional unsat core size     : 0
% 9.35/1.65  #    Propositional preprocessing time  : 0.000
% 9.35/1.65  #    Propositional encoding time       : 0.000
% 9.35/1.65  #    Propositional solver time         : 0.000
% 9.35/1.65  #    Success case prop preproc time    : 0.000
% 9.35/1.65  #    Success case prop encoding time   : 0.000
% 9.35/1.65  #    Success case prop solver time     : 0.000
% 9.35/1.65  # Current number of processed clauses  : 5557
% 9.35/1.65  #    Positive orientable unit clauses  : 3312
% 9.35/1.65  #    Positive unorientable unit clauses: 3
% 9.35/1.65  #    Negative unit clauses             : 12
% 9.35/1.65  #    Non-unit-clauses                  : 2230
% 9.35/1.65  # Current number of unprocessed clauses: 41905
% 9.35/1.65  # ...number of literals in the above   : 105131
% 9.35/1.65  # Current number of archived formulas  : 0
% 9.35/1.65  # Current number of archived clauses   : 230
% 9.35/1.65  # Clause-clause subsumption calls (NU) : 449511
% 9.35/1.65  # Rec. Clause-clause subsumption calls : 380227
% 9.35/1.65  # Non-unit clause-clause subsumptions  : 414
% 9.35/1.65  # Unit Clause-clause subsumption calls : 629991
% 9.35/1.65  # Rewrite failures with RHS unbound    : 0
% 9.35/1.65  # BW rewrite match attempts            : 311476
% 9.35/1.65  # BW rewrite match successes           : 152
% 9.35/1.65  # Condensation attempts                : 0
% 9.35/1.65  # Condensation successes               : 0
% 9.35/1.65  # Termbank termtop insertions          : 1029328
% 9.35/1.65  # Search garbage collected termcells   : 10458
% 9.35/1.65  
% 9.35/1.65  # -------------------------------------------------
% 9.35/1.65  # User time                : 1.046 s
% 9.35/1.65  # System time              : 0.061 s
% 9.35/1.65  # Total time               : 1.107 s
% 9.35/1.65  # Maximum resident set size: 5660 pages
% 9.35/1.65  
% 9.35/1.65  # -------------------------------------------------
% 9.35/1.65  # User time                : 3.177 s
% 9.35/1.65  # System time              : 0.151 s
% 9.35/1.65  # Total time               : 3.328 s
% 9.35/1.65  # Maximum resident set size: 2580 pages
% 9.35/1.65  % E---3.1 exiting
%------------------------------------------------------------------------------