TSTP Solution File: SWW473+6 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n009.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 Aug 22 11:07:26 EDT 2023

% Result   : Theorem 186.45s 136.46s
% Output   : CNFRefutation 186.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  172
% Syntax   : Number of formulae    :  200 (  18 unt; 162 typ;   0 def)
%            Number of atoms       :   64 (  13 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   46 (  20   ~;  22   |;   1   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  370 ( 141   >; 229   *;   0   +;   0  <<)
%            Number of predicates  :   29 (  27 usr;   1 prp; 0-2 aty)
%            Number of functors    :  135 ( 135 usr;  21 con; 0-7 aty)
%            Number of variables   :   41 (;  41   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ zero_neq_one > zero > preorder > ordered_ab_group_add > ordere779506340up_add > ordere236663937imp_le > ordere223160158up_add > ordere216010020id_add > order > ord > one > monoid_add > minus > linordered_semidom > linordered_idom > linorder > linord219039673up_add > hBOOL > group_add > finite_finite_1 > dense_linorder > comm_monoid_add > cancel_semigroup_add > cancel146912293up_add > bot > ab_semigroup_add > ab_group_add > hAPP > combs > combc > combb > ti > sum_sum > sum_Plus > image > fun > finite_comp_fun_idem > finite1357897459simple > combk > #nlpp > zero_zero > undefined > the_elem > the_1 > the > plus_plus > partial_flat_lub > ord_less_eq > ord_less > option > one_one > nat_case > minus_minus > member > insert > finite_folding_one > finite_finite > finite_card > finite2073411215e_idem > fequal > combi > collect > bot_bot > x_a > wt > u > suc > pname > pn > p > nat > na > mgt_call > mgt > g > fimplies > fdisj > fconj > fTrue > fNot > fFalse > com > bool > body > #skF_32 > #skF_47 > #skF_49 > #skF_64 > #skF_38 > #skF_75 > #skF_31 > #skF_65 > #skF_34 > #skF_57 > #skF_62 > #skF_63 > #skF_56 > #skF_26 > #skF_44 > #skF_53 > #skF_40 > #skF_17 > #skF_45 > #skF_22 > #skF_60 > #skF_78 > #skF_4 > #skF_39 > #skF_20 > #skF_14 > #skF_15 > #skF_12 > #skF_8 > #skF_70 > #skF_30 > #skF_11 > #skF_48 > #skF_18 > #skF_23 > #skF_19 > #skF_67 > #skF_7 > #skF_2 > #skF_68 > #skF_54 > #skF_58 > #skF_66 > #skF_6 > #skF_37 > #skF_71 > #skF_51 > #skF_29 > #skF_77 > #skF_74 > #skF_28 > #skF_1 > #skF_43 > #skF_24 > #skF_13 > #skF_55 > #skF_52 > #skF_50 > #skF_73 > #skF_25 > #skF_59 > #skF_76 > #skF_9 > #skF_21 > #skF_79 > #skF_3 > #skF_33 > #skF_36 > #skF_41 > #skF_35 > #skF_27 > #skF_46 > #skF_61 > #skF_16 > #skF_72 > #skF_5 > #skF_42 > #skF_69 > #skF_10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(fconj,type,
    fconj: $i ).

tff(hAPP,type,
    hAPP: ( $i * $i * $i * $i ) > $i ).

tff('#skF_32',type,
    '#skF_32': ( $i * $i * $i ) > $i ).

tff('#skF_47',type,
    '#skF_47': ( $i * $i ) > $i ).

tff(partial_flat_lub,type,
    partial_flat_lub: $i > $i ).

tff('#skF_49',type,
    '#skF_49': ( $i * $i * $i ) > $i ).

tff(minus,type,
    minus: $i > $o ).

tff(ord_less_eq,type,
    ord_less_eq: $i > $i ).

tff('#skF_64',type,
    '#skF_64': ( $i * $i * $i ) > $i ).

tff('#skF_38',type,
    '#skF_38': ( $i * $i * $i ) > $i ).

tff('#skF_75',type,
    '#skF_75': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(suc,type,
    suc: $i ).

tff('#skF_31',type,
    '#skF_31': ( $i * $i * $i ) > $i ).

tff('#skF_65',type,
    '#skF_65': ( $i * $i * $i * $i ) > $i ).

tff('#skF_34',type,
    '#skF_34': ( $i * $i * $i * $i * $i ) > $i ).

tff('#skF_57',type,
    '#skF_57': ( $i * $i * $i ) > $i ).

tff(group_add,type,
    group_add: $i > $o ).

tff('#skF_62',type,
    '#skF_62': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_63',type,
    '#skF_63': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_56',type,
    '#skF_56': ( $i * $i ) > $i ).

tff(bot_bot,type,
    bot_bot: $i > $i ).

tff(one_one,type,
    one_one: $i > $i ).

tff(combk,type,
    combk: ( $i * $i ) > $i ).

tff(combs,type,
    combs: ( $i * $i * $i ) > $i ).

tff(monoid_add,type,
    monoid_add: $i > $o ).

tff(the_elem,type,
    the_elem: $i > $i ).

tff('#skF_26',type,
    '#skF_26': ( $i * $i ) > $i ).

tff(linordered_semidom,type,
    linordered_semidom: $i > $o ).

tff('#skF_44',type,
    '#skF_44': ( $i * $i ) > $i ).

tff(ab_semigroup_add,type,
    ab_semigroup_add: $i > $o ).

tff(member,type,
    member: $i > $i ).

tff('#skF_53',type,
    '#skF_53': ( $i * $i ) > $i ).

tff('#skF_40',type,
    '#skF_40': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_17',type,
    '#skF_17': ( $i * $i ) > $i ).

tff(combb,type,
    combb: ( $i * $i * $i ) > $i ).

tff(mgt,type,
    mgt: $i ).

tff('#skF_45',type,
    '#skF_45': ( $i * $i ) > $i ).

tff(sum_Plus,type,
    sum_Plus: ( $i * $i ) > $i ).

tff(fimplies,type,
    fimplies: $i ).

tff('#skF_22',type,
    '#skF_22': ( $i * $i * $i ) > $i ).

tff(ord,type,
    ord: $i > $o ).

tff(zero_neq_one,type,
    zero_neq_one: $i > $o ).

tff('#skF_60',type,
    '#skF_60': ( $i * $i ) > $i ).

tff(fNot,type,
    fNot: $i ).

tff(sum_sum,type,
    sum_sum: ( $i * $i ) > $i ).

tff('#skF_78',type,
    '#skF_78': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(u,type,
    u: $i ).

tff(bool,type,
    bool: $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

tff(collect,type,
    collect: $i > $i ).

tff('#skF_39',type,
    '#skF_39': ( $i * $i * $i ) > $i ).

tff(com,type,
    com: $i ).

tff(linord219039673up_add,type,
    linord219039673up_add: $i > $o ).

tff('#skF_20',type,
    '#skF_20': ( $i * $i * $i * $i ) > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i ) > $i ).

tff(nat,type,
    nat: $i ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i * $i ) > $i ).

tff(fun,type,
    fun: ( $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i * $i * $i * $i ) > $i ).

tff(ordere779506340up_add,type,
    ordere779506340up_add: $i > $o ).

tff('#skF_70',type,
    '#skF_70': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_30',type,
    '#skF_30': ( $i * $i * $i ) > $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i * $i * $i * $i ) > $i ).

tff('#skF_48',type,
    '#skF_48': ( $i * $i * $i ) > $i ).

tff('#skF_18',type,
    '#skF_18': ( $i * $i ) > $i ).

tff(wt,type,
    wt: $i ).

tff('#skF_23',type,
    '#skF_23': ( $i * $i * $i ) > $i ).

tff('#skF_19',type,
    '#skF_19': ( $i * $i ) > $i ).

tff('#skF_67',type,
    '#skF_67': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(nat_case,type,
    nat_case: $i > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i * $i * $i * $i ) > $i ).

tff(body,type,
    body: $i ).

tff(bot,type,
    bot: $i > $o ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i * $i * $i ) > $i ).

tff('#skF_68',type,
    '#skF_68': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_54',type,
    '#skF_54': ( $i * $i * $i * $i ) > $i ).

tff(ordere236663937imp_le,type,
    ordere236663937imp_le: $i > $o ).

tff('#skF_58',type,
    '#skF_58': ( $i * $i * $i ) > $i ).

tff(fequal,type,
    fequal: $i > $i ).

tff(cancel146912293up_add,type,
    cancel146912293up_add: $i > $o ).

tff('#skF_66',type,
    '#skF_66': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(undefined,type,
    undefined: $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i * $i ) > $i ).

tff('#skF_37',type,
    '#skF_37': ( $i * $i * $i ) > $i ).

tff(combi,type,
    combi: $i > $i ).

tff('#skF_71',type,
    '#skF_71': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(comm_monoid_add,type,
    comm_monoid_add: $i > $o ).

tff(insert,type,
    insert: $i > $i ).

tff('#skF_51',type,
    '#skF_51': ( $i * $i ) > $i ).

tff(ordere223160158up_add,type,
    ordere223160158up_add: $i > $o ).

tff(the_1,type,
    the_1: $i > $i ).

tff('#skF_29',type,
    '#skF_29': ( $i * $i * $i * $i ) > $i ).

tff('#skF_77',type,
    '#skF_77': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(pn,type,
    pn: $i ).

tff(fdisj,type,
    fdisj: $i ).

tff(ordered_ab_group_add,type,
    ordered_ab_group_add: $i > $o ).

tff(finite_finite,type,
    finite_finite: $i > $i ).

tff(image,type,
    image: ( $i * $i ) > $i ).

tff(g,type,
    g: $i ).

tff('#skF_74',type,
    '#skF_74': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_28',type,
    '#skF_28': ( $i * $i ) > $i ).

tff(mgt_call,type,
    mgt_call: $i ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i * $i * $i * $i ) > $i ).

tff('#skF_43',type,
    '#skF_43': ( $i * $i * $i * $i ) > $i ).

tff('#skF_24',type,
    '#skF_24': ( $i * $i ) > $i ).

tff(finite1357897459simple,type,
    finite1357897459simple: ( $i * $i ) > $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

tff(minus_minus,type,
    minus_minus: $i > $i ).

tff(ti,type,
    ti: ( $i * $i ) > $i ).

tff(pname,type,
    pname: $i ).

tff(finite2073411215e_idem,type,
    finite2073411215e_idem: $i > $i ).

tff(fTrue,type,
    fTrue: $i ).

tff(x_a,type,
    x_a: $i ).

tff(linordered_idom,type,
    linordered_idom: $i > $o ).

tff(na,type,
    na: $i ).

tff('#skF_55',type,
    '#skF_55': ( $i * $i * $i * $i ) > $i ).

tff('#skF_52',type,
    '#skF_52': ( $i * $i ) > $i ).

tff('#skF_50',type,
    '#skF_50': ( $i * $i * $i ) > $i ).

tff('#skF_73',type,
    '#skF_73': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_25',type,
    '#skF_25': ( $i * $i ) > $i ).

tff(ab_group_add,type,
    ab_group_add: $i > $o ).

tff(option,type,
    option: $i > $i ).

tff(ordere216010020id_add,type,
    ordere216010020id_add: $i > $o ).

tff(hBOOL,type,
    hBOOL: $i > $o ).

tff('#skF_59',type,
    '#skF_59': ( $i * $i * $i ) > $i ).

tff('#skF_76',type,
    '#skF_76': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i * $i * $i ) > $i ).

tff('#skF_21',type,
    '#skF_21': ( $i * $i * $i * $i ) > $i ).

tff(cancel_semigroup_add,type,
    cancel_semigroup_add: $i > $o ).

tff(the,type,
    the: $i > $i ).

tff(zero_zero,type,
    zero_zero: $i > $i ).

tff(preorder,type,
    preorder: $i > $o ).

tff('#skF_79',type,
    '#skF_79': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i * $i ) > $i ).

tff(dense_linorder,type,
    dense_linorder: $i > $o ).

tff(ord_less,type,
    ord_less: $i > $i ).

tff('#skF_33',type,
    '#skF_33': ( $i * $i * $i * $i * $i ) > $i ).

tff('#skF_36',type,
    '#skF_36': ( $i * $i * $i * $i ) > $i ).

tff(plus_plus,type,
    plus_plus: $i > $i ).

tff('#skF_41',type,
    '#skF_41': ( $i * $i * $i ) > $i ).

tff(p,type,
    p: $i ).

tff(finite_folding_one,type,
    finite_folding_one: $i > $i ).

tff(one,type,
    one: $i > $o ).

tff('#skF_35',type,
    '#skF_35': ( $i * $i * $i * $i ) > $i ).

tff('#skF_27',type,
    '#skF_27': ( $i * $i ) > $i ).

tff('#skF_46',type,
    '#skF_46': $i > $i ).

tff(finite_finite_1,type,
    finite_finite_1: $i > $o ).

tff('#skF_61',type,
    '#skF_61': ( $i * $i ) > $i ).

tff(fFalse,type,
    fFalse: $i ).

tff('#skF_16',type,
    '#skF_16': ( $i * $i ) > $i ).

tff(finite_comp_fun_idem,type,
    finite_comp_fun_idem: ( $i * $i ) > $i ).

tff(order,type,
    order: $i > $o ).

tff('#skF_72',type,
    '#skF_72': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff(zero,type,
    zero: $i > $o ).

tff(combc,type,
    combc: ( $i * $i * $i ) > $i ).

tff(finite_card,type,
    finite_card: $i > $i ).

tff('#skF_42',type,
    '#skF_42': ( $i * $i * $i ) > $i ).

tff('#skF_69',type,
    '#skF_69': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i * $i ) > $i ).

tff(linorder,type,
    linorder: $i > $o ).

tff(f_3295,hypothesis,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

tff(f_543,axiom,
    ! [X_c,X_b,F,X_1,A_3] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3))
     => hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_imageI) ).

tff(f_3258,axiom,
    ~ hBOOL(fFalse),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

tff(f_3292,hypothesis,
    hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

tff(f_121,axiom,
    ! [X_c,X_a,B_1_1,B_2_1] : ( ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).

tff(f_3211,axiom,
    ! [P] :
      ( hBOOL(P)
      | hBOOL(hAPP(bool,bool,fNot,P)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

tff(f_3262,axiom,
    ! [P] :
      ( ( ti(bool,P) = fTrue )
      | ( ti(bool,P) = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

tff(f_125,hypothesis,
    ! [B_1_1] :
      ( hBOOL(ti(bool,B_1_1))
    <=> hBOOL(B_1_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).

tff(f_3299,negated_conjecture,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

tff(f_563,axiom,
    ! [X_b,X_1,A_3,B_2] :
      ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_3)),B_2))
    <=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))
        & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_3),B_2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_insert__subset) ).

tff(c_1678,plain,
    hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    inference(cnfTransformation,[status(thm)],[f_3295]) ).

tff(c_326,plain,
    ! [A_3_308,X_b_305,X_c_304,F_306,X_1_307] :
      ( hBOOL(hAPP(fun(X_c_304,bool),bool,hAPP(X_c_304,fun(fun(X_c_304,bool),bool),member(X_c_304),hAPP(X_b_305,X_c_304,F_306,X_1_307)),hAPP(fun(X_b_305,bool),fun(X_c_304,bool),hAPP(fun(X_b_305,X_c_304),fun(fun(X_b_305,bool),fun(X_c_304,bool)),image(X_b_305,X_c_304),F_306),A_3_308)))
      | ~ hBOOL(hAPP(fun(X_b_305,bool),bool,hAPP(X_b_305,fun(fun(X_b_305,bool),bool),member(X_b_305),X_1_307),A_3_308)) ),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

tff(c_1656,plain,
    ~ hBOOL(fFalse),
    inference(cnfTransformation,[status(thm)],[f_3258]) ).

tff(c_1672,plain,
    hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(cnfTransformation,[status(thm)],[f_3292]) ).

tff(c_6204,plain,
    ! [X_c_2312,X_a_2313,B_1_1_2314,B_2_1_2315] : ( ti(X_c_2312,hAPP(X_a_2313,X_c_2312,B_1_1_2314,B_2_1_2315)) = hAPP(X_a_2313,X_c_2312,B_1_1_2314,B_2_1_2315) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_1632,plain,
    ! [P_2075] :
      ( hBOOL(hAPP(bool,bool,fNot,P_2075))
      | hBOOL(P_2075) ),
    inference(cnfTransformation,[status(thm)],[f_3211]) ).

tff(c_2196,plain,
    ! [P_2144] :
      ( ( ti(bool,P_2144) = fFalse )
      | ( ti(bool,P_2144) = fTrue ) ),
    inference(cnfTransformation,[status(thm)],[f_3262]) ).

tff(c_86,plain,
    ! [B_1_1_54] :
      ( hBOOL(B_1_1_54)
      | ~ hBOOL(ti(bool,B_1_1_54)) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_2220,plain,
    ! [P_2144] :
      ( hBOOL(P_2144)
      | ~ hBOOL(fTrue)
      | ( ti(bool,P_2144) = fFalse ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2196,c_86]) ).

tff(c_5826,plain,
    ~ hBOOL(fTrue),
    inference(splitLeft,[status(thm)],[c_2220]) ).

tff(c_88,plain,
    ! [B_1_1_54] :
      ( hBOOL(ti(bool,B_1_1_54))
      | ~ hBOOL(B_1_1_54) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_2217,plain,
    ! [P_2144] :
      ( hBOOL(fTrue)
      | ~ hBOOL(P_2144)
      | ( ti(bool,P_2144) = fFalse ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2196,c_88]) ).

tff(c_5828,plain,
    ! [P_2285] :
      ( ~ hBOOL(P_2285)
      | ( ti(bool,P_2285) = fFalse ) ),
    inference(negUnitSimplification,[status(thm)],[c_5826,c_2217]) ).

tff(c_5927,plain,
    ! [P_2294] :
      ( ( ti(bool,hAPP(bool,bool,fNot,P_2294)) = fFalse )
      | hBOOL(P_2294) ),
    inference(resolution,[status(thm)],[c_1632,c_5828]) ).

tff(c_5939,plain,
    ! [P_2294] :
      ( hBOOL(fFalse)
      | ~ hBOOL(hAPP(bool,bool,fNot,P_2294))
      | hBOOL(P_2294) ),
    inference(superposition,[status(thm),theory(equality)],[c_5927,c_88]) ).

tff(c_5955,plain,
    ! [P_2295] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,P_2295))
      | hBOOL(P_2295) ),
    inference(negUnitSimplification,[status(thm)],[c_1656,c_5939]) ).

tff(c_5959,plain,
    ! [P_2075] : hBOOL(P_2075),
    inference(resolution,[status(thm)],[c_1632,c_5955]) ).

tff(c_6020,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5959,c_5826]) ).

tff(c_6023,plain,
    ! [P_2300] :
      ( hBOOL(P_2300)
      | ( ti(bool,P_2300) = fFalse ) ),
    inference(splitRight,[status(thm)],[c_2220]) ).

tff(c_1682,plain,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(cnfTransformation,[status(thm)],[f_3299]) ).

tff(c_6039,plain,
    ti(bool,hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) = fFalse,
    inference(resolution,[status(thm)],[c_6023,c_1682]) ).

tff(c_6210,plain,
    hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)) = fFalse,
    inference(superposition,[status(thm),theory(equality)],[c_6204,c_6039]) ).

tff(c_325839,plain,
    ! [X_b_5176,X_1_5177,A_3_5178,B_2_5179] :
      ( hBOOL(hAPP(fun(X_b_5176,bool),bool,hAPP(fun(X_b_5176,bool),fun(fun(X_b_5176,bool),bool),ord_less_eq(fun(X_b_5176,bool)),hAPP(fun(X_b_5176,bool),fun(X_b_5176,bool),hAPP(X_b_5176,fun(fun(X_b_5176,bool),fun(X_b_5176,bool)),insert(X_b_5176),X_1_5177),A_3_5178)),B_2_5179))
      | ~ hBOOL(hAPP(fun(X_b_5176,bool),bool,hAPP(fun(X_b_5176,bool),fun(fun(X_b_5176,bool),bool),ord_less_eq(fun(X_b_5176,bool)),A_3_5178),B_2_5179))
      | ~ hBOOL(hAPP(fun(X_b_5176,bool),bool,hAPP(X_b_5176,fun(fun(X_b_5176,bool),bool),member(X_b_5176),X_1_5177),B_2_5179)) ),
    inference(cnfTransformation,[status(thm)],[f_563]) ).

tff(c_326131,plain,
    ( hBOOL(fFalse)
    | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
    | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
    inference(superposition,[status(thm),theory(equality)],[c_6210,c_325839]) ).

tff(c_326227,plain,
    ( hBOOL(fFalse)
    | ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1672,c_326131]) ).

tff(c_326228,plain,
    ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
    inference(negUnitSimplification,[status(thm)],[c_1656,c_326227]) ).

tff(c_326347,plain,
    ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
    inference(resolution,[status(thm)],[c_326,c_326228]) ).

tff(c_326366,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1678,c_326347]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.38  % Computer : n009.cluster.edu
% 0.14/0.38  % Model    : x86_64 x86_64
% 0.14/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38  % Memory   : 8042.1875MB
% 0.14/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38  % CPULimit : 300
% 0.14/0.38  % WCLimit  : 300
% 0.14/0.38  % DateTime : Thu Aug  3 19:08:54 EDT 2023
% 0.14/0.38  % CPUTime  : 
% 186.45/136.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 186.45/136.46  
% 186.45/136.46  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 186.61/136.50  
% 186.61/136.50  Inference rules
% 186.61/136.50  ----------------------
% 186.61/136.50  #Ref     : 140
% 186.61/136.50  #Sup     : 73162
% 186.61/136.50  #Fact    : 16
% 186.61/136.50  #Define  : 0
% 186.61/136.50  #Split   : 51
% 186.61/136.50  #Chain   : 0
% 186.61/136.50  #Close   : 0
% 186.61/136.50  
% 186.61/136.50  Ordering : KBO
% 186.61/136.50  
% 186.61/136.50  Simplification rules
% 186.61/136.50  ----------------------
% 186.61/136.50  #Subsume      : 27476
% 186.61/136.50  #Demod        : 65187
% 186.61/136.50  #Tautology    : 13971
% 186.61/136.50  #SimpNegUnit  : 9552
% 186.61/136.50  #BackRed      : 85
% 186.61/136.50  
% 186.61/136.50  #Partial instantiations: 0
% 186.61/136.50  #Strategies tried      : 1
% 186.61/136.50  
% 186.61/136.50  Timing (in seconds)
% 186.61/136.50  ----------------------
% 186.61/136.50  Preprocessing        : 2.48
% 186.61/136.50  Parsing              : 1.34
% 186.61/136.50  CNF conversion       : 0.18
% 186.61/136.50  Main loop            : 132.86
% 186.61/136.50  Inferencing          : 12.89
% 186.61/136.50  Reduction            : 92.08
% 186.61/136.50  Demodulation         : 83.08
% 186.61/136.50  BG Simplification    : 0.93
% 186.61/136.50  Subsumption          : 22.34
% 186.61/136.50  Abstraction          : 1.64
% 186.61/136.50  MUC search           : 0.00
% 186.61/136.50  Cooper               : 0.00
% 186.61/136.50  Total                : 135.40
% 186.61/136.50  Index Insertion      : 0.00
% 186.61/136.50  Index Deletion       : 0.00
% 186.61/136.50  Index Matching       : 0.00
% 186.61/136.50  BG Taut test         : 0.00
%------------------------------------------------------------------------------