TSTP Solution File: NUM611+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM611+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 : Thu Aug 31 10:39:16 EDT 2023

% Result   : Theorem 4.26s 4.51s
% Output   : CNFRefutation 4.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  103
% Syntax   : Number of formulae    :  136 (  20 unt;  92 typ;   0 def)
%            Number of atoms       :  126 (  30 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  124 (  42   ~;  39   |;  30   &)
%                                         (   2 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  141 (  74   >;  67   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-2 aty)
%            Number of functors    :   79 (  79 usr;  18 con; 0-4 aty)
%            Number of variables   :   34 (   0 sgn;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aSet0: $i > $o ).

tff(decl_23,type,
    aElement0: $i > $o ).

tff(decl_24,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_25,type,
    isFinite0: $i > $o ).

tff(decl_26,type,
    slcrc0: $i ).

tff(decl_27,type,
    isCountable0: $i > $o ).

tff(decl_28,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(decl_29,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_30,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(decl_31,type,
    szNzAzT0: $i ).

tff(decl_32,type,
    sz00: $i ).

tff(decl_33,type,
    szszuzczcdt0: $i > $i ).

tff(decl_34,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_35,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_36,type,
    sbrdtbr0: $i > $i ).

tff(decl_37,type,
    szmzizndt0: $i > $i ).

tff(decl_38,type,
    szmzazxdt0: $i > $i ).

tff(decl_39,type,
    slbdtrb0: $i > $i ).

tff(decl_40,type,
    slbdtsldtrb0: ( $i * $i ) > $i ).

tff(decl_41,type,
    aFunction0: $i > $o ).

tff(decl_42,type,
    szDzozmdt0: $i > $i ).

tff(decl_43,type,
    sdtlpdtrp0: ( $i * $i ) > $i ).

tff(decl_44,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(decl_45,type,
    sdtlcdtrc0: ( $i * $i ) > $i ).

tff(decl_46,type,
    sdtexdt0: ( $i * $i ) > $i ).

tff(decl_47,type,
    szDzizrdt0: $i > $i ).

tff(decl_48,type,
    xT: $i ).

tff(decl_49,type,
    xK: $i ).

tff(decl_50,type,
    xS: $i ).

tff(decl_51,type,
    xc: $i ).

tff(decl_52,type,
    xk: $i ).

tff(decl_53,type,
    xN: $i ).

tff(decl_54,type,
    xC: $i ).

tff(decl_55,type,
    xe: $i ).

tff(decl_56,type,
    xd: $i ).

tff(decl_57,type,
    xO: $i ).

tff(decl_58,type,
    xQ: $i ).

tff(decl_59,type,
    xp: $i ).

tff(decl_60,type,
    xP: $i ).

tff(decl_61,type,
    epred1_1: $i > $o ).

tff(decl_62,type,
    epred2_1: $i > $o ).

tff(decl_63,type,
    epred3_1: $i > $o ).

tff(decl_64,type,
    epred4_1: $i > $o ).

tff(decl_65,type,
    esk1_1: $i > $i ).

tff(decl_66,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk5_1: $i > $i ).

tff(decl_70,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_73,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_74,type,
    esk10_1: $i > $i ).

tff(decl_75,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_83,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_84,type,
    esk20_1: $i > $i ).

tff(decl_85,type,
    esk21_1: $i > $i ).

tff(decl_86,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_87,type,
    esk23_3: ( $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk27_3: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_94,type,
    esk30_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk31_1: $i > $i ).

tff(decl_96,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_97,type,
    esk33_2: ( $i * $i ) > $i ).

tff(decl_98,type,
    esk34_1: $i > $i ).

tff(decl_99,type,
    esk35_2: ( $i * $i ) > $i ).

tff(decl_100,type,
    esk36_2: ( $i * $i ) > $i ).

tff(decl_101,type,
    esk37_1: $i > $i ).

tff(decl_102,type,
    esk38_1: $i > $i ).

tff(decl_103,type,
    esk39_1: $i > $i ).

tff(decl_104,type,
    esk40_0: $i ).

tff(decl_105,type,
    esk41_0: $i ).

tff(decl_106,type,
    esk42_2: ( $i * $i ) > $i ).

tff(decl_107,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_109,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_110,type,
    esk46_3: ( $i * $i * $i ) > $i ).

tff(decl_111,type,
    esk47_1: $i > $i ).

tff(decl_112,type,
    esk48_1: $i > $i ).

tff(decl_113,type,
    esk49_2: ( $i * $i ) > $i ).

fof(mCardNum,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
      <=> isFinite0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).

fof(m__5078,hypothesis,
    ( aSet0(xQ)
    & ! [X1] :
        ( aElementOf0(X1,xQ)
       => aElementOf0(X1,xO) )
    & aSubsetOf0(xQ,xO)
    & sbrdtbr0(xQ) = xK
    & aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).

fof(mSubFSet,axiom,
    ! [X1] :
      ( ( aSet0(X1)
        & isFinite0(X1) )
     => ! [X2] :
          ( aSubsetOf0(X2,X1)
         => isFinite0(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).

fof(m__3418,hypothesis,
    aElementOf0(xK,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).

fof(m__5164,hypothesis,
    ( aSet0(xP)
    & ! [X1] :
        ( aElementOf0(X1,xQ)
       => sdtlseqdt0(szmzizndt0(xQ),X1) )
    & ! [X1] :
        ( aElementOf0(X1,xP)
      <=> ( aElement0(X1)
          & aElementOf0(X1,xQ)
          & X1 != szmzizndt0(xQ) ) )
    & xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).

fof(m__5147,hypothesis,
    ( aElementOf0(xp,xQ)
    & ! [X1] :
        ( aElementOf0(X1,xQ)
       => sdtlseqdt0(xp,X1) )
    & xp = szmzizndt0(xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).

fof(m__5195,hypothesis,
    ( ! [X1] :
        ( aElementOf0(X1,xP)
       => aElementOf0(X1,xQ) )
    & aSubsetOf0(xP,xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).

fof(mSuccEquSucc,axiom,
    ! [X1,X2] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0) )
     => ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEquSucc) ).

fof(mCardDiff,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( ( isFinite0(X1)
            & aElementOf0(X2,X1) )
         => szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).

fof(m__3533,hypothesis,
    ( aElementOf0(xk,szNzAzT0)
    & szszuzczcdt0(xk) = xK ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).

fof(m__,conjecture,
    sbrdtbr0(xP) = xk,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(c_0_11,plain,
    ! [X76] :
      ( ( ~ aElementOf0(sbrdtbr0(X76),szNzAzT0)
        | isFinite0(X76)
        | ~ aSet0(X76) )
      & ( ~ isFinite0(X76)
        | aElementOf0(sbrdtbr0(X76),szNzAzT0)
        | ~ aSet0(X76) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).

fof(c_0_12,hypothesis,
    ! [X246] :
      ( aSet0(xQ)
      & ( ~ aElementOf0(X246,xQ)
        | aElementOf0(X246,xO) )
      & aSubsetOf0(xQ,xO)
      & sbrdtbr0(xQ) = xK
      & aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5078])])]) ).

fof(c_0_13,plain,
    ! [X21,X22] :
      ( ~ aSet0(X21)
      | ~ isFinite0(X21)
      | ~ aSubsetOf0(X22,X21)
      | isFinite0(X22) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])]) ).

cnf(c_0_14,plain,
    ( isFinite0(X1)
    | ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,hypothesis,
    sbrdtbr0(xQ) = xK,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,hypothesis,
    aElementOf0(xK,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__3418]) ).

cnf(c_0_17,hypothesis,
    aSet0(xQ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_18,hypothesis,
    ! [X253,X254] :
      ( aSet0(xP)
      & ( ~ aElementOf0(X253,xQ)
        | sdtlseqdt0(szmzizndt0(xQ),X253) )
      & ( aElement0(X254)
        | ~ aElementOf0(X254,xP) )
      & ( aElementOf0(X254,xQ)
        | ~ aElementOf0(X254,xP) )
      & ( X254 != szmzizndt0(xQ)
        | ~ aElementOf0(X254,xP) )
      & ( ~ aElement0(X254)
        | ~ aElementOf0(X254,xQ)
        | X254 = szmzizndt0(xQ)
        | aElementOf0(X254,xP) )
      & xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5164])])])]) ).

fof(c_0_19,hypothesis,
    ! [X252] :
      ( aElementOf0(xp,xQ)
      & ( ~ aElementOf0(X252,xQ)
        | sdtlseqdt0(xp,X252) )
      & xp = szmzizndt0(xQ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5147])])]) ).

cnf(c_0_20,plain,
    ( isFinite0(X2)
    | ~ aSet0(X1)
    | ~ isFinite0(X1)
    | ~ aSubsetOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,hypothesis,
    isFinite0(xQ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

fof(c_0_22,hypothesis,
    ! [X256] :
      ( ( ~ aElementOf0(X256,xP)
        | aElementOf0(X256,xQ) )
      & aSubsetOf0(xP,xQ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5195])])]) ).

fof(c_0_23,plain,
    ! [X56,X57] :
      ( ~ aElementOf0(X56,szNzAzT0)
      | ~ aElementOf0(X57,szNzAzT0)
      | szszuzczcdt0(X56) != szszuzczcdt0(X57)
      | X56 = X57 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEquSucc])]) ).

fof(c_0_24,plain,
    ! [X80,X81] :
      ( ~ aSet0(X80)
      | ~ isFinite0(X80)
      | ~ aElementOf0(X81,X80)
      | szszuzczcdt0(sbrdtbr0(sdtmndt0(X80,X81))) = sbrdtbr0(X80) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).

cnf(c_0_25,hypothesis,
    xP = sdtmndt0(xQ,szmzizndt0(xQ)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,hypothesis,
    xp = szmzizndt0(xQ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_27,hypothesis,
    ( isFinite0(X1)
    | ~ aSubsetOf0(X1,xQ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_17])]) ).

cnf(c_0_28,hypothesis,
    aSubsetOf0(xP,xQ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    ( X1 = X2
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0)
    | szszuzczcdt0(X1) != szszuzczcdt0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,hypothesis,
    szszuzczcdt0(xk) = xK,
    inference(split_conjunct,[status(thm)],[m__3533]) ).

cnf(c_0_31,hypothesis,
    aElementOf0(xk,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__3533]) ).

cnf(c_0_32,plain,
    ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
    | ~ aSet0(X1)
    | ~ isFinite0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,hypothesis,
    sdtmndt0(xQ,xp) = xP,
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,hypothesis,
    aElementOf0(xp,xQ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_35,plain,
    ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
    | ~ isFinite0(X1)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_36,hypothesis,
    isFinite0(xP),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_37,hypothesis,
    aSet0(xP),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_38,negated_conjecture,
    sbrdtbr0(xP) != xk,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_39,hypothesis,
    ( X1 = xk
    | szszuzczcdt0(X1) != xK
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

cnf(c_0_40,hypothesis,
    szszuzczcdt0(sbrdtbr0(xP)) = xK,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_15]),c_0_21]),c_0_34]),c_0_17])]) ).

cnf(c_0_41,hypothesis,
    aElementOf0(sbrdtbr0(xP),szNzAzT0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).

cnf(c_0_42,negated_conjecture,
    sbrdtbr0(xP) != xk,
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_43,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),c_0_42]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM611+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 13:48:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 4.26/4.51  % Version  : CSE_E---1.5
% 4.26/4.51  % Problem  : theBenchmark.p
% 4.26/4.51  % Proof found
% 4.26/4.51  % SZS status Theorem for theBenchmark.p
% 4.26/4.51  % SZS output start Proof
% See solution above
% 4.26/4.52  % Total time : 3.915000 s
% 4.26/4.52  % SZS output end Proof
% 4.26/4.52  % Total time : 3.924000 s
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