TSTP Solution File: NUM604+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM604+1 : 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 : n018.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 10:39:11 EDT 2023

% Result   : Theorem 0.77s 0.84s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   74
% Syntax   : Number of formulae    :  106 (  17 unt;  63 typ;   0 def)
%            Number of atoms       :  128 (  31 equ)
%            Maximal formula atoms :   19 (   2 avg)
%            Number of connectives :  137 (  52   ~;  53   |;  22   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   89 (  48   >;  41   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   54 (  54 usr;  15 con; 0-4 aty)
%            Number of variables   :   39 (   0 sgn;  24   !;   1   ?;   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,
    xx: $i ).

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

tff(decl_60,type,
    esk1_1: $i > $i ).

tff(decl_61,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_62,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk5_1: $i > $i ).

tff(decl_65,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk10_1: $i > $i ).

tff(decl_70,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_78,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_79,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk22_1: $i > $i ).

tff(decl_82,type,
    esk23_1: $i > $i ).

tff(decl_83,type,
    esk24_1: $i > $i ).

tff(decl_84,type,
    esk25_1: $i > $i ).

fof(mDefSub,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aSubsetOf0(X2,X1)
        <=> ( aSet0(X2)
            & ! [X3] :
                ( aElementOf0(X3,X2)
               => aElementOf0(X3,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

fof(mDefMin,axiom,
    ! [X1] :
      ( ( aSubsetOf0(X1,szNzAzT0)
        & X1 != slcrc0 )
     => ! [X2] :
          ( X2 = szmzizndt0(X1)
        <=> ( aElementOf0(X2,X1)
            & ! [X3] :
                ( aElementOf0(X3,X1)
               => sdtlseqdt0(X2,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).

fof(m__3671,hypothesis,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).

fof(m__4660,hypothesis,
    ( aFunction0(xe)
    & szDzozmdt0(xe) = szNzAzT0
    & ! [X1] :
        ( aElementOf0(X1,szNzAzT0)
       => sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).

fof(m__3435,hypothesis,
    ( aSubsetOf0(xS,szNzAzT0)
    & isCountable0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).

fof(mNATSet,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

fof(m__5034,hypothesis,
    ( aElementOf0(xi,szNzAzT0)
    & sdtlpdtrp0(xe,xi) = xx ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5034) ).

fof(mDefEmp,axiom,
    ! [X1] :
      ( X1 = slcrc0
    <=> ( aSet0(X1)
        & ~ ? [X2] : aElementOf0(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

fof(m__5045,hypothesis,
    aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5045) ).

fof(m__,conjecture,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mCountNFin_01,axiom,
    ! [X1] :
      ( ( aSet0(X1)
        & isCountable0(X1) )
     => X1 != slcrc0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).

fof(c_0_11,plain,
    ! [X15,X16,X17,X18] :
      ( ( aSet0(X16)
        | ~ aSubsetOf0(X16,X15)
        | ~ aSet0(X15) )
      & ( ~ aElementOf0(X17,X16)
        | aElementOf0(X17,X15)
        | ~ aSubsetOf0(X16,X15)
        | ~ aSet0(X15) )
      & ( aElementOf0(esk2_2(X15,X18),X18)
        | ~ aSet0(X18)
        | aSubsetOf0(X18,X15)
        | ~ aSet0(X15) )
      & ( ~ aElementOf0(esk2_2(X15,X18),X15)
        | ~ aSet0(X18)
        | aSubsetOf0(X18,X15)
        | ~ aSet0(X15) ) ),
    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)],[mDefSub])])])])])]) ).

fof(c_0_12,plain,
    ! [X86,X87,X88,X89] :
      ( ( aElementOf0(X87,X86)
        | X87 != szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 )
      & ( ~ aElementOf0(X88,X86)
        | sdtlseqdt0(X87,X88)
        | X87 != szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 )
      & ( aElementOf0(esk7_2(X86,X89),X86)
        | ~ aElementOf0(X89,X86)
        | X89 = szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 )
      & ( ~ sdtlseqdt0(X89,esk7_2(X86,X89))
        | ~ aElementOf0(X89,X86)
        | X89 = szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 ) ),
    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)],[mDefMin])])])])])]) ).

fof(c_0_13,hypothesis,
    ! [X175] :
      ( ( aSubsetOf0(sdtlpdtrp0(xN,X175),szNzAzT0)
        | ~ aElementOf0(X175,szNzAzT0) )
      & ( isCountable0(sdtlpdtrp0(xN,X175))
        | ~ aElementOf0(X175,szNzAzT0) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])]) ).

fof(c_0_14,hypothesis,
    ! [X195] :
      ( aFunction0(xe)
      & szDzozmdt0(xe) = szNzAzT0
      & ( ~ aElementOf0(X195,szNzAzT0)
        | sdtlpdtrp0(xe,X195) = szmzizndt0(sdtlpdtrp0(xN,X195)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])]) ).

cnf(c_0_15,plain,
    ( aSet0(X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,hypothesis,
    aSubsetOf0(xS,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__3435]) ).

cnf(c_0_17,plain,
    aSet0(szNzAzT0),
    inference(split_conjunct,[status(thm)],[mNATSet]) ).

cnf(c_0_18,plain,
    ( aElementOf0(X1,X2)
    | X2 = slcrc0
    | X1 != szmzizndt0(X2)
    | ~ aSubsetOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,hypothesis,
    ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,hypothesis,
    aElementOf0(xi,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__5034]) ).

cnf(c_0_21,hypothesis,
    ( sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1))
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,hypothesis,
    sdtlpdtrp0(xe,xi) = xx,
    inference(split_conjunct,[status(thm)],[m__5034]) ).

fof(c_0_23,plain,
    ! [X9,X10,X11] :
      ( ( aSet0(X9)
        | X9 != slcrc0 )
      & ( ~ aElementOf0(X10,X9)
        | X9 != slcrc0 )
      & ( ~ aSet0(X11)
        | aElementOf0(esk1_1(X11),X11)
        | X11 = slcrc0 ) ),
    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)],[mDefEmp])])])])])]) ).

cnf(c_0_24,plain,
    ( aElementOf0(X1,X3)
    | ~ aElementOf0(X1,X2)
    | ~ aSubsetOf0(X2,X3)
    | ~ aSet0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_25,hypothesis,
    aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
    inference(split_conjunct,[status(thm)],[m__5045]) ).

cnf(c_0_26,hypothesis,
    aSet0(xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

cnf(c_0_27,plain,
    ( X1 = slcrc0
    | aElementOf0(szmzizndt0(X1),X1)
    | ~ aSubsetOf0(X1,szNzAzT0) ),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_28,hypothesis,
    aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_29,hypothesis,
    szmzizndt0(sdtlpdtrp0(xN,xi)) = xx,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).

fof(c_0_30,negated_conjecture,
    ~ aElementOf0(xx,xS),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

fof(c_0_31,plain,
    ! [X14] :
      ( ~ aSet0(X14)
      | ~ isCountable0(X14)
      | X14 != slcrc0 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCountNFin_01])]) ).

cnf(c_0_32,plain,
    ( aSet0(X1)
    | X1 != slcrc0 ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_33,hypothesis,
    ( isCountable0(sdtlpdtrp0(xN,X1))
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_34,hypothesis,
    ( aElementOf0(X1,xS)
    | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).

cnf(c_0_35,hypothesis,
    ( sdtlpdtrp0(xN,xi) = slcrc0
    | aElementOf0(xx,sdtlpdtrp0(xN,xi)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_36,negated_conjecture,
    ~ aElementOf0(xx,xS),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_37,plain,
    ( ~ aSet0(X1)
    | ~ isCountable0(X1)
    | X1 != slcrc0 ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_38,plain,
    aSet0(slcrc0),
    inference(er,[status(thm)],[c_0_32]) ).

cnf(c_0_39,hypothesis,
    isCountable0(sdtlpdtrp0(xN,xi)),
    inference(spm,[status(thm)],[c_0_33,c_0_20]) ).

cnf(c_0_40,hypothesis,
    sdtlpdtrp0(xN,xi) = slcrc0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_41,plain,
    ~ isCountable0(slcrc0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_38])]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM604+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Aug 25 15:44:59 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.59  start to proof: theBenchmark
% 0.77/0.84  % Version  : CSE_E---1.5
% 0.77/0.84  % Problem  : theBenchmark.p
% 0.77/0.84  % Proof found
% 0.77/0.84  % SZS status Theorem for theBenchmark.p
% 0.77/0.84  % SZS output start Proof
% See solution above
% 0.77/0.85  % Total time : 0.238000 s
% 0.77/0.85  % SZS output end Proof
% 0.77/0.85  % Total time : 0.244000 s
%------------------------------------------------------------------------------