TSTP Solution File: NUM609+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM609+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n015.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 10:39:13 EDT 2023

% Result   : Theorem 0.20s 0.70s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   75
% Syntax   : Number of formulae    :  103 (  18 unt;  64 typ;   0 def)
%            Number of atoms       :  154 (  29 equ)
%            Maximal formula atoms :   54 (   3 avg)
%            Number of connectives :  195 (  80   ~;  87   |;  18   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Maximal term depth    :    4 (   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    :   55 (  55 usr;  16 con; 0-4 aty)
%            Number of variables   :   47 (   0 sgn;  25   !;   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,
    esk1_1: $i > $i ).

tff(decl_62,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk5_1: $i > $i ).

tff(decl_66,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk10_1: $i > $i ).

tff(decl_71,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_79,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_80,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk22_1: $i > $i ).

tff(decl_83,type,
    esk23_1: $i > $i ).

tff(decl_84,type,
    esk24_1: $i > $i ).

tff(decl_85,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/sandbox/benchmark/theBenchmark.p',mDefSub) ).

fof(mDefCons,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aElement0(X2) )
     => ! [X3] :
          ( X3 = sdtpldt0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aElement0(X4)
                  & ( aElementOf0(X4,X1)
                    | X4 = X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

fof(mConsDiff,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).

fof(m__5164,hypothesis,
    ( aSet0(xP)
    & xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).

fof(m__5147,hypothesis,
    xp = szmzizndt0(xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).

fof(m__5093,hypothesis,
    ( aSubsetOf0(xQ,xO)
    & xQ != slcrc0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).

fof(m__4891,hypothesis,
    ( aSet0(xO)
    & xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).

fof(m__5173,hypothesis,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).

fof(m__5182,hypothesis,
    aElementOf0(xp,xO),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5182) ).

fof(m__,conjecture,
    aSubsetOf0(xP,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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,
    ! [X28,X29,X30,X31,X32,X33] :
      ( ( aSet0(X30)
        | X30 != sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( aElement0(X31)
        | ~ aElementOf0(X31,X30)
        | X30 != sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( aElementOf0(X31,X28)
        | X31 = X29
        | ~ aElementOf0(X31,X30)
        | X30 != sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( ~ aElementOf0(X32,X28)
        | ~ aElement0(X32)
        | aElementOf0(X32,X30)
        | X30 != sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( X32 != X29
        | ~ aElement0(X32)
        | aElementOf0(X32,X30)
        | X30 != sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( ~ aElementOf0(esk3_3(X28,X29,X33),X28)
        | ~ aElement0(esk3_3(X28,X29,X33))
        | ~ aElementOf0(esk3_3(X28,X29,X33),X33)
        | ~ aSet0(X33)
        | X33 = sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( esk3_3(X28,X29,X33) != X29
        | ~ aElement0(esk3_3(X28,X29,X33))
        | ~ aElementOf0(esk3_3(X28,X29,X33),X33)
        | ~ aSet0(X33)
        | X33 = sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( aElement0(esk3_3(X28,X29,X33))
        | aElementOf0(esk3_3(X28,X29,X33),X33)
        | ~ aSet0(X33)
        | X33 = sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) )
      & ( aElementOf0(esk3_3(X28,X29,X33),X28)
        | esk3_3(X28,X29,X33) = X29
        | aElementOf0(esk3_3(X28,X29,X33),X33)
        | ~ aSet0(X33)
        | X33 = sdtpldt0(X28,X29)
        | ~ aSet0(X28)
        | ~ aElement0(X29) ) ),
    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)],[mDefCons])])])])])]) ).

fof(c_0_13,plain,
    ! [X7,X8] :
      ( ~ aSet0(X7)
      | ~ aElementOf0(X8,X7)
      | aElement0(X8) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

fof(c_0_14,plain,
    ! [X42,X43] :
      ( ~ aSet0(X42)
      | ~ aElementOf0(X43,X42)
      | sdtpldt0(sdtmndt0(X42,X43),X43) = X42 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])]) ).

cnf(c_0_15,hypothesis,
    xP = sdtmndt0(xQ,szmzizndt0(xQ)),
    inference(split_conjunct,[status(thm)],[m__5164]) ).

cnf(c_0_16,hypothesis,
    xp = szmzizndt0(xQ),
    inference(split_conjunct,[status(thm)],[m__5147]) ).

cnf(c_0_17,plain,
    ( aSet0(X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,hypothesis,
    aSubsetOf0(xQ,xO),
    inference(split_conjunct,[status(thm)],[m__5093]) ).

cnf(c_0_19,hypothesis,
    aSet0(xO),
    inference(split_conjunct,[status(thm)],[m__4891]) ).

cnf(c_0_20,plain,
    ( aElementOf0(X1,X3)
    | ~ aElementOf0(X1,X2)
    | ~ aElement0(X1)
    | X3 != sdtpldt0(X2,X4)
    | ~ aSet0(X2)
    | ~ aElement0(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_21,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,plain,
    ( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,hypothesis,
    aElementOf0(xp,xQ),
    inference(split_conjunct,[status(thm)],[m__5173]) ).

cnf(c_0_24,hypothesis,
    sdtmndt0(xQ,xp) = xP,
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_25,hypothesis,
    aSet0(xQ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).

cnf(c_0_26,hypothesis,
    aElementOf0(xp,xO),
    inference(split_conjunct,[status(thm)],[m__5182]) ).

cnf(c_0_27,plain,
    ( aElementOf0(X1,X2)
    | X2 != sdtpldt0(X3,X4)
    | ~ aElementOf0(X1,X3)
    | ~ aElement0(X4)
    | ~ aSet0(X3) ),
    inference(csr,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,hypothesis,
    sdtpldt0(xP,xp) = xQ,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).

cnf(c_0_29,hypothesis,
    aElement0(xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_19])]) ).

cnf(c_0_30,hypothesis,
    aSet0(xP),
    inference(split_conjunct,[status(thm)],[m__5164]) ).

cnf(c_0_31,hypothesis,
    ( aElementOf0(X1,X2)
    | X2 != xQ
    | ~ aElementOf0(X1,xP) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).

cnf(c_0_32,hypothesis,
    ( aElementOf0(X1,xQ)
    | ~ aElementOf0(X1,xP) ),
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_33,plain,
    ( aElementOf0(esk2_2(X1,X2),X2)
    | aSubsetOf0(X2,X1)
    | ~ aSet0(X2)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_34,negated_conjecture,
    ~ aSubsetOf0(xP,xQ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_35,plain,
    ( aSubsetOf0(X2,X1)
    | ~ aElementOf0(esk2_2(X1,X2),X1)
    | ~ aSet0(X2)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_36,hypothesis,
    ( aSubsetOf0(xP,X1)
    | aElementOf0(esk2_2(X1,xP),xQ)
    | ~ aSet0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30])]) ).

cnf(c_0_37,negated_conjecture,
    ~ aSubsetOf0(xP,xQ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_38,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_30]),c_0_25])]),c_0_37]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM609+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n015.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   : Fri Aug 25 18:10:52 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.70  % Version  : CSE_E---1.5
% 0.20/0.70  % Problem  : theBenchmark.p
% 0.20/0.70  % Proof found
% 0.20/0.70  % SZS status Theorem for theBenchmark.p
% 0.20/0.70  % SZS output start Proof
% See solution above
% 0.20/0.71  % Total time : 0.110000 s
% 0.20/0.71  % SZS output end Proof
% 0.20/0.71  % Total time : 0.114000 s
%------------------------------------------------------------------------------