TSTP Solution File: NUM566+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM566+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 : n023.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 10:38:48 EDT 2023

% Result   : Theorem 0.46s 0.62s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   63
% Syntax   : Number of formulae    :   97 (  16 unt;  52 typ;   0 def)
%            Number of atoms       :  118 (  13 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  126 (  53   ~;  48   |;  16   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   87 (  45   >;  42   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   43 (  43 usr;   7 con; 0-4 aty)
%            Number of variables   :   43 (   0 sgn;  19   !;   4   ?;   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,
    esk1_1: $i > $i ).

tff(decl_53,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk5_1: $i > $i ).

tff(decl_57,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_60,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk10_1: $i > $i ).

tff(decl_62,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk22_2: ( $i * $i ) > $i ).

fof(m__,conjecture,
    ? [X1] :
      ( aElementOf0(X1,xT)
      & ? [X2] :
          ( aSubsetOf0(X2,xS)
          & isCountable0(X2)
          & ! [X3] :
              ( aElementOf0(X3,slbdtsldtrb0(X2,xK))
             => sdtlpdtrp0(xc,X3) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__3507,hypothesis,
    ! [X1] :
      ( aElementOf0(X1,slbdtsldtrb0(xS,sz00))
     => sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3507) ).

fof(m__3453,hypothesis,
    ( aFunction0(xc)
    & szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
    & aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).

fof(m__3462,hypothesis,
    xK = sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).

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

fof(m__3291,hypothesis,
    ( aSet0(xT)
    & isFinite0(xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).

fof(mImgRng,axiom,
    ! [X1] :
      ( aFunction0(X1)
     => ! [X2] :
          ( aElementOf0(X2,szDzozmdt0(X1))
         => aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).

fof(m__3476,hypothesis,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3476) ).

fof(mSubRefl,axiom,
    ! [X1] :
      ( aSet0(X1)
     => aSubsetOf0(X1,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).

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

fof(c_0_11,negated_conjecture,
    ~ ? [X1] :
        ( aElementOf0(X1,xT)
        & ? [X2] :
            ( aSubsetOf0(X2,xS)
            & isCountable0(X2)
            & ! [X3] :
                ( aElementOf0(X3,slbdtsldtrb0(X2,xK))
               => sdtlpdtrp0(xc,X3) = X1 ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_12,hypothesis,
    ! [X174] :
      ( ~ aElementOf0(X174,slbdtsldtrb0(xS,sz00))
      | sdtlpdtrp0(xc,X174) = sdtlpdtrp0(xc,slcrc0) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3507])]) ).

cnf(c_0_13,hypothesis,
    szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
    inference(split_conjunct,[status(thm)],[m__3453]) ).

cnf(c_0_14,hypothesis,
    xK = sz00,
    inference(split_conjunct,[status(thm)],[m__3462]) ).

fof(c_0_15,negated_conjecture,
    ! [X175,X176] :
      ( ( aElementOf0(esk22_2(X175,X176),slbdtsldtrb0(X176,xK))
        | ~ aSubsetOf0(X176,xS)
        | ~ isCountable0(X176)
        | ~ aElementOf0(X175,xT) )
      & ( sdtlpdtrp0(xc,esk22_2(X175,X176)) != X175
        | ~ aSubsetOf0(X176,xS)
        | ~ isCountable0(X176)
        | ~ aElementOf0(X175,xT) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).

cnf(c_0_16,hypothesis,
    ( sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0)
    | ~ aElementOf0(X1,slbdtsldtrb0(xS,sz00)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,hypothesis,
    slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    ( aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,xK))
    | ~ aSubsetOf0(X2,xS)
    | ~ isCountable0(X2)
    | ~ aElementOf0(X1,xT) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_19,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])])])])])]) ).

cnf(c_0_20,negated_conjecture,
    ( sdtlpdtrp0(xc,esk22_2(X1,X2)) != X1
    | ~ aSubsetOf0(X2,xS)
    | ~ isCountable0(X2)
    | ~ aElementOf0(X1,xT) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,hypothesis,
    ( sdtlpdtrp0(xc,X1) = sdtlpdtrp0(xc,slcrc0)
    | ~ aElementOf0(X1,szDzozmdt0(xc)) ),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    ( aElementOf0(esk22_2(X1,X2),slbdtsldtrb0(X2,sz00))
    | ~ aSubsetOf0(X2,xS)
    | ~ isCountable0(X2)
    | ~ aElementOf0(X1,xT) ),
    inference(rw,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_23,hypothesis,
    isCountable0(xS),
    inference(split_conjunct,[status(thm)],[m__3435]) ).

cnf(c_0_24,plain,
    ( aElementOf0(X1,X3)
    | ~ aElementOf0(X1,X2)
    | ~ aSubsetOf0(X2,X3)
    | ~ aSet0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,hypothesis,
    aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
    inference(split_conjunct,[status(thm)],[m__3453]) ).

cnf(c_0_26,hypothesis,
    aSet0(xT),
    inference(split_conjunct,[status(thm)],[m__3291]) ).

fof(c_0_27,plain,
    ! [X155,X156] :
      ( ~ aFunction0(X155)
      | ~ aElementOf0(X156,szDzozmdt0(X155))
      | aElementOf0(sdtlpdtrp0(X155,X156),sdtlcdtrc0(X155,szDzozmdt0(X155))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mImgRng])])]) ).

cnf(c_0_28,hypothesis,
    ( ~ aSubsetOf0(X1,xS)
    | ~ isCountable0(X1)
    | ~ aElementOf0(esk22_2(sdtlpdtrp0(xc,slcrc0),X1),szDzozmdt0(xc))
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]) ).

cnf(c_0_29,hypothesis,
    ( aElementOf0(esk22_2(X1,xS),szDzozmdt0(xc))
    | ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(X1,xT) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_23])]) ).

cnf(c_0_30,hypothesis,
    ( aElementOf0(X1,xT)
    | ~ aElementOf0(X1,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).

cnf(c_0_31,plain,
    ( aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,szDzozmdt0(X1)))
    | ~ aFunction0(X1)
    | ~ aElementOf0(X2,szDzozmdt0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_32,hypothesis,
    aFunction0(xc),
    inference(split_conjunct,[status(thm)],[m__3453]) ).

cnf(c_0_33,hypothesis,
    aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
    inference(split_conjunct,[status(thm)],[m__3476]) ).

cnf(c_0_34,hypothesis,
    ( ~ aSubsetOf0(xS,xS)
    | ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_23])]) ).

cnf(c_0_35,hypothesis,
    ( aElementOf0(sdtlpdtrp0(xc,X1),xT)
    | ~ aElementOf0(X1,szDzozmdt0(xc)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).

cnf(c_0_36,hypothesis,
    aElementOf0(slcrc0,szDzozmdt0(xc)),
    inference(rw,[status(thm)],[c_0_33,c_0_17]) ).

fof(c_0_37,plain,
    ! [X22] :
      ( ~ aSet0(X22)
      | aSubsetOf0(X22,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubRefl])]) ).

cnf(c_0_38,plain,
    ( aSet0(X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_39,hypothesis,
    aSubsetOf0(xS,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__3435]) ).

cnf(c_0_40,plain,
    aSet0(szNzAzT0),
    inference(split_conjunct,[status(thm)],[mNATSet]) ).

cnf(c_0_41,hypothesis,
    ~ aSubsetOf0(xS,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).

cnf(c_0_42,plain,
    ( aSubsetOf0(X1,X1)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_43,hypothesis,
    aSet0(xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).

cnf(c_0_44,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM566+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % 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 12:53:57 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.46/0.57  start to proof: theBenchmark
% 0.46/0.62  % Version  : CSE_E---1.5
% 0.46/0.62  % Problem  : theBenchmark.p
% 0.46/0.62  % Proof found
% 0.46/0.62  % SZS status Theorem for theBenchmark.p
% 0.46/0.62  % SZS output start Proof
% See solution above
% 0.46/0.63  % Total time : 0.042000 s
% 0.46/0.63  % SZS output end Proof
% 0.46/0.63  % Total time : 0.047000 s
%------------------------------------------------------------------------------