TSTP Solution File: NUM630+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM630+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 : n013.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 10:39:30 EDT 2023

% Result   : Theorem 1.11s 1.22s
% Output   : CNFRefutation 1.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   79
% Syntax   : Number of formulae    :  107 (  24 unt;  66 typ;   0 def)
%            Number of atoms       :  100 (  34 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :   92 (  33   ~;  29   |;  22   &)
%                                         (   1 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    5 (   2 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    :   57 (  57 usr;  18 con; 0-4 aty)
%            Number of variables   :   25 (   0 sgn;  17   !;   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,
    xn: $i ).

tff(decl_62,type,
    xD: $i ).

tff(decl_63,type,
    esk1_1: $i > $i ).

tff(decl_64,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk5_1: $i > $i ).

tff(decl_68,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk10_1: $i > $i ).

tff(decl_73,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_81,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_82,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk22_1: $i > $i ).

tff(decl_85,type,
    esk23_1: $i > $i ).

tff(decl_86,type,
    esk24_1: $i > $i ).

tff(decl_87,type,
    esk25_1: $i > $i ).

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(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(m__,conjecture,
    sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__5309,hypothesis,
    ( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aElementOf0(xn,szNzAzT0)
    & sdtlpdtrp0(xe,xn) = xp ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).

fof(mConsDiff,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).

fof(m__5164,hypothesis,
    ( aSet0(xP)
    & xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).

fof(m__5147,hypothesis,
    xp = szmzizndt0(xQ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).

fof(m__5093,hypothesis,
    ( aSubsetOf0(xQ,xO)
    & xQ != slcrc0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).

fof(m__4891,hypothesis,
    ( aSet0(xO)
    & xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).

fof(m__4151,hypothesis,
    ( aFunction0(xC)
    & szDzozmdt0(xC) = szNzAzT0
    & ! [X1] :
        ( aElementOf0(X1,szNzAzT0)
       => ( aFunction0(sdtlpdtrp0(xC,X1))
          & szDzozmdt0(sdtlpdtrp0(xC,X1)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)
          & ! [X2] :
              ( ( aSet0(X2)
                & aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) )
             => sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) = sdtlpdtrp0(xc,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).

fof(m__5173,hypothesis,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).

fof(m__5585,hypothesis,
    xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).

fof(m__5599,hypothesis,
    aElementOf0(xP,slbdtsldtrb0(xD,xk)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5599) ).

fof(c_0_13,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])])]) ).

fof(c_0_14,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_15,negated_conjecture,
    sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_16,hypothesis,
    ( sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1))
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,hypothesis,
    aElementOf0(xn,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__5309]) ).

cnf(c_0_18,hypothesis,
    sdtlpdtrp0(xe,xn) = xp,
    inference(split_conjunct,[status(thm)],[m__5309]) ).

fof(c_0_19,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_20,hypothesis,
    xP = sdtmndt0(xQ,szmzizndt0(xQ)),
    inference(split_conjunct,[status(thm)],[m__5164]) ).

cnf(c_0_21,hypothesis,
    xp = szmzizndt0(xQ),
    inference(split_conjunct,[status(thm)],[m__5147]) ).

cnf(c_0_22,plain,
    ( aSet0(X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,hypothesis,
    aSubsetOf0(xQ,xO),
    inference(split_conjunct,[status(thm)],[m__5093]) ).

cnf(c_0_24,hypothesis,
    aSet0(xO),
    inference(split_conjunct,[status(thm)],[m__4891]) ).

fof(c_0_25,hypothesis,
    ! [X182,X183] :
      ( aFunction0(xC)
      & szDzozmdt0(xC) = szNzAzT0
      & ( aFunction0(sdtlpdtrp0(xC,X182))
        | ~ aElementOf0(X182,szNzAzT0) )
      & ( szDzozmdt0(sdtlpdtrp0(xC,X182)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X182),szmzizndt0(sdtlpdtrp0(xN,X182))),xk)
        | ~ aElementOf0(X182,szNzAzT0) )
      & ( ~ aSet0(X183)
        | ~ aElementOf0(X183,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X182),szmzizndt0(sdtlpdtrp0(xN,X182))),xk))
        | sdtlpdtrp0(sdtlpdtrp0(xC,X182),X183) = sdtlpdtrp0(xc,sdtpldt0(X183,szmzizndt0(sdtlpdtrp0(xN,X182))))
        | ~ aElementOf0(X182,szNzAzT0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4151])])])]) ).

cnf(c_0_26,negated_conjecture,
    sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_27,hypothesis,
    szmzizndt0(sdtlpdtrp0(xN,xn)) = xp,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_28,plain,
    ( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_29,hypothesis,
    aElementOf0(xp,xQ),
    inference(split_conjunct,[status(thm)],[m__5173]) ).

cnf(c_0_30,hypothesis,
    sdtmndt0(xQ,xp) = xP,
    inference(rw,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_31,hypothesis,
    aSet0(xQ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_32,hypothesis,
    ( sdtlpdtrp0(sdtlpdtrp0(xC,X2),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X2))))
    | ~ aSet0(X1)
    | ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X2),szmzizndt0(sdtlpdtrp0(xN,X2))),xk))
    | ~ aElementOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_33,hypothesis,
    xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
    inference(split_conjunct,[status(thm)],[m__5585]) ).

cnf(c_0_34,negated_conjecture,
    sdtlpdtrp0(xc,sdtpldt0(xP,xp)) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_35,hypothesis,
    sdtpldt0(xP,xp) = xQ,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).

cnf(c_0_36,hypothesis,
    ( sdtlpdtrp0(xc,sdtpldt0(X1,xp)) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),X1)
    | ~ aElementOf0(X1,slbdtsldtrb0(xD,xk))
    | ~ aSet0(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_17]),c_0_33]),c_0_27]) ).

cnf(c_0_37,hypothesis,
    aElementOf0(xP,slbdtsldtrb0(xD,xk)),
    inference(split_conjunct,[status(thm)],[m__5599]) ).

cnf(c_0_38,hypothesis,
    aSet0(xP),
    inference(split_conjunct,[status(thm)],[m__5164]) ).

cnf(c_0_39,negated_conjecture,
    sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) != sdtlpdtrp0(xc,xQ),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_35]),c_0_38])]),c_0_39]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM630+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n013.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 12:08:02 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 1.11/1.22  % Version  : CSE_E---1.5
% 1.11/1.22  % Problem  : theBenchmark.p
% 1.11/1.22  % Proof found
% 1.11/1.22  % SZS status Theorem for theBenchmark.p
% 1.11/1.22  % SZS output start Proof
% See solution above
% 1.11/1.22  % Total time : 0.641000 s
% 1.11/1.22  % SZS output end Proof
% 1.11/1.22  % Total time : 0.647000 s
%------------------------------------------------------------------------------