TSTP Solution File: RNG108+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG108+4 : 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 : n017.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 13:49:13 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   58
% Syntax   : Number of formulae    :   81 (  11 unt;  51 typ;   0 def)
%            Number of atoms       :  221 (  63 equ)
%            Maximal formula atoms :   96 (   7 avg)
%            Number of connectives :  328 ( 137   ~; 124   |;  59   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  43   >;  42   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;   8 con; 0-4 aty)
%            Number of variables   :   47 (   0 sgn;  27   !;  12   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aElement0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    sz10: $i ).

tff(decl_25,type,
    smndt0: $i > $i ).

tff(decl_26,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_28,type,
    aSet0: $i > $o ).

tff(decl_29,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_30,type,
    sdtpldt1: ( $i * $i ) > $i ).

tff(decl_31,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(decl_32,type,
    aIdeal0: $i > $o ).

tff(decl_33,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

tff(decl_34,type,
    aNaturalNumber0: $i > $o ).

tff(decl_35,type,
    sbrdtbr0: $i > $i ).

tff(decl_36,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_37,type,
    doDivides0: ( $i * $i ) > $o ).

tff(decl_38,type,
    aDivisorOf0: ( $i * $i ) > $o ).

tff(decl_39,type,
    aGcdOfAnd0: ( $i * $i * $i ) > $o ).

tff(decl_40,type,
    misRelativelyPrime0: ( $i * $i ) > $o ).

tff(decl_41,type,
    slsdtgt0: $i > $i ).

tff(decl_42,type,
    xa: $i ).

tff(decl_43,type,
    xb: $i ).

tff(decl_44,type,
    xc: $i ).

tff(decl_45,type,
    xI: $i ).

tff(decl_46,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk9_1: $i > $i ).

tff(decl_55,type,
    esk10_1: $i > $i ).

tff(decl_56,type,
    esk11_1: $i > $i ).

tff(decl_57,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk13_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_59,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_60,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_62,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk21_0: $i ).

tff(decl_67,type,
    esk22_0: $i ).

tff(decl_68,type,
    esk23_1: $i > $i ).

tff(decl_69,type,
    esk24_1: $i > $i ).

tff(decl_70,type,
    esk25_1: $i > $i ).

tff(decl_71,type,
    esk26_1: $i > $i ).

tff(decl_72,type,
    esk27_1: $i > $i ).

fof(m__2174,hypothesis,
    ( aSet0(xI)
    & ! [X1] :
        ( aElementOf0(X1,xI)
       => ( ! [X2] :
              ( aElementOf0(X2,xI)
             => aElementOf0(sdtpldt0(X1,X2),xI) )
          & ! [X2] :
              ( aElement0(X2)
             => aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
    & aIdeal0(xI)
    & ! [X1] :
        ( aElementOf0(X1,slsdtgt0(xa))
      <=> ? [X2] :
            ( aElement0(X2)
            & sdtasdt0(xa,X2) = X1 ) )
    & ! [X1] :
        ( aElementOf0(X1,slsdtgt0(xb))
      <=> ? [X2] :
            ( aElement0(X2)
            & sdtasdt0(xb,X2) = X1 ) )
    & ! [X1] :
        ( aElementOf0(X1,xI)
      <=> ? [X2,X3] :
            ( aElementOf0(X2,slsdtgt0(xa))
            & aElementOf0(X3,slsdtgt0(xb))
            & sdtpldt0(X2,X3) = X1 ) )
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).

fof(m__,conjecture,
    ( ( ? [X1] :
          ( aElement0(X1)
          & sdtasdt0(xa,X1) = sz00 )
      | aElementOf0(sz00,slsdtgt0(xa)) )
    & ( ? [X1] :
          ( aElement0(X1)
          & sdtasdt0(xa,X1) = xa )
      | aElementOf0(xa,slsdtgt0(xa)) )
    & ( ? [X1] :
          ( aElement0(X1)
          & sdtasdt0(xb,X1) = sz00 )
      | aElementOf0(sz00,slsdtgt0(xb)) )
    & ( ? [X1] :
          ( aElement0(X1)
          & sdtasdt0(xb,X1) = xb )
      | aElementOf0(xb,slsdtgt0(xb)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mMulZero,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

fof(mSortsC,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

fof(m__2091,hypothesis,
    ( aElement0(xa)
    & aElement0(xb) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).

fof(mMulUnit,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).

fof(mSortsC_01,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

fof(c_0_7,hypothesis,
    ! [X117,X118,X119,X120,X122,X123,X124,X126,X127,X128,X131,X132,X133] :
      ( aSet0(xI)
      & ( ~ aElementOf0(X118,xI)
        | aElementOf0(sdtpldt0(X117,X118),xI)
        | ~ aElementOf0(X117,xI) )
      & ( ~ aElement0(X119)
        | aElementOf0(sdtasdt0(X119,X117),xI)
        | ~ aElementOf0(X117,xI) )
      & aIdeal0(xI)
      & ( aElement0(esk24_1(X120))
        | ~ aElementOf0(X120,slsdtgt0(xa)) )
      & ( sdtasdt0(xa,esk24_1(X120)) = X120
        | ~ aElementOf0(X120,slsdtgt0(xa)) )
      & ( ~ aElement0(X123)
        | sdtasdt0(xa,X123) != X122
        | aElementOf0(X122,slsdtgt0(xa)) )
      & ( aElement0(esk25_1(X124))
        | ~ aElementOf0(X124,slsdtgt0(xb)) )
      & ( sdtasdt0(xb,esk25_1(X124)) = X124
        | ~ aElementOf0(X124,slsdtgt0(xb)) )
      & ( ~ aElement0(X127)
        | sdtasdt0(xb,X127) != X126
        | aElementOf0(X126,slsdtgt0(xb)) )
      & ( aElementOf0(esk26_1(X128),slsdtgt0(xa))
        | ~ aElementOf0(X128,xI) )
      & ( aElementOf0(esk27_1(X128),slsdtgt0(xb))
        | ~ aElementOf0(X128,xI) )
      & ( sdtpldt0(esk26_1(X128),esk27_1(X128)) = X128
        | ~ aElementOf0(X128,xI) )
      & ( ~ aElementOf0(X132,slsdtgt0(xa))
        | ~ aElementOf0(X133,slsdtgt0(xb))
        | sdtpldt0(X132,X133) != X131
        | aElementOf0(X131,xI) )
      & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    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)],[m__2174])])])])])]) ).

fof(c_0_8,negated_conjecture,
    ~ ( ( ? [X1] :
            ( aElement0(X1)
            & sdtasdt0(xa,X1) = sz00 )
        | aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ? [X1] :
            ( aElement0(X1)
            & sdtasdt0(xa,X1) = xa )
        | aElementOf0(xa,slsdtgt0(xa)) )
      & ( ? [X1] :
            ( aElement0(X1)
            & sdtasdt0(xb,X1) = sz00 )
        | aElementOf0(sz00,slsdtgt0(xb)) )
      & ( ? [X1] :
            ( aElement0(X1)
            & sdtasdt0(xb,X1) = xb )
        | aElementOf0(xb,slsdtgt0(xb)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_9,hypothesis,
    ( aElementOf0(X2,slsdtgt0(xa))
    | ~ aElement0(X1)
    | sdtasdt0(xa,X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X29] :
      ( ( sdtasdt0(X29,sz00) = sz00
        | ~ aElement0(X29) )
      & ( sz00 = sdtasdt0(sz00,X29)
        | ~ aElement0(X29) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).

fof(c_0_11,negated_conjecture,
    ! [X134,X135,X136,X137] :
      ( ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElement0(X134)
        | sdtasdt0(xa,X134) != sz00 )
      & ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElement0(X135)
        | sdtasdt0(xa,X135) != xa
        | ~ aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElement0(X136)
        | sdtasdt0(xb,X136) != sz00
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ~ aElement0(X137)
        | sdtasdt0(xb,X137) != xb
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElementOf0(sz00,slsdtgt0(xa)) )
      & ( ~ aElementOf0(xb,slsdtgt0(xb))
        | ~ aElementOf0(sz00,slsdtgt0(xb))
        | ~ aElementOf0(xa,slsdtgt0(xa))
        | ~ aElementOf0(sz00,slsdtgt0(xa)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

cnf(c_0_12,hypothesis,
    ( aElementOf0(sdtasdt0(xa,X1),slsdtgt0(xa))
    | ~ aElement0(X1) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    aElement0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_15,hypothesis,
    aElement0(xa),
    inference(split_conjunct,[status(thm)],[m__2091]) ).

cnf(c_0_16,hypothesis,
    ( aElementOf0(X2,slsdtgt0(xb))
    | ~ aElement0(X1)
    | sdtasdt0(xb,X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ aElementOf0(xb,slsdtgt0(xb))
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(sz00,slsdtgt0(xa)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,hypothesis,
    aElementOf0(sz00,slsdtgt0(xa)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).

cnf(c_0_19,hypothesis,
    ( aElementOf0(sdtasdt0(xb,X1),slsdtgt0(xb))
    | ~ aElement0(X1) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_20,hypothesis,
    aElement0(xb),
    inference(split_conjunct,[status(thm)],[m__2091]) ).

fof(c_0_21,plain,
    ! [X24] :
      ( ( sdtasdt0(X24,sz10) = X24
        | ~ aElement0(X24) )
      & ( X24 = sdtasdt0(sz10,X24)
        | ~ aElement0(X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).

cnf(c_0_22,negated_conjecture,
    ( ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(xb,slsdtgt0(xb)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).

cnf(c_0_23,hypothesis,
    aElementOf0(sz00,slsdtgt0(xb)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_14]),c_0_20])]) ).

cnf(c_0_24,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_25,plain,
    aElement0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(xb,slsdtgt0(xb)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).

cnf(c_0_27,hypothesis,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_24]),c_0_25]),c_0_20])]) ).

cnf(c_0_28,negated_conjecture,
    ~ aElementOf0(xa,slsdtgt0(xa)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).

cnf(c_0_29,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_24]),c_0_25]),c_0_15])]),c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : RNG108+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun Aug 27 01:12:56 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.017000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.021000 s
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