TSTP Solution File: RNG114+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG114+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 : 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 13:49:15 EDT 2023

% Result   : Theorem 0.21s 0.66s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   68
% Syntax   : Number of formulae    :   87 (   8 unt;  65 typ;   0 def)
%            Number of atoms       :  116 (  34 equ)
%            Maximal formula atoms :   33 (   5 avg)
%            Number of connectives :  138 (  44   ~;  35   |;  51   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   6 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  :   15 (  13 usr;   3 prp; 0-3 aty)
%            Number of functors    :   52 (  52 usr;  18 con; 0-4 aty)
%            Number of variables   :   49 (   0 sgn;  26   !;  16   ?;   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,
    xu: $i ).

tff(decl_47,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk9_1: $i > $i ).

tff(decl_56,type,
    esk10_1: $i > $i ).

tff(decl_57,type,
    esk11_1: $i > $i ).

tff(decl_58,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk13_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_62,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk21_0: $i ).

tff(decl_68,type,
    esk22_0: $i ).

tff(decl_69,type,
    esk23_1: $i > $i ).

tff(decl_70,type,
    esk24_1: $i > $i ).

tff(decl_71,type,
    esk25_1: $i > $i ).

tff(decl_72,type,
    esk26_1: $i > $i ).

tff(decl_73,type,
    esk27_1: $i > $i ).

tff(decl_74,type,
    esk28_0: $i ).

tff(decl_75,type,
    esk29_0: $i ).

tff(decl_76,type,
    esk30_0: $i ).

tff(decl_77,type,
    esk31_0: $i ).

tff(decl_78,type,
    esk32_0: $i ).

tff(decl_79,type,
    esk33_1: $i > $i ).

tff(decl_80,type,
    esk34_1: $i > $i ).

tff(decl_81,type,
    esk35_0: $i ).

tff(decl_82,type,
    esk36_0: $i ).

tff(decl_83,type,
    esk37_0: $i ).

tff(decl_84,type,
    esk38_0: $i ).

tff(decl_85,type,
    epred1_0: $o ).

tff(decl_86,type,
    epred2_0: $o ).

fof(m__2273,hypothesis,
    ( ? [X1,X2] :
        ( aElementOf0(X1,slsdtgt0(xa))
        & aElementOf0(X2,slsdtgt0(xb))
        & sdtpldt0(X1,X2) = xu )
    & aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( ( ? [X2,X3] :
                ( aElementOf0(X2,slsdtgt0(xa))
                & aElementOf0(X3,slsdtgt0(xb))
                & sdtpldt0(X2,X3) = X1 )
            | aElementOf0(X1,xI) )
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).

fof(m__,conjecture,
    ? [X1,X2] :
      ( aElement0(X1)
      & aElement0(X2)
      & xu = sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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(c_0_3,hypothesis,
    ( ? [X1,X2] :
        ( aElementOf0(X1,slsdtgt0(xa))
        & aElementOf0(X2,slsdtgt0(xb))
        & sdtpldt0(X1,X2) = xu )
    & aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( ( ? [X2,X3] :
                ( aElementOf0(X2,slsdtgt0(xa))
                & aElementOf0(X3,slsdtgt0(xb))
                & sdtpldt0(X2,X3) = X1 )
            | aElementOf0(X1,xI) )
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_simplification,[status(thm)],[m__2273]) ).

fof(c_0_4,negated_conjecture,
    ~ ? [X1,X2] :
        ( aElement0(X1)
        & aElement0(X2)
        & xu = sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_5,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_6,hypothesis,
    ! [X149,X150,X151] :
      ( aElementOf0(esk37_0,slsdtgt0(xa))
      & aElementOf0(esk38_0,slsdtgt0(xb))
      & sdtpldt0(esk37_0,esk38_0) = xu
      & aElementOf0(xu,xI)
      & xu != sz00
      & ( ~ aElementOf0(X150,slsdtgt0(xa))
        | ~ aElementOf0(X151,slsdtgt0(xb))
        | sdtpldt0(X150,X151) != X149
        | X149 = sz00
        | ~ iLess0(sbrdtbr0(X149),sbrdtbr0(xu)) )
      & ( ~ aElementOf0(X149,xI)
        | X149 = sz00
        | ~ iLess0(sbrdtbr0(X149),sbrdtbr0(xu)) ) ),
    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_3])])])])]) ).

fof(c_0_7,negated_conjecture,
    ! [X154,X155] :
      ( ~ aElement0(X154)
      | ~ aElement0(X155)
      | xu != sdtpldt0(sdtasdt0(xa,X154),sdtasdt0(xb,X155)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

cnf(c_0_8,hypothesis,
    ( sdtasdt0(xa,esk24_1(X1)) = X1
    | ~ aElementOf0(X1,slsdtgt0(xa)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,hypothesis,
    aElementOf0(esk37_0,slsdtgt0(xa)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,hypothesis,
    ( aElement0(esk24_1(X1))
    | ~ aElementOf0(X1,slsdtgt0(xa)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,negated_conjecture,
    ( ~ aElement0(X1)
    | ~ aElement0(X2)
    | xu != sdtpldt0(sdtasdt0(xa,X1),sdtasdt0(xb,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,hypothesis,
    sdtasdt0(xa,esk24_1(esk37_0)) = esk37_0,
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,hypothesis,
    aElement0(esk24_1(esk37_0)),
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_14,hypothesis,
    ( sdtasdt0(xb,esk25_1(X1)) = X1
    | ~ aElementOf0(X1,slsdtgt0(xb)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,hypothesis,
    aElementOf0(esk38_0,slsdtgt0(xb)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_16,hypothesis,
    ( aElement0(esk25_1(X1))
    | ~ aElementOf0(X1,slsdtgt0(xb)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_17,negated_conjecture,
    ( sdtpldt0(esk37_0,sdtasdt0(xb,X1)) != xu
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).

cnf(c_0_18,hypothesis,
    sdtasdt0(xb,esk25_1(esk38_0)) = esk38_0,
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,hypothesis,
    sdtpldt0(esk37_0,esk38_0) = xu,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_20,hypothesis,
    aElement0(esk25_1(esk38_0)),
    inference(spm,[status(thm)],[c_0_16,c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem    : RNG114+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35  % Computer : n015.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun Aug 27 02:43:08 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.21/0.60  start to proof: theBenchmark
% 0.21/0.66  % Version  : CSE_E---1.5
% 0.21/0.66  % Problem  : theBenchmark.p
% 0.21/0.66  % Proof found
% 0.21/0.66  % SZS status Theorem for theBenchmark.p
% 0.21/0.66  % SZS output start Proof
% See solution above
% 0.21/0.67  % Total time : 0.049000 s
% 0.21/0.67  % SZS output end Proof
% 0.21/0.67  % Total time : 0.053000 s
%------------------------------------------------------------------------------