TSTP Solution File: RNG122+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG122+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 : n020.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 13:49:19 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   63
% Syntax   : Number of formulae    :   98 (  17 unt;  50 typ;   0 def)
%            Number of atoms       :  145 (  34 equ)
%            Maximal formula atoms :   29 (   3 avg)
%            Number of connectives :  157 (  60   ~;  54   |;  30   &)
%                                         (   1 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   80 (  38   >;  42   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   39 (  39 usr;  12 con; 0-4 aty)
%            Number of variables   :   47 (   0 sgn;  34   !;   0   ?;   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,
    xq: $i ).

tff(decl_48,type,
    xr: $i ).

tff(decl_49,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk9_1: $i > $i ).

tff(decl_58,type,
    esk10_1: $i > $i ).

tff(decl_59,type,
    esk11_1: $i > $i ).

tff(decl_60,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk13_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk21_0: $i ).

tff(decl_70,type,
    esk22_0: $i ).

tff(decl_71,type,
    esk23_0: $i ).

fof(mDefIdeal,axiom,
    ! [X1] :
      ( aIdeal0(X1)
    <=> ( aSet0(X1)
        & ! [X2] :
            ( aElementOf0(X2,X1)
           => ( ! [X3] :
                  ( aElementOf0(X3,X1)
                 => aElementOf0(sdtpldt0(X2,X3),X1) )
              & ! [X3] :
                  ( aElement0(X3)
                 => aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

fof(m__2174,hypothesis,
    ( aIdeal0(xI)
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

fof(mAddAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

fof(m__2666,hypothesis,
    ( aElement0(xq)
    & aElement0(xr)
    & xb = sdtpldt0(sdtasdt0(xq,xu),xr)
    & ( xr = sz00
      | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).

fof(m__,conjecture,
    xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__2690,hypothesis,
    aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2690) ).

fof(mAddInvr,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).

fof(m__2091,hypothesis,
    ( aElement0(xa)
    & aElement0(xb) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).

fof(m__2273,hypothesis,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).

fof(mAddZero,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(c_0_13,plain,
    ! [X60,X61,X62,X63,X64] :
      ( ( aSet0(X60)
        | ~ aIdeal0(X60) )
      & ( ~ aElementOf0(X62,X60)
        | aElementOf0(sdtpldt0(X61,X62),X60)
        | ~ aElementOf0(X61,X60)
        | ~ aIdeal0(X60) )
      & ( ~ aElement0(X63)
        | aElementOf0(sdtasdt0(X63,X61),X60)
        | ~ aElementOf0(X61,X60)
        | ~ aIdeal0(X60) )
      & ( aElementOf0(esk9_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( aElement0(esk11_1(X64))
        | aElementOf0(esk10_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
        | aElementOf0(esk10_1(X64),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( aElement0(esk11_1(X64))
        | ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) )
      & ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
        | ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
        | ~ aSet0(X64)
        | aIdeal0(X64) ) ),
    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)],[mDefIdeal])])])])])]) ).

fof(c_0_14,plain,
    ! [X12,X13] :
      ( ~ aElement0(X12)
      | ~ aElement0(X13)
      | sdtpldt0(X12,X13) = sdtpldt0(X13,X12) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

fof(c_0_15,plain,
    ! [X32,X33] :
      ( ~ aSet0(X32)
      | ~ aElementOf0(X33,X32)
      | aElement0(X33) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

cnf(c_0_16,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,hypothesis,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[m__2174]) ).

fof(c_0_18,plain,
    ! [X14,X15,X16] :
      ( ~ aElement0(X14)
      | ~ aElement0(X15)
      | ~ aElement0(X16)
      | sdtpldt0(sdtpldt0(X14,X15),X16) = sdtpldt0(X14,sdtpldt0(X15,X16)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

cnf(c_0_19,hypothesis,
    xb = sdtpldt0(sdtasdt0(xq,xu),xr),
    inference(split_conjunct,[status(thm)],[m__2666]) ).

cnf(c_0_20,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,hypothesis,
    aElement0(xr),
    inference(split_conjunct,[status(thm)],[m__2666]) ).

fof(c_0_22,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_23,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,hypothesis,
    aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(split_conjunct,[status(thm)],[m__2690]) ).

cnf(c_0_25,hypothesis,
    aSet0(xI),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_26,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,hypothesis,
    ( sdtpldt0(xr,sdtasdt0(xq,xu)) = xb
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

fof(c_0_28,plain,
    ! [X18] :
      ( ( sdtpldt0(X18,smndt0(X18)) = sz00
        | ~ aElement0(X18) )
      & ( sz00 = sdtpldt0(smndt0(X18),X18)
        | ~ aElement0(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).

cnf(c_0_29,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,hypothesis,
    aElement0(smndt0(sdtasdt0(xq,xu))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_31,hypothesis,
    aElement0(xb),
    inference(split_conjunct,[status(thm)],[m__2091]) ).

cnf(c_0_32,hypothesis,
    ( sdtpldt0(xr,sdtpldt0(sdtasdt0(xq,xu),X1)) = sdtpldt0(xb,X1)
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21])]) ).

cnf(c_0_33,plain,
    ( sdtpldt0(X1,smndt0(X1)) = sz00
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_34,hypothesis,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_simplification,[status(thm)],[m__2273]) ).

cnf(c_0_35,negated_conjecture,
    sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_30]),c_0_31])]) ).

cnf(c_0_36,hypothesis,
    ( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) = sdtpldt0(xr,sz00)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30])]) ).

fof(c_0_37,plain,
    ! [X17] :
      ( ( sdtpldt0(X17,sz00) = X17
        | ~ aElement0(X17) )
      & ( X17 = sdtpldt0(sz00,X17)
        | ~ aElement0(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).

fof(c_0_38,hypothesis,
    ! [X112] :
      ( aElementOf0(xu,xI)
      & xu != sz00
      & ( ~ aElementOf0(X112,xI)
        | X112 = sz00
        | ~ iLess0(sbrdtbr0(X112),sbrdtbr0(xu)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).

cnf(c_0_39,negated_conjecture,
    ( sdtpldt0(xr,sz00) != xr
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

fof(c_0_41,plain,
    ! [X10,X11] :
      ( ~ aElement0(X10)
      | ~ aElement0(X11)
      | aElement0(sdtasdt0(X10,X11)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_42,hypothesis,
    aElementOf0(xu,xI),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_43,negated_conjecture,
    ~ aElement0(sdtasdt0(xq,xu)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_21])]) ).

cnf(c_0_44,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_45,hypothesis,
    aElement0(xu),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_42]),c_0_25])]) ).

cnf(c_0_46,hypothesis,
    aElement0(xq),
    inference(split_conjunct,[status(thm)],[m__2666]) ).

cnf(c_0_47,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG122+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34  % Computer : n020.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit   : 300
% 0.17/0.34  % WCLimit    : 300
% 0.17/0.34  % DateTime   : Sun Aug 27 03:06:44 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.031000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.035000 s
%------------------------------------------------------------------------------