TSTP Solution File: RNG071+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG071+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 : n026.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 13:48:55 EDT 2023

% Result   : Theorem 0.22s 0.67s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   53
% Syntax   : Number of formulae    :  104 (  32 unt;  33 typ;   0 def)
%            Number of atoms       :  164 (  17 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  159 (  66   ~;  59   |;  25   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  15   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  18 con; 0-2 aty)
%            Number of variables   :   44 (   0 sgn;  26   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aNaturalNumber0: $i > $o ).

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

tff(decl_24,type,
    szszuzczcdt0: $i > $i ).

tff(decl_25,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_26,type,
    aScalar0: $i > $o ).

tff(decl_27,type,
    sz0z00: $i ).

tff(decl_28,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_29,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_30,type,
    smndt0: $i > $i ).

tff(decl_31,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_32,type,
    aVector0: $i > $o ).

tff(decl_33,type,
    aDimensionOf0: $i > $i ).

tff(decl_34,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(decl_35,type,
    sziznziztdt0: $i > $i ).

tff(decl_36,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(decl_37,type,
    xs: $i ).

tff(decl_38,type,
    xt: $i ).

tff(decl_39,type,
    xp: $i ).

tff(decl_40,type,
    xq: $i ).

tff(decl_41,type,
    xA: $i ).

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

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

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

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

tff(decl_46,type,
    xF: $i ).

tff(decl_47,type,
    xG: $i ).

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

tff(decl_49,type,
    xR: $i ).

tff(decl_50,type,
    xP: $i ).

tff(decl_51,type,
    xS: $i ).

tff(decl_52,type,
    xN: $i ).

tff(decl_53,type,
    esk1_1: $i > $i ).

tff(decl_54,type,
    esk2_2: ( $i * $i ) > $i ).

fof(mScSqPos,axiom,
    ! [X1] :
      ( aVector0(X1)
     => sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).

fof(mSqPos,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).

fof(mPosMon,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( ( sdtlseqdt0(sz0z00,X1)
          & sdtlseqdt0(sz0z00,X2) )
       => ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
          & sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).

fof(m__1800,hypothesis,
    ( aScalar0(xD)
    & xD = sdtasasdt0(xq,xq) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).

fof(m__1726,hypothesis,
    ( aVector0(xq)
    & xq = sziznziztdt0(xt) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).

fof(m__1837,hypothesis,
    ( aScalar0(xF)
    & xF = sdtasdt0(xA,xA) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

fof(m__1746,hypothesis,
    ( aScalar0(xA)
    & xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).

fof(m__,conjecture,
    ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
    & sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__1854,hypothesis,
    ( aScalar0(xG)
    & xG = sdtasdt0(xB,xB) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).

fof(m__1766,hypothesis,
    ( aScalar0(xB)
    & xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).

fof(m__1783,hypothesis,
    ( aScalar0(xC)
    & xC = sdtasasdt0(xp,xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).

fof(m__1709,hypothesis,
    ( aVector0(xp)
    & xp = sziznziztdt0(xs) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).

fof(m__2590,hypothesis,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2590) ).

fof(mLEMon,axiom,
    ! [X1,X2,X3,X4] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3)
        & aScalar0(X4) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X3,X4) )
       => sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).

fof(mLETrn,axiom,
    ! [X1,X2,X3] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).

fof(m__1930,hypothesis,
    ( aScalar0(xS)
    & xS = sdtasdt0(xF,xD) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).

fof(m__1892,hypothesis,
    ( aScalar0(xR)
    & xR = sdtasdt0(xC,xG) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).

fof(m__1911,hypothesis,
    ( aScalar0(xP)
    & xP = sdtasdt0(xE,xH) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).

fof(mSZeroSc,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).

fof(mLETot,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | sdtlseqdt0(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).

fof(c_0_20,plain,
    ! [X68] :
      ( ~ aVector0(X68)
      | sdtlseqdt0(sz0z00,sdtasasdt0(X68,X68)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).

fof(c_0_21,plain,
    ! [X49] :
      ( ~ aScalar0(X49)
      | sdtlseqdt0(sz0z00,sdtasdt0(X49,X49)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).

fof(c_0_22,plain,
    ! [X47,X48] :
      ( ( sdtlseqdt0(sz0z00,sdtpldt0(X47,X48))
        | ~ sdtlseqdt0(sz0z00,X47)
        | ~ sdtlseqdt0(sz0z00,X48)
        | ~ aScalar0(X47)
        | ~ aScalar0(X48) )
      & ( sdtlseqdt0(sz0z00,sdtasdt0(X47,X48))
        | ~ sdtlseqdt0(sz0z00,X47)
        | ~ sdtlseqdt0(sz0z00,X48)
        | ~ aScalar0(X47)
        | ~ aScalar0(X48) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])]) ).

cnf(c_0_23,plain,
    ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
    | ~ aVector0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,hypothesis,
    xD = sdtasasdt0(xq,xq),
    inference(split_conjunct,[status(thm)],[m__1800]) ).

cnf(c_0_25,hypothesis,
    aVector0(xq),
    inference(split_conjunct,[status(thm)],[m__1726]) ).

cnf(c_0_26,plain,
    ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,hypothesis,
    xF = sdtasdt0(xA,xA),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_28,hypothesis,
    aScalar0(xA),
    inference(split_conjunct,[status(thm)],[m__1746]) ).

fof(c_0_29,negated_conjecture,
    ~ ( sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
      & sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_30,hypothesis,
    xG = sdtasdt0(xB,xB),
    inference(split_conjunct,[status(thm)],[m__1854]) ).

cnf(c_0_31,hypothesis,
    aScalar0(xB),
    inference(split_conjunct,[status(thm)],[m__1766]) ).

cnf(c_0_32,hypothesis,
    xC = sdtasasdt0(xp,xp),
    inference(split_conjunct,[status(thm)],[m__1783]) ).

cnf(c_0_33,hypothesis,
    aVector0(xp),
    inference(split_conjunct,[status(thm)],[m__1709]) ).

fof(c_0_34,hypothesis,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    inference(fof_simplification,[status(thm)],[m__2590]) ).

fof(c_0_35,plain,
    ! [X37,X38,X39,X40] :
      ( ~ aScalar0(X37)
      | ~ aScalar0(X38)
      | ~ aScalar0(X39)
      | ~ aScalar0(X40)
      | ~ sdtlseqdt0(X37,X38)
      | ~ sdtlseqdt0(X39,X40)
      | sdtlseqdt0(sdtpldt0(X37,X39),sdtpldt0(X38,X40)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])]) ).

fof(c_0_36,plain,
    ! [X34,X35,X36] :
      ( ~ aScalar0(X34)
      | ~ aScalar0(X35)
      | ~ aScalar0(X36)
      | ~ sdtlseqdt0(X34,X35)
      | ~ sdtlseqdt0(X35,X36)
      | sdtlseqdt0(X34,X36) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])]) ).

cnf(c_0_37,plain,
    ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
    | ~ sdtlseqdt0(sz0z00,X1)
    | ~ sdtlseqdt0(sz0z00,X2)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_38,hypothesis,
    xS = sdtasdt0(xF,xD),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

cnf(c_0_39,hypothesis,
    sdtlseqdt0(sz0z00,xD),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_40,hypothesis,
    sdtlseqdt0(sz0z00,xF),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_41,hypothesis,
    aScalar0(xD),
    inference(split_conjunct,[status(thm)],[m__1800]) ).

cnf(c_0_42,hypothesis,
    aScalar0(xF),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_43,negated_conjecture,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
    inference(fof_nnf,[status(thm)],[c_0_29]) ).

cnf(c_0_44,hypothesis,
    xR = sdtasdt0(xC,xG),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

cnf(c_0_45,hypothesis,
    sdtlseqdt0(sz0z00,xG),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_31])]) ).

cnf(c_0_46,hypothesis,
    sdtlseqdt0(sz0z00,xC),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_32]),c_0_33])]) ).

cnf(c_0_47,hypothesis,
    aScalar0(xG),
    inference(split_conjunct,[status(thm)],[m__1854]) ).

cnf(c_0_48,hypothesis,
    aScalar0(xC),
    inference(split_conjunct,[status(thm)],[m__1783]) ).

cnf(c_0_49,hypothesis,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_50,plain,
    ( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3)
    | ~ aScalar0(X4)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_51,hypothesis,
    aScalar0(xS),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

cnf(c_0_52,hypothesis,
    aScalar0(xP),
    inference(split_conjunct,[status(thm)],[m__1911]) ).

cnf(c_0_53,hypothesis,
    aScalar0(xR),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

cnf(c_0_54,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_55,hypothesis,
    sdtlseqdt0(sz0z00,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]) ).

cnf(c_0_56,plain,
    aScalar0(sz0z00),
    inference(split_conjunct,[status(thm)],[mSZeroSc]) ).

fof(c_0_57,plain,
    ! [X45,X46] :
      ( ~ aScalar0(X45)
      | ~ aScalar0(X46)
      | sdtlseqdt0(X45,X46)
      | sdtlseqdt0(X46,X45) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])]) ).

cnf(c_0_58,negated_conjecture,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_59,plain,
    ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
    | ~ sdtlseqdt0(sz0z00,X1)
    | ~ sdtlseqdt0(sz0z00,X2)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_60,hypothesis,
    sdtlseqdt0(sz0z00,xR),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_44]),c_0_45]),c_0_46]),c_0_47]),c_0_48])]) ).

cnf(c_0_61,hypothesis,
    ( ~ sdtlseqdt0(xP,xS)
    | ~ sdtlseqdt0(xP,xR) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).

cnf(c_0_62,hypothesis,
    ( sdtlseqdt0(X1,xS)
    | ~ sdtlseqdt0(X1,sz0z00)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_51]),c_0_56])]) ).

cnf(c_0_63,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_64,negated_conjecture,
    ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_51]),c_0_53])]),c_0_55]),c_0_60])]) ).

cnf(c_0_65,hypothesis,
    ( ~ sdtlseqdt0(xP,xR)
    | ~ sdtlseqdt0(xP,sz0z00) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_52])]) ).

cnf(c_0_66,hypothesis,
    ( sdtlseqdt0(X1,xR)
    | ~ sdtlseqdt0(X1,sz0z00)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_60]),c_0_53]),c_0_56])]) ).

cnf(c_0_67,hypothesis,
    ( sdtlseqdt0(X1,xP)
    | sdtlseqdt0(xP,X1)
    | ~ aScalar0(X1) ),
    inference(spm,[status(thm)],[c_0_63,c_0_52]) ).

cnf(c_0_68,negated_conjecture,
    ~ sdtlseqdt0(sz0z00,xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_59]),c_0_52])]) ).

cnf(c_0_69,hypothesis,
    ~ sdtlseqdt0(xP,sz0z00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_52])]) ).

cnf(c_0_70,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_56]),c_0_68]),c_0_69]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : RNG071+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.37  % Computer : n026.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Sun Aug 27 01:44:49 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.22/0.63  start to proof: theBenchmark
% 0.22/0.67  % Version  : CSE_E---1.5
% 0.22/0.67  % Problem  : theBenchmark.p
% 0.22/0.67  % Proof found
% 0.22/0.67  % SZS status Theorem for theBenchmark.p
% 0.22/0.67  % SZS output start Proof
% See solution above
% 0.22/0.67  % Total time : 0.031000 s
% 0.22/0.67  % SZS output end Proof
% 0.22/0.67  % Total time : 0.034000 s
%------------------------------------------------------------------------------