TSTP Solution File: RNG059+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG059+2 : 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 : n032.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 13:48:49 EDT 2023

% Result   : Theorem 0.17s 0.59s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   86 (  22 unt;  33 typ;   0 def)
%            Number of atoms       :  142 (  57 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  141 (  52   ~;  49   |;  34   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    4 (   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   :   40 (   1 sgn;  22   !;   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(mMNeg,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
        & sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).

fof(mScZero,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => ( sdtpldt0(X1,sz0z00) = X1
        & sdtpldt0(sz0z00,X1) = X1
        & sdtasdt0(X1,sz0z00) = sz0z00
        & sdtasdt0(sz0z00,X1) = sz0z00
        & sdtpldt0(X1,smndt0(X1)) = sz0z00
        & sdtpldt0(smndt0(X1),X1) = sz0z00
        & smndt0(smndt0(X1)) = X1
        & smndt0(sz0z00) = sz0z00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

fof(mMulSc,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => aScalar0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

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

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

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

fof(mNegSc,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => aScalar0(smndt0(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

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

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

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

fof(mMDNeg,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).

fof(mArith,axiom,
    ! [X1,X2,X3] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3) )
     => ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
        & sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
        & sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
        & sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).

fof(m__,conjecture,
    sdtasdt0(smndt0(xS),xR) = smndt0(xN),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__1949,hypothesis,
    ( aScalar0(xN)
    & xN = sdtasdt0(xR,xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).

fof(c_0_14,plain,
    ! [X27,X28] :
      ( ( sdtasdt0(X27,smndt0(X28)) = smndt0(sdtasdt0(X27,X28))
        | ~ aScalar0(X27)
        | ~ aScalar0(X28) )
      & ( sdtasdt0(smndt0(X27),X28) = smndt0(sdtasdt0(X27,X28))
        | ~ aScalar0(X27)
        | ~ aScalar0(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).

fof(c_0_15,plain,
    ! [X16] :
      ( ( sdtpldt0(X16,sz0z00) = X16
        | ~ aScalar0(X16) )
      & ( sdtpldt0(sz0z00,X16) = X16
        | ~ aScalar0(X16) )
      & ( sdtasdt0(X16,sz0z00) = sz0z00
        | ~ aScalar0(X16) )
      & ( sdtasdt0(sz0z00,X16) = sz0z00
        | ~ aScalar0(X16) )
      & ( sdtpldt0(X16,smndt0(X16)) = sz0z00
        | ~ aScalar0(X16) )
      & ( sdtpldt0(smndt0(X16),X16) = sz0z00
        | ~ aScalar0(X16) )
      & ( smndt0(smndt0(X16)) = X16
        | ~ aScalar0(X16) )
      & ( smndt0(sz0z00) = sz0z00
        | ~ aScalar0(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).

fof(c_0_16,plain,
    ! [X13,X14] :
      ( ~ aScalar0(X13)
      | ~ aScalar0(X14)
      | aScalar0(sdtasdt0(X13,X14)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).

cnf(c_0_17,plain,
    ( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,hypothesis,
    xS = sdtasdt0(xF,xD),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

cnf(c_0_19,hypothesis,
    aScalar0(xD),
    inference(split_conjunct,[status(thm)],[m__1800]) ).

cnf(c_0_20,hypothesis,
    aScalar0(xF),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_21,plain,
    ( smndt0(smndt0(X1)) = X1
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,plain,
    ( aScalar0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,hypothesis,
    sdtasdt0(smndt0(xF),xD) = smndt0(xS),
    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])]) ).

fof(c_0_25,plain,
    ! [X15] :
      ( ~ aScalar0(X15)
      | aScalar0(smndt0(X15)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).

cnf(c_0_26,hypothesis,
    xR = sdtasdt0(xC,xG),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

cnf(c_0_27,hypothesis,
    aScalar0(xG),
    inference(split_conjunct,[status(thm)],[m__1854]) ).

cnf(c_0_28,hypothesis,
    aScalar0(xC),
    inference(split_conjunct,[status(thm)],[m__1783]) ).

fof(c_0_29,plain,
    ! [X29,X30] :
      ( ~ aScalar0(X29)
      | ~ aScalar0(X30)
      | sdtasdt0(smndt0(X29),smndt0(X30)) = sdtasdt0(X29,X30) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])]) ).

cnf(c_0_30,plain,
    ( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_31,hypothesis,
    sdtasdt0(xF,smndt0(xD)) = smndt0(xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_19]),c_0_20])]) ).

cnf(c_0_32,hypothesis,
    ( aScalar0(smndt0(xS))
    | ~ aScalar0(smndt0(xF)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19])]) ).

cnf(c_0_33,plain,
    ( aScalar0(smndt0(X1))
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_34,plain,
    ! [X17,X18,X19] :
      ( ( sdtpldt0(sdtpldt0(X17,X18),X19) = sdtpldt0(X17,sdtpldt0(X18,X19))
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) )
      & ( sdtpldt0(X17,X18) = sdtpldt0(X18,X17)
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) )
      & ( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) )
      & ( sdtasdt0(X17,X18) = sdtasdt0(X18,X17)
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).

cnf(c_0_35,hypothesis,
    sdtasdt0(xC,smndt0(xG)) = smndt0(xR),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_27]),c_0_28])]) ).

fof(c_0_36,negated_conjecture,
    sdtasdt0(smndt0(xS),xR) != smndt0(xN),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_37,plain,
    ( sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_38,hypothesis,
    smndt0(smndt0(xS)) = xS,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_18]),c_0_19]),c_0_20])]) ).

cnf(c_0_39,hypothesis,
    aScalar0(smndt0(xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_20])]) ).

cnf(c_0_40,hypothesis,
    xN = sdtasdt0(xR,xS),
    inference(split_conjunct,[status(thm)],[m__1949]) ).

cnf(c_0_41,hypothesis,
    aScalar0(xS),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

cnf(c_0_42,hypothesis,
    aScalar0(xR),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

cnf(c_0_43,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_44,hypothesis,
    aScalar0(xN),
    inference(split_conjunct,[status(thm)],[m__1949]) ).

cnf(c_0_45,hypothesis,
    ( aScalar0(smndt0(xR))
    | ~ aScalar0(smndt0(xG)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_35]),c_0_28])]) ).

cnf(c_0_46,negated_conjecture,
    sdtasdt0(smndt0(xS),xR) != smndt0(xN),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_47,hypothesis,
    ( sdtasdt0(smndt0(xS),X1) = sdtasdt0(xS,smndt0(X1))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).

cnf(c_0_48,hypothesis,
    sdtasdt0(smndt0(xR),xS) = smndt0(xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_40]),c_0_41]),c_0_42])]) ).

cnf(c_0_49,hypothesis,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_50,hypothesis,
    aScalar0(smndt0(xR)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_33]),c_0_27])]) ).

cnf(c_0_51,negated_conjecture,
    sdtasdt0(xS,smndt0(xR)) != smndt0(xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42])]) ).

cnf(c_0_52,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_41])]),c_0_51]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : RNG059+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32  % Computer : n032.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Sun Aug 27 02:16:59 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 0.17/0.50  start to proof: theBenchmark
% 0.17/0.59  % Version  : CSE_E---1.5
% 0.17/0.59  % Problem  : theBenchmark.p
% 0.17/0.59  % Proof found
% 0.17/0.59  % SZS status Theorem for theBenchmark.p
% 0.17/0.59  % SZS output start Proof
% See solution above
% 0.17/0.60  % Total time : 0.085000 s
% 0.17/0.60  % SZS output end Proof
% 0.17/0.60  % Total time : 0.089000 s
%------------------------------------------------------------------------------