TSTP Solution File: RNG099+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG099+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 : n027.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 13:49:08 EDT 2023

% Result   : Theorem 0.20s 0.62s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   67 (  17 unt;  32 typ;   0 def)
%            Number of atoms       :  106 (   3 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  111 (  40   ~;  35   |;  26   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   46 (  23   >;  23   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   27 (  27 usr;   9 con; 0-4 aty)
%            Number of variables   :   34 (   0 sgn;  25   !;   2   ?;   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,
    xI: $i ).

tff(decl_35,type,
    xJ: $i ).

tff(decl_36,type,
    xx: $i ).

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

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

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

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

tff(decl_41,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_42,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_43,type,
    esk3_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_47,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_49,type,
    esk9_1: $i > $i ).

tff(decl_50,type,
    esk10_1: $i > $i ).

tff(decl_51,type,
    esk11_1: $i > $i ).

tff(decl_52,type,
    esk12_1: $i > $i ).

tff(decl_53,type,
    esk13_1: $i > $i ).

fof(m__,conjecture,
    ? [X1] :
      ( aElement0(X1)
      & ( aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
        | sdteqdtlpzmzozddtrp0(X1,xx,xI) )
      & ( aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
        | sdteqdtlpzmzozddtrp0(X1,xy,xJ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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

fof(m__1332,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1332) ).

fof(m__1409,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).

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

fof(m__1205,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)
    & aSet0(xJ)
    & ! [X1] :
        ( aElementOf0(X1,xJ)
       => ( ! [X2] :
              ( aElementOf0(X2,xJ)
             => aElementOf0(sdtpldt0(X1,X2),xJ) )
          & ! [X2] :
              ( aElement0(X2)
             => aElementOf0(sdtasdt0(X2,X1),xJ) ) ) )
    & aIdeal0(xJ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).

fof(m__1319,hypothesis,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).

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

fof(m__1294,hypothesis,
    ( aElementOf0(xa,xI)
    & aElementOf0(xb,xJ)
    & sdtpldt0(xa,xb) = sz10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).

fof(m__1217,hypothesis,
    ( aElement0(xx)
    & aElement0(xy) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).

fof(c_0_10,negated_conjecture,
    ~ ? [X1] :
        ( aElement0(X1)
        & ( aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
          | sdteqdtlpzmzozddtrp0(X1,xx,xI) )
        & ( aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
          | sdteqdtlpzmzozddtrp0(X1,xy,xJ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_11,negated_conjecture,
    ! [X84] :
      ( ( ~ aElementOf0(sdtpldt0(X84,smndt0(xy)),xJ)
        | ~ aElementOf0(sdtpldt0(X84,smndt0(xx)),xI)
        | ~ aElement0(X84) )
      & ( ~ sdteqdtlpzmzozddtrp0(X84,xy,xJ)
        | ~ aElementOf0(sdtpldt0(X84,smndt0(xx)),xI)
        | ~ aElement0(X84) )
      & ( ~ aElementOf0(sdtpldt0(X84,smndt0(xy)),xJ)
        | ~ sdteqdtlpzmzozddtrp0(X84,xx,xI)
        | ~ aElement0(X84) )
      & ( ~ sdteqdtlpzmzozddtrp0(X84,xy,xJ)
        | ~ sdteqdtlpzmzozddtrp0(X84,xx,xI)
        | ~ aElement0(X84) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_12,plain,
    ! [X8,X9] :
      ( ~ aElement0(X8)
      | ~ aElement0(X9)
      | aElement0(sdtpldt0(X8,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ aElementOf0(sdtpldt0(X1,smndt0(xy)),xJ)
    | ~ aElementOf0(sdtpldt0(X1,smndt0(xx)),xI)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_14,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    inference(split_conjunct,[status(thm)],[m__1332]) ).

cnf(c_0_15,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    inference(split_conjunct,[status(thm)],[m__1409]) ).

fof(c_0_16,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])])]) ).

fof(c_0_17,hypothesis,
    ! [X75,X76,X77,X78,X79,X80] :
      ( aSet0(xI)
      & ( ~ aElementOf0(X76,xI)
        | aElementOf0(sdtpldt0(X75,X76),xI)
        | ~ aElementOf0(X75,xI) )
      & ( ~ aElement0(X77)
        | aElementOf0(sdtasdt0(X77,X75),xI)
        | ~ aElementOf0(X75,xI) )
      & aIdeal0(xI)
      & aSet0(xJ)
      & ( ~ aElementOf0(X79,xJ)
        | aElementOf0(sdtpldt0(X78,X79),xJ)
        | ~ aElementOf0(X78,xJ) )
      & ( ~ aElement0(X80)
        | aElementOf0(sdtasdt0(X80,X78),xJ)
        | ~ aElementOf0(X78,xJ) )
      & aIdeal0(xJ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1205])])])]) ).

cnf(c_0_18,plain,
    ( aElement0(sdtpldt0(X1,X2))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,hypothesis,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    inference(split_conjunct,[status(thm)],[m__1319]) ).

cnf(c_0_20,hypothesis,
    ~ aElement0(xw),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

fof(c_0_21,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_22,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,hypothesis,
    aElementOf0(xb,xJ),
    inference(split_conjunct,[status(thm)],[m__1294]) ).

cnf(c_0_24,hypothesis,
    aSet0(xJ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,hypothesis,
    ( ~ aElement0(sdtasdt0(xx,xb))
    | ~ aElement0(sdtasdt0(xy,xa)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

cnf(c_0_26,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,hypothesis,
    aElement0(xb),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_28,hypothesis,
    aElement0(xx),
    inference(split_conjunct,[status(thm)],[m__1217]) ).

cnf(c_0_29,hypothesis,
    aElementOf0(xa,xI),
    inference(split_conjunct,[status(thm)],[m__1294]) ).

cnf(c_0_30,hypothesis,
    aSet0(xI),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_31,hypothesis,
    ~ aElement0(sdtasdt0(xy,xa)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).

cnf(c_0_32,hypothesis,
    aElement0(xa),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_30])]) ).

cnf(c_0_33,hypothesis,
    aElement0(xy),
    inference(split_conjunct,[status(thm)],[m__1217]) ).

cnf(c_0_34,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_32]),c_0_33])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : RNG099+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n027.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 03:09:05 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.62  % Version  : CSE_E---1.5
% 0.20/0.62  % Problem  : theBenchmark.p
% 0.20/0.62  % Proof found
% 0.20/0.62  % SZS status Theorem for theBenchmark.p
% 0.20/0.62  % SZS output start Proof
% See solution above
% 0.20/0.63  % Total time : 0.071000 s
% 0.20/0.63  % SZS output end Proof
% 0.20/0.63  % Total time : 0.075000 s
%------------------------------------------------------------------------------