TSTP Solution File: RNG124+1 by CSE

TSTP Solution File: RNG124+1 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG124+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 : n002.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 13:49:20 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   54
% Syntax   : Number of formulae    :   62 (   6 unt;  50 typ;   0 def)
%            Number of atoms       :   31 (  12 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   32 (  13   ~;   6   |;  11   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   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   :    4 (   0 sgn;   3   !;   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(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(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__2673,hypothesis,
    xr != sz00,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2673) ).

fof(m__2729,hypothesis,
    aElementOf0(xr,xI),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2729) ).

fof(c_0_4,hypothesis,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_simplification,[status(thm)],[m__2273]) ).

fof(c_0_5,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_4])])]) ).

cnf(c_0_6,hypothesis,
    ( xr = sz00
    | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
    inference(split_conjunct,[status(thm)],[m__2666]) ).

cnf(c_0_7,hypothesis,
    xr != sz00,
    inference(split_conjunct,[status(thm)],[m__2673]) ).

cnf(c_0_8,hypothesis,
    ( X1 = sz00
    | ~ aElementOf0(X1,xI)
    | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,hypothesis,
    iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
    inference(sr,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,hypothesis,
    aElementOf0(xr,xI),
    inference(split_conjunct,[status(thm)],[m__2729]) ).

cnf(c_0_11,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),c_0_7]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : RNG124+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun Aug 27 03:14:33 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.021000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.025000 s
%------------------------------------------------------------------------------