TSTP Solution File: COM018+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COM018+4 : 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 : n014.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 : Wed Aug 30 18:36:19 EDT 2023

% Result   : Theorem 0.19s 0.71s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   48
% Syntax   : Number of formulae    :   59 (   6 unt;  43 typ;   0 def)
%            Number of atoms       :  222 (  23 equ)
%            Maximal formula atoms :   96 (  13 avg)
%            Number of connectives :  295 (  89   ~; 132   |;  69   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   62 (  30   >;  32   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   33 (  33 usr;  13 con; 0-4 aty)
%            Number of variables   :   34 (   1 sgn;  18   !;  13   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aElement0: $i > $o ).

tff(decl_23,type,
    aRewritingSystem0: $i > $o ).

tff(decl_24,type,
    aReductOfIn0: ( $i * $i * $i ) > $o ).

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

tff(decl_26,type,
    sdtmndtplgtdt0: ( $i * $i * $i ) > $o ).

tff(decl_27,type,
    sdtmndtasgtdt0: ( $i * $i * $i ) > $o ).

tff(decl_28,type,
    isConfluent0: $i > $o ).

tff(decl_29,type,
    isLocallyConfluent0: $i > $o ).

tff(decl_30,type,
    isTerminating0: $i > $o ).

tff(decl_31,type,
    aNormalFormOfIn0: ( $i * $i * $i ) > $o ).

tff(decl_32,type,
    xR: $i ).

tff(decl_33,type,
    xa: $i ).

tff(decl_34,type,
    xb: $i ).

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

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

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

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

tff(decl_39,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk2_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_41,type,
    esk3_1: $i > $i ).

tff(decl_42,type,
    esk4_1: $i > $i ).

tff(decl_43,type,
    esk5_1: $i > $i ).

tff(decl_44,type,
    esk6_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk7_1: $i > $i ).

tff(decl_46,type,
    esk8_1: $i > $i ).

tff(decl_47,type,
    esk9_1: $i > $i ).

tff(decl_48,type,
    esk10_1: $i > $i ).

tff(decl_49,type,
    esk11_1: $i > $i ).

tff(decl_50,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk20_0: $i ).

tff(decl_59,type,
    esk21_0: $i ).

tff(decl_60,type,
    esk22_0: $i ).

tff(decl_61,type,
    esk23_0: $i ).

tff(decl_62,type,
    esk24_0: $i ).

tff(decl_63,type,
    esk25_0: $i ).

tff(decl_64,type,
    esk26_1: $i > $i ).

fof(m__,conjecture,
    ? [X1] :
      ( ( aElement0(X1)
        & ( xw = X1
          | aReductOfIn0(X1,xw,xR)
          | ? [X2] :
              ( aElement0(X2)
              & aReductOfIn0(X2,xw,xR)
              & sdtmndtplgtdt0(X2,xR,X1) )
          | sdtmndtplgtdt0(xw,xR,X1)
          | sdtmndtasgtdt0(xw,xR,X1) )
        & ~ ? [X2] : aReductOfIn0(X2,X1,xR) )
      | aNormalFormOfIn0(X1,xw,xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mTermNF,axiom,
    ! [X1] :
      ( ( aRewritingSystem0(X1)
        & isTerminating0(X1) )
     => ! [X2] :
          ( aElement0(X2)
         => ? [X3] : aNormalFormOfIn0(X3,X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).

fof(m__656_01,hypothesis,
    ( ! [X1,X2,X3] :
        ( ( aElement0(X1)
          & aElement0(X2)
          & aElement0(X3)
          & aReductOfIn0(X2,X1,xR)
          & aReductOfIn0(X3,X1,xR) )
       => ? [X4] :
            ( aElement0(X4)
            & ( X2 = X4
              | ( ( aReductOfIn0(X4,X2,xR)
                  | ? [X5] :
                      ( aElement0(X5)
                      & aReductOfIn0(X5,X2,xR)
                      & sdtmndtplgtdt0(X5,xR,X4) ) )
                & sdtmndtplgtdt0(X2,xR,X4) ) )
            & sdtmndtasgtdt0(X2,xR,X4)
            & ( X3 = X4
              | ( ( aReductOfIn0(X4,X3,xR)
                  | ? [X5] :
                      ( aElement0(X5)
                      & aReductOfIn0(X5,X3,xR)
                      & sdtmndtplgtdt0(X5,xR,X4) ) )
                & sdtmndtplgtdt0(X3,xR,X4) ) )
            & sdtmndtasgtdt0(X3,xR,X4) ) )
    & isLocallyConfluent0(xR)
    & ! [X1,X2] :
        ( ( aElement0(X1)
          & aElement0(X2) )
       => ( ( aReductOfIn0(X2,X1,xR)
            | ? [X3] :
                ( aElement0(X3)
                & aReductOfIn0(X3,X1,xR)
                & sdtmndtplgtdt0(X3,xR,X2) )
            | sdtmndtplgtdt0(X1,xR,X2) )
         => iLess0(X2,X1) ) )
    & isTerminating0(xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).

fof(m__799,hypothesis,
    ( aElement0(xw)
    & ( xu = xw
      | ( ( aReductOfIn0(xw,xu,xR)
          | ? [X1] :
              ( aElement0(X1)
              & aReductOfIn0(X1,xu,xR)
              & sdtmndtplgtdt0(X1,xR,xw) ) )
        & sdtmndtplgtdt0(xu,xR,xw) ) )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( xv = xw
      | ( ( aReductOfIn0(xw,xv,xR)
          | ? [X1] :
              ( aElement0(X1)
              & aReductOfIn0(X1,xv,xR)
              & sdtmndtplgtdt0(X1,xR,xw) ) )
        & sdtmndtplgtdt0(xv,xR,xw) ) )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).

fof(m__656,hypothesis,
    aRewritingSystem0(xR),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).

fof(c_0_5,negated_conjecture,
    ~ ? [X1] :
        ( ( aElement0(X1)
          & ( xw = X1
            | aReductOfIn0(X1,xw,xR)
            | ? [X2] :
                ( aElement0(X2)
                & aReductOfIn0(X2,xw,xR)
                & sdtmndtplgtdt0(X2,xR,X1) )
            | sdtmndtplgtdt0(xw,xR,X1)
            | sdtmndtasgtdt0(xw,xR,X1) )
          & ~ ? [X2] : aReductOfIn0(X2,X1,xR) )
        | aNormalFormOfIn0(X1,xw,xR) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_6,negated_conjecture,
    ! [X80,X81,X83] :
      ( ( xw != X80
        | ~ aElement0(X80)
        | aReductOfIn0(esk26_1(X80),X80,xR) )
      & ( ~ aReductOfIn0(X80,xw,xR)
        | ~ aElement0(X80)
        | aReductOfIn0(esk26_1(X80),X80,xR) )
      & ( ~ aElement0(X81)
        | ~ aReductOfIn0(X81,xw,xR)
        | ~ sdtmndtplgtdt0(X81,xR,X80)
        | ~ aElement0(X80)
        | aReductOfIn0(esk26_1(X80),X80,xR) )
      & ( ~ sdtmndtplgtdt0(xw,xR,X80)
        | ~ aElement0(X80)
        | aReductOfIn0(esk26_1(X80),X80,xR) )
      & ( ~ sdtmndtasgtdt0(xw,xR,X80)
        | ~ aElement0(X80)
        | aReductOfIn0(esk26_1(X80),X80,xR) )
      & ~ aNormalFormOfIn0(X83,xw,xR) ),
    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)],[c_0_5])])])])])]) ).

fof(c_0_7,plain,
    ! [X54,X55] :
      ( ~ aRewritingSystem0(X54)
      | ~ isTerminating0(X54)
      | ~ aElement0(X55)
      | aNormalFormOfIn0(esk13_2(X54,X55),X55,X54) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTermNF])])])]) ).

fof(c_0_8,hypothesis,
    ! [X57,X58,X59,X63,X64,X65] :
      ( ( aElement0(esk14_3(X57,X58,X59))
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( aElement0(esk15_3(X57,X58,X59))
        | aReductOfIn0(esk14_3(X57,X58,X59),X58,xR)
        | X58 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( aReductOfIn0(esk15_3(X57,X58,X59),X58,xR)
        | aReductOfIn0(esk14_3(X57,X58,X59),X58,xR)
        | X58 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( sdtmndtplgtdt0(esk15_3(X57,X58,X59),xR,esk14_3(X57,X58,X59))
        | aReductOfIn0(esk14_3(X57,X58,X59),X58,xR)
        | X58 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( sdtmndtplgtdt0(X58,xR,esk14_3(X57,X58,X59))
        | X58 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( sdtmndtasgtdt0(X58,xR,esk14_3(X57,X58,X59))
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( aElement0(esk16_3(X57,X58,X59))
        | aReductOfIn0(esk14_3(X57,X58,X59),X59,xR)
        | X59 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( aReductOfIn0(esk16_3(X57,X58,X59),X59,xR)
        | aReductOfIn0(esk14_3(X57,X58,X59),X59,xR)
        | X59 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( sdtmndtplgtdt0(esk16_3(X57,X58,X59),xR,esk14_3(X57,X58,X59))
        | aReductOfIn0(esk14_3(X57,X58,X59),X59,xR)
        | X59 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( sdtmndtplgtdt0(X59,xR,esk14_3(X57,X58,X59))
        | X59 = esk14_3(X57,X58,X59)
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & ( sdtmndtasgtdt0(X59,xR,esk14_3(X57,X58,X59))
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ aReductOfIn0(X58,X57,xR)
        | ~ aReductOfIn0(X59,X57,xR) )
      & isLocallyConfluent0(xR)
      & ( ~ aReductOfIn0(X64,X63,xR)
        | iLess0(X64,X63)
        | ~ aElement0(X63)
        | ~ aElement0(X64) )
      & ( ~ aElement0(X65)
        | ~ aReductOfIn0(X65,X63,xR)
        | ~ sdtmndtplgtdt0(X65,xR,X64)
        | iLess0(X64,X63)
        | ~ aElement0(X63)
        | ~ aElement0(X64) )
      & ( ~ sdtmndtplgtdt0(X63,xR,X64)
        | iLess0(X64,X63)
        | ~ aElement0(X63)
        | ~ aElement0(X64) )
      & isTerminating0(xR) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__656_01])])])])]) ).

fof(c_0_9,hypothesis,
    ( aElement0(xw)
    & ( aElement0(esk24_0)
      | aReductOfIn0(xw,xu,xR)
      | xu = xw )
    & ( aReductOfIn0(esk24_0,xu,xR)
      | aReductOfIn0(xw,xu,xR)
      | xu = xw )
    & ( sdtmndtplgtdt0(esk24_0,xR,xw)
      | aReductOfIn0(xw,xu,xR)
      | xu = xw )
    & ( sdtmndtplgtdt0(xu,xR,xw)
      | xu = xw )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( aElement0(esk25_0)
      | aReductOfIn0(xw,xv,xR)
      | xv = xw )
    & ( aReductOfIn0(esk25_0,xv,xR)
      | aReductOfIn0(xw,xv,xR)
      | xv = xw )
    & ( sdtmndtplgtdt0(esk25_0,xR,xw)
      | aReductOfIn0(xw,xv,xR)
      | xv = xw )
    & ( sdtmndtplgtdt0(xv,xR,xw)
      | xv = xw )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__799])])]) ).

cnf(c_0_10,negated_conjecture,
    ~ aNormalFormOfIn0(X1,xw,xR),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( aNormalFormOfIn0(esk13_2(X1,X2),X2,X1)
    | ~ aRewritingSystem0(X1)
    | ~ isTerminating0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,hypothesis,
    isTerminating0(xR),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,hypothesis,
    aRewritingSystem0(xR),
    inference(split_conjunct,[status(thm)],[m__656]) ).

cnf(c_0_14,hypothesis,
    aElement0(xw),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n014.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   : Tue Aug 29 12:53:00 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.71  % Version  : CSE_E---1.5
% 0.19/0.71  % Problem  : theBenchmark.p
% 0.19/0.71  % Proof found
% 0.19/0.71  % SZS status Theorem for theBenchmark.p
% 0.19/0.71  % SZS output start Proof
% See solution above
% 0.19/0.71  % Total time : 0.124000 s
% 0.19/0.71  % SZS output end Proof
% 0.19/0.71  % Total time : 0.127000 s
%------------------------------------------------------------------------------