TSTP Solution File: COM017+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COM017+1 : 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 : n028.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 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   59 (   7 unt;  30 typ;   0 def)
%            Number of atoms       :  150 (   0 equ)
%            Maximal formula atoms :   44 (   5 avg)
%            Number of connectives :  212 (  91   ~;  90   |;  26   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   46 (  24   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;   6 con; 0-4 aty)
%            Number of variables   :   51 (   0 sgn;  16   !;   3   ?;   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,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk2_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_40,type,
    esk3_1: $i > $i ).

tff(decl_41,type,
    esk4_1: $i > $i ).

tff(decl_42,type,
    esk5_1: $i > $i ).

tff(decl_43,type,
    esk6_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk7_1: $i > $i ).

tff(decl_45,type,
    esk8_1: $i > $i ).

tff(decl_46,type,
    esk9_1: $i > $i ).

tff(decl_47,type,
    esk10_1: $i > $i ).

tff(decl_48,type,
    esk11_1: $i > $i ).

tff(decl_49,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk14_3: ( $i * $i * $i ) > $i ).

fof(m__,conjecture,
    ? [X1] :
      ( aElement0(X1)
      & sdtmndtasgtdt0(xu,xR,X1)
      & sdtmndtasgtdt0(xv,xR,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mWCRDef,axiom,
    ! [X1] :
      ( aRewritingSystem0(X1)
     => ( isLocallyConfluent0(X1)
      <=> ! [X2,X3,X4] :
            ( ( aElement0(X2)
              & aElement0(X3)
              & aElement0(X4)
              & aReductOfIn0(X3,X2,X1)
              & aReductOfIn0(X4,X2,X1) )
           => ? [X5] :
                ( aElement0(X5)
                & sdtmndtasgtdt0(X3,X1,X5)
                & sdtmndtasgtdt0(X4,X1,X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mWCRDef) ).

fof(mReduct,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aRewritingSystem0(X2) )
     => ! [X3] :
          ( aReductOfIn0(X3,X1,X2)
         => aElement0(X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).

fof(m__656_01,hypothesis,
    ( isLocallyConfluent0(xR)
    & isTerminating0(xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).

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

fof(m__779,hypothesis,
    ( aElement0(xv)
    & aReductOfIn0(xv,xa,xR)
    & sdtmndtasgtdt0(xv,xR,xc) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__779) ).

fof(m__755,hypothesis,
    ( aElement0(xu)
    & aReductOfIn0(xu,xa,xR)
    & sdtmndtasgtdt0(xu,xR,xb) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).

fof(m__731,hypothesis,
    ( aElement0(xa)
    & aElement0(xb)
    & aElement0(xc) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).

fof(c_0_8,negated_conjecture,
    ~ ? [X1] :
        ( aElement0(X1)
        & sdtmndtasgtdt0(xu,xR,X1)
        & sdtmndtasgtdt0(xv,xR,X1) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_9,plain,
    ! [X34,X35,X36,X37,X42] :
      ( ( aElement0(esk6_4(X34,X35,X36,X37))
        | ~ aElement0(X35)
        | ~ aElement0(X36)
        | ~ aElement0(X37)
        | ~ aReductOfIn0(X36,X35,X34)
        | ~ aReductOfIn0(X37,X35,X34)
        | ~ isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( sdtmndtasgtdt0(X36,X34,esk6_4(X34,X35,X36,X37))
        | ~ aElement0(X35)
        | ~ aElement0(X36)
        | ~ aElement0(X37)
        | ~ aReductOfIn0(X36,X35,X34)
        | ~ aReductOfIn0(X37,X35,X34)
        | ~ isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( sdtmndtasgtdt0(X37,X34,esk6_4(X34,X35,X36,X37))
        | ~ aElement0(X35)
        | ~ aElement0(X36)
        | ~ aElement0(X37)
        | ~ aReductOfIn0(X36,X35,X34)
        | ~ aReductOfIn0(X37,X35,X34)
        | ~ isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( aElement0(esk7_1(X34))
        | isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( aElement0(esk8_1(X34))
        | isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( aElement0(esk9_1(X34))
        | isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( aReductOfIn0(esk8_1(X34),esk7_1(X34),X34)
        | isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( aReductOfIn0(esk9_1(X34),esk7_1(X34),X34)
        | isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) )
      & ( ~ aElement0(X42)
        | ~ sdtmndtasgtdt0(esk8_1(X34),X34,X42)
        | ~ sdtmndtasgtdt0(esk9_1(X34),X34,X42)
        | isLocallyConfluent0(X34)
        | ~ aRewritingSystem0(X34) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mWCRDef])])])])]) ).

fof(c_0_10,plain,
    ! [X6,X7,X8] :
      ( ~ aElement0(X6)
      | ~ aRewritingSystem0(X7)
      | ~ aReductOfIn0(X8,X6,X7)
      | aElement0(X8) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mReduct])])]) ).

fof(c_0_11,negated_conjecture,
    ! [X61] :
      ( ~ aElement0(X61)
      | ~ sdtmndtasgtdt0(xu,xR,X61)
      | ~ sdtmndtasgtdt0(xv,xR,X61) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).

cnf(c_0_12,plain,
    ( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X4,X1))
    | ~ aElement0(X3)
    | ~ aElement0(X4)
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X4,X3,X2)
    | ~ aReductOfIn0(X1,X3,X2)
    | ~ isLocallyConfluent0(X2)
    | ~ aRewritingSystem0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( aElement0(X3)
    | ~ aElement0(X1)
    | ~ aRewritingSystem0(X2)
    | ~ aReductOfIn0(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    ( ~ aElement0(X1)
    | ~ sdtmndtasgtdt0(xu,xR,X1)
    | ~ sdtmndtasgtdt0(xv,xR,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X4,X1))
    | ~ isLocallyConfluent0(X2)
    | ~ aReductOfIn0(X4,X3,X2)
    | ~ aReductOfIn0(X1,X3,X2)
    | ~ aRewritingSystem0(X2)
    | ~ aElement0(X3) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).

cnf(c_0_16,hypothesis,
    isLocallyConfluent0(xR),
    inference(split_conjunct,[status(thm)],[m__656_01]) ).

cnf(c_0_17,hypothesis,
    aRewritingSystem0(xR),
    inference(split_conjunct,[status(thm)],[m__656]) ).

cnf(c_0_18,plain,
    ( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X1,X4))
    | ~ aElement0(X3)
    | ~ aElement0(X1)
    | ~ aElement0(X4)
    | ~ aReductOfIn0(X1,X3,X2)
    | ~ aReductOfIn0(X4,X3,X2)
    | ~ isLocallyConfluent0(X2)
    | ~ aRewritingSystem0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xu,xR,esk6_4(xR,X1,X2,xv))
    | ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(X2,X1,xR)
    | ~ aElement0(esk6_4(xR,X1,X2,xv))
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_20,plain,
    ( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X1,X4))
    | ~ isLocallyConfluent0(X2)
    | ~ aReductOfIn0(X4,X3,X2)
    | ~ aReductOfIn0(X1,X3,X2)
    | ~ aRewritingSystem0(X2)
    | ~ aElement0(X3) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_18,c_0_13]),c_0_13]) ).

cnf(c_0_21,plain,
    ( aElement0(esk6_4(X1,X2,X3,X4))
    | ~ aElement0(X2)
    | ~ aElement0(X3)
    | ~ aElement0(X4)
    | ~ aReductOfIn0(X3,X2,X1)
    | ~ aReductOfIn0(X4,X2,X1)
    | ~ isLocallyConfluent0(X1)
    | ~ aRewritingSystem0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_22,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(esk6_4(xR,X1,xu,xv))
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]),c_0_17])]) ).

cnf(c_0_23,plain,
    ( aElement0(esk6_4(X1,X2,X3,X4))
    | ~ isLocallyConfluent0(X1)
    | ~ aReductOfIn0(X4,X2,X1)
    | ~ aReductOfIn0(X3,X2,X1)
    | ~ aRewritingSystem0(X1)
    | ~ aElement0(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_21,c_0_13]),c_0_13]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ aReductOfIn0(xv,X1,xR)
    | ~ aReductOfIn0(xu,X1,xR)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]),c_0_17])]) ).

cnf(c_0_25,hypothesis,
    aReductOfIn0(xv,xa,xR),
    inference(split_conjunct,[status(thm)],[m__779]) ).

cnf(c_0_26,hypothesis,
    aReductOfIn0(xu,xa,xR),
    inference(split_conjunct,[status(thm)],[m__755]) ).

cnf(c_0_27,hypothesis,
    aElement0(xa),
    inference(split_conjunct,[status(thm)],[m__731]) ).

cnf(c_0_28,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : COM017+1 : 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
% 0.13/0.34  % Computer : n028.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 13:19:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.021000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.024000 s
%------------------------------------------------------------------------------