TSTP Solution File: COM023+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : COM023+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 : n012.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 18:36:22 EDT 2023

% Result   : Theorem 0.19s 0.55s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   50 (   7 unt;  25 typ;   0 def)
%            Number of atoms       :  145 (   0 equ)
%            Maximal formula atoms :   44 (   5 avg)
%            Number of connectives :  212 (  92   ~;  94   |;  22   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    3 (   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    :   15 (  15 usr;   1 con; 0-4 aty)
%            Number of variables   :   36 (   0 sgn;  15   !;   2   ?;   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,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    esk2_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_35,type,
    esk3_1: $i > $i ).

tff(decl_36,type,
    esk4_1: $i > $i ).

tff(decl_37,type,
    esk5_1: $i > $i ).

tff(decl_38,type,
    esk6_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_39,type,
    esk7_1: $i > $i ).

tff(decl_40,type,
    esk8_1: $i > $i ).

tff(decl_41,type,
    esk9_1: $i > $i ).

tff(decl_42,type,
    esk10_1: $i > $i ).

tff(decl_43,type,
    esk11_1: $i > $i ).

tff(decl_44,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk14_3: ( $i * $i * $i ) > $i ).

fof(mCRDef,axiom,
    ! [X1] :
      ( aRewritingSystem0(X1)
     => ( isConfluent0(X1)
      <=> ! [X2,X3,X4] :
            ( ( aElement0(X2)
              & aElement0(X3)
              & aElement0(X4)
              & sdtmndtasgtdt0(X2,X1,X3)
              & sdtmndtasgtdt0(X2,X1,X4) )
           => ? [X5] :
                ( aElement0(X5)
                & sdtmndtasgtdt0(X3,X1,X5)
                & sdtmndtasgtdt0(X4,X1,X5) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCRDef) ).

fof(m__715,hypothesis,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3)
        & sdtmndtasgtdt0(X1,xR,X2)
        & sdtmndtasgtdt0(X1,xR,X3) )
     => ? [X4] :
          ( aElement0(X4)
          & sdtmndtasgtdt0(X2,xR,X4)
          & sdtmndtasgtdt0(X3,xR,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__715) ).

fof(m__,conjecture,
    isConfluent0(xR),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__656,hypothesis,
    aRewritingSystem0(xR),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).

fof(c_0_4,plain,
    ! [X25,X26,X27,X28,X33] :
      ( ( aElement0(esk2_4(X25,X26,X27,X28))
        | ~ aElement0(X26)
        | ~ aElement0(X27)
        | ~ aElement0(X28)
        | ~ sdtmndtasgtdt0(X26,X25,X27)
        | ~ sdtmndtasgtdt0(X26,X25,X28)
        | ~ isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( sdtmndtasgtdt0(X27,X25,esk2_4(X25,X26,X27,X28))
        | ~ aElement0(X26)
        | ~ aElement0(X27)
        | ~ aElement0(X28)
        | ~ sdtmndtasgtdt0(X26,X25,X27)
        | ~ sdtmndtasgtdt0(X26,X25,X28)
        | ~ isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( sdtmndtasgtdt0(X28,X25,esk2_4(X25,X26,X27,X28))
        | ~ aElement0(X26)
        | ~ aElement0(X27)
        | ~ aElement0(X28)
        | ~ sdtmndtasgtdt0(X26,X25,X27)
        | ~ sdtmndtasgtdt0(X26,X25,X28)
        | ~ isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( aElement0(esk3_1(X25))
        | isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( aElement0(esk4_1(X25))
        | isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( aElement0(esk5_1(X25))
        | isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( sdtmndtasgtdt0(esk3_1(X25),X25,esk4_1(X25))
        | isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( sdtmndtasgtdt0(esk3_1(X25),X25,esk5_1(X25))
        | isConfluent0(X25)
        | ~ aRewritingSystem0(X25) )
      & ( ~ aElement0(X33)
        | ~ sdtmndtasgtdt0(esk4_1(X25),X25,X33)
        | ~ sdtmndtasgtdt0(esk5_1(X25),X25,X33)
        | isConfluent0(X25)
        | ~ aRewritingSystem0(X25) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCRDef])])])])]) ).

fof(c_0_5,hypothesis,
    ! [X57,X58,X59] :
      ( ( aElement0(esk14_3(X57,X58,X59))
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ sdtmndtasgtdt0(X57,xR,X58)
        | ~ sdtmndtasgtdt0(X57,xR,X59) )
      & ( sdtmndtasgtdt0(X58,xR,esk14_3(X57,X58,X59))
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ sdtmndtasgtdt0(X57,xR,X58)
        | ~ sdtmndtasgtdt0(X57,xR,X59) )
      & ( sdtmndtasgtdt0(X59,xR,esk14_3(X57,X58,X59))
        | ~ aElement0(X57)
        | ~ aElement0(X58)
        | ~ aElement0(X59)
        | ~ sdtmndtasgtdt0(X57,xR,X58)
        | ~ sdtmndtasgtdt0(X57,xR,X59) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__715])])])]) ).

fof(c_0_6,negated_conjecture,
    ~ isConfluent0(xR),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_7,plain,
    ( isConfluent0(X2)
    | ~ aElement0(X1)
    | ~ sdtmndtasgtdt0(esk4_1(X2),X2,X1)
    | ~ sdtmndtasgtdt0(esk5_1(X2),X2,X1)
    | ~ aRewritingSystem0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,hypothesis,
    ( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X3,X1))
    | ~ aElement0(X2)
    | ~ aElement0(X3)
    | ~ aElement0(X1)
    | ~ sdtmndtasgtdt0(X2,xR,X3)
    | ~ sdtmndtasgtdt0(X2,xR,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,hypothesis,
    aRewritingSystem0(xR),
    inference(split_conjunct,[status(thm)],[m__656]) ).

cnf(c_0_10,negated_conjecture,
    ~ isConfluent0(xR),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,hypothesis,
    ( aElement0(esk14_3(X1,X2,X3))
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3)
    | ~ sdtmndtasgtdt0(X1,xR,X2)
    | ~ sdtmndtasgtdt0(X1,xR,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,hypothesis,
    ( ~ sdtmndtasgtdt0(esk4_1(xR),xR,esk14_3(X1,X2,esk5_1(xR)))
    | ~ sdtmndtasgtdt0(X1,xR,esk5_1(xR))
    | ~ sdtmndtasgtdt0(X1,xR,X2)
    | ~ aElement0(esk5_1(xR))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),c_0_10]),c_0_11]) ).

cnf(c_0_13,hypothesis,
    ( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X1,X3))
    | ~ aElement0(X2)
    | ~ aElement0(X1)
    | ~ aElement0(X3)
    | ~ sdtmndtasgtdt0(X2,xR,X1)
    | ~ sdtmndtasgtdt0(X2,xR,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,hypothesis,
    ( ~ sdtmndtasgtdt0(X1,xR,esk5_1(xR))
    | ~ sdtmndtasgtdt0(X1,xR,esk4_1(xR))
    | ~ aElement0(esk5_1(xR))
    | ~ aElement0(esk4_1(xR))
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,plain,
    ( sdtmndtasgtdt0(esk3_1(X1),X1,esk5_1(X1))
    | isConfluent0(X1)
    | ~ aRewritingSystem0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_16,hypothesis,
    ( ~ sdtmndtasgtdt0(esk3_1(xR),xR,esk4_1(xR))
    | ~ aElement0(esk5_1(xR))
    | ~ aElement0(esk4_1(xR))
    | ~ aElement0(esk3_1(xR)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_9])]),c_0_10]) ).

cnf(c_0_17,plain,
    ( sdtmndtasgtdt0(esk3_1(X1),X1,esk4_1(X1))
    | isConfluent0(X1)
    | ~ aRewritingSystem0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_18,hypothesis,
    ( ~ aElement0(esk5_1(xR))
    | ~ aElement0(esk4_1(xR))
    | ~ aElement0(esk3_1(xR)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_9])]),c_0_10]) ).

cnf(c_0_19,plain,
    ( aElement0(esk5_1(X1))
    | isConfluent0(X1)
    | ~ aRewritingSystem0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_20,hypothesis,
    ( ~ aElement0(esk4_1(xR))
    | ~ aElement0(esk3_1(xR)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_9])]),c_0_10]) ).

cnf(c_0_21,plain,
    ( aElement0(esk4_1(X1))
    | isConfluent0(X1)
    | ~ aRewritingSystem0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_22,hypothesis,
    ~ aElement0(esk3_1(xR)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_9])]),c_0_10]) ).

cnf(c_0_23,plain,
    ( aElement0(esk3_1(X1))
    | isConfluent0(X1)
    | ~ aRewritingSystem0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_24,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_9])]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COM023+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34  % Computer : n012.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Tue Aug 29 13:08:39 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.19/0.53  start to proof: theBenchmark
% 0.19/0.55  % Version  : CSE_E---1.5
% 0.19/0.55  % Problem  : theBenchmark.p
% 0.19/0.55  % Proof found
% 0.19/0.55  % SZS status Theorem for theBenchmark.p
% 0.19/0.55  % SZS output start Proof
% See solution above
% 0.19/0.55  % Total time : 0.011000 s
% 0.19/0.55  % SZS output end Proof
% 0.19/0.55  % Total time : 0.014000 s
%------------------------------------------------------------------------------