TSTP Solution File: SWV167+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWV167+1 : TPTP v5.0.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 12:21:10 EST 2010

% Result   : Theorem 0.32s
% Output   : CNFRefutation 0.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   39 (  10 unt;   0 def)
%            Number of atoms       :  329 (  91 equ)
%            Maximal formula atoms :   45 (   8 avg)
%            Number of connectives :  419 ( 129   ~; 126   |; 119   &)
%                                         (   1 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  16 con; 0-3 aty)
%            Number of variables   :   88 (   0 sgn  78   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2] :
      ( ( leq(X1,X2)
        & X1 != X2 )
     => gt(X2,X1) ),
    file('/tmp/tmpXDXDCS/sel_SWV167+1.p_1',leq_gt2) ).

fof(22,axiom,
    ! [X1,X2] :
      ( leq(X1,pred(X2))
    <=> gt(X2,X1) ),
    file('/tmp/tmpXDXDCS/sel_SWV167+1.p_1',leq_gt_pred) ).

fof(56,conjecture,
    ( ( a_select2(mu_init,pv40) = init
      & a_select2(sigma_init,pv40) = init
      & leq(n0,pv40)
      & leq(pv40,n4)
      & ! [X4] :
          ( ( leq(n0,X4)
            & leq(X4,n135299) )
         => ! [X5] :
              ( ( leq(n0,X5)
                & leq(X5,n4) )
             => a_select3(q_init,X4,X5) = init ) )
      & ! [X6] :
          ( ( leq(n0,X6)
            & leq(X6,n4) )
         => a_select2(rho_init,X6) = init )
      & ! [X7] :
          ( ( leq(n0,X7)
            & leq(X7,pred(pv40)) )
         => a_select2(mu_init,X7) = init )
      & ! [X8] :
          ( ( leq(n0,X8)
            & leq(X8,pred(pv40)) )
         => a_select2(sigma_init,X8) = init )
      & ! [X9] :
          ( ( leq(n0,X9)
            & leq(X9,n4) )
         => a_select3(center_init,X9,n0) = init )
      & ( gt(loopcounter,n1)
       => ! [X10] :
            ( ( leq(n0,X10)
              & leq(X10,n4) )
           => a_select2(muold_init,X10) = init ) )
      & ( gt(loopcounter,n1)
       => ! [X11] :
            ( ( leq(n0,X11)
              & leq(X11,n4) )
           => a_select2(rhoold_init,X11) = init ) )
      & ( gt(loopcounter,n1)
       => ! [X12] :
            ( ( leq(n0,X12)
              & leq(X12,n4) )
           => a_select2(sigmaold_init,X12) = init ) ) )
   => ! [X13] :
        ( ( leq(n0,X13)
          & leq(X13,pv40) )
       => a_select2(mu_init,X13) = init ) ),
    file('/tmp/tmpXDXDCS/sel_SWV167+1.p_1',cl5_nebula_init_0011) ).

fof(67,negated_conjecture,
    ~ ( ( a_select2(mu_init,pv40) = init
        & a_select2(sigma_init,pv40) = init
        & leq(n0,pv40)
        & leq(pv40,n4)
        & ! [X4] :
            ( ( leq(n0,X4)
              & leq(X4,n135299) )
           => ! [X5] :
                ( ( leq(n0,X5)
                  & leq(X5,n4) )
               => a_select3(q_init,X4,X5) = init ) )
        & ! [X6] :
            ( ( leq(n0,X6)
              & leq(X6,n4) )
           => a_select2(rho_init,X6) = init )
        & ! [X7] :
            ( ( leq(n0,X7)
              & leq(X7,pred(pv40)) )
           => a_select2(mu_init,X7) = init )
        & ! [X8] :
            ( ( leq(n0,X8)
              & leq(X8,pred(pv40)) )
           => a_select2(sigma_init,X8) = init )
        & ! [X9] :
            ( ( leq(n0,X9)
              & leq(X9,n4) )
           => a_select3(center_init,X9,n0) = init )
        & ( gt(loopcounter,n1)
         => ! [X10] :
              ( ( leq(n0,X10)
                & leq(X10,n4) )
             => a_select2(muold_init,X10) = init ) )
        & ( gt(loopcounter,n1)
         => ! [X11] :
              ( ( leq(n0,X11)
                & leq(X11,n4) )
             => a_select2(rhoold_init,X11) = init ) )
        & ( gt(loopcounter,n1)
         => ! [X12] :
              ( ( leq(n0,X12)
                & leq(X12,n4) )
             => a_select2(sigmaold_init,X12) = init ) ) )
     => ! [X13] :
          ( ( leq(n0,X13)
            & leq(X13,pv40) )
         => a_select2(mu_init,X13) = init ) ),
    inference(assume_negation,[status(cth)],[56]) ).

fof(69,plain,
    ( epred1_0
   => ( a_select2(mu_init,pv40) = init
      & a_select2(sigma_init,pv40) = init
      & leq(n0,pv40)
      & leq(pv40,n4)
      & ! [X4] :
          ( ( leq(n0,X4)
            & leq(X4,n135299) )
         => ! [X5] :
              ( ( leq(n0,X5)
                & leq(X5,n4) )
             => a_select3(q_init,X4,X5) = init ) )
      & ! [X6] :
          ( ( leq(n0,X6)
            & leq(X6,n4) )
         => a_select2(rho_init,X6) = init )
      & ! [X7] :
          ( ( leq(n0,X7)
            & leq(X7,pred(pv40)) )
         => a_select2(mu_init,X7) = init )
      & ! [X8] :
          ( ( leq(n0,X8)
            & leq(X8,pred(pv40)) )
         => a_select2(sigma_init,X8) = init )
      & ! [X9] :
          ( ( leq(n0,X9)
            & leq(X9,n4) )
         => a_select3(center_init,X9,n0) = init )
      & ( gt(loopcounter,n1)
       => ! [X10] :
            ( ( leq(n0,X10)
              & leq(X10,n4) )
           => a_select2(muold_init,X10) = init ) )
      & ( gt(loopcounter,n1)
       => ! [X11] :
            ( ( leq(n0,X11)
              & leq(X11,n4) )
           => a_select2(rhoold_init,X11) = init ) )
      & ( gt(loopcounter,n1)
       => ! [X12] :
            ( ( leq(n0,X12)
              & leq(X12,n4) )
           => a_select2(sigmaold_init,X12) = init ) ) ) ),
    introduced(definition) ).

fof(70,negated_conjecture,
    ~ ( epred1_0
     => ! [X13] :
          ( ( leq(n0,X13)
            & leq(X13,pv40) )
         => a_select2(mu_init,X13) = init ) ),
    inference(apply_def,[status(esa)],[67,69,theory(equality)]) ).

fof(79,plain,
    ! [X1,X2] :
      ( ~ leq(X1,X2)
      | X1 = X2
      | gt(X2,X1) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(80,plain,
    ! [X3,X4] :
      ( ~ leq(X3,X4)
      | X3 = X4
      | gt(X4,X3) ),
    inference(variable_rename,[status(thm)],[79]) ).

cnf(81,plain,
    ( gt(X1,X2)
    | X2 = X1
    | ~ leq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[80]) ).

fof(120,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,pred(X2))
        | gt(X2,X1) )
      & ( ~ gt(X2,X1)
        | leq(X1,pred(X2)) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(121,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,pred(X4))
        | gt(X4,X3) )
      & ( ~ gt(X4,X3)
        | leq(X3,pred(X4)) ) ),
    inference(variable_rename,[status(thm)],[120]) ).

cnf(122,plain,
    ( leq(X1,pred(X2))
    | ~ gt(X2,X1) ),
    inference(split_conjunct,[status(thm)],[121]) ).

fof(173,negated_conjecture,
    ( epred1_0
    & ? [X13] :
        ( leq(n0,X13)
        & leq(X13,pv40)
        & a_select2(mu_init,X13) != init ) ),
    inference(fof_nnf,[status(thm)],[70]) ).

fof(174,negated_conjecture,
    ( epred1_0
    & ? [X14] :
        ( leq(n0,X14)
        & leq(X14,pv40)
        & a_select2(mu_init,X14) != init ) ),
    inference(variable_rename,[status(thm)],[173]) ).

fof(175,negated_conjecture,
    ( epred1_0
    & leq(n0,esk1_0)
    & leq(esk1_0,pv40)
    & a_select2(mu_init,esk1_0) != init ),
    inference(skolemize,[status(esa)],[174]) ).

cnf(176,negated_conjecture,
    a_select2(mu_init,esk1_0) != init,
    inference(split_conjunct,[status(thm)],[175]) ).

cnf(177,negated_conjecture,
    leq(esk1_0,pv40),
    inference(split_conjunct,[status(thm)],[175]) ).

cnf(178,negated_conjecture,
    leq(n0,esk1_0),
    inference(split_conjunct,[status(thm)],[175]) ).

cnf(179,negated_conjecture,
    epred1_0,
    inference(split_conjunct,[status(thm)],[175]) ).

fof(192,plain,
    ( ~ epred1_0
    | ( a_select2(mu_init,pv40) = init
      & a_select2(sigma_init,pv40) = init
      & leq(n0,pv40)
      & leq(pv40,n4)
      & ! [X4] :
          ( ~ leq(n0,X4)
          | ~ leq(X4,n135299)
          | ! [X5] :
              ( ~ leq(n0,X5)
              | ~ leq(X5,n4)
              | a_select3(q_init,X4,X5) = init ) )
      & ! [X6] :
          ( ~ leq(n0,X6)
          | ~ leq(X6,n4)
          | a_select2(rho_init,X6) = init )
      & ! [X7] :
          ( ~ leq(n0,X7)
          | ~ leq(X7,pred(pv40))
          | a_select2(mu_init,X7) = init )
      & ! [X8] :
          ( ~ leq(n0,X8)
          | ~ leq(X8,pred(pv40))
          | a_select2(sigma_init,X8) = init )
      & ! [X9] :
          ( ~ leq(n0,X9)
          | ~ leq(X9,n4)
          | a_select3(center_init,X9,n0) = init )
      & ( ~ gt(loopcounter,n1)
        | ! [X10] :
            ( ~ leq(n0,X10)
            | ~ leq(X10,n4)
            | a_select2(muold_init,X10) = init ) )
      & ( ~ gt(loopcounter,n1)
        | ! [X11] :
            ( ~ leq(n0,X11)
            | ~ leq(X11,n4)
            | a_select2(rhoold_init,X11) = init ) )
      & ( ~ gt(loopcounter,n1)
        | ! [X12] :
            ( ~ leq(n0,X12)
            | ~ leq(X12,n4)
            | a_select2(sigmaold_init,X12) = init ) ) ) ),
    inference(fof_nnf,[status(thm)],[69]) ).

fof(193,plain,
    ( ~ epred1_0
    | ( a_select2(mu_init,pv40) = init
      & a_select2(sigma_init,pv40) = init
      & leq(n0,pv40)
      & leq(pv40,n4)
      & ! [X13] :
          ( ~ leq(n0,X13)
          | ~ leq(X13,n135299)
          | ! [X14] :
              ( ~ leq(n0,X14)
              | ~ leq(X14,n4)
              | a_select3(q_init,X13,X14) = init ) )
      & ! [X15] :
          ( ~ leq(n0,X15)
          | ~ leq(X15,n4)
          | a_select2(rho_init,X15) = init )
      & ! [X16] :
          ( ~ leq(n0,X16)
          | ~ leq(X16,pred(pv40))
          | a_select2(mu_init,X16) = init )
      & ! [X17] :
          ( ~ leq(n0,X17)
          | ~ leq(X17,pred(pv40))
          | a_select2(sigma_init,X17) = init )
      & ! [X18] :
          ( ~ leq(n0,X18)
          | ~ leq(X18,n4)
          | a_select3(center_init,X18,n0) = init )
      & ( ~ gt(loopcounter,n1)
        | ! [X19] :
            ( ~ leq(n0,X19)
            | ~ leq(X19,n4)
            | a_select2(muold_init,X19) = init ) )
      & ( ~ gt(loopcounter,n1)
        | ! [X20] :
            ( ~ leq(n0,X20)
            | ~ leq(X20,n4)
            | a_select2(rhoold_init,X20) = init ) )
      & ( ~ gt(loopcounter,n1)
        | ! [X21] :
            ( ~ leq(n0,X21)
            | ~ leq(X21,n4)
            | a_select2(sigmaold_init,X21) = init ) ) ) ),
    inference(variable_rename,[status(thm)],[192]) ).

fof(194,plain,
    ! [X13,X14,X15,X16,X17,X18,X19,X20,X21] :
      ( ( ( ~ leq(n0,X21)
          | ~ leq(X21,n4)
          | a_select2(sigmaold_init,X21) = init
          | ~ gt(loopcounter,n1) )
        & ( ~ leq(n0,X20)
          | ~ leq(X20,n4)
          | a_select2(rhoold_init,X20) = init
          | ~ gt(loopcounter,n1) )
        & ( ~ leq(n0,X19)
          | ~ leq(X19,n4)
          | a_select2(muold_init,X19) = init
          | ~ gt(loopcounter,n1) )
        & ( ~ leq(n0,X18)
          | ~ leq(X18,n4)
          | a_select3(center_init,X18,n0) = init )
        & ( ~ leq(n0,X17)
          | ~ leq(X17,pred(pv40))
          | a_select2(sigma_init,X17) = init )
        & ( ~ leq(n0,X16)
          | ~ leq(X16,pred(pv40))
          | a_select2(mu_init,X16) = init )
        & ( ~ leq(n0,X15)
          | ~ leq(X15,n4)
          | a_select2(rho_init,X15) = init )
        & ( ~ leq(n0,X14)
          | ~ leq(X14,n4)
          | a_select3(q_init,X13,X14) = init
          | ~ leq(n0,X13)
          | ~ leq(X13,n135299) )
        & a_select2(mu_init,pv40) = init
        & a_select2(sigma_init,pv40) = init
        & leq(n0,pv40)
        & leq(pv40,n4) )
      | ~ epred1_0 ),
    inference(shift_quantors,[status(thm)],[193]) ).

fof(195,plain,
    ! [X13,X14,X15,X16,X17,X18,X19,X20,X21] :
      ( ( ~ leq(n0,X21)
        | ~ leq(X21,n4)
        | a_select2(sigmaold_init,X21) = init
        | ~ gt(loopcounter,n1)
        | ~ epred1_0 )
      & ( ~ leq(n0,X20)
        | ~ leq(X20,n4)
        | a_select2(rhoold_init,X20) = init
        | ~ gt(loopcounter,n1)
        | ~ epred1_0 )
      & ( ~ leq(n0,X19)
        | ~ leq(X19,n4)
        | a_select2(muold_init,X19) = init
        | ~ gt(loopcounter,n1)
        | ~ epred1_0 )
      & ( ~ leq(n0,X18)
        | ~ leq(X18,n4)
        | a_select3(center_init,X18,n0) = init
        | ~ epred1_0 )
      & ( ~ leq(n0,X17)
        | ~ leq(X17,pred(pv40))
        | a_select2(sigma_init,X17) = init
        | ~ epred1_0 )
      & ( ~ leq(n0,X16)
        | ~ leq(X16,pred(pv40))
        | a_select2(mu_init,X16) = init
        | ~ epred1_0 )
      & ( ~ leq(n0,X15)
        | ~ leq(X15,n4)
        | a_select2(rho_init,X15) = init
        | ~ epred1_0 )
      & ( ~ leq(n0,X14)
        | ~ leq(X14,n4)
        | a_select3(q_init,X13,X14) = init
        | ~ leq(n0,X13)
        | ~ leq(X13,n135299)
        | ~ epred1_0 )
      & ( a_select2(mu_init,pv40) = init
        | ~ epred1_0 )
      & ( a_select2(sigma_init,pv40) = init
        | ~ epred1_0 )
      & ( leq(n0,pv40)
        | ~ epred1_0 )
      & ( leq(pv40,n4)
        | ~ epred1_0 ) ),
    inference(distribute,[status(thm)],[194]) ).

cnf(199,plain,
    ( a_select2(mu_init,pv40) = init
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[195]) ).

cnf(202,plain,
    ( a_select2(mu_init,X1) = init
    | ~ epred1_0
    | ~ leq(X1,pred(pv40))
    | ~ leq(n0,X1) ),
    inference(split_conjunct,[status(thm)],[195]) ).

cnf(236,plain,
    ( a_select2(mu_init,pv40) = init
    | $false ),
    inference(rw,[status(thm)],[199,179,theory(equality)]) ).

cnf(237,plain,
    a_select2(mu_init,pv40) = init,
    inference(cn,[status(thm)],[236,theory(equality)]) ).

cnf(327,plain,
    ( a_select2(mu_init,X1) = init
    | $false
    | ~ leq(n0,X1)
    | ~ leq(X1,pred(pv40)) ),
    inference(rw,[status(thm)],[202,179,theory(equality)]) ).

cnf(328,plain,
    ( a_select2(mu_init,X1) = init
    | ~ leq(n0,X1)
    | ~ leq(X1,pred(pv40)) ),
    inference(cn,[status(thm)],[327,theory(equality)]) ).

cnf(330,plain,
    ( a_select2(mu_init,X1) = init
    | ~ leq(n0,X1)
    | ~ gt(pv40,X1) ),
    inference(spm,[status(thm)],[328,122,theory(equality)]) ).

cnf(1744,plain,
    ( ~ gt(pv40,esk1_0)
    | ~ leq(n0,esk1_0) ),
    inference(spm,[status(thm)],[176,330,theory(equality)]) ).

cnf(1745,plain,
    ( ~ gt(pv40,esk1_0)
    | $false ),
    inference(rw,[status(thm)],[1744,178,theory(equality)]) ).

cnf(1746,plain,
    ~ gt(pv40,esk1_0),
    inference(cn,[status(thm)],[1745,theory(equality)]) ).

cnf(1747,plain,
    ( pv40 = esk1_0
    | ~ leq(esk1_0,pv40) ),
    inference(spm,[status(thm)],[1746,81,theory(equality)]) ).

cnf(1751,plain,
    ( pv40 = esk1_0
    | $false ),
    inference(rw,[status(thm)],[1747,177,theory(equality)]) ).

cnf(1752,plain,
    pv40 = esk1_0,
    inference(cn,[status(thm)],[1751,theory(equality)]) ).

cnf(1766,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[176,1752,theory(equality)]),237,theory(equality)]) ).

cnf(1767,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[1766,theory(equality)]) ).

cnf(1768,negated_conjecture,
    $false,
    1767,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV167+1.p
% --creating new selector for [SWV003+0.ax]
% -running prover on /tmp/tmpXDXDCS/sel_SWV167+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV167+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV167+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV167+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------