TSTP Solution File: SWV181+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWV181+1 : TPTP v5.0.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 12:22:11 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   76 (  33 unt;   0 def)
%            Number of atoms       :  317 (  72 equ)
%            Maximal formula atoms :   31 (   4 avg)
%            Number of connectives :  358 ( 117   ~; 120   |;  83   &)
%                                         (   1 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  15 con; 0-3 aty)
%            Number of variables   :  109 (   0 sgn  78   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1,X2,X3] :
      ( ( leq(X1,X2)
        & leq(X2,X3) )
     => leq(X1,X3) ),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',transitivity_leq) ).

fof(5,axiom,
    ! [X1,X2] :
      ( gt(X2,X1)
     => leq(X1,X2) ),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',leq_gt1) ).

fof(6,axiom,
    ! [X1] : plus(n1,X1) = succ(X1),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',succ_plus_1_l) ).

fof(14,axiom,
    ! [X1] : plus(X1,n1) = succ(X1),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',succ_plus_1_r) ).

fof(15,axiom,
    ! [X1] : ~ gt(X1,X1),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',irreflexivity_gt) ).

fof(16,axiom,
    ! [X1] : gt(succ(X1),X1),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',gt_succ) ).

fof(21,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> gt(succ(X2),X1) ),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',leq_succ_gt_equiv) ).

fof(36,axiom,
    gt(n1,n0),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',gt_1_0) ).

fof(39,conjecture,
    ( ( leq(tptp_float_0_001,pv76)
      & leq(n1,loopcounter)
      & gt(n1,loopcounter)
      & ! [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_select3(center_init,X6,n0) = init )
      & ( gt(loopcounter,n0)
       => ! [X7] :
            ( ( leq(n0,X7)
              & leq(X7,n4) )
           => a_select2(mu_init,X7) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X8] :
            ( ( leq(n0,X8)
              & leq(X8,n4) )
           => a_select2(rho_init,X8) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X9] :
            ( ( leq(n0,X9)
              & leq(X9,n4) )
           => a_select2(sigma_init,X9) = init ) ) )
   => ! [X10] :
        ( ( leq(n0,X10)
          & leq(X10,n4) )
       => a_select2(muold_init,X10) = init ) ),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',cl5_nebula_init_0081) ).

fof(54,axiom,
    ! [X1] :
      ( ( leq(n0,X1)
        & leq(X1,n1) )
     => ( X1 = n0
        | X1 = n1 ) ),
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',finite_domain_1) ).

fof(59,axiom,
    succ(n0) = n1,
    file('/tmp/tmpxzD-ZG/sel_SWV181+1.p_1',successor_1) ).

fof(64,negated_conjecture,
    ~ ( ( leq(tptp_float_0_001,pv76)
        & leq(n1,loopcounter)
        & gt(n1,loopcounter)
        & ! [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_select3(center_init,X6,n0) = init )
        & ( gt(loopcounter,n0)
         => ! [X7] :
              ( ( leq(n0,X7)
                & leq(X7,n4) )
             => a_select2(mu_init,X7) = init ) )
        & ( gt(loopcounter,n0)
         => ! [X8] :
              ( ( leq(n0,X8)
                & leq(X8,n4) )
             => a_select2(rho_init,X8) = init ) )
        & ( gt(loopcounter,n0)
         => ! [X9] :
              ( ( leq(n0,X9)
                & leq(X9,n4) )
             => a_select2(sigma_init,X9) = init ) ) )
     => ! [X10] :
          ( ( leq(n0,X10)
            & leq(X10,n4) )
         => a_select2(muold_init,X10) = init ) ),
    inference(assume_negation,[status(cth)],[39]) ).

fof(65,plain,
    ! [X1] : ~ gt(X1,X1),
    inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).

fof(66,plain,
    ( epred1_0
   => ( leq(tptp_float_0_001,pv76)
      & leq(n1,loopcounter)
      & gt(n1,loopcounter)
      & ! [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_select3(center_init,X6,n0) = init )
      & ( gt(loopcounter,n0)
       => ! [X7] :
            ( ( leq(n0,X7)
              & leq(X7,n4) )
           => a_select2(mu_init,X7) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X8] :
            ( ( leq(n0,X8)
              & leq(X8,n4) )
           => a_select2(rho_init,X8) = init ) )
      & ( gt(loopcounter,n0)
       => ! [X9] :
            ( ( leq(n0,X9)
              & leq(X9,n4) )
           => a_select2(sigma_init,X9) = init ) ) ) ),
    introduced(definition) ).

fof(67,negated_conjecture,
    ~ ( epred1_0
     => ! [X10] :
          ( ( leq(n0,X10)
            & leq(X10,n4) )
         => a_select2(muold_init,X10) = init ) ),
    inference(apply_def,[status(esa)],[64,66,theory(equality)]) ).

fof(73,plain,
    ! [X1,X2,X3] :
      ( ~ leq(X1,X2)
      | ~ leq(X2,X3)
      | leq(X1,X3) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(74,plain,
    ! [X4,X5,X6] :
      ( ~ leq(X4,X5)
      | ~ leq(X5,X6)
      | leq(X4,X6) ),
    inference(variable_rename,[status(thm)],[73]) ).

cnf(75,plain,
    ( leq(X1,X2)
    | ~ leq(X3,X2)
    | ~ leq(X1,X3) ),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(79,plain,
    ! [X1,X2] :
      ( ~ gt(X2,X1)
      | leq(X1,X2) ),
    inference(fof_nnf,[status(thm)],[5]) ).

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

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

fof(82,plain,
    ! [X2] : plus(n1,X2) = succ(X2),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(83,plain,
    plus(n1,X1) = succ(X1),
    inference(split_conjunct,[status(thm)],[82]) ).

fof(99,plain,
    ! [X2] : plus(X2,n1) = succ(X2),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(100,plain,
    plus(X1,n1) = succ(X1),
    inference(split_conjunct,[status(thm)],[99]) ).

fof(101,plain,
    ! [X2] : ~ gt(X2,X2),
    inference(variable_rename,[status(thm)],[65]) ).

cnf(102,plain,
    ~ gt(X1,X1),
    inference(split_conjunct,[status(thm)],[101]) ).

fof(103,plain,
    ! [X2] : gt(succ(X2),X2),
    inference(variable_rename,[status(thm)],[16]) ).

cnf(104,plain,
    gt(succ(X1),X1),
    inference(split_conjunct,[status(thm)],[103]) ).

fof(113,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | gt(succ(X2),X1) )
      & ( ~ gt(succ(X2),X1)
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(114,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | gt(succ(X4),X3) )
      & ( ~ gt(succ(X4),X3)
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[113]) ).

cnf(115,plain,
    ( leq(X1,X2)
    | ~ gt(succ(X2),X1) ),
    inference(split_conjunct,[status(thm)],[114]) ).

cnf(116,plain,
    ( gt(succ(X1),X2)
    | ~ leq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[114]) ).

cnf(135,plain,
    gt(n1,n0),
    inference(split_conjunct,[status(thm)],[36]) ).

fof(138,negated_conjecture,
    ( epred1_0
    & ? [X10] :
        ( leq(n0,X10)
        & leq(X10,n4)
        & a_select2(muold_init,X10) != init ) ),
    inference(fof_nnf,[status(thm)],[67]) ).

fof(139,negated_conjecture,
    ( epred1_0
    & ? [X11] :
        ( leq(n0,X11)
        & leq(X11,n4)
        & a_select2(muold_init,X11) != init ) ),
    inference(variable_rename,[status(thm)],[138]) ).

fof(140,negated_conjecture,
    ( epred1_0
    & leq(n0,esk1_0)
    & leq(esk1_0,n4)
    & a_select2(muold_init,esk1_0) != init ),
    inference(skolemize,[status(esa)],[139]) ).

cnf(144,negated_conjecture,
    epred1_0,
    inference(split_conjunct,[status(thm)],[140]) ).

fof(169,plain,
    ! [X1] :
      ( ~ leq(n0,X1)
      | ~ leq(X1,n1)
      | X1 = n0
      | X1 = n1 ),
    inference(fof_nnf,[status(thm)],[54]) ).

fof(170,plain,
    ! [X2] :
      ( ~ leq(n0,X2)
      | ~ leq(X2,n1)
      | X2 = n0
      | X2 = n1 ),
    inference(variable_rename,[status(thm)],[169]) ).

cnf(171,plain,
    ( X1 = n1
    | X1 = n0
    | ~ leq(X1,n1)
    | ~ leq(n0,X1) ),
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(176,plain,
    succ(n0) = n1,
    inference(split_conjunct,[status(thm)],[59]) ).

fof(181,plain,
    ( ~ epred1_0
    | ( leq(tptp_float_0_001,pv76)
      & leq(n1,loopcounter)
      & gt(n1,loopcounter)
      & ! [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_select3(center_init,X6,n0) = init )
      & ( ~ gt(loopcounter,n0)
        | ! [X7] :
            ( ~ leq(n0,X7)
            | ~ leq(X7,n4)
            | a_select2(mu_init,X7) = init ) )
      & ( ~ gt(loopcounter,n0)
        | ! [X8] :
            ( ~ leq(n0,X8)
            | ~ leq(X8,n4)
            | a_select2(rho_init,X8) = init ) )
      & ( ~ gt(loopcounter,n0)
        | ! [X9] :
            ( ~ leq(n0,X9)
            | ~ leq(X9,n4)
            | a_select2(sigma_init,X9) = init ) ) ) ),
    inference(fof_nnf,[status(thm)],[66]) ).

fof(182,plain,
    ( ~ epred1_0
    | ( leq(tptp_float_0_001,pv76)
      & leq(n1,loopcounter)
      & gt(n1,loopcounter)
      & ! [X10] :
          ( ~ leq(n0,X10)
          | ~ leq(X10,n135299)
          | ! [X11] :
              ( ~ leq(n0,X11)
              | ~ leq(X11,n4)
              | a_select3(q_init,X10,X11) = init ) )
      & ! [X12] :
          ( ~ leq(n0,X12)
          | ~ leq(X12,n4)
          | a_select3(center_init,X12,n0) = init )
      & ( ~ gt(loopcounter,n0)
        | ! [X13] :
            ( ~ leq(n0,X13)
            | ~ leq(X13,n4)
            | a_select2(mu_init,X13) = init ) )
      & ( ~ gt(loopcounter,n0)
        | ! [X14] :
            ( ~ leq(n0,X14)
            | ~ leq(X14,n4)
            | a_select2(rho_init,X14) = init ) )
      & ( ~ gt(loopcounter,n0)
        | ! [X15] :
            ( ~ leq(n0,X15)
            | ~ leq(X15,n4)
            | a_select2(sigma_init,X15) = init ) ) ) ),
    inference(variable_rename,[status(thm)],[181]) ).

fof(183,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ( ( ~ leq(n0,X15)
          | ~ leq(X15,n4)
          | a_select2(sigma_init,X15) = init
          | ~ gt(loopcounter,n0) )
        & ( ~ leq(n0,X14)
          | ~ leq(X14,n4)
          | a_select2(rho_init,X14) = init
          | ~ gt(loopcounter,n0) )
        & ( ~ leq(n0,X13)
          | ~ leq(X13,n4)
          | a_select2(mu_init,X13) = init
          | ~ gt(loopcounter,n0) )
        & ( ~ leq(n0,X12)
          | ~ leq(X12,n4)
          | a_select3(center_init,X12,n0) = init )
        & ( ~ leq(n0,X11)
          | ~ leq(X11,n4)
          | a_select3(q_init,X10,X11) = init
          | ~ leq(n0,X10)
          | ~ leq(X10,n135299) )
        & leq(tptp_float_0_001,pv76)
        & leq(n1,loopcounter)
        & gt(n1,loopcounter) )
      | ~ epred1_0 ),
    inference(shift_quantors,[status(thm)],[182]) ).

fof(184,plain,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ( ~ leq(n0,X15)
        | ~ leq(X15,n4)
        | a_select2(sigma_init,X15) = init
        | ~ gt(loopcounter,n0)
        | ~ epred1_0 )
      & ( ~ leq(n0,X14)
        | ~ leq(X14,n4)
        | a_select2(rho_init,X14) = init
        | ~ gt(loopcounter,n0)
        | ~ epred1_0 )
      & ( ~ leq(n0,X13)
        | ~ leq(X13,n4)
        | a_select2(mu_init,X13) = init
        | ~ gt(loopcounter,n0)
        | ~ epred1_0 )
      & ( ~ leq(n0,X12)
        | ~ leq(X12,n4)
        | a_select3(center_init,X12,n0) = init
        | ~ epred1_0 )
      & ( ~ leq(n0,X11)
        | ~ leq(X11,n4)
        | a_select3(q_init,X10,X11) = init
        | ~ leq(n0,X10)
        | ~ leq(X10,n135299)
        | ~ epred1_0 )
      & ( leq(tptp_float_0_001,pv76)
        | ~ epred1_0 )
      & ( leq(n1,loopcounter)
        | ~ epred1_0 )
      & ( gt(n1,loopcounter)
        | ~ epred1_0 ) ),
    inference(distribute,[status(thm)],[183]) ).

cnf(185,plain,
    ( gt(n1,loopcounter)
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[184]) ).

cnf(186,plain,
    ( leq(n1,loopcounter)
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[184]) ).

cnf(194,plain,
    plus(n0,n1) = n1,
    inference(rw,[status(thm)],[176,100,theory(equality)]),
    [unfolding] ).

cnf(195,plain,
    plus(n1,X1) = plus(X1,n1),
    inference(rw,[status(thm)],[83,100,theory(equality)]),
    [unfolding] ).

cnf(197,plain,
    gt(plus(X1,n1),X1),
    inference(rw,[status(thm)],[104,100,theory(equality)]),
    [unfolding] ).

cnf(209,plain,
    ( leq(X1,X2)
    | ~ gt(plus(X2,n1),X1) ),
    inference(rw,[status(thm)],[115,100,theory(equality)]),
    [unfolding] ).

cnf(212,plain,
    ( gt(plus(X1,n1),X2)
    | ~ leq(X2,X1) ),
    inference(rw,[status(thm)],[116,100,theory(equality)]),
    [unfolding] ).

cnf(215,plain,
    ( leq(n1,loopcounter)
    | $false ),
    inference(rw,[status(thm)],[186,144,theory(equality)]) ).

cnf(216,plain,
    leq(n1,loopcounter),
    inference(cn,[status(thm)],[215,theory(equality)]) ).

cnf(219,plain,
    ( gt(n1,loopcounter)
    | $false ),
    inference(rw,[status(thm)],[185,144,theory(equality)]) ).

cnf(220,plain,
    gt(n1,loopcounter),
    inference(cn,[status(thm)],[219,theory(equality)]) ).

cnf(225,plain,
    ( leq(X1,loopcounter)
    | ~ leq(X1,n1) ),
    inference(spm,[status(thm)],[75,216,theory(equality)]) ).

cnf(227,plain,
    ( leq(X1,X2)
    | ~ leq(X1,X3)
    | ~ gt(X2,X3) ),
    inference(spm,[status(thm)],[75,81,theory(equality)]) ).

cnf(234,plain,
    plus(n1,n0) = n1,
    inference(rw,[status(thm)],[194,195,theory(equality)]) ).

cnf(249,plain,
    ~ leq(plus(X1,n1),X1),
    inference(spm,[status(thm)],[102,212,theory(equality)]) ).

cnf(250,plain,
    leq(X1,X1),
    inference(spm,[status(thm)],[209,197,theory(equality)]) ).

cnf(256,plain,
    ( n0 = X1
    | n1 = X1
    | ~ leq(n0,X1)
    | ~ gt(n1,X1) ),
    inference(spm,[status(thm)],[171,81,theory(equality)]) ).

cnf(405,plain,
    ~ leq(plus(n1,X1),X1),
    inference(spm,[status(thm)],[249,195,theory(equality)]) ).

cnf(498,plain,
    ~ leq(n1,n0),
    inference(spm,[status(thm)],[405,234,theory(equality)]) ).

cnf(541,plain,
    ( leq(X1,n1)
    | ~ leq(X1,n0) ),
    inference(spm,[status(thm)],[227,135,theory(equality)]) ).

cnf(583,plain,
    leq(n0,n1),
    inference(spm,[status(thm)],[541,250,theory(equality)]) ).

cnf(1045,plain,
    ( n1 = loopcounter
    | n0 = loopcounter
    | ~ gt(n1,loopcounter)
    | ~ leq(n0,n1) ),
    inference(spm,[status(thm)],[256,225,theory(equality)]) ).

cnf(1065,plain,
    ( n1 = loopcounter
    | n0 = loopcounter
    | $false
    | ~ leq(n0,n1) ),
    inference(rw,[status(thm)],[1045,220,theory(equality)]) ).

cnf(1066,plain,
    ( n1 = loopcounter
    | n0 = loopcounter
    | $false
    | $false ),
    inference(rw,[status(thm)],[1065,583,theory(equality)]) ).

cnf(1067,plain,
    ( n1 = loopcounter
    | n0 = loopcounter ),
    inference(cn,[status(thm)],[1066,theory(equality)]) ).

cnf(1089,plain,
    ( leq(n1,n0)
    | loopcounter = n1 ),
    inference(spm,[status(thm)],[216,1067,theory(equality)]) ).

cnf(1093,plain,
    loopcounter = n1,
    inference(sr,[status(thm)],[1089,498,theory(equality)]) ).

cnf(1096,plain,
    gt(n1,n1),
    inference(rw,[status(thm)],[220,1093,theory(equality)]) ).

cnf(1097,plain,
    $false,
    inference(sr,[status(thm)],[1096,102,theory(equality)]) ).

cnf(1098,plain,
    $false,
    1097,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV181+1.p
% --creating new selector for [SWV003+0.ax]
% -running prover on /tmp/tmpxzD-ZG/sel_SWV181+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV181+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV181+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV181+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
% 
%------------------------------------------------------------------------------