TSTP Solution File: SWV394+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWV394+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 12:36:48 EST 2010

% Result   : Theorem 238.97s
% Output   : CNFRefutation 238.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   65 (  10 unt;   0 def)
%            Number of atoms       :  201 (  13 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  223 (  87   ~;  87   |;  35   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   6 usr;   2 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :  180 (  12 sgn 115   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
     => remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',ax43) ).

fof(12,axiom,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & strictly_less_than(X4,lookup_slb(X2,X4)) )
     => remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',ax45) ).

fof(13,axiom,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & less_than(lookup_slb(X2,X4),X4) )
     => remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',ax44) ).

fof(15,axiom,
    ! [X1,X2] :
      ( ok(triple(X1,X2,bad))
    <=> ~ $true ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',ax40) ).

fof(20,axiom,
    ! [X1,X2] :
      ( less_than(X1,X2)
      | less_than(X2,X1) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',totality) ).

fof(21,axiom,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',stricly_smaller_definition) ).

fof(36,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
        & ok(remove_cpq(triple(X1,X2,X3),X4)) )
     => ! [X5] :
          ( pair_in_list(X2,X4,X5)
         => less_than(X5,X4) ) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',l30_co) ).

fof(37,axiom,
    ! [X1,X2,X3,X4,X5] :
      ( ( pair_in_list(X2,X4,X5)
        & strictly_less_than(X4,X5)
        & ok(remove_cpq(triple(X1,X2,X3),X4)) )
     => pair_in_list(remove_slb(X2,X4),X4,X5) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',l30_li3132) ).

fof(38,axiom,
    ! [X1,X2,X3] :
      ( check_cpq(triple(X1,X2,X3))
    <=> ! [X4,X5] :
          ( pair_in_list(X2,X4,X5)
         => less_than(X5,X4) ) ),
    file('/tmp/tmpIC5Y9q/sel_SWV394+1.p_5',l30_li4142) ).

fof(39,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
          & ok(remove_cpq(triple(X1,X2,X3),X4)) )
       => ! [X5] :
            ( pair_in_list(X2,X4,X5)
           => less_than(X5,X4) ) ),
    inference(assume_negation,[status(cth)],[36]) ).

fof(40,plain,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
     => remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
    inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).

fof(42,plain,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[21,theory(equality)]) ).

fof(46,plain,
    ! [X1,X2,X3,X4] :
      ( contains_slb(X2,X4)
      | remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
    inference(fof_nnf,[status(thm)],[40]) ).

fof(47,plain,
    ! [X5,X6,X7,X8] :
      ( contains_slb(X6,X8)
      | remove_cpq(triple(X5,X6,X7),X8) = triple(X5,X6,bad) ),
    inference(variable_rename,[status(thm)],[46]) ).

cnf(48,plain,
    ( remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad)
    | contains_slb(X2,X4) ),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(81,plain,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
      | ~ strictly_less_than(X4,lookup_slb(X2,X4))
      | remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(82,plain,
    ! [X5,X6,X7,X8] :
      ( ~ contains_slb(X6,X8)
      | ~ strictly_less_than(X8,lookup_slb(X6,X8))
      | remove_cpq(triple(X5,X6,X7),X8) = triple(remove_pqp(X5,X8),remove_slb(X6,X8),bad) ),
    inference(variable_rename,[status(thm)],[81]) ).

cnf(83,plain,
    ( remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad)
    | ~ strictly_less_than(X4,lookup_slb(X2,X4))
    | ~ contains_slb(X2,X4) ),
    inference(split_conjunct,[status(thm)],[82]) ).

fof(84,plain,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
      | ~ less_than(lookup_slb(X2,X4),X4)
      | remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(85,plain,
    ! [X5,X6,X7,X8] :
      ( ~ contains_slb(X6,X8)
      | ~ less_than(lookup_slb(X6,X8),X8)
      | remove_cpq(triple(X5,X6,X7),X8) = triple(remove_pqp(X5,X8),remove_slb(X6,X8),X7) ),
    inference(variable_rename,[status(thm)],[84]) ).

cnf(86,plain,
    ( remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3)
    | ~ less_than(lookup_slb(X2,X4),X4)
    | ~ contains_slb(X2,X4) ),
    inference(split_conjunct,[status(thm)],[85]) ).

fof(89,plain,
    ! [X1,X2] :
      ( ( ~ ok(triple(X1,X2,bad))
        | ~ $true )
      & ( $true
        | ok(triple(X1,X2,bad)) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(90,plain,
    ! [X3,X4] :
      ( ( ~ ok(triple(X3,X4,bad))
        | ~ $true )
      & ( $true
        | ok(triple(X3,X4,bad)) ) ),
    inference(variable_rename,[status(thm)],[89]) ).

cnf(92,plain,
    ( $false
    | ~ ok(triple(X1,X2,bad)) ),
    inference(split_conjunct,[status(thm)],[90]) ).

fof(107,plain,
    ! [X3,X4] :
      ( less_than(X3,X4)
      | less_than(X4,X3) ),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(108,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[107]) ).

fof(109,plain,
    ! [X1,X2] :
      ( ( ~ strictly_less_than(X1,X2)
        | ( less_than(X1,X2)
          & ~ less_than(X2,X1) ) )
      & ( ~ less_than(X1,X2)
        | less_than(X2,X1)
        | strictly_less_than(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(110,plain,
    ! [X3,X4] :
      ( ( ~ strictly_less_than(X3,X4)
        | ( less_than(X3,X4)
          & ~ less_than(X4,X3) ) )
      & ( ~ less_than(X3,X4)
        | less_than(X4,X3)
        | strictly_less_than(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[109]) ).

fof(111,plain,
    ! [X3,X4] :
      ( ( less_than(X3,X4)
        | ~ strictly_less_than(X3,X4) )
      & ( ~ less_than(X4,X3)
        | ~ strictly_less_than(X3,X4) )
      & ( ~ less_than(X3,X4)
        | less_than(X4,X3)
        | strictly_less_than(X3,X4) ) ),
    inference(distribute,[status(thm)],[110]) ).

cnf(112,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[111]) ).

fof(153,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( check_cpq(remove_cpq(triple(X1,X2,X3),X4))
      & ok(remove_cpq(triple(X1,X2,X3),X4))
      & ? [X5] :
          ( pair_in_list(X2,X4,X5)
          & ~ less_than(X5,X4) ) ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(154,negated_conjecture,
    ? [X6,X7,X8,X9] :
      ( check_cpq(remove_cpq(triple(X6,X7,X8),X9))
      & ok(remove_cpq(triple(X6,X7,X8),X9))
      & ? [X10] :
          ( pair_in_list(X7,X9,X10)
          & ~ less_than(X10,X9) ) ),
    inference(variable_rename,[status(thm)],[153]) ).

fof(155,negated_conjecture,
    ( check_cpq(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0))
    & ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0))
    & pair_in_list(esk2_0,esk4_0,esk5_0)
    & ~ less_than(esk5_0,esk4_0) ),
    inference(skolemize,[status(esa)],[154]) ).

cnf(156,negated_conjecture,
    ~ less_than(esk5_0,esk4_0),
    inference(split_conjunct,[status(thm)],[155]) ).

cnf(157,negated_conjecture,
    pair_in_list(esk2_0,esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[155]) ).

cnf(158,negated_conjecture,
    ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)),
    inference(split_conjunct,[status(thm)],[155]) ).

cnf(159,negated_conjecture,
    check_cpq(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)),
    inference(split_conjunct,[status(thm)],[155]) ).

fof(160,plain,
    ! [X1,X2,X3,X4,X5] :
      ( ~ pair_in_list(X2,X4,X5)
      | ~ strictly_less_than(X4,X5)
      | ~ ok(remove_cpq(triple(X1,X2,X3),X4))
      | pair_in_list(remove_slb(X2,X4),X4,X5) ),
    inference(fof_nnf,[status(thm)],[37]) ).

fof(161,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ~ pair_in_list(X7,X9,X10)
      | ~ strictly_less_than(X9,X10)
      | ~ ok(remove_cpq(triple(X6,X7,X8),X9))
      | pair_in_list(remove_slb(X7,X9),X9,X10) ),
    inference(variable_rename,[status(thm)],[160]) ).

cnf(162,plain,
    ( pair_in_list(remove_slb(X1,X2),X2,X3)
    | ~ ok(remove_cpq(triple(X4,X1,X5),X2))
    | ~ strictly_less_than(X2,X3)
    | ~ pair_in_list(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[161]) ).

fof(163,plain,
    ! [X1,X2,X3] :
      ( ( ~ check_cpq(triple(X1,X2,X3))
        | ! [X4,X5] :
            ( ~ pair_in_list(X2,X4,X5)
            | less_than(X5,X4) ) )
      & ( ? [X4,X5] :
            ( pair_in_list(X2,X4,X5)
            & ~ less_than(X5,X4) )
        | check_cpq(triple(X1,X2,X3)) ) ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(164,plain,
    ! [X6,X7,X8] :
      ( ( ~ check_cpq(triple(X6,X7,X8))
        | ! [X9,X10] :
            ( ~ pair_in_list(X7,X9,X10)
            | less_than(X10,X9) ) )
      & ( ? [X11,X12] :
            ( pair_in_list(X7,X11,X12)
            & ~ less_than(X12,X11) )
        | check_cpq(triple(X6,X7,X8)) ) ),
    inference(variable_rename,[status(thm)],[163]) ).

fof(165,plain,
    ! [X6,X7,X8] :
      ( ( ~ check_cpq(triple(X6,X7,X8))
        | ! [X9,X10] :
            ( ~ pair_in_list(X7,X9,X10)
            | less_than(X10,X9) ) )
      & ( ( pair_in_list(X7,esk6_3(X6,X7,X8),esk7_3(X6,X7,X8))
          & ~ less_than(esk7_3(X6,X7,X8),esk6_3(X6,X7,X8)) )
        | check_cpq(triple(X6,X7,X8)) ) ),
    inference(skolemize,[status(esa)],[164]) ).

fof(166,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( ~ pair_in_list(X7,X9,X10)
        | less_than(X10,X9)
        | ~ check_cpq(triple(X6,X7,X8)) )
      & ( ( pair_in_list(X7,esk6_3(X6,X7,X8),esk7_3(X6,X7,X8))
          & ~ less_than(esk7_3(X6,X7,X8),esk6_3(X6,X7,X8)) )
        | check_cpq(triple(X6,X7,X8)) ) ),
    inference(shift_quantors,[status(thm)],[165]) ).

fof(167,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( ~ pair_in_list(X7,X9,X10)
        | less_than(X10,X9)
        | ~ check_cpq(triple(X6,X7,X8)) )
      & ( pair_in_list(X7,esk6_3(X6,X7,X8),esk7_3(X6,X7,X8))
        | check_cpq(triple(X6,X7,X8)) )
      & ( ~ less_than(esk7_3(X6,X7,X8),esk6_3(X6,X7,X8))
        | check_cpq(triple(X6,X7,X8)) ) ),
    inference(distribute,[status(thm)],[166]) ).

cnf(170,plain,
    ( less_than(X4,X5)
    | ~ check_cpq(triple(X1,X2,X3))
    | ~ pair_in_list(X2,X5,X4) ),
    inference(split_conjunct,[status(thm)],[167]) ).

cnf(183,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[112,108]) ).

cnf(198,negated_conjecture,
    ( ok(triple(esk1_0,esk2_0,bad))
    | contains_slb(esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[158,48,theory(equality)]) ).

cnf(200,negated_conjecture,
    contains_slb(esk2_0,esk4_0),
    inference(sr,[status(thm)],[198,92,theory(equality)]) ).

cnf(214,negated_conjecture,
    ( pair_in_list(remove_slb(esk2_0,esk4_0),esk4_0,X1)
    | ~ pair_in_list(esk2_0,esk4_0,X1)
    | ~ strictly_less_than(esk4_0,X1) ),
    inference(spm,[status(thm)],[162,158,theory(equality)]) ).

cnf(251,plain,
    ( less_than(X1,X2)
    | ~ pair_in_list(remove_slb(X3,X4),X2,X1)
    | ~ check_cpq(remove_cpq(triple(X5,X3,X6),X4))
    | ~ less_than(lookup_slb(X3,X4),X4)
    | ~ contains_slb(X3,X4) ),
    inference(spm,[status(thm)],[170,86,theory(equality)]) ).

cnf(261,plain,
    ( ~ ok(remove_cpq(triple(X1,X3,X4),X2))
    | ~ strictly_less_than(X2,lookup_slb(X3,X2))
    | ~ contains_slb(X3,X2) ),
    inference(spm,[status(thm)],[92,83,theory(equality)]) ).

cnf(1491,negated_conjecture,
    ( ~ strictly_less_than(esk4_0,lookup_slb(esk2_0,esk4_0))
    | ~ contains_slb(esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[261,158,theory(equality)]) ).

cnf(1498,negated_conjecture,
    ( ~ strictly_less_than(esk4_0,lookup_slb(esk2_0,esk4_0))
    | $false ),
    inference(rw,[status(thm)],[1491,200,theory(equality)]) ).

cnf(1499,negated_conjecture,
    ~ strictly_less_than(esk4_0,lookup_slb(esk2_0,esk4_0)),
    inference(cn,[status(thm)],[1498,theory(equality)]) ).

cnf(1509,negated_conjecture,
    less_than(lookup_slb(esk2_0,esk4_0),esk4_0),
    inference(spm,[status(thm)],[1499,183,theory(equality)]) ).

cnf(3036,negated_conjecture,
    ( less_than(X1,X2)
    | ~ pair_in_list(remove_slb(esk2_0,esk4_0),X2,X1)
    | ~ less_than(lookup_slb(esk2_0,esk4_0),esk4_0)
    | ~ contains_slb(esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[251,159,theory(equality)]) ).

cnf(3046,negated_conjecture,
    ( less_than(X1,X2)
    | ~ pair_in_list(remove_slb(esk2_0,esk4_0),X2,X1)
    | $false
    | ~ contains_slb(esk2_0,esk4_0) ),
    inference(rw,[status(thm)],[3036,1509,theory(equality)]) ).

cnf(3047,negated_conjecture,
    ( less_than(X1,X2)
    | ~ pair_in_list(remove_slb(esk2_0,esk4_0),X2,X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3046,200,theory(equality)]) ).

cnf(3048,negated_conjecture,
    ( less_than(X1,X2)
    | ~ pair_in_list(remove_slb(esk2_0,esk4_0),X2,X1) ),
    inference(cn,[status(thm)],[3047,theory(equality)]) ).

cnf(3056,negated_conjecture,
    ( less_than(X1,esk4_0)
    | ~ pair_in_list(esk2_0,esk4_0,X1)
    | ~ strictly_less_than(esk4_0,X1) ),
    inference(spm,[status(thm)],[3048,214,theory(equality)]) ).

cnf(3057,negated_conjecture,
    ( less_than(X1,esk4_0)
    | ~ pair_in_list(esk2_0,esk4_0,X1) ),
    inference(csr,[status(thm)],[3056,183]) ).

cnf(3058,negated_conjecture,
    less_than(esk5_0,esk4_0),
    inference(spm,[status(thm)],[3057,157,theory(equality)]) ).

cnf(3059,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[3058,156,theory(equality)]) ).

cnf(3060,negated_conjecture,
    $false,
    3059,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV394+1.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax, SWV007+3.ax]
% eprover: CPU time limit exceeded, terminating
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpIC5Y9q/sel_SWV394+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpIC5Y9q/sel_SWV394+1.p_2 with time limit 80
% -prover status ResourceOut
% --creating new selector for [SWV007+0.ax, SWV007+2.ax, SWV007+3.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpIC5Y9q/sel_SWV394+1.p_3 with time limit 74
% -prover status ResourceOut
% --creating new selector for [SWV007+0.ax, SWV007+2.ax, SWV007+3.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpIC5Y9q/sel_SWV394+1.p_4 with time limit 55
% -prover status ResourceOut
% --creating new selector for [SWV007+0.ax, SWV007+2.ax, SWV007+3.ax]
% -running prover on /tmp/tmpIC5Y9q/sel_SWV394+1.p_5 with time limit 52
% -prover status Theorem
% Problem SWV394+1.p solved in phase 4.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV394+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV394+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
% 
%------------------------------------------------------------------------------