TSTP Solution File: SWV408+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWV408+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 12:39:41 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   38 (  12 unt;   0 def)
%            Number of atoms       :  111 (  10 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  122 (  49   ~;  47   |;  22   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :   66 (   5 sgn  42   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(5,axiom,
    ! [X1] : ~ contains_slb(create_slb,X1),
    file('/tmp/tmpACb3YE/sel_SWV408+1.p_1',ax20) ).

fof(12,axiom,
    ! [X1,X2,X3,X4] :
      ( X2 != create_slb
     => findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
    file('/tmp/tmpACb3YE/sel_SWV408+1.p_1',ax51) ).

fof(19,axiom,
    ! [X1,X2,X3] :
      ( ( contains_slb(X1,X2)
        & strictly_less_than(X2,X3) )
     => ( pair_in_list(update_slb(X1,X3),X2,X3)
        | ? [X4] :
            ( pair_in_list(update_slb(X1,X3),X2,X4)
            & less_than(X3,X4) ) ) ),
    file('/tmp/tmpACb3YE/sel_SWV408+1.p_1',l44_l45) ).

fof(20,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
     => ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
        | ? [X5] :
            ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
            & less_than(findmin_pqp_res(X1),X5) ) ) ),
    file('/tmp/tmpACb3YE/sel_SWV408+1.p_1',l44_co) ).

fof(21,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( contains_slb(X2,X4)
          & strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
       => ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
          | ? [X5] :
              ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
              & less_than(findmin_pqp_res(X1),X5) ) ) ),
    inference(assume_negation,[status(cth)],[20]) ).

fof(22,plain,
    ! [X1] : ~ contains_slb(create_slb,X1),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(40,plain,
    ! [X2] : ~ contains_slb(create_slb,X2),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(41,plain,
    ~ contains_slb(create_slb,X1),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(61,plain,
    ! [X1,X2,X3,X4] :
      ( X2 = create_slb
      | findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(62,plain,
    ! [X5,X6,X7,X8] :
      ( X6 = create_slb
      | findmin_cpq_res(triple(X5,X6,X7)) = findmin_pqp_res(X5) ),
    inference(variable_rename,[status(thm)],[61]) ).

cnf(63,plain,
    ( findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1)
    | X2 = create_slb ),
    inference(split_conjunct,[status(thm)],[62]) ).

fof(83,plain,
    ! [X1,X2,X3] :
      ( ~ contains_slb(X1,X2)
      | ~ strictly_less_than(X2,X3)
      | pair_in_list(update_slb(X1,X3),X2,X3)
      | ? [X4] :
          ( pair_in_list(update_slb(X1,X3),X2,X4)
          & less_than(X3,X4) ) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(84,plain,
    ! [X5,X6,X7] :
      ( ~ contains_slb(X5,X6)
      | ~ strictly_less_than(X6,X7)
      | pair_in_list(update_slb(X5,X7),X6,X7)
      | ? [X8] :
          ( pair_in_list(update_slb(X5,X7),X6,X8)
          & less_than(X7,X8) ) ),
    inference(variable_rename,[status(thm)],[83]) ).

fof(85,plain,
    ! [X5,X6,X7] :
      ( ~ contains_slb(X5,X6)
      | ~ strictly_less_than(X6,X7)
      | pair_in_list(update_slb(X5,X7),X6,X7)
      | ( pair_in_list(update_slb(X5,X7),X6,esk1_3(X5,X6,X7))
        & less_than(X7,esk1_3(X5,X6,X7)) ) ),
    inference(skolemize,[status(esa)],[84]) ).

fof(86,plain,
    ! [X5,X6,X7] :
      ( ( pair_in_list(update_slb(X5,X7),X6,esk1_3(X5,X6,X7))
        | pair_in_list(update_slb(X5,X7),X6,X7)
        | ~ contains_slb(X5,X6)
        | ~ strictly_less_than(X6,X7) )
      & ( less_than(X7,esk1_3(X5,X6,X7))
        | pair_in_list(update_slb(X5,X7),X6,X7)
        | ~ contains_slb(X5,X6)
        | ~ strictly_less_than(X6,X7) ) ),
    inference(distribute,[status(thm)],[85]) ).

cnf(87,plain,
    ( pair_in_list(update_slb(X3,X2),X1,X2)
    | less_than(X2,esk1_3(X3,X1,X2))
    | ~ strictly_less_than(X1,X2)
    | ~ contains_slb(X3,X1) ),
    inference(split_conjunct,[status(thm)],[86]) ).

cnf(88,plain,
    ( pair_in_list(update_slb(X3,X2),X1,X2)
    | pair_in_list(update_slb(X3,X2),X1,esk1_3(X3,X1,X2))
    | ~ strictly_less_than(X1,X2)
    | ~ contains_slb(X3,X1) ),
    inference(split_conjunct,[status(thm)],[86]) ).

fof(89,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( contains_slb(X2,X4)
      & strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3)))
      & ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
      & ! [X5] :
          ( ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
          | ~ less_than(findmin_pqp_res(X1),X5) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(90,negated_conjecture,
    ? [X6,X7,X8,X9] :
      ( contains_slb(X7,X9)
      & strictly_less_than(X9,findmin_cpq_res(triple(X6,X7,X8)))
      & ~ pair_in_list(update_slb(X7,findmin_pqp_res(X6)),X9,findmin_pqp_res(X6))
      & ! [X10] :
          ( ~ pair_in_list(update_slb(X7,findmin_pqp_res(X6)),X9,X10)
          | ~ less_than(findmin_pqp_res(X6),X10) ) ),
    inference(variable_rename,[status(thm)],[89]) ).

fof(91,negated_conjecture,
    ( contains_slb(esk3_0,esk5_0)
    & strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0)))
    & ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    & ! [X10] :
        ( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X10)
        | ~ less_than(findmin_pqp_res(esk2_0),X10) ) ),
    inference(skolemize,[status(esa)],[90]) ).

fof(92,negated_conjecture,
    ! [X10] :
      ( ( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X10)
        | ~ less_than(findmin_pqp_res(esk2_0),X10) )
      & ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
      & contains_slb(esk3_0,esk5_0)
      & strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0))) ),
    inference(shift_quantors,[status(thm)],[91]) ).

cnf(93,negated_conjecture,
    strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0))),
    inference(split_conjunct,[status(thm)],[92]) ).

cnf(94,negated_conjecture,
    contains_slb(esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[92]) ).

cnf(95,negated_conjecture,
    ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0)),
    inference(split_conjunct,[status(thm)],[92]) ).

cnf(96,negated_conjecture,
    ( ~ less_than(findmin_pqp_res(esk2_0),X1)
    | ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X1) ),
    inference(split_conjunct,[status(thm)],[92]) ).

cnf(109,negated_conjecture,
    ( strictly_less_than(esk5_0,findmin_pqp_res(esk2_0))
    | create_slb = esk3_0 ),
    inference(spm,[status(thm)],[93,63,theory(equality)]) ).

cnf(139,plain,
    ( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    | ~ less_than(findmin_pqp_res(esk2_0),esk1_3(esk3_0,esk5_0,findmin_pqp_res(esk2_0)))
    | ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0))
    | ~ contains_slb(esk3_0,esk5_0) ),
    inference(spm,[status(thm)],[96,88,theory(equality)]) ).

cnf(143,plain,
    ( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    | ~ less_than(findmin_pqp_res(esk2_0),esk1_3(esk3_0,esk5_0,findmin_pqp_res(esk2_0)))
    | ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0))
    | $false ),
    inference(rw,[status(thm)],[139,94,theory(equality)]) ).

cnf(144,plain,
    ( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    | ~ less_than(findmin_pqp_res(esk2_0),esk1_3(esk3_0,esk5_0,findmin_pqp_res(esk2_0)))
    | ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0)) ),
    inference(cn,[status(thm)],[143,theory(equality)]) ).

cnf(145,plain,
    ( ~ less_than(findmin_pqp_res(esk2_0),esk1_3(esk3_0,esk5_0,findmin_pqp_res(esk2_0)))
    | ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0)) ),
    inference(sr,[status(thm)],[144,95,theory(equality)]) ).

cnf(190,plain,
    ( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    | ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0))
    | ~ contains_slb(esk3_0,esk5_0) ),
    inference(spm,[status(thm)],[145,87,theory(equality)]) ).

cnf(191,plain,
    ( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    | ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0))
    | $false ),
    inference(rw,[status(thm)],[190,94,theory(equality)]) ).

cnf(192,plain,
    ( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    | ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0)) ),
    inference(cn,[status(thm)],[191,theory(equality)]) ).

cnf(193,plain,
    ~ strictly_less_than(esk5_0,findmin_pqp_res(esk2_0)),
    inference(sr,[status(thm)],[192,95,theory(equality)]) ).

cnf(195,negated_conjecture,
    esk3_0 = create_slb,
    inference(sr,[status(thm)],[109,193,theory(equality)]) ).

cnf(198,negated_conjecture,
    contains_slb(create_slb,esk5_0),
    inference(rw,[status(thm)],[94,195,theory(equality)]) ).

cnf(199,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[198,41,theory(equality)]) ).

cnf(200,negated_conjecture,
    $false,
    199,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV408+1.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax, SWV007+3.ax]
% -running prover on /tmp/tmpACb3YE/sel_SWV408+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV408+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV408+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV408+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
% 
%------------------------------------------------------------------------------