TSTP Solution File: SWV408+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWV408+2 : 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 12:39:45 EST 2010

% Result   : Theorem 0.25s
% Output   : CNFRefutation 0.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   42 (   7 unt;   0 def)
%            Number of atoms       :  121 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  132 (  53   ~;  46   |;  26   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   96 (   0 sgn  58   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(10,axiom,
    ! [X1,X2] :
      ( less_than(X1,X2)
      | less_than(X2,X1) ),
    file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',totality) ).

fof(11,axiom,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',stricly_smaller_definition) ).

fof(19,axiom,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & strictly_less_than(X3,X4) )
     => pair_in_list(update_slb(X1,X4),X2,X4) ),
    file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',l48_li3839) ).

fof(20,axiom,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & less_than(X4,X3) )
     => pair_in_list(update_slb(X1,X4),X2,X3) ),
    file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',l49_li3637) ).

fof(21,axiom,
    ! [X1,X2] :
      ( contains_slb(X1,X2)
     => ? [X3] : pair_in_list(X1,X2,X3) ),
    file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',l45_li4647) ).

fof(22,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/tmpz3GHNm/sel_SWV408+2.p_1',l44_co) ).

fof(23,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)],[22]) ).

fof(25,plain,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).

fof(55,plain,
    ! [X3,X4] :
      ( less_than(X3,X4)
      | less_than(X4,X3) ),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(56,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(57,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)],[25]) ).

fof(58,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)],[57]) ).

fof(59,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)],[58]) ).

cnf(60,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[59]) ).

fof(85,plain,
    ! [X1,X2,X3,X4] :
      ( ~ pair_in_list(X1,X2,X3)
      | ~ strictly_less_than(X3,X4)
      | pair_in_list(update_slb(X1,X4),X2,X4) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(86,plain,
    ! [X5,X6,X7,X8] :
      ( ~ pair_in_list(X5,X6,X7)
      | ~ strictly_less_than(X7,X8)
      | pair_in_list(update_slb(X5,X8),X6,X8) ),
    inference(variable_rename,[status(thm)],[85]) ).

cnf(87,plain,
    ( pair_in_list(update_slb(X1,X2),X3,X2)
    | ~ strictly_less_than(X4,X2)
    | ~ pair_in_list(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[86]) ).

fof(88,plain,
    ! [X1,X2,X3,X4] :
      ( ~ pair_in_list(X1,X2,X3)
      | ~ less_than(X4,X3)
      | pair_in_list(update_slb(X1,X4),X2,X3) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(89,plain,
    ! [X5,X6,X7,X8] :
      ( ~ pair_in_list(X5,X6,X7)
      | ~ less_than(X8,X7)
      | pair_in_list(update_slb(X5,X8),X6,X7) ),
    inference(variable_rename,[status(thm)],[88]) ).

cnf(90,plain,
    ( pair_in_list(update_slb(X1,X2),X3,X4)
    | ~ less_than(X2,X4)
    | ~ pair_in_list(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[89]) ).

fof(91,plain,
    ! [X1,X2] :
      ( ~ contains_slb(X1,X2)
      | ? [X3] : pair_in_list(X1,X2,X3) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(92,plain,
    ! [X4,X5] :
      ( ~ contains_slb(X4,X5)
      | ? [X6] : pair_in_list(X4,X5,X6) ),
    inference(variable_rename,[status(thm)],[91]) ).

fof(93,plain,
    ! [X4,X5] :
      ( ~ contains_slb(X4,X5)
      | pair_in_list(X4,X5,esk1_2(X4,X5)) ),
    inference(skolemize,[status(esa)],[92]) ).

cnf(94,plain,
    ( pair_in_list(X1,X2,esk1_2(X1,X2))
    | ~ contains_slb(X1,X2) ),
    inference(split_conjunct,[status(thm)],[93]) ).

fof(95,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)],[23]) ).

fof(96,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)],[95]) ).

fof(97,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)],[96]) ).

fof(98,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)],[97]) ).

cnf(100,negated_conjecture,
    contains_slb(esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[98]) ).

cnf(101,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)],[98]) ).

cnf(102,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)],[98]) ).

cnf(109,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[60,56]) ).

cnf(123,plain,
    ( ~ less_than(findmin_pqp_res(esk2_0),X1)
    | ~ pair_in_list(esk3_0,esk5_0,X1) ),
    inference(spm,[status(thm)],[102,90,theory(equality)]) ).

cnf(124,plain,
    ( pair_in_list(update_slb(X1,X2),X3,X2)
    | ~ strictly_less_than(esk1_2(X1,X3),X2)
    | ~ contains_slb(X1,X3) ),
    inference(spm,[status(thm)],[87,94,theory(equality)]) ).

cnf(254,plain,
    ( pair_in_list(update_slb(X1,X2),X3,X2)
    | less_than(X2,esk1_2(X1,X3))
    | ~ contains_slb(X1,X3) ),
    inference(spm,[status(thm)],[124,109,theory(equality)]) ).

cnf(1304,negated_conjecture,
    ( pair_in_list(update_slb(esk3_0,X1),esk5_0,X1)
    | less_than(X1,esk1_2(esk3_0,esk5_0)) ),
    inference(spm,[status(thm)],[254,100,theory(equality)]) ).

cnf(1395,negated_conjecture,
    ( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
    | ~ pair_in_list(esk3_0,esk5_0,esk1_2(esk3_0,esk5_0)) ),
    inference(spm,[status(thm)],[123,1304,theory(equality)]) ).

cnf(1404,negated_conjecture,
    ~ pair_in_list(esk3_0,esk5_0,esk1_2(esk3_0,esk5_0)),
    inference(sr,[status(thm)],[1395,101,theory(equality)]) ).

cnf(1429,plain,
    ~ contains_slb(esk3_0,esk5_0),
    inference(spm,[status(thm)],[1404,94,theory(equality)]) ).

cnf(1430,plain,
    $false,
    inference(rw,[status(thm)],[1429,100,theory(equality)]) ).

cnf(1431,plain,
    $false,
    inference(cn,[status(thm)],[1430,theory(equality)]) ).

cnf(1432,plain,
    $false,
    1431,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV408+2.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax, SWV007+3.ax]
% -running prover on /tmp/tmpz3GHNm/sel_SWV408+2.p_1 with time limit 29
% -prover status Theorem
% Problem SWV408+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV408+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV408+2.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
% 
%------------------------------------------------------------------------------