TSTP Solution File: LCL894+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : LCL894+1 : TPTP v5.5.0. Released v5.5.0.
% 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 @ 2800MHz
% Memory   : 2005MB
% OS       : Linux 2.6.32.26-175.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Mon Oct 22 18:23:41 EDT 2012

% Result   : Theorem 1.81s
% Output   : CNFRefutation 1.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   91 (  36 unt;   0 def)
%            Number of atoms       :  174 (  13 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  147 (  64   ~;  66   |;  10   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  144 (  12 sgn  56   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] : '>='(X1,'0'),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_08) ).

fof(2,axiom,
    ! [X2,X3,X4] :
      ( '>='(X2,X3)
     => '>='('+'(X2,X4),'+'(X3,X4)) ),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_09) ).

fof(3,conjecture,
    ( ( '>='(c,a)
      & '>='(c,b) )
  <=> '>='(c,'+'(a,'==>'(a,b))) ),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',goals_13) ).

fof(4,axiom,
    ! [X1,X5] : equal('+'(X1,X5),'+'(X5,X1)),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_02) ).

fof(5,axiom,
    ! [X1] : equal('+'(X1,'0'),X1),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_03) ).

fof(7,axiom,
    ! [X7,X8] :
      ( ( '>='(X7,X8)
        & '>='(X8,X7) )
     => equal(X7,X8) ),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_06) ).

fof(8,axiom,
    ! [X9,X10,X11] :
      ( '>='('+'(X9,X10),X11)
    <=> '>='(X10,'==>'(X9,X11)) ),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_07) ).

fof(9,axiom,
    ! [X1] : '>='(X1,X1),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_04) ).

fof(10,axiom,
    ! [X12,X13,X14] :
      ( ( '>='(X12,X13)
        & '>='(X13,X14) )
     => '>='(X12,X14) ),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_05) ).

fof(12,axiom,
    ! [X18,X19,X20] :
      ( '>='(X18,X19)
     => '>='('==>'(X19,X20),'==>'(X18,X20)) ),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_10) ).

fof(13,axiom,
    ! [X1,X5] : equal('+'(X1,'==>'(X1,X5)),'+'(X5,'==>'(X5,X1))),
    file('/tmp/tmpLNyzZM/sel_LCL894+1.p_1',sos_12) ).

fof(14,negated_conjecture,
    ~ ( ( '>='(c,a)
        & '>='(c,b) )
    <=> '>='(c,'+'(a,'==>'(a,b))) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(15,plain,
    ! [X2] : '>='(X2,'0'),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(16,plain,
    '>='(X1,'0'),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(17,plain,
    ! [X2,X3,X4] :
      ( ~ '>='(X2,X3)
      | '>='('+'(X2,X4),'+'(X3,X4)) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(18,plain,
    ! [X5,X6,X7] :
      ( ~ '>='(X5,X6)
      | '>='('+'(X5,X7),'+'(X6,X7)) ),
    inference(variable_rename,[status(thm)],[17]) ).

cnf(19,plain,
    ( '>='('+'(X1,X2),'+'(X3,X2))
    | ~ '>='(X1,X3) ),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(20,negated_conjecture,
    ( ( ~ '>='(c,a)
      | ~ '>='(c,b)
      | ~ '>='(c,'+'(a,'==>'(a,b))) )
    & ( ( '>='(c,a)
        & '>='(c,b) )
      | '>='(c,'+'(a,'==>'(a,b))) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(21,negated_conjecture,
    ( ( ~ '>='(c,a)
      | ~ '>='(c,b)
      | ~ '>='(c,'+'(a,'==>'(a,b))) )
    & ( '>='(c,a)
      | '>='(c,'+'(a,'==>'(a,b))) )
    & ( '>='(c,b)
      | '>='(c,'+'(a,'==>'(a,b))) ) ),
    inference(distribute,[status(thm)],[20]) ).

cnf(22,negated_conjecture,
    ( '>='(c,'+'(a,'==>'(a,b)))
    | '>='(c,b) ),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(23,negated_conjecture,
    ( '>='(c,'+'(a,'==>'(a,b)))
    | '>='(c,a) ),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(24,negated_conjecture,
    ( ~ '>='(c,'+'(a,'==>'(a,b)))
    | ~ '>='(c,b)
    | ~ '>='(c,a) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(25,plain,
    ! [X6,X7] : equal('+'(X6,X7),'+'(X7,X6)),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(26,plain,
    '+'(X1,X2) = '+'(X2,X1),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(27,plain,
    ! [X2] : equal('+'(X2,'0'),X2),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(28,plain,
    '+'(X1,'0') = X1,
    inference(split_conjunct,[status(thm)],[27]) ).

fof(31,plain,
    ! [X7,X8] :
      ( ~ '>='(X7,X8)
      | ~ '>='(X8,X7)
      | equal(X7,X8) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(32,plain,
    ! [X9,X10] :
      ( ~ '>='(X9,X10)
      | ~ '>='(X10,X9)
      | equal(X9,X10) ),
    inference(variable_rename,[status(thm)],[31]) ).

cnf(33,plain,
    ( X1 = X2
    | ~ '>='(X2,X1)
    | ~ '>='(X1,X2) ),
    inference(split_conjunct,[status(thm)],[32]) ).

fof(34,plain,
    ! [X9,X10,X11] :
      ( ( ~ '>='('+'(X9,X10),X11)
        | '>='(X10,'==>'(X9,X11)) )
      & ( ~ '>='(X10,'==>'(X9,X11))
        | '>='('+'(X9,X10),X11) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(35,plain,
    ! [X12,X13,X14] :
      ( ( ~ '>='('+'(X12,X13),X14)
        | '>='(X13,'==>'(X12,X14)) )
      & ( ~ '>='(X13,'==>'(X12,X14))
        | '>='('+'(X12,X13),X14) ) ),
    inference(variable_rename,[status(thm)],[34]) ).

cnf(36,plain,
    ( '>='('+'(X1,X2),X3)
    | ~ '>='(X2,'==>'(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(37,plain,
    ( '>='(X1,'==>'(X2,X3))
    | ~ '>='('+'(X2,X1),X3) ),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(38,plain,
    ! [X2] : '>='(X2,X2),
    inference(variable_rename,[status(thm)],[9]) ).

cnf(39,plain,
    '>='(X1,X1),
    inference(split_conjunct,[status(thm)],[38]) ).

fof(40,plain,
    ! [X12,X13,X14] :
      ( ~ '>='(X12,X13)
      | ~ '>='(X13,X14)
      | '>='(X12,X14) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(41,plain,
    ! [X15,X16,X17] :
      ( ~ '>='(X15,X16)
      | ~ '>='(X16,X17)
      | '>='(X15,X17) ),
    inference(variable_rename,[status(thm)],[40]) ).

cnf(42,plain,
    ( '>='(X1,X2)
    | ~ '>='(X3,X2)
    | ~ '>='(X1,X3) ),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(46,plain,
    ! [X18,X19,X20] :
      ( ~ '>='(X18,X19)
      | '>='('==>'(X19,X20),'==>'(X18,X20)) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(47,plain,
    ! [X21,X22,X23] :
      ( ~ '>='(X21,X22)
      | '>='('==>'(X22,X23),'==>'(X21,X23)) ),
    inference(variable_rename,[status(thm)],[46]) ).

cnf(48,plain,
    ( '>='('==>'(X1,X2),'==>'(X3,X2))
    | ~ '>='(X3,X1) ),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(49,plain,
    ! [X6,X7] : equal('+'(X6,'==>'(X6,X7)),'+'(X7,'==>'(X7,X6))),
    inference(variable_rename,[status(thm)],[13]) ).

cnf(50,plain,
    '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(51,plain,
    '+'('0',X1) = X1,
    inference(spm,[status(thm)],[28,26,theory(equality)]) ).

cnf(53,plain,
    ( '0' = X1
    | ~ '>='('0',X1) ),
    inference(spm,[status(thm)],[33,16,theory(equality)]) ).

cnf(63,plain,
    ( '>='('+'(X2,X1),'+'(X3,X2))
    | ~ '>='(X1,X3) ),
    inference(spm,[status(thm)],[19,26,theory(equality)]) ).

cnf(79,plain,
    ( '==>'(X1,X2) = X3
    | ~ '>='('==>'(X1,X2),X3)
    | ~ '>='('+'(X1,X3),X2) ),
    inference(spm,[status(thm)],[33,37,theory(equality)]) ).

cnf(80,plain,
    ( '>='(X1,'==>'(X2,X3))
    | ~ '>='(X1,X4)
    | ~ '>='('+'(X2,X4),X3) ),
    inference(spm,[status(thm)],[42,37,theory(equality)]) ).

cnf(81,plain,
    '>='('+'(X1,'==>'(X1,X2)),X2),
    inference(spm,[status(thm)],[36,39,theory(equality)]) ).

cnf(113,plain,
    ( '>='('+'(X1,X2),X2)
    | ~ '>='(X1,'0') ),
    inference(spm,[status(thm)],[19,51,theory(equality)]) ).

cnf(117,plain,
    ( '>='('+'(X1,X2),X2)
    | $false ),
    inference(rw,[status(thm)],[113,16,theory(equality)]) ).

cnf(118,plain,
    '>='('+'(X1,X2),X2),
    inference(cn,[status(thm)],[117,theory(equality)]) ).

cnf(121,plain,
    '>='('==>'('0',X1),X1),
    inference(spm,[status(thm)],[81,51,theory(equality)]) ).

cnf(125,plain,
    ( '>='(X1,X2)
    | ~ '>='(X1,'+'(X3,'==>'(X3,X2))) ),
    inference(spm,[status(thm)],[42,81,theory(equality)]) ).

cnf(130,plain,
    '>='('+'(X2,X1),X2),
    inference(spm,[status(thm)],[118,26,theory(equality)]) ).

cnf(147,plain,
    ( '>='(X1,X2)
    | ~ '>='(X1,'+'(X2,X3)) ),
    inference(spm,[status(thm)],[42,130,theory(equality)]) ).

cnf(156,plain,
    ( '0' = '==>'(X1,X2)
    | ~ '>='('+'(X1,'0'),X2) ),
    inference(spm,[status(thm)],[53,37,theory(equality)]) ).

cnf(157,plain,
    ( '0' = '==>'(X1,X2)
    | ~ '>='(X1,X2) ),
    inference(rw,[status(thm)],[156,28,theory(equality)]) ).

cnf(380,negated_conjecture,
    '>='(c,a),
    inference(spm,[status(thm)],[147,23,theory(equality)]) ).

cnf(392,negated_conjecture,
    ( '>='(X1,a)
    | ~ '>='(X1,c) ),
    inference(spm,[status(thm)],[42,380,theory(equality)]) ).

cnf(399,negated_conjecture,
    ( ~ '>='(c,'+'(a,'==>'(a,b)))
    | $false
    | ~ '>='(c,b) ),
    inference(rw,[status(thm)],[24,380,theory(equality)]) ).

cnf(400,negated_conjecture,
    ( ~ '>='(c,'+'(a,'==>'(a,b)))
    | ~ '>='(c,b) ),
    inference(cn,[status(thm)],[399,theory(equality)]) ).

cnf(405,negated_conjecture,
    '>='('+'(X1,'==>'(X1,c)),a),
    inference(spm,[status(thm)],[392,81,theory(equality)]) ).

cnf(512,plain,
    ( '>='('+'(X2,'==>'(X2,X1)),'+'(X3,X1))
    | ~ '>='('==>'(X1,X2),X3) ),
    inference(spm,[status(thm)],[63,50,theory(equality)]) ).

cnf(774,plain,
    ( '>='('0','==>'(X3,X2))
    | ~ '>='(X3,X1)
    | ~ '>='(X1,X2) ),
    inference(spm,[status(thm)],[48,157,theory(equality)]) ).

cnf(1478,plain,
    ( '==>'('0',X1) = X1
    | ~ '>='('+'('0',X1),X1) ),
    inference(spm,[status(thm)],[79,121,theory(equality)]) ).

cnf(1498,plain,
    ( '==>'('0',X1) = X1
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1478,51,theory(equality)]),39,theory(equality)]) ).

cnf(1499,plain,
    '==>'('0',X1) = X1,
    inference(cn,[status(thm)],[1498,theory(equality)]) ).

cnf(1525,plain,
    ( '>='(X1,'==>'(X2,X1))
    | ~ '>='(X2,'0') ),
    inference(spm,[status(thm)],[48,1499,theory(equality)]) ).

cnf(1608,plain,
    ( '>='(X1,'==>'(X2,X1))
    | $false ),
    inference(rw,[status(thm)],[1525,16,theory(equality)]) ).

cnf(1609,plain,
    '>='(X1,'==>'(X2,X1)),
    inference(cn,[status(thm)],[1608,theory(equality)]) ).

cnf(1730,negated_conjecture,
    ( '>='(X1,'==>'(X2,a))
    | ~ '>='(X1,'==>'(X2,c)) ),
    inference(spm,[status(thm)],[80,405,theory(equality)]) ).

cnf(3734,negated_conjecture,
    '>='(c,b),
    inference(spm,[status(thm)],[125,22,theory(equality)]) ).

cnf(3781,negated_conjecture,
    ( ~ '>='(c,'+'(a,'==>'(a,b)))
    | $false ),
    inference(rw,[status(thm)],[400,3734,theory(equality)]) ).

cnf(3782,negated_conjecture,
    ~ '>='(c,'+'(a,'==>'(a,b))),
    inference(cn,[status(thm)],[3781,theory(equality)]) ).

cnf(19368,negated_conjecture,
    ( '>='('0','==>'(c,X1))
    | ~ '>='(b,X1) ),
    inference(spm,[status(thm)],[774,3734,theory(equality)]) ).

cnf(19536,negated_conjecture,
    ( '>='('+'(c,'0'),X1)
    | ~ '>='(b,X1) ),
    inference(spm,[status(thm)],[36,19368,theory(equality)]) ).

cnf(19565,negated_conjecture,
    ( '>='(c,X1)
    | ~ '>='(b,X1) ),
    inference(rw,[status(thm)],[19536,28,theory(equality)]) ).

cnf(19581,negated_conjecture,
    '>='(c,'==>'(X1,b)),
    inference(spm,[status(thm)],[19565,1609,theory(equality)]) ).

cnf(19604,negated_conjecture,
    '>='('+'(X1,c),b),
    inference(spm,[status(thm)],[36,19581,theory(equality)]) ).

cnf(19626,negated_conjecture,
    '>='('+'(c,X1),b),
    inference(spm,[status(thm)],[19604,26,theory(equality)]) ).

cnf(19796,negated_conjecture,
    ( '>='(X1,'==>'(c,b))
    | ~ '>='(X1,X2) ),
    inference(spm,[status(thm)],[80,19626,theory(equality)]) ).

cnf(25923,negated_conjecture,
    '>='(X1,'==>'(c,b)),
    inference(spm,[status(thm)],[19796,39,theory(equality)]) ).

cnf(26273,negated_conjecture,
    '0' = '==>'(c,b),
    inference(spm,[status(thm)],[53,25923,theory(equality)]) ).

cnf(26376,negated_conjecture,
    ( '>='('+'(c,'0'),'+'(X1,b))
    | ~ '>='('==>'(b,c),X1) ),
    inference(spm,[status(thm)],[512,26273,theory(equality)]) ).

cnf(26481,negated_conjecture,
    ( '>='(c,'+'(X1,b))
    | ~ '>='('==>'(b,c),X1) ),
    inference(rw,[status(thm)],[26376,28,theory(equality)]) ).

cnf(49370,negated_conjecture,
    '>='('==>'(X1,c),'==>'(X1,a)),
    inference(spm,[status(thm)],[1730,39,theory(equality)]) ).

cnf(49572,negated_conjecture,
    '>='(c,'+'('==>'(b,a),b)),
    inference(spm,[status(thm)],[26481,49370,theory(equality)]) ).

cnf(49612,negated_conjecture,
    '>='(c,'+'(a,'==>'(a,b))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[49572,26,theory(equality)]),50,theory(equality)]) ).

cnf(49613,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[49612,3782,theory(equality)]) ).

cnf(49614,negated_conjecture,
    $false,
    49613,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LCL/LCL894+1.p
% --creating new selector for []
% -running prover on /tmp/tmpLNyzZM/sel_LCL894+1.p_1 with time limit 29
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/tmp/tmpLNyzZM/sel_LCL894+1.p_1']
% -prover status Theorem
% Problem LCL894+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LCL/LCL894+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LCL/LCL894+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
% 
%------------------------------------------------------------------------------