TSTP Solution File: GRP659+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GRP659+1 : TPTP v5.0.0. Released v4.0.0.
% 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 : Sat Dec 25 11:21:06 EST 2010

% Result   : Theorem 0.55s
% Output   : CNFRefutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   47
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   91 (  85 unt;   0 def)
%            Number of atoms       :   97 (  94 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   16 (  10   ~;   4   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 1-2 aty)
%            Number of variables   :  171 (   0 sgn  27   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] : mult(mult(X3,mult(X2,X1)),X2) = mult(mult(X3,X2),mult(X1,X2)),
    file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f05) ).

fof(2,axiom,
    ! [X2,X3] : rd(mult(X3,X2),X2) = X3,
    file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f04) ).

fof(3,axiom,
    ! [X2,X3] : mult(X3,ld(X3,X2)) = X2,
    file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f01) ).

fof(4,conjecture,
    ? [X4] :
    ! [X5] :
      ( mult(X5,X4) = X5
      & mult(X4,X5) = X5 ),
    file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',goals) ).

fof(5,axiom,
    ! [X2,X3] : mult(rd(X3,X2),X2) = X3,
    file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f03) ).

fof(6,axiom,
    ! [X2,X3] : ld(X3,mult(X3,X2)) = X2,
    file('/tmp/tmp82WwnO/sel_GRP659+1.p_1',f02) ).

fof(7,negated_conjecture,
    ~ ? [X4] :
      ! [X5] :
        ( mult(X5,X4) = X5
        & mult(X4,X5) = X5 ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(8,plain,
    ! [X4,X5,X6] : mult(mult(X6,mult(X5,X4)),X5) = mult(mult(X6,X5),mult(X4,X5)),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(9,plain,
    mult(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),mult(X3,X2)),
    inference(split_conjunct,[status(thm)],[8]) ).

fof(10,plain,
    ! [X4,X5] : rd(mult(X5,X4),X4) = X5,
    inference(variable_rename,[status(thm)],[2]) ).

cnf(11,plain,
    rd(mult(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[10]) ).

fof(12,plain,
    ! [X4,X5] : mult(X5,ld(X5,X4)) = X4,
    inference(variable_rename,[status(thm)],[3]) ).

cnf(13,plain,
    mult(X1,ld(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[12]) ).

fof(14,negated_conjecture,
    ! [X4] :
    ? [X5] :
      ( mult(X5,X4) != X5
      | mult(X4,X5) != X5 ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(15,negated_conjecture,
    ! [X6] :
    ? [X7] :
      ( mult(X7,X6) != X7
      | mult(X6,X7) != X7 ),
    inference(variable_rename,[status(thm)],[14]) ).

fof(16,negated_conjecture,
    ! [X6] :
      ( mult(esk1_1(X6),X6) != esk1_1(X6)
      | mult(X6,esk1_1(X6)) != esk1_1(X6) ),
    inference(skolemize,[status(esa)],[15]) ).

cnf(17,negated_conjecture,
    ( mult(X1,esk1_1(X1)) != esk1_1(X1)
    | mult(esk1_1(X1),X1) != esk1_1(X1) ),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,plain,
    ! [X4,X5] : mult(rd(X5,X4),X4) = X5,
    inference(variable_rename,[status(thm)],[5]) ).

cnf(19,plain,
    mult(rd(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[18]) ).

fof(20,plain,
    ! [X4,X5] : ld(X5,mult(X5,X4)) = X4,
    inference(variable_rename,[status(thm)],[6]) ).

cnf(21,plain,
    ld(X1,mult(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,plain,
    ld(rd(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[21,19,theory(equality)]) ).

cnf(23,plain,
    rd(X2,ld(X1,X2)) = X1,
    inference(spm,[status(thm)],[11,13,theory(equality)]) ).

cnf(24,plain,
    mult(mult(X1,X3),X2) = mult(mult(X1,X2),mult(ld(X2,X3),X2)),
    inference(spm,[status(thm)],[9,13,theory(equality)]) ).

cnf(25,plain,
    ld(mult(X1,mult(X2,X3)),mult(mult(X1,X2),mult(X3,X2))) = X2,
    inference(spm,[status(thm)],[21,9,theory(equality)]) ).

cnf(27,plain,
    mult(X1,X2) = mult(mult(rd(X1,mult(X2,X3)),X2),mult(X3,X2)),
    inference(spm,[status(thm)],[9,19,theory(equality)]) ).

cnf(28,plain,
    rd(mult(mult(X1,X2),mult(X3,X2)),X2) = mult(X1,mult(X2,X3)),
    inference(spm,[status(thm)],[11,9,theory(equality)]) ).

cnf(42,plain,
    mult(X1,mult(ld(X2,X3),X2)) = mult(mult(rd(X1,X2),X3),X2),
    inference(spm,[status(thm)],[24,19,theory(equality)]) ).

cnf(53,plain,
    mult(X1,X2) = mult(X1,mult(ld(X2,X2),X2)),
    inference(spm,[status(thm)],[42,19,theory(equality)]) ).

cnf(65,plain,
    ld(X1,mult(X1,X2)) = mult(ld(X2,X2),X2),
    inference(spm,[status(thm)],[21,53,theory(equality)]) ).

cnf(76,plain,
    X2 = mult(ld(X2,X2),X2),
    inference(rw,[status(thm)],[65,21,theory(equality)]) ).

cnf(88,plain,
    rd(X1,X1) = ld(X1,X1),
    inference(spm,[status(thm)],[11,76,theory(equality)]) ).

cnf(89,plain,
    mult(mult(X1,X2),ld(X2,X2)) = mult(mult(X1,ld(X2,X2)),mult(X2,ld(X2,X2))),
    inference(spm,[status(thm)],[9,76,theory(equality)]) ).

cnf(91,plain,
    mult(X1,mult(ld(X1,X2),X1)) = mult(mult(ld(X1,X1),X2),X1),
    inference(spm,[status(thm)],[24,76,theory(equality)]) ).

cnf(93,plain,
    mult(mult(X1,X2),ld(X2,X2)) = mult(mult(X1,ld(X2,X2)),X2),
    inference(rw,[status(thm)],[89,13,theory(equality)]) ).

cnf(105,plain,
    mult(X1,X1) = mult(mult(X1,X1),ld(X1,X1)),
    inference(spm,[status(thm)],[93,13,theory(equality)]) ).

cnf(158,plain,
    ld(mult(X1,mult(X2,X2)),mult(mult(X1,mult(X2,X2)),mult(ld(X2,X2),mult(X2,X2)))) = mult(X2,X2),
    inference(spm,[status(thm)],[25,105,theory(equality)]) ).

cnf(167,plain,
    mult(ld(X2,X2),mult(X2,X2)) = mult(X2,X2),
    inference(rw,[status(thm)],[158,21,theory(equality)]) ).

cnf(270,plain,
    rd(mult(X1,mult(X3,X2)),X2) = mult(rd(X1,X2),mult(X2,X3)),
    inference(spm,[status(thm)],[28,19,theory(equality)]) ).

cnf(309,plain,
    rd(mult(X1,X2),mult(X3,X2)) = mult(rd(X1,mult(X2,X3)),X2),
    inference(spm,[status(thm)],[11,27,theory(equality)]) ).

cnf(416,plain,
    rd(mult(X1,X2),X3) = mult(rd(X1,X3),mult(X3,rd(X2,X3))),
    inference(spm,[status(thm)],[270,19,theory(equality)]) ).

cnf(432,plain,
    rd(mult(X1,X1),X1) = mult(rd(ld(X1,X1),X1),mult(X1,X1)),
    inference(spm,[status(thm)],[270,167,theory(equality)]) ).

cnf(455,plain,
    X1 = mult(rd(ld(X1,X1),X1),mult(X1,X1)),
    inference(rw,[status(thm)],[432,11,theory(equality)]) ).

cnf(462,plain,
    rd(X1,mult(X1,X1)) = rd(ld(X1,X1),X1),
    inference(spm,[status(thm)],[11,455,theory(equality)]) ).

cnf(484,plain,
    mult(rd(X1,mult(X1,X1)),X1) = ld(X1,X1),
    inference(spm,[status(thm)],[19,462,theory(equality)]) ).

cnf(537,plain,
    mult(rd(X1,mult(X2,X1)),X2) = ld(mult(X1,X2),mult(X1,X2)),
    inference(spm,[status(thm)],[88,309,theory(equality)]) ).

cnf(576,plain,
    ld(mult(X1,X1),mult(X1,X1)) = mult(rd(mult(X1,X1),mult(ld(X1,X1),mult(X1,X1))),ld(X1,X1)),
    inference(spm,[status(thm)],[537,105,theory(equality)]) ).

cnf(598,plain,
    ld(X1,X1) = mult(rd(mult(X1,X1),mult(ld(X1,X1),mult(X1,X1))),ld(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[576,537,theory(equality)]),484,theory(equality)]) ).

cnf(599,plain,
    ld(X1,X1) = mult(ld(X1,X1),ld(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[598,167,theory(equality)]),88,theory(equality)]),537,theory(equality)]),484,theory(equality)]) ).

cnf(620,plain,
    mult(ld(X1,X1),X1) = mult(X1,mult(ld(X1,ld(X1,X1)),X1)),
    inference(spm,[status(thm)],[91,599,theory(equality)]) ).

cnf(640,plain,
    X1 = mult(X1,mult(ld(X1,ld(X1,X1)),X1)),
    inference(rw,[status(thm)],[620,76,theory(equality)]) ).

cnf(718,plain,
    ld(X1,X1) = mult(ld(X1,ld(X1,X1)),X1),
    inference(spm,[status(thm)],[21,640,theory(equality)]) ).

cnf(772,plain,
    mult(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[640,718,theory(equality)]) ).

cnf(1694,plain,
    mult(X1,mult(X2,rd(X3,X2))) = rd(mult(mult(X1,X2),X3),X2),
    inference(spm,[status(thm)],[416,11,theory(equality)]) ).

cnf(1791,plain,
    rd(mult(X1,X2),X2) = mult(X1,mult(X2,rd(ld(mult(X1,X2),mult(X1,X2)),X2))),
    inference(spm,[status(thm)],[1694,772,theory(equality)]) ).

cnf(1823,plain,
    X1 = mult(X1,mult(X2,rd(ld(mult(X1,X2),mult(X1,X2)),X2))),
    inference(rw,[status(thm)],[1791,11,theory(equality)]) ).

cnf(1824,plain,
    X1 = mult(X1,mult(X2,rd(X1,mult(X2,X1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1823,537,theory(equality)]),11,theory(equality)]) ).

cnf(1831,plain,
    ld(X1,X1) = mult(X2,rd(X1,mult(X2,X1))),
    inference(spm,[status(thm)],[21,1824,theory(equality)]) ).

cnf(1908,plain,
    mult(rd(X1,X2),rd(X2,X1)) = ld(X2,X2),
    inference(spm,[status(thm)],[1831,19,theory(equality)]) ).

cnf(2134,plain,
    mult(X2,rd(ld(X2,X1),X1)) = ld(ld(X2,X1),ld(X2,X1)),
    inference(spm,[status(thm)],[1908,23,theory(equality)]) ).

cnf(2137,plain,
    mult(ld(X2,X2),X2) = mult(X1,mult(ld(X2,rd(X2,X1)),X2)),
    inference(spm,[status(thm)],[42,1908,theory(equality)]) ).

cnf(2189,plain,
    X2 = mult(X1,mult(ld(X2,rd(X2,X1)),X2)),
    inference(rw,[status(thm)],[2137,76,theory(equality)]) ).

cnf(2453,plain,
    ld(X1,X2) = mult(ld(X2,rd(X2,X1)),X2),
    inference(spm,[status(thm)],[21,2189,theory(equality)]) ).

cnf(2525,plain,
    rd(ld(X2,X1),X1) = ld(X1,rd(X1,X2)),
    inference(spm,[status(thm)],[11,2453,theory(equality)]) ).

cnf(2529,plain,
    mult(ld(X1,X2),X1) = ld(ld(X2,X1),X1),
    inference(spm,[status(thm)],[2453,23,theory(equality)]) ).

cnf(2566,plain,
    mult(ld(X1,rd(X1,X2)),rd(X1,ld(X2,X1))) = ld(X1,X1),
    inference(spm,[status(thm)],[1831,2453,theory(equality)]) ).

cnf(2590,plain,
    mult(ld(X1,rd(X1,X2)),X2) = ld(X1,X1),
    inference(rw,[status(thm)],[2566,23,theory(equality)]) ).

cnf(2595,plain,
    rd(X2,X1) = ld(X1,rd(X1,rd(X1,X2))),
    inference(spm,[status(thm)],[2525,22,theory(equality)]) ).

cnf(2637,plain,
    rd(X1,mult(ld(X1,X2),X1)) = ld(X2,X1),
    inference(spm,[status(thm)],[23,2529,theory(equality)]) ).

cnf(2666,plain,
    rd(ld(X1,X1),X2) = ld(X1,rd(X1,X2)),
    inference(spm,[status(thm)],[11,2590,theory(equality)]) ).

cnf(2670,plain,
    mult(ld(X1,X2),ld(X2,X1)) = ld(X1,X1),
    inference(spm,[status(thm)],[2590,23,theory(equality)]) ).

cnf(2762,plain,
    mult(X1,rd(X2,X1)) = rd(X1,rd(X1,X2)),
    inference(spm,[status(thm)],[13,2595,theory(equality)]) ).

cnf(2876,plain,
    rd(ld(X1,X2),ld(X2,rd(X2,X1))) = mult(ld(X1,X2),rd(X2,ld(X1,X2))),
    inference(spm,[status(thm)],[2762,2525,theory(equality)]) ).

cnf(2897,plain,
    rd(ld(X1,X2),ld(X2,rd(X2,X1))) = mult(ld(X1,X2),X1),
    inference(rw,[status(thm)],[2876,23,theory(equality)]) ).

cnf(2903,plain,
    rd(X1,mult(X2,X1)) = ld(mult(X1,X2),X1),
    inference(spm,[status(thm)],[2637,21,theory(equality)]) ).

cnf(2993,plain,
    rd(X1,ld(X2,X2)) = ld(mult(X1,ld(X2,rd(X2,X1))),X1),
    inference(spm,[status(thm)],[2903,2590,theory(equality)]) ).

cnf(3037,plain,
    ld(ld(X1,X2),ld(X1,X1)) = ld(X2,X1),
    inference(spm,[status(thm)],[21,2670,theory(equality)]) ).

cnf(3274,plain,
    rd(ld(X1,X1),X2) = ld(ld(X1,X1),rd(ld(X1,X1),X2)),
    inference(spm,[status(thm)],[2666,3037,theory(equality)]) ).

cnf(3315,plain,
    ld(X1,rd(X1,X2)) = ld(ld(X1,X1),rd(ld(X1,X1),X2)),
    inference(rw,[status(thm)],[3274,2666,theory(equality)]) ).

cnf(3316,plain,
    ld(X1,rd(X1,X2)) = ld(ld(X1,X1),ld(X1,rd(X1,X2))),
    inference(rw,[status(thm)],[3315,2666,theory(equality)]) ).

cnf(3763,plain,
    ld(ld(X2,X1),ld(X2,X1)) = mult(X2,ld(X1,rd(X1,X2))),
    inference(rw,[status(thm)],[2134,2525,theory(equality)]) ).

cnf(9665,plain,
    ld(ld(ld(X1,X2),ld(X1,X2)),ld(ld(X1,X2),mult(ld(X1,X2),X1))) = ld(ld(X1,X2),mult(ld(X1,X2),X1)),
    inference(spm,[status(thm)],[3316,2897,theory(equality)]) ).

cnf(9726,plain,
    rd(X1,ld(X2,X2)) = ld(ld(X1,X2),mult(ld(X1,X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[9665,3763,theory(equality)]),21,theory(equality)]),2993,theory(equality)]) ).

cnf(9727,plain,
    rd(X1,ld(X2,X2)) = X1,
    inference(rw,[status(thm)],[9726,21,theory(equality)]) ).

cnf(9729,plain,
    mult(X1,ld(X2,X2)) = X1,
    inference(spm,[status(thm)],[19,9727,theory(equality)]) ).

cnf(9852,plain,
    ld(mult(X1,X2),mult(mult(X1,X2),mult(ld(X3,X3),X2))) = X2,
    inference(spm,[status(thm)],[25,9729,theory(equality)]) ).

cnf(9955,plain,
    mult(ld(X3,X3),X2) = X2,
    inference(rw,[status(thm)],[9852,21,theory(equality)]) ).

cnf(10320,negated_conjecture,
    mult(esk1_1(ld(X1,X1)),ld(X1,X1)) != esk1_1(ld(X1,X1)),
    inference(spm,[status(thm)],[17,9955,theory(equality)]) ).

cnf(10461,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[10320,9729,theory(equality)]) ).

cnf(10462,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[10461,theory(equality)]) ).

cnf(10463,negated_conjecture,
    $false,
    10462,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP659+1.p
% --creating new selector for []
% -running prover on /tmp/tmp82WwnO/sel_GRP659+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP659+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP659+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP659+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
% 
%------------------------------------------------------------------------------