TSTP Solution File: GRP660+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GRP660+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 11:21:18 EST 2010

% Result   : Theorem 1.41s
% Output   : CNFRefutation 1.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   94 (  88 unt;   0 def)
%            Number of atoms       :  100 (  97 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   :  184 (   0 sgn  27   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] : mult(mult(mult(X3,X2),X1),X3) = mult(X3,mult(X2,mult(X1,X3))),
    file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f05) ).

fof(2,axiom,
    ! [X2,X3] : rd(mult(X3,X2),X2) = X3,
    file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f04) ).

fof(3,axiom,
    ! [X2,X3] : mult(X3,ld(X3,X2)) = X2,
    file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f01) ).

fof(4,conjecture,
    ? [X4] :
    ! [X5] :
      ( mult(X5,X4) = X5
      & mult(X4,X5) = X5 ),
    file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',goals) ).

fof(5,axiom,
    ! [X2,X3] : mult(rd(X3,X2),X2) = X3,
    file('/tmp/tmppMCQuq/sel_GRP660+1.p_1',f03) ).

fof(6,axiom,
    ! [X2,X3] : ld(X3,mult(X3,X2)) = X2,
    file('/tmp/tmppMCQuq/sel_GRP660+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(mult(X6,X5),X4),X6) = mult(X6,mult(X5,mult(X4,X6))),
    inference(variable_rename,[status(thm)],[1]) ).

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

cnf(26,plain,
    ld(mult(mult(X1,X2),X3),mult(X1,mult(X2,mult(X3,X1)))) = X1,
    inference(spm,[status(thm)],[21,9,theory(equality)]) ).

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

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

cnf(40,plain,
    ld(X1,mult(mult(X2,X3),X1)) = mult(ld(X1,X2),mult(X3,X1)),
    inference(spm,[status(thm)],[21,24,theory(equality)]) ).

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

cnf(51,plain,
    ld(X1,mult(X3,X1)) = mult(ld(X1,X2),mult(ld(X2,X3),X1)),
    inference(spm,[status(thm)],[40,13,theory(equality)]) ).

cnf(54,plain,
    ld(X1,mult(X2,X1)) = mult(ld(X1,rd(X2,X3)),mult(X3,X1)),
    inference(spm,[status(thm)],[40,19,theory(equality)]) ).

cnf(87,plain,
    rd(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),rd(X3,X1)),
    inference(spm,[status(thm)],[28,19,theory(equality)]) ).

cnf(101,plain,
    rd(mult(X1,X3),X1) = mult(mult(X1,X2),rd(ld(X2,X3),X1)),
    inference(spm,[status(thm)],[87,13,theory(equality)]) ).

cnf(103,plain,
    rd(mult(X1,X2),X1) = mult(mult(X1,rd(X2,X3)),rd(X3,X1)),
    inference(spm,[status(thm)],[87,19,theory(equality)]) ).

cnf(122,plain,
    ld(ld(X1,X2),ld(X1,mult(X3,X1))) = mult(ld(X2,X3),X1),
    inference(spm,[status(thm)],[21,51,theory(equality)]) ).

cnf(145,plain,
    rd(ld(X1,mult(X2,X1)),mult(X3,X1)) = ld(X1,rd(X2,X3)),
    inference(spm,[status(thm)],[11,54,theory(equality)]) ).

cnf(242,plain,
    mult(X2,rd(ld(ld(X1,X2),X3),X1)) = rd(mult(X1,X3),X1),
    inference(spm,[status(thm)],[101,13,theory(equality)]) ).

cnf(280,plain,
    rd(rd(mult(X1,X2),X1),rd(X3,X1)) = mult(X1,rd(X2,X3)),
    inference(spm,[status(thm)],[11,103,theory(equality)]) ).

cnf(287,plain,
    mult(mult(ld(X1,X2),rd(X3,X2)),X1) = rd(mult(ld(X1,X2),X3),ld(X1,X2)),
    inference(spm,[status(thm)],[103,23,theory(equality)]) ).

cnf(315,plain,
    ld(X2,ld(X1,mult(X3,X1))) = mult(ld(mult(X1,X2),X3),X1),
    inference(spm,[status(thm)],[122,21,theory(equality)]) ).

cnf(316,plain,
    ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
    inference(spm,[status(thm)],[122,21,theory(equality)]) ).

cnf(340,plain,
    ld(X2,X1) = mult(ld(mult(X1,X2),X1),X1),
    inference(spm,[status(thm)],[316,21,theory(equality)]) ).

cnf(341,plain,
    ld(X2,rd(X1,X2)) = mult(ld(X1,rd(X1,X2)),rd(X1,X2)),
    inference(spm,[status(thm)],[316,22,theory(equality)]) ).

cnf(342,plain,
    rd(X1,mult(ld(X2,X1),X1)) = ld(X1,X2),
    inference(spm,[status(thm)],[23,316,theory(equality)]) ).

cnf(357,plain,
    rd(ld(X2,X1),X1) = ld(mult(X1,X2),X1),
    inference(spm,[status(thm)],[11,340,theory(equality)]) ).

cnf(408,plain,
    rd(X1,mult(X2,X1)) = ld(X1,rd(X1,X2)),
    inference(spm,[status(thm)],[342,22,theory(equality)]) ).

cnf(425,plain,
    rd(rd(X1,X2),rd(X1,mult(X2,X1))) = X1,
    inference(spm,[status(thm)],[23,408,theory(equality)]) ).

cnf(742,plain,
    ld(X1,ld(X2,X3)) = mult(ld(mult(X2,X1),rd(X3,X2)),X2),
    inference(spm,[status(thm)],[315,19,theory(equality)]) ).

cnf(969,plain,
    ld(X1,rd(X2,X2)) = ld(mult(mult(X2,X1),X1),mult(X2,X1)),
    inference(spm,[status(thm)],[357,145,theory(equality)]) ).

cnf(1028,plain,
    ld(X1,rd(mult(X2,X3),X2)) = rd(ld(ld(X2,X1),X3),X2),
    inference(spm,[status(thm)],[21,242,theory(equality)]) ).

cnf(1102,plain,
    rd(ld(rd(X1,mult(X2,X1)),X3),X1) = ld(rd(X1,X2),rd(mult(X1,X3),X1)),
    inference(spm,[status(thm)],[1028,408,theory(equality)]) ).

cnf(1221,plain,
    rd(rd(X2,X1),rd(X3,X1)) = mult(X1,rd(ld(X1,X2),X3)),
    inference(spm,[status(thm)],[280,13,theory(equality)]) ).

cnf(1644,plain,
    mult(rd(X1,mult(X2,X1)),rd(X1,X2)) = ld(X2,rd(X1,X2)),
    inference(rw,[status(thm)],[341,408,theory(equality)]) ).

cnf(2073,plain,
    mult(ld(X2,rd(X3,X1)),X1) = ld(ld(X1,X2),ld(X1,X3)),
    inference(spm,[status(thm)],[742,13,theory(equality)]) ).

cnf(2455,plain,
    ld(rd(mult(X1,X1),X1),mult(X1,rd(X1,X1))) = ld(rd(X1,X1),rd(X1,X1)),
    inference(spm,[status(thm)],[969,103,theory(equality)]) ).

cnf(2493,plain,
    rd(X1,X1) = ld(rd(X1,X1),rd(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2455,11,theory(equality)]),21,theory(equality)]) ).

cnf(2509,plain,
    mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
    inference(spm,[status(thm)],[13,2493,theory(equality)]) ).

cnf(2510,plain,
    rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
    inference(spm,[status(thm)],[23,2493,theory(equality)]) ).

cnf(2529,plain,
    mult(X1,ld(mult(X1,X1),X1)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2510,1221,theory(equality)]),357,theory(equality)]) ).

cnf(2562,plain,
    mult(rd(X1,X1),mult(X1,rd(X1,X1))) = mult(mult(X1,rd(X1,X1)),rd(X1,X1)),
    inference(spm,[status(thm)],[27,2509,theory(equality)]) ).

cnf(2597,plain,
    mult(rd(X1,X1),mult(X1,rd(X1,X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2562,103,theory(equality)]),11,theory(equality)]) ).

cnf(2625,plain,
    ld(X1,rd(X1,X1)) = ld(mult(X1,X1),X1),
    inference(spm,[status(thm)],[21,2529,theory(equality)]) ).

cnf(2670,plain,
    rd(X1,mult(X1,X1)) = ld(mult(X1,X1),X1),
    inference(rw,[status(thm)],[2625,408,theory(equality)]) ).

cnf(2695,plain,
    rd(rd(X1,X1),ld(mult(X1,X1),X1)) = X1,
    inference(spm,[status(thm)],[425,2670,theory(equality)]) ).

cnf(2704,plain,
    mult(ld(mult(X1,X1),X1),rd(X1,X1)) = ld(X1,rd(X1,X1)),
    inference(spm,[status(thm)],[1644,2670,theory(equality)]) ).

cnf(2718,plain,
    mult(ld(mult(X1,X1),X1),rd(X1,X1)) = ld(mult(X1,X1),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2704,408,theory(equality)]),2670,theory(equality)]) ).

cnf(2775,plain,
    ld(mult(mult(rd(X1,X1),rd(X1,X1)),X1),mult(rd(X1,X1),X1)) = rd(X1,X1),
    inference(spm,[status(thm)],[26,2597,theory(equality)]) ).

cnf(2812,plain,
    ld(X1,X1) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2775,2509,theory(equality)]),19,theory(equality)]),19,theory(equality)]) ).

cnf(2849,plain,
    ld(X1,ld(X1,X1)) = rd(X1,mult(X1,X1)),
    inference(spm,[status(thm)],[408,2812,theory(equality)]) ).

cnf(2870,plain,
    mult(ld(X1,X1),ld(X1,X1)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2509,2812,theory(equality)]),2812,theory(equality)]) ).

cnf(2871,plain,
    mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
    inference(rw,[status(thm)],[2870,2812,theory(equality)]) ).

cnf(2878,plain,
    ld(X1,ld(X1,X1)) = ld(mult(X1,X1),X1),
    inference(rw,[status(thm)],[2849,2670,theory(equality)]) ).

cnf(3550,plain,
    rd(ld(X1,X1),ld(mult(X1,X1),X1)) = X1,
    inference(rw,[status(thm)],[2695,2812,theory(equality)]) ).

cnf(6102,plain,
    mult(ld(mult(X1,X1),X1),ld(X1,X1)) = ld(mult(X1,X1),X1),
    inference(rw,[status(thm)],[2718,2812,theory(equality)]) ).

cnf(26672,plain,
    rd(ld(rd(ld(X1,X1),ld(mult(X1,X1),X1)),X2),ld(X1,X1)) = ld(rd(ld(X1,X1),ld(mult(X1,X1),X1)),rd(mult(ld(X1,X1),X2),ld(X1,X1))),
    inference(spm,[status(thm)],[1102,6102,theory(equality)]) ).

cnf(26831,plain,
    rd(ld(X1,X2),ld(X1,X1)) = ld(rd(ld(X1,X1),ld(mult(X1,X1),X1)),rd(mult(ld(X1,X1),X2),ld(X1,X1))),
    inference(rw,[status(thm)],[26672,3550,theory(equality)]) ).

cnf(26832,plain,
    rd(ld(X1,X2),ld(X1,X1)) = mult(ld(mult(X1,X1),X1),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[26831,3550,theory(equality)]),287,theory(equality)]),42,theory(equality)]),2878,theory(equality)]),21,theory(equality)]) ).

cnf(26898,plain,
    rd(X2,ld(X1,X1)) = mult(ld(mult(X1,X1),X1),mult(X1,X2)),
    inference(spm,[status(thm)],[26832,21,theory(equality)]) ).

cnf(27208,plain,
    mult(ld(ld(X1,X1),ld(X1,X1)),mult(ld(X1,X1),X2)) = rd(X2,ld(ld(X1,X1),ld(X1,X1))),
    inference(spm,[status(thm)],[26898,2871,theory(equality)]) ).

cnf(27369,plain,
    mult(ld(X1,X1),mult(ld(X1,X1),X2)) = rd(X2,ld(ld(X1,X1),ld(X1,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[27208,2073,theory(equality)]),408,theory(equality)]),2670,theory(equality)]),340,theory(equality)]) ).

cnf(27370,plain,
    mult(ld(X1,X1),mult(ld(X1,X1),X2)) = rd(X2,ld(X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[27369,2073,theory(equality)]),408,theory(equality)]),2670,theory(equality)]),340,theory(equality)]) ).

cnf(27708,plain,
    ld(mult(mult(ld(X1,X1),ld(X1,X1)),X2),rd(mult(X2,ld(X1,X1)),ld(X1,X1))) = ld(X1,X1),
    inference(spm,[status(thm)],[26,27370,theory(equality)]) ).

cnf(27883,plain,
    ld(mult(ld(X1,X1),X2),X2) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[27708,2871,theory(equality)]),11,theory(equality)]) ).

cnf(28027,plain,
    mult(mult(ld(X1,X1),X2),ld(X1,X1)) = X2,
    inference(spm,[status(thm)],[13,27883,theory(equality)]) ).

cnf(28029,plain,
    rd(X1,ld(X2,X2)) = mult(ld(X2,X2),X1),
    inference(spm,[status(thm)],[23,27883,theory(equality)]) ).

cnf(28255,plain,
    mult(ld(X2,X2),mult(X1,ld(X2,X2))) = X1,
    inference(spm,[status(thm)],[11,28029,theory(equality)]) ).

cnf(29252,plain,
    rd(X2,ld(X1,X1)) = mult(mult(ld(X1,X1),X2),rd(ld(X1,X1),ld(X1,X1))),
    inference(spm,[status(thm)],[87,28255,theory(equality)]) ).

cnf(29410,plain,
    mult(ld(X1,X1),X2) = mult(mult(ld(X1,X1),X2),rd(ld(X1,X1),ld(X1,X1))),
    inference(rw,[status(thm)],[29252,28029,theory(equality)]) ).

cnf(29411,plain,
    mult(ld(X1,X1),X2) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[29410,2812,theory(equality)]),2073,theory(equality)]),408,theory(equality)]),2670,theory(equality)]),340,theory(equality)]),28027,theory(equality)]) ).

cnf(29818,negated_conjecture,
    mult(esk1_1(ld(X1,X1)),ld(X1,X1)) != esk1_1(ld(X1,X1)),
    inference(spm,[status(thm)],[17,29411,theory(equality)]) ).

cnf(29819,plain,
    mult(X2,ld(X1,X1)) = X2,
    inference(rw,[status(thm)],[28255,29411,theory(equality)]) ).

cnf(31001,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[29818,29819,theory(equality)]) ).

cnf(31002,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[31001,theory(equality)]) ).

cnf(31003,negated_conjecture,
    $false,
    31002,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP660+1.p
% --creating new selector for []
% -running prover on /tmp/tmppMCQuq/sel_GRP660+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP660+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP660+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP660+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
% 
%------------------------------------------------------------------------------