TSTP Solution File: REL042+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : REL042+2 : 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 : Sun Dec 26 01:37:41 EST 2010

% Result   : Theorem 1.04s
% Output   : CNFRefutation 1.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  117 ( 111 unt;   0 def)
%            Number of atoms       :  123 ( 121 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   7   ~;   0   |;   4   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  152 (  11 sgn  56   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',modular_law_1) ).

fof(3,axiom,
    ! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',converse_multiplicativity) ).

fof(4,axiom,
    ! [X1] : converse(converse(X1)) = X1,
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',converse_idempotence) ).

fof(5,axiom,
    ! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',composition_distributivity) ).

fof(6,axiom,
    ! [X1] : composition(X1,one) = X1,
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',composition_identity) ).

fof(7,axiom,
    ! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',converse_additivity) ).

fof(8,axiom,
    ! [X1,X2] : join(X1,X2) = join(X2,X1),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',maddux1_join_commutativity) ).

fof(11,axiom,
    ! [X1] : zero = meet(X1,complement(X1)),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',def_zero) ).

fof(12,axiom,
    ! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',converse_cancellativity) ).

fof(13,axiom,
    ! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',maddux4_definiton_of_meet) ).

fof(14,axiom,
    ! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',maddux2_join_associativity) ).

fof(15,axiom,
    ! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',maddux3_a_kind_of_de_Morgan) ).

fof(16,conjecture,
    ! [X1] :
      ( ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero
     => join(composition(converse(X1),X1),one) = one ),
    file('/tmp/tmpLMLWwi/sel_REL042+2.p_1',goals) ).

fof(17,negated_conjecture,
    ~ ! [X1] :
        ( ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero
       => join(composition(converse(X1),X1),one) = one ),
    inference(assume_negation,[status(cth)],[16]) ).

fof(20,plain,
    ! [X4,X5,X6] : join(meet(composition(X4,X5),X6),meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6)) = meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6),
    inference(variable_rename,[status(thm)],[2]) ).

cnf(21,plain,
    join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(22,plain,
    ! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(23,plain,
    converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(24,plain,
    ! [X2] : converse(converse(X2)) = X2,
    inference(variable_rename,[status(thm)],[4]) ).

cnf(25,plain,
    converse(converse(X1)) = X1,
    inference(split_conjunct,[status(thm)],[24]) ).

fof(26,plain,
    ! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(27,plain,
    composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(28,plain,
    ! [X2] : composition(X2,one) = X2,
    inference(variable_rename,[status(thm)],[6]) ).

cnf(29,plain,
    composition(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[28]) ).

fof(30,plain,
    ! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(31,plain,
    converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(32,plain,
    ! [X3,X4] : join(X3,X4) = join(X4,X3),
    inference(variable_rename,[status(thm)],[8]) ).

cnf(33,plain,
    join(X1,X2) = join(X2,X1),
    inference(split_conjunct,[status(thm)],[32]) ).

fof(38,plain,
    ! [X2] : zero = meet(X2,complement(X2)),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(39,plain,
    zero = meet(X1,complement(X1)),
    inference(split_conjunct,[status(thm)],[38]) ).

fof(40,plain,
    ! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
    inference(variable_rename,[status(thm)],[12]) ).

cnf(41,plain,
    join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(42,plain,
    ! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
    inference(variable_rename,[status(thm)],[13]) ).

cnf(43,plain,
    meet(X1,X2) = complement(join(complement(X1),complement(X2))),
    inference(split_conjunct,[status(thm)],[42]) ).

fof(44,plain,
    ! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(45,plain,
    join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(46,plain,
    ! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(47,plain,
    X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(48,negated_conjecture,
    ? [X1] :
      ( ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero
      & join(composition(converse(X1),X1),one) != one ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(49,negated_conjecture,
    ? [X3] :
      ( ! [X4] : meet(composition(X3,X4),composition(X3,complement(X4))) = zero
      & join(composition(converse(X3),X3),one) != one ),
    inference(variable_rename,[status(thm)],[48]) ).

fof(50,negated_conjecture,
    ( ! [X4] : meet(composition(esk1_0,X4),composition(esk1_0,complement(X4))) = zero
    & join(composition(converse(esk1_0),esk1_0),one) != one ),
    inference(skolemize,[status(esa)],[49]) ).

fof(51,negated_conjecture,
    ! [X4] :
      ( meet(composition(esk1_0,X4),composition(esk1_0,complement(X4))) = zero
      & join(composition(converse(esk1_0),esk1_0),one) != one ),
    inference(shift_quantors,[status(thm)],[50]) ).

cnf(52,negated_conjecture,
    join(composition(converse(esk1_0),esk1_0),one) != one,
    inference(split_conjunct,[status(thm)],[51]) ).

cnf(53,negated_conjecture,
    meet(composition(esk1_0,X1),composition(esk1_0,complement(X1))) = zero,
    inference(split_conjunct,[status(thm)],[51]) ).

cnf(54,plain,
    complement(join(complement(X1),complement(complement(X1)))) = zero,
    inference(rw,[status(thm)],[39,43,theory(equality)]),
    [unfolding] ).

cnf(55,negated_conjecture,
    complement(join(complement(composition(esk1_0,X1)),complement(composition(esk1_0,complement(X1))))) = zero,
    inference(rw,[status(thm)],[53,43,theory(equality)]),
    [unfolding] ).

cnf(56,plain,
    join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3)))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[21,43,theory(equality)]),43,theory(equality)]),43,theory(equality)]),43,theory(equality)]),43,theory(equality)]),
    [unfolding] ).

cnf(59,negated_conjecture,
    join(one,composition(converse(esk1_0),esk1_0)) != one,
    inference(rw,[status(thm)],[52,33,theory(equality)]) ).

cnf(62,plain,
    composition(converse(X1),X2) = converse(composition(converse(X2),X1)),
    inference(spm,[status(thm)],[23,25,theory(equality)]) ).

cnf(63,plain,
    join(X1,converse(X2)) = converse(join(converse(X1),X2)),
    inference(spm,[status(thm)],[31,25,theory(equality)]) ).

cnf(64,plain,
    join(converse(X1),X2) = converse(join(X1,converse(X2))),
    inference(spm,[status(thm)],[31,25,theory(equality)]) ).

cnf(88,plain,
    join(converse(composition(X2,X1)),composition(X3,converse(X2))) = composition(join(converse(X1),X3),converse(X2)),
    inference(spm,[status(thm)],[27,23,theory(equality)]) ).

cnf(101,plain,
    join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
    inference(rw,[status(thm)],[41,33,theory(equality)]) ).

cnf(109,negated_conjecture,
    complement(join(complement(esk1_0),complement(composition(esk1_0,complement(one))))) = zero,
    inference(spm,[status(thm)],[55,29,theory(equality)]) ).

cnf(116,plain,
    join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
    inference(rw,[status(thm)],[47,33,theory(equality)]) ).

cnf(129,plain,
    join(complement(join(X2,complement(X1))),complement(join(complement(X1),complement(X2)))) = X1,
    inference(spm,[status(thm)],[116,33,theory(equality)]) ).

cnf(138,plain,
    join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
    inference(rw,[status(thm)],[56,33,theory(equality)]) ).

cnf(139,plain,
    join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),
    inference(rw,[status(thm)],[138,33,theory(equality)]) ).

cnf(140,plain,
    join(complement(join(complement(composition(converse(X1),X2)),complement(X3))),complement(join(complement(X3),complement(composition(converse(X1),complement(join(complement(X2),complement(composition(X1,X3))))))))) = complement(join(complement(X3),complement(composition(converse(X1),complement(join(complement(X2),complement(composition(X1,X3)))))))),
    inference(spm,[status(thm)],[139,25,theory(equality)]) ).

cnf(309,plain,
    converse(converse(X1)) = composition(converse(one),X1),
    inference(spm,[status(thm)],[62,29,theory(equality)]) ).

cnf(327,plain,
    X1 = composition(converse(one),X1),
    inference(rw,[status(thm)],[309,25,theory(equality)]) ).

cnf(343,plain,
    one = converse(one),
    inference(spm,[status(thm)],[29,327,theory(equality)]) ).

cnf(380,plain,
    join(one,converse(X1)) = converse(join(one,X1)),
    inference(spm,[status(thm)],[31,343,theory(equality)]) ).

cnf(389,plain,
    composition(one,X1) = X1,
    inference(rw,[status(thm)],[327,343,theory(equality)]) ).

cnf(403,plain,
    join(complement(X1),composition(converse(one),complement(X1))) = complement(X1),
    inference(spm,[status(thm)],[101,389,theory(equality)]) ).

cnf(414,plain,
    join(complement(X1),complement(X1)) = complement(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[403,343,theory(equality)]),389,theory(equality)]) ).

cnf(457,plain,
    join(zero,zero) = zero,
    inference(spm,[status(thm)],[414,54,theory(equality)]) ).

cnf(460,plain,
    join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))) = X1,
    inference(spm,[status(thm)],[116,414,theory(equality)]) ).

cnf(472,plain,
    join(zero,complement(complement(X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[460,54,theory(equality)]),33,theory(equality)]) ).

cnf(486,plain,
    join(zero,X1) = join(zero,join(zero,X1)),
    inference(spm,[status(thm)],[45,457,theory(equality)]) ).

cnf(649,plain,
    join(zero,X1) = X1,
    inference(spm,[status(thm)],[486,472,theory(equality)]) ).

cnf(658,plain,
    converse(converse(X1)) = join(converse(zero),X1),
    inference(spm,[status(thm)],[64,649,theory(equality)]) ).

cnf(660,plain,
    X1 = join(X1,zero),
    inference(spm,[status(thm)],[33,649,theory(equality)]) ).

cnf(665,plain,
    complement(complement(X1)) = X1,
    inference(rw,[status(thm)],[472,649,theory(equality)]) ).

cnf(669,plain,
    X1 = join(converse(zero),X1),
    inference(rw,[status(thm)],[658,25,theory(equality)]) ).

cnf(683,plain,
    join(X1,X1) = X1,
    inference(spm,[status(thm)],[414,665,theory(equality)]) ).

cnf(684,plain,
    complement(join(X1,complement(X1))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[54,665,theory(equality)]),33,theory(equality)]) ).

cnf(720,plain,
    complement(zero) = join(X1,complement(X1)),
    inference(spm,[status(thm)],[665,684,theory(equality)]) ).

cnf(823,plain,
    join(X1,X2) = join(X1,join(X1,X2)),
    inference(spm,[status(thm)],[45,683,theory(equality)]) ).

cnf(878,plain,
    complement(complement(converse(zero))) = zero,
    inference(spm,[status(thm)],[684,669,theory(equality)]) ).

cnf(891,plain,
    converse(zero) = zero,
    inference(rw,[status(thm)],[878,665,theory(equality)]) ).

cnf(895,plain,
    composition(zero,converse(X1)) = converse(composition(X1,zero)),
    inference(spm,[status(thm)],[23,891,theory(equality)]) ).

cnf(1067,plain,
    converse(zero) = composition(zero,converse(one)),
    inference(spm,[status(thm)],[895,389,theory(equality)]) ).

cnf(1086,plain,
    zero = composition(zero,converse(one)),
    inference(rw,[status(thm)],[1067,891,theory(equality)]) ).

cnf(1087,plain,
    zero = composition(zero,one),
    inference(rw,[status(thm)],[1086,343,theory(equality)]) ).

cnf(1163,plain,
    join(complement(join(complement(X1),X2)),X1) = X1,
    inference(spm,[status(thm)],[823,116,theory(equality)]) ).

cnf(1175,plain,
    join(X1,complement(zero)) = complement(zero),
    inference(spm,[status(thm)],[823,720,theory(equality)]) ).

cnf(1194,plain,
    join(X1,complement(join(complement(X1),X2))) = X1,
    inference(rw,[status(thm)],[1163,33,theory(equality)]) ).

cnf(1220,plain,
    converse(complement(zero)) = join(X1,converse(complement(zero))),
    inference(spm,[status(thm)],[63,1175,theory(equality)]) ).

cnf(1224,plain,
    complement(zero) = join(complement(zero),X1),
    inference(spm,[status(thm)],[33,1175,theory(equality)]) ).

cnf(1520,plain,
    converse(complement(zero)) = complement(zero),
    inference(spm,[status(thm)],[1224,1220,theory(equality)]) ).

cnf(1548,plain,
    composition(complement(zero),converse(X1)) = converse(composition(X1,complement(zero))),
    inference(spm,[status(thm)],[23,1520,theory(equality)]) ).

cnf(1631,plain,
    join(converse(zero),composition(X1,converse(zero))) = composition(join(converse(one),X1),converse(zero)),
    inference(spm,[status(thm)],[88,1087,theory(equality)]) ).

cnf(1668,plain,
    composition(X1,zero) = composition(join(converse(one),X1),converse(zero)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1631,891,theory(equality)]),891,theory(equality)]),649,theory(equality)]) ).

cnf(1669,plain,
    composition(X1,zero) = composition(join(one,X1),zero),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1668,343,theory(equality)]),891,theory(equality)]) ).

cnf(2972,plain,
    converse(complement(zero)) = composition(complement(zero),converse(one)),
    inference(spm,[status(thm)],[1548,389,theory(equality)]) ).

cnf(2998,plain,
    complement(zero) = composition(complement(zero),converse(one)),
    inference(rw,[status(thm)],[2972,1520,theory(equality)]) ).

cnf(2999,plain,
    complement(zero) = composition(complement(zero),one),
    inference(rw,[status(thm)],[2998,343,theory(equality)]) ).

cnf(3020,plain,
    join(converse(complement(zero)),composition(X1,converse(complement(zero)))) = composition(join(converse(one),X1),converse(complement(zero))),
    inference(spm,[status(thm)],[88,2999,theory(equality)]) ).

cnf(3040,plain,
    complement(zero) = composition(join(converse(one),X1),converse(complement(zero))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3020,1520,theory(equality)]),1520,theory(equality)]),1224,theory(equality)]) ).

cnf(3041,plain,
    complement(zero) = composition(join(one,X1),complement(zero)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[3040,343,theory(equality)]),1520,theory(equality)]) ).

cnf(3057,plain,
    join(complement(complement(zero)),composition(converse(join(one,X1)),complement(complement(zero)))) = complement(complement(zero)),
    inference(spm,[status(thm)],[101,3041,theory(equality)]) ).

cnf(3092,plain,
    composition(converse(X1),zero) = complement(complement(zero)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[3057,665,theory(equality)]),380,theory(equality)]),665,theory(equality)]),1669,theory(equality)]),649,theory(equality)]) ).

cnf(3093,plain,
    composition(converse(X1),zero) = zero,
    inference(rw,[status(thm)],[3092,665,theory(equality)]) ).

cnf(3120,plain,
    composition(X1,zero) = zero,
    inference(spm,[status(thm)],[3093,25,theory(equality)]) ).

cnf(4744,negated_conjecture,
    join(complement(join(zero,X1)),complement(join(zero,complement(X1)))) = join(complement(esk1_0),complement(composition(esk1_0,complement(one)))),
    inference(spm,[status(thm)],[116,109,theory(equality)]) ).

cnf(4773,negated_conjecture,
    complement(zero) = join(complement(esk1_0),complement(composition(esk1_0,complement(one)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4744,649,theory(equality)]),649,theory(equality)]),665,theory(equality)]),33,theory(equality)]),720,theory(equality)]) ).

cnf(9702,negated_conjecture,
    join(complement(join(complement(composition(converse(esk1_0),esk1_0)),complement(complement(one)))),complement(join(complement(complement(one)),complement(composition(converse(esk1_0),complement(complement(zero))))))) = complement(join(complement(complement(one)),complement(composition(converse(esk1_0),complement(complement(zero)))))),
    inference(spm,[status(thm)],[140,4773,theory(equality)]) ).

cnf(9809,negated_conjecture,
    complement(join(one,complement(composition(converse(esk1_0),esk1_0)))) = complement(join(complement(complement(one)),complement(composition(converse(esk1_0),complement(complement(zero)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[9702,665,theory(equality)]),33,theory(equality)]),665,theory(equality)]),665,theory(equality)]),3120,theory(equality)]),1175,theory(equality)]),665,theory(equality)]),660,theory(equality)]) ).

cnf(9810,negated_conjecture,
    complement(join(one,complement(composition(converse(esk1_0),esk1_0)))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[9809,665,theory(equality)]),665,theory(equality)]),3120,theory(equality)]),1175,theory(equality)]),665,theory(equality)]) ).

cnf(10371,negated_conjecture,
    join(complement(join(zero,X1)),complement(join(zero,complement(X1)))) = join(one,complement(composition(converse(esk1_0),esk1_0))),
    inference(spm,[status(thm)],[116,9810,theory(equality)]) ).

cnf(10420,negated_conjecture,
    complement(zero) = join(one,complement(composition(converse(esk1_0),esk1_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[10371,649,theory(equality)]),649,theory(equality)]),665,theory(equality)]),33,theory(equality)]),720,theory(equality)]) ).

cnf(10490,negated_conjecture,
    join(complement(complement(zero)),complement(join(complement(composition(converse(esk1_0),esk1_0)),complement(one)))) = composition(converse(esk1_0),esk1_0),
    inference(spm,[status(thm)],[129,10420,theory(equality)]) ).

cnf(10514,negated_conjecture,
    complement(join(complement(one),complement(composition(converse(esk1_0),esk1_0)))) = composition(converse(esk1_0),esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[10490,665,theory(equality)]),33,theory(equality)]),649,theory(equality)]) ).

cnf(23653,negated_conjecture,
    join(one,composition(converse(esk1_0),esk1_0)) = one,
    inference(spm,[status(thm)],[1194,10514,theory(equality)]) ).

cnf(23760,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[23653,59,theory(equality)]) ).

cnf(23761,negated_conjecture,
    $false,
    23760,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL042+2.p
% --creating new selector for [REL001+0.ax, REL001+1.ax]
% -running prover on /tmp/tmpLMLWwi/sel_REL042+2.p_1 with time limit 29
% -prover status Theorem
% Problem REL042+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL042+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL042+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
% 
%------------------------------------------------------------------------------