TSTP Solution File: KLE080+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE080+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 12:12:29 EST 2010
% Result : Theorem 2.08s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 118 ( 112 unt; 0 def)
% Number of atoms : 130 ( 127 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 6 ~; 0 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 168 ( 12 sgn 52 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',additive_identity) ).
fof(3,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',left_distributivity) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',additive_commutativity) ).
fof(5,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',additive_idempotence) ).
fof(7,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',left_annihilation) ).
fof(8,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',additive_associativity) ).
fof(9,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',multiplicative_right_identity) ).
fof(10,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',domain3) ).
fof(11,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',domain2) ).
fof(12,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',domain1) ).
fof(13,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',multiplicative_left_identity) ).
fof(14,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',right_distributivity) ).
fof(15,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',domain5) ).
fof(16,axiom,
domain(zero) = zero,
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',domain4) ).
fof(17,conjecture,
! [X4] :
( ! [X5] :
( addition(domain(X5),antidomain(X5)) = one
& multiplication(domain(X5),antidomain(X5)) = zero )
=> antidomain(antidomain(X4)) = domain(X4) ),
file('/tmp/tmpQIHrqI/sel_KLE080+1.p_1',goals) ).
fof(18,negated_conjecture,
~ ! [X4] :
( ! [X5] :
( addition(domain(X5),antidomain(X5)) = one
& multiplication(domain(X5),antidomain(X5)) = zero )
=> antidomain(antidomain(X4)) = domain(X4) ),
inference(assume_negation,[status(cth)],[17]) ).
fof(21,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(22,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(24,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[5]) ).
cnf(28,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[27]) ).
fof(31,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[7]) ).
cnf(32,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[8]) ).
cnf(34,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[9]) ).
cnf(36,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X5] : addition(domain(X5),one) = one,
inference(variable_rename,[status(thm)],[10]) ).
cnf(38,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X6,X7] : domain(multiplication(X6,X7)) = domain(multiplication(X6,domain(X7))),
inference(variable_rename,[status(thm)],[11]) ).
cnf(40,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X5] : addition(X5,multiplication(domain(X5),X5)) = multiplication(domain(X5),X5),
inference(variable_rename,[status(thm)],[12]) ).
cnf(42,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[13]) ).
cnf(44,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[43]) ).
fof(45,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(46,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X6,X7] : domain(addition(X6,X7)) = addition(domain(X6),domain(X7)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(48,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,plain,
domain(zero) = zero,
inference(split_conjunct,[status(thm)],[16]) ).
fof(50,negated_conjecture,
? [X4] :
( ! [X5] :
( addition(domain(X5),antidomain(X5)) = one
& multiplication(domain(X5),antidomain(X5)) = zero )
& antidomain(antidomain(X4)) != domain(X4) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(51,negated_conjecture,
? [X6] :
( ! [X7] :
( addition(domain(X7),antidomain(X7)) = one
& multiplication(domain(X7),antidomain(X7)) = zero )
& antidomain(antidomain(X6)) != domain(X6) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,negated_conjecture,
( ! [X7] :
( addition(domain(X7),antidomain(X7)) = one
& multiplication(domain(X7),antidomain(X7)) = zero )
& antidomain(antidomain(esk1_0)) != domain(esk1_0) ),
inference(skolemize,[status(esa)],[51]) ).
fof(53,negated_conjecture,
! [X7] :
( addition(domain(X7),antidomain(X7)) = one
& multiplication(domain(X7),antidomain(X7)) = zero
& antidomain(antidomain(esk1_0)) != domain(esk1_0) ),
inference(shift_quantors,[status(thm)],[52]) ).
cnf(54,negated_conjecture,
antidomain(antidomain(esk1_0)) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,negated_conjecture,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,negated_conjecture,
addition(domain(X1),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[53]) ).
cnf(58,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[22,26,theory(equality)]) ).
cnf(62,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[38,26,theory(equality)]) ).
cnf(90,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[34,28,theory(equality)]) ).
cnf(105,plain,
addition(domain(addition(X1,X2)),X3) = addition(domain(X1),addition(domain(X2),X3)),
inference(spm,[status(thm)],[34,48,theory(equality)]) ).
cnf(114,plain,
domain(domain(X1)) = domain(multiplication(one,X1)),
inference(spm,[status(thm)],[40,44,theory(equality)]) ).
cnf(123,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[114,44,theory(equality)]) ).
cnf(130,plain,
addition(one,domain(one)) = domain(one),
inference(spm,[status(thm)],[42,36,theory(equality)]) ).
cnf(141,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[46,36,theory(equality)]) ).
cnf(146,negated_conjecture,
addition(zero,multiplication(domain(X1),X2)) = multiplication(domain(X1),addition(antidomain(X1),X2)),
inference(spm,[status(thm)],[46,55,theory(equality)]) ).
cnf(178,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[24,44,theory(equality)]) ).
cnf(181,negated_conjecture,
addition(zero,multiplication(X2,antidomain(X1))) = multiplication(addition(domain(X1),X2),antidomain(X1)),
inference(spm,[status(thm)],[24,55,theory(equality)]) ).
cnf(182,negated_conjecture,
addition(multiplication(X1,antidomain(X2)),zero) = multiplication(addition(X1,domain(X2)),antidomain(X2)),
inference(spm,[status(thm)],[24,55,theory(equality)]) ).
cnf(201,negated_conjecture,
multiplication(X1,antidomain(X2)) = multiplication(addition(X1,domain(X2)),antidomain(X2)),
inference(rw,[status(thm)],[182,22,theory(equality)]) ).
cnf(223,plain,
one = domain(one),
inference(rw,[status(thm)],[130,62,theory(equality)]) ).
cnf(228,plain,
addition(one,domain(X1)) = domain(addition(one,X1)),
inference(spm,[status(thm)],[48,223,theory(equality)]) ).
cnf(233,plain,
one = domain(addition(one,X1)),
inference(rw,[status(thm)],[228,62,theory(equality)]) ).
cnf(244,negated_conjecture,
addition(domain(X1),antidomain(domain(X1))) = one,
inference(spm,[status(thm)],[56,123,theory(equality)]) ).
cnf(245,plain,
addition(domain(X1),domain(X2)) = domain(addition(domain(X1),X2)),
inference(spm,[status(thm)],[48,123,theory(equality)]) ).
cnf(253,plain,
domain(addition(X1,X2)) = domain(addition(domain(X1),X2)),
inference(rw,[status(thm)],[245,48,theory(equality)]) ).
cnf(265,plain,
domain(multiplication(X1,one)) = domain(multiplication(X1,addition(one,X2))),
inference(spm,[status(thm)],[40,233,theory(equality)]) ).
cnf(279,plain,
domain(X1) = domain(multiplication(X1,addition(one,X2))),
inference(rw,[status(thm)],[265,36,theory(equality)]) ).
cnf(476,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[90,26,theory(equality)]) ).
cnf(500,negated_conjecture,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[476,56,theory(equality)]) ).
cnf(522,negated_conjecture,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[500,26,theory(equality)]) ).
cnf(744,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[42,178,theory(equality)]),62,theory(equality)]) ).
cnf(745,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[744,44,theory(equality)]) ).
cnf(772,plain,
multiplication(domain(multiplication(X1,X2)),multiplication(X1,domain(X2))) = multiplication(X1,domain(X2)),
inference(spm,[status(thm)],[745,40,theory(equality)]) ).
cnf(773,plain,
addition(X1,multiplication(domain(X1),X2)) = multiplication(domain(X1),addition(X1,X2)),
inference(spm,[status(thm)],[46,745,theory(equality)]) ).
cnf(839,negated_conjecture,
domain(one) = domain(addition(X1,antidomain(X1))),
inference(spm,[status(thm)],[253,56,theory(equality)]) ).
cnf(870,negated_conjecture,
one = domain(addition(X1,antidomain(X1))),
inference(rw,[status(thm)],[839,223,theory(equality)]) ).
cnf(903,negated_conjecture,
domain(multiplication(X1,one)) = domain(multiplication(X1,addition(X2,antidomain(X2)))),
inference(spm,[status(thm)],[40,870,theory(equality)]) ).
cnf(927,negated_conjecture,
domain(X1) = domain(multiplication(X1,addition(X2,antidomain(X2)))),
inference(rw,[status(thm)],[903,36,theory(equality)]) ).
cnf(2477,negated_conjecture,
addition(domain(X1),one) = addition(domain(addition(X1,X2)),antidomain(X2)),
inference(spm,[status(thm)],[105,56,theory(equality)]) ).
cnf(2553,negated_conjecture,
one = addition(domain(addition(X1,X2)),antidomain(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2477,26,theory(equality)]),62,theory(equality)]) ).
cnf(2837,negated_conjecture,
addition(domain(multiplication(X1,addition(one,X2))),antidomain(multiplication(X1,X2))) = one,
inference(spm,[status(thm)],[2553,141,theory(equality)]) ).
cnf(2899,negated_conjecture,
addition(domain(X1),antidomain(multiplication(X1,X2))) = one,
inference(rw,[status(thm)],[2837,279,theory(equality)]) ).
cnf(7527,negated_conjecture,
multiplication(domain(X1),addition(antidomain(X1),X2)) = multiplication(domain(X1),X2),
inference(rw,[status(thm)],[146,58,theory(equality)]) ).
cnf(7576,negated_conjecture,
domain(multiplication(domain(X1),antidomain(antidomain(X1)))) = domain(domain(X1)),
inference(spm,[status(thm)],[927,7527,theory(equality)]) ).
cnf(7666,negated_conjecture,
domain(multiplication(domain(X1),antidomain(antidomain(X1)))) = domain(X1),
inference(rw,[status(thm)],[7576,123,theory(equality)]) ).
cnf(10712,negated_conjecture,
multiplication(domain(addition(X1,X2)),antidomain(X2)) = multiplication(domain(X1),antidomain(X2)),
inference(spm,[status(thm)],[201,48,theory(equality)]) ).
cnf(10954,negated_conjecture,
multiplication(addition(domain(X1),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
inference(rw,[status(thm)],[181,58,theory(equality)]) ).
cnf(10973,negated_conjecture,
multiplication(one,antidomain(X1)) = multiplication(antidomain(domain(X1)),antidomain(X1)),
inference(spm,[status(thm)],[10954,244,theory(equality)]) ).
cnf(11002,negated_conjecture,
multiplication(one,antidomain(X1)) = multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)),
inference(spm,[status(thm)],[10954,2899,theory(equality)]) ).
cnf(11067,negated_conjecture,
antidomain(X1) = multiplication(antidomain(domain(X1)),antidomain(X1)),
inference(rw,[status(thm)],[10973,44,theory(equality)]) ).
cnf(11107,negated_conjecture,
antidomain(X1) = multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)),
inference(rw,[status(thm)],[11002,44,theory(equality)]) ).
cnf(11239,negated_conjecture,
addition(antidomain(domain(X1)),antidomain(X1)) = multiplication(antidomain(domain(X1)),addition(one,antidomain(X1))),
inference(spm,[status(thm)],[141,11067,theory(equality)]) ).
cnf(11308,negated_conjecture,
addition(antidomain(X1),antidomain(domain(X1))) = multiplication(antidomain(domain(X1)),addition(one,antidomain(X1))),
inference(rw,[status(thm)],[11239,26,theory(equality)]) ).
cnf(11309,negated_conjecture,
addition(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[11308,522,theory(equality)]),36,theory(equality)]) ).
cnf(11991,negated_conjecture,
multiplication(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(spm,[status(thm)],[11107,745,theory(equality)]) ).
cnf(12282,negated_conjecture,
addition(antidomain(X1),antidomain(domain(X1))) = multiplication(antidomain(X1),addition(one,antidomain(domain(X1)))),
inference(spm,[status(thm)],[141,11991,theory(equality)]) ).
cnf(12357,negated_conjecture,
antidomain(domain(X1)) = multiplication(antidomain(X1),addition(one,antidomain(domain(X1)))),
inference(rw,[status(thm)],[12282,11309,theory(equality)]) ).
cnf(12358,negated_conjecture,
antidomain(domain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[12357,522,theory(equality)]),36,theory(equality)]) ).
cnf(12468,negated_conjecture,
antidomain(domain(X1)) = antidomain(multiplication(domain(X1),antidomain(antidomain(X1)))),
inference(spm,[status(thm)],[12358,7666,theory(equality)]) ).
cnf(12578,negated_conjecture,
antidomain(X1) = antidomain(multiplication(domain(X1),antidomain(antidomain(X1)))),
inference(rw,[status(thm)],[12468,12358,theory(equality)]) ).
cnf(37514,negated_conjecture,
multiplication(domain(zero),multiplication(domain(X1),domain(antidomain(X1)))) = multiplication(domain(X1),domain(antidomain(X1))),
inference(spm,[status(thm)],[772,55,theory(equality)]) ).
cnf(37711,negated_conjecture,
zero = multiplication(domain(X1),domain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[37514,49,theory(equality)]),32,theory(equality)]) ).
cnf(37968,negated_conjecture,
addition(X1,zero) = multiplication(domain(X1),addition(X1,domain(antidomain(X1)))),
inference(spm,[status(thm)],[773,37711,theory(equality)]) ).
cnf(38110,negated_conjecture,
X1 = multiplication(domain(X1),addition(X1,domain(antidomain(X1)))),
inference(rw,[status(thm)],[37968,22,theory(equality)]) ).
cnf(75817,negated_conjecture,
multiplication(domain(one),antidomain(antidomain(X1))) = multiplication(domain(domain(X1)),antidomain(antidomain(X1))),
inference(spm,[status(thm)],[10712,56,theory(equality)]) ).
cnf(76056,negated_conjecture,
antidomain(antidomain(X1)) = multiplication(domain(domain(X1)),antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[75817,223,theory(equality)]),44,theory(equality)]) ).
cnf(76057,negated_conjecture,
antidomain(antidomain(X1)) = multiplication(domain(X1),antidomain(antidomain(X1))),
inference(rw,[status(thm)],[76056,123,theory(equality)]) ).
cnf(76535,negated_conjecture,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[12578,76057,theory(equality)]) ).
cnf(76536,negated_conjecture,
domain(antidomain(antidomain(X1))) = domain(X1),
inference(rw,[status(thm)],[7666,76057,theory(equality)]) ).
cnf(77255,negated_conjecture,
multiplication(domain(X1),addition(antidomain(antidomain(X1)),domain(antidomain(antidomain(antidomain(X1)))))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[38110,76536,theory(equality)]) ).
cnf(77447,negated_conjecture,
domain(X1) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[77255,76535,theory(equality)]),26,theory(equality)]),56,theory(equality)]),36,theory(equality)]) ).
cnf(77718,negated_conjecture,
$false,
inference(rw,[status(thm)],[54,77447,theory(equality)]) ).
cnf(77719,negated_conjecture,
$false,
inference(cn,[status(thm)],[77718,theory(equality)]) ).
cnf(77720,negated_conjecture,
$false,
77719,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE080+1.p
% --creating new selector for [KLE001+0.ax, KLE001+5.ax]
% -running prover on /tmp/tmpQIHrqI/sel_KLE080+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE080+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE080+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE080+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
%
%------------------------------------------------------------------------------