TSTP Solution File: KLE010+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE010+2 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 11:39:57 EST 2010
% Result : Theorem 3.66s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 16
% Syntax : Number of formulae : 195 ( 72 unt; 0 def)
% Number of atoms : 423 ( 261 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 412 ( 184 ~; 189 |; 30 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 205 ( 5 sgn 73 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',right_annihilation) ).
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',multiplicative_left_identity) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',additive_identity) ).
fof(4,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',left_distributivity) ).
fof(5,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',additive_associativity) ).
fof(6,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',additive_commutativity) ).
fof(7,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',additive_idempotence) ).
fof(9,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',left_annihilation) ).
fof(10,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',test_4) ).
fof(11,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',test_3) ).
fof(12,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',test_2) ).
fof(13,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',test_1) ).
fof(14,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',multiplicative_right_identity) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',right_distributivity) ).
fof(16,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',order) ).
fof(17,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
file('/tmp/tmpEW3ZCw/sel_KLE010+2.p_1',goals) ).
fof(18,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[17]) ).
fof(19,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(20,plain,
! [X2] : multiplication(X2,zero) = zero,
inference(variable_rename,[status(thm)],[1]) ).
cnf(21,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(23,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(25,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(27,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[5]) ).
cnf(29,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[7]) ).
cnf(33,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[32]) ).
fof(36,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[9]) ).
cnf(37,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X4] :
( test(X4)
| c(X4) = zero ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(39,plain,
! [X5] :
( test(X5)
| c(X5) = zero ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( c(X1) = zero
| test(X1) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5] :
( ~ test(X4)
| ( ( c(X4) != X5
| complement(X4,X5) )
& ( ~ complement(X4,X5)
| c(X4) = X5 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(42,plain,
! [X6,X7] :
( ~ test(X6)
| ( ( c(X6) != X7
| complement(X6,X7) )
& ( ~ complement(X6,X7)
| c(X6) = X7 ) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X6,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(X6) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(44,plain,
( c(X1) = X2
| ~ test(X1)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(46,plain,
! [X4,X5] :
( ( ~ complement(X5,X4)
| ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) )
& ( multiplication(X4,X5) != zero
| multiplication(X5,X4) != zero
| addition(X4,X5) != one
| complement(X5,X4) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(47,plain,
! [X6,X7] :
( ( ~ complement(X7,X6)
| ( multiplication(X6,X7) = zero
& multiplication(X7,X6) = zero
& addition(X6,X7) = one ) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| addition(X6,X7) != one
| complement(X7,X6) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,plain,
! [X6,X7] :
( ( multiplication(X6,X7) = zero
| ~ complement(X7,X6) )
& ( multiplication(X7,X6) = zero
| ~ complement(X7,X6) )
& ( addition(X6,X7) = one
| ~ complement(X7,X6) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| addition(X6,X7) != one
| complement(X7,X6) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(49,plain,
( complement(X1,X2)
| addition(X2,X1) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(51,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(52,plain,
( multiplication(X2,X1) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(53,plain,
! [X4] :
( ( ~ test(X4)
| ? [X5] : complement(X5,X4) )
& ( ! [X5] : ~ complement(X5,X4)
| test(X4) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(54,plain,
! [X6] :
( ( ~ test(X6)
| ? [X7] : complement(X7,X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X6] :
( ( ~ test(X6)
| complement(esk1_1(X6),X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(skolemize,[status(esa)],[54]) ).
fof(56,plain,
! [X6,X8] :
( ( ~ complement(X8,X6)
| test(X6) )
& ( ~ test(X6)
| complement(esk1_1(X6),X6) ) ),
inference(shift_quantors,[status(thm)],[55]) ).
cnf(57,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,plain,
( test(X1)
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(59,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[14]) ).
cnf(60,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[59]) ).
fof(61,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(62,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(64,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[63]) ).
cnf(65,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(67,negated_conjecture,
? [X4,X5] :
( test(X5)
& test(X4)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
| ~ leq(addition(addition(addition(addition(multiplication(X5,X4),multiplication(c(X5),X4)),multiplication(X4,X5)),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(68,negated_conjecture,
? [X6,X7] :
( test(X7)
& test(X6)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(X7,X6),multiplication(c(X7),X6)),multiplication(X6,X7)),multiplication(c(X6),X7)),multiplication(c(X6),c(X7))))
| ~ leq(addition(addition(addition(addition(multiplication(X7,X6),multiplication(c(X7),X6)),multiplication(X6,X7)),multiplication(c(X6),X7)),multiplication(c(X6),c(X7))),one) ) ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ) ),
inference(skolemize,[status(esa)],[68]) ).
cnf(70,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0)))) ),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(71,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(72,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(73,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[25,31,theory(equality)]) ).
cnf(81,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[50,57,theory(equality)]) ).
cnf(82,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[52,57,theory(equality)]) ).
cnf(84,negated_conjecture,
( complement(esk2_0,X1)
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[45,71,theory(equality)]) ).
cnf(85,negated_conjecture,
( complement(esk3_0,X1)
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[45,72,theory(equality)]) ).
cnf(86,plain,
( complement(X1,X2)
| c(X1) = zero
| c(X1) != X2 ),
inference(spm,[status(thm)],[45,40,theory(equality)]) ).
cnf(87,plain,
( c(esk1_1(X1)) = X1
| ~ test(esk1_1(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[44,57,theory(equality)]) ).
cnf(107,plain,
addition(X1,addition(X2,addition(X1,X2))) = addition(X1,X2),
inference(spm,[status(thm)],[33,29,theory(equality)]) ).
cnf(108,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[29,33,theory(equality)]) ).
cnf(110,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[31,29,theory(equality)]) ).
cnf(119,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[62,60,theory(equality)]) ).
cnf(130,plain,
addition(multiplication(X1,addition(X2,X3)),X4) = addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)),
inference(spm,[status(thm)],[29,62,theory(equality)]) ).
cnf(182,plain,
( test(X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(spm,[status(thm)],[58,49,theory(equality)]) ).
cnf(186,plain,
( c(X1) = X2
| ~ test(X1)
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| addition(X2,X1) != one ),
inference(spm,[status(thm)],[44,49,theory(equality)]) ).
cnf(187,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| ~ leq(addition(addition(addition(addition(multiplication(esk3_0,esk2_0),multiplication(c(esk3_0),esk2_0)),multiplication(esk2_0,esk3_0)),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ),
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)],[70,27,theory(equality)]),31,theory(equality)]),29,theory(equality)]),31,theory(equality)]),29,theory(equality)]),29,theory(equality)]),31,theory(equality)]) ).
cnf(188,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))),one) ),
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)],[187,27,theory(equality)]),31,theory(equality)]),29,theory(equality)]),31,theory(equality)]),29,theory(equality)]),29,theory(equality)]),31,theory(equality)]) ).
cnf(189,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| addition(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))),one) != one ),
inference(spm,[status(thm)],[188,65,theory(equality)]) ).
cnf(190,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))))
| addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),addition(one,multiplication(addition(esk3_0,c(esk3_0)),esk2_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[189,29,theory(equality)]),29,theory(equality)]),29,theory(equality)]),31,theory(equality)]) ).
cnf(198,negated_conjecture,
( addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),addition(one,multiplication(addition(esk3_0,c(esk3_0)),esk2_0))))) != one
| addition(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0))))) != addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))) ),
inference(spm,[status(thm)],[190,65,theory(equality)]) ).
cnf(200,negated_conjecture,
( addition(X1,esk2_0) = one
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[50,84,theory(equality)]) ).
cnf(201,negated_conjecture,
( multiplication(X1,esk2_0) = zero
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[52,84,theory(equality)]) ).
cnf(202,negated_conjecture,
( multiplication(esk2_0,X1) = zero
| c(esk2_0) != X1 ),
inference(spm,[status(thm)],[51,84,theory(equality)]) ).
cnf(207,negated_conjecture,
addition(c(esk2_0),esk2_0) = one,
inference(er,[status(thm)],[200,theory(equality)]) ).
cnf(208,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[207,31,theory(equality)]) ).
cnf(210,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(er,[status(thm)],[201,theory(equality)]) ).
cnf(212,negated_conjecture,
addition(zero,multiplication(c(esk2_0),X1)) = multiplication(c(esk2_0),addition(esk2_0,X1)),
inference(spm,[status(thm)],[62,210,theory(equality)]) ).
cnf(215,negated_conjecture,
addition(multiplication(X1,esk2_0),zero) = multiplication(addition(X1,c(esk2_0)),esk2_0),
inference(spm,[status(thm)],[27,210,theory(equality)]) ).
cnf(217,negated_conjecture,
multiplication(c(esk2_0),X1) = multiplication(c(esk2_0),addition(esk2_0,X1)),
inference(rw,[status(thm)],[212,73,theory(equality)]) ).
cnf(220,negated_conjecture,
multiplication(X1,esk2_0) = multiplication(addition(X1,c(esk2_0)),esk2_0),
inference(rw,[status(thm)],[215,25,theory(equality)]) ).
cnf(223,plain,
( one = esk1_1(zero)
| ~ test(zero) ),
inference(spm,[status(thm)],[73,81,theory(equality)]) ).
cnf(224,negated_conjecture,
( test(X1)
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[58,85,theory(equality)]) ).
cnf(225,negated_conjecture,
( addition(X1,esk3_0) = one
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[50,85,theory(equality)]) ).
cnf(226,negated_conjecture,
( multiplication(X1,esk3_0) = zero
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[52,85,theory(equality)]) ).
cnf(227,negated_conjecture,
( multiplication(esk3_0,X1) = zero
| c(esk3_0) != X1 ),
inference(spm,[status(thm)],[51,85,theory(equality)]) ).
cnf(255,plain,
( zero = esk1_1(one)
| ~ test(one) ),
inference(spm,[status(thm)],[23,82,theory(equality)]) ).
cnf(260,plain,
( addition(zero,multiplication(X2,esk1_1(X1))) = multiplication(addition(X1,X2),esk1_1(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[27,82,theory(equality)]) ).
cnf(266,plain,
( multiplication(X2,esk1_1(X1)) = multiplication(addition(X1,X2),esk1_1(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[260,73,theory(equality)]) ).
cnf(269,plain,
( complement(zero,one)
| ~ test(one) ),
inference(spm,[status(thm)],[57,255,theory(equality)]) ).
cnf(313,negated_conjecture,
addition(c(esk3_0),esk3_0) = one,
inference(er,[status(thm)],[225,theory(equality)]) ).
cnf(314,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[313,31,theory(equality)]) ).
cnf(316,negated_conjecture,
( addition(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))))) != addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),multiplication(addition(esk3_0,c(esk3_0)),esk2_0))))
| addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),addition(one,multiplication(addition(esk3_0,c(esk3_0)),esk2_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[198,314,theory(equality)]),23,theory(equality)]),31,theory(equality)]) ).
cnf(317,negated_conjecture,
( addition(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))))) != addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))))
| addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(c(esk2_0),c(esk3_0)),addition(one,multiplication(addition(esk3_0,c(esk3_0)),esk2_0))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[316,314,theory(equality)]),23,theory(equality)]),31,theory(equality)]) ).
cnf(318,negated_conjecture,
( addition(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))))) != addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))))
| addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,addition(one,multiplication(c(esk2_0),c(esk3_0)))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[317,314,theory(equality)]),23,theory(equality)]),31,theory(equality)]),31,theory(equality)]),29,theory(equality)]) ).
cnf(347,plain,
( test(X1)
| c(X2) = zero
| c(X2) != X1 ),
inference(spm,[status(thm)],[58,86,theory(equality)]) ).
cnf(387,plain,
( c(one) = zero
| ~ test(one)
| ~ test(zero) ),
inference(spm,[status(thm)],[87,223,theory(equality)]) ).
cnf(389,plain,
( c(one) = zero
| ~ test(zero) ),
inference(csr,[status(thm)],[387,40]) ).
cnf(408,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),one)) = one,
inference(spm,[status(thm)],[107,208,theory(equality)]) ).
cnf(428,negated_conjecture,
addition(esk2_0,addition(one,c(esk2_0))) = one,
inference(rw,[status(thm)],[408,31,theory(equality)]) ).
cnf(459,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[108,81,theory(equality)]) ).
cnf(561,negated_conjecture,
( addition(one,multiplication(esk2_0,esk3_0)) != addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,multiplication(c(esk2_0),c(esk3_0)))))
| addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,addition(one,multiplication(c(esk2_0),c(esk3_0)))))) != one ),
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)],[318,110,theory(equality)]),62,theory(equality)]),31,theory(equality)]),314,theory(equality)]),60,theory(equality)]),208,theory(equality)]),31,theory(equality)]),108,theory(equality)]) ).
cnf(562,negated_conjecture,
( $false
| addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(esk2_0,addition(one,multiplication(c(esk2_0),c(esk3_0)))))) != one ),
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)],[561,110,theory(equality)]),62,theory(equality)]),31,theory(equality)]),314,theory(equality)]),60,theory(equality)]),208,theory(equality)]),31,theory(equality)]) ).
cnf(563,negated_conjecture,
( $false
| addition(one,multiplication(esk2_0,esk3_0)) != one ),
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)],[562,110,theory(equality)]),29,theory(equality)]),62,theory(equality)]),31,theory(equality)]),314,theory(equality)]),60,theory(equality)]),428,theory(equality)]),31,theory(equality)]) ).
cnf(564,negated_conjecture,
addition(one,multiplication(esk2_0,esk3_0)) != one,
inference(cn,[status(thm)],[563,theory(equality)]) ).
cnf(789,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(er,[status(thm)],[202,theory(equality)]) ).
cnf(794,negated_conjecture,
addition(multiplication(esk2_0,X1),zero) = multiplication(esk2_0,addition(X1,c(esk2_0))),
inference(spm,[status(thm)],[62,789,theory(equality)]) ).
cnf(801,negated_conjecture,
multiplication(esk2_0,X1) = multiplication(esk2_0,addition(X1,c(esk2_0))),
inference(rw,[status(thm)],[794,25,theory(equality)]) ).
cnf(1103,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(er,[status(thm)],[226,theory(equality)]) ).
cnf(1109,negated_conjecture,
addition(zero,multiplication(c(esk3_0),X1)) = multiplication(c(esk3_0),addition(esk3_0,X1)),
inference(spm,[status(thm)],[62,1103,theory(equality)]) ).
cnf(1116,negated_conjecture,
multiplication(c(esk3_0),X1) = multiplication(c(esk3_0),addition(esk3_0,X1)),
inference(rw,[status(thm)],[1109,73,theory(equality)]) ).
cnf(1184,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(er,[status(thm)],[227,theory(equality)]) ).
cnf(1238,plain,
( addition(multiplication(X1,X2),one) = addition(multiplication(X1,addition(X2,X3)),esk1_1(multiplication(X1,X3)))
| ~ test(multiplication(X1,X3)) ),
inference(spm,[status(thm)],[130,81,theory(equality)]) ).
cnf(1299,plain,
( addition(one,multiplication(X1,X2)) = addition(multiplication(X1,addition(X2,X3)),esk1_1(multiplication(X1,X3)))
| ~ test(multiplication(X1,X3)) ),
inference(rw,[status(thm)],[1238,31,theory(equality)]) ).
cnf(1491,negated_conjecture,
multiplication(one,esk2_0) = multiplication(esk2_0,esk2_0),
inference(spm,[status(thm)],[220,208,theory(equality)]) ).
cnf(1505,negated_conjecture,
esk2_0 = multiplication(esk2_0,esk2_0),
inference(rw,[status(thm)],[1491,23,theory(equality)]) ).
cnf(1514,negated_conjecture,
addition(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,addition(esk2_0,X1)),
inference(spm,[status(thm)],[62,1505,theory(equality)]) ).
cnf(1522,negated_conjecture,
multiplication(esk2_0,addition(one,X1)) = multiplication(esk2_0,addition(esk2_0,X1)),
inference(rw,[status(thm)],[1514,119,theory(equality)]) ).
cnf(3334,plain,
( test(X1)
| multiplication(X1,zero) != zero
| multiplication(zero,X1) != zero
| X1 != one ),
inference(spm,[status(thm)],[182,25,theory(equality)]) ).
cnf(3339,plain,
( test(zero)
| multiplication(zero,X1) != zero
| multiplication(X1,zero) != zero
| X1 != one ),
inference(spm,[status(thm)],[182,73,theory(equality)]) ).
cnf(3375,plain,
( test(X1)
| $false
| multiplication(zero,X1) != zero
| X1 != one ),
inference(rw,[status(thm)],[3334,21,theory(equality)]) ).
cnf(3376,plain,
( test(X1)
| $false
| $false
| X1 != one ),
inference(rw,[status(thm)],[3375,37,theory(equality)]) ).
cnf(3377,plain,
( test(X1)
| X1 != one ),
inference(cn,[status(thm)],[3376,theory(equality)]) ).
cnf(3382,plain,
( test(zero)
| $false
| multiplication(X1,zero) != zero
| X1 != one ),
inference(rw,[status(thm)],[3339,37,theory(equality)]) ).
cnf(3383,plain,
( test(zero)
| $false
| $false
| X1 != one ),
inference(rw,[status(thm)],[3382,21,theory(equality)]) ).
cnf(3384,plain,
( test(zero)
| X1 != one ),
inference(cn,[status(thm)],[3383,theory(equality)]) ).
cnf(3451,plain,
complement(zero,one),
inference(spm,[status(thm)],[269,3377,theory(equality)]) ).
cnf(3458,plain,
test(one),
inference(spm,[status(thm)],[58,3451,theory(equality)]) ).
cnf(3470,plain,
( complement(one,X1)
| c(one) != X1 ),
inference(spm,[status(thm)],[45,3458,theory(equality)]) ).
cnf(3517,plain,
test(zero),
inference(er,[status(thm)],[3384,theory(equality)]) ).
cnf(3523,plain,
( c(one) = zero
| $false ),
inference(rw,[status(thm)],[389,3517,theory(equality)]) ).
cnf(3524,plain,
c(one) = zero,
inference(cn,[status(thm)],[3523,theory(equality)]) ).
cnf(3701,negated_conjecture,
( c(c(esk3_0)) = esk3_0
| multiplication(esk3_0,c(esk3_0)) != zero
| multiplication(c(esk3_0),esk3_0) != zero
| ~ test(c(esk3_0)) ),
inference(spm,[status(thm)],[186,314,theory(equality)]) ).
cnf(3752,negated_conjecture,
( c(c(esk3_0)) = esk3_0
| $false
| multiplication(c(esk3_0),esk3_0) != zero
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[3701,1184,theory(equality)]) ).
cnf(3753,negated_conjecture,
( c(c(esk3_0)) = esk3_0
| $false
| $false
| ~ test(c(esk3_0)) ),
inference(rw,[status(thm)],[3752,1103,theory(equality)]) ).
cnf(3754,negated_conjecture,
( c(c(esk3_0)) = esk3_0
| ~ test(c(esk3_0)) ),
inference(cn,[status(thm)],[3753,theory(equality)]) ).
cnf(3839,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[3754,224,theory(equality)]) ).
cnf(3848,negated_conjecture,
( esk3_0 = zero
| test(X1)
| esk3_0 != X1 ),
inference(spm,[status(thm)],[347,3839,theory(equality)]) ).
cnf(3861,negated_conjecture,
( addition(X1,one) = one
| zero = esk3_0
| esk3_0 != X1 ),
inference(spm,[status(thm)],[459,3848,theory(equality)]) ).
cnf(3862,plain,
( complement(one,X1)
| zero != X1 ),
inference(rw,[status(thm)],[3470,3524,theory(equality)]) ).
cnf(3863,plain,
( test(X1)
| zero != X1 ),
inference(spm,[status(thm)],[58,3862,theory(equality)]) ).
cnf(3864,plain,
( addition(X1,one) = one
| zero != X1 ),
inference(spm,[status(thm)],[50,3862,theory(equality)]) ).
cnf(4004,negated_conjecture,
( multiplication(c(esk2_0),one) = multiplication(c(esk2_0),esk1_1(esk2_0))
| ~ test(esk2_0) ),
inference(spm,[status(thm)],[217,81,theory(equality)]) ).
cnf(4027,negated_conjecture,
( c(esk2_0) = multiplication(c(esk2_0),esk1_1(esk2_0))
| ~ test(esk2_0) ),
inference(rw,[status(thm)],[4004,60,theory(equality)]) ).
cnf(4028,negated_conjecture,
( c(esk2_0) = multiplication(c(esk2_0),esk1_1(esk2_0))
| $false ),
inference(rw,[status(thm)],[4027,71,theory(equality)]) ).
cnf(4029,negated_conjecture,
c(esk2_0) = multiplication(c(esk2_0),esk1_1(esk2_0)),
inference(cn,[status(thm)],[4028,theory(equality)]) ).
cnf(4047,plain,
( one = addition(one,X1)
| zero != X1 ),
inference(spm,[status(thm)],[31,3864,theory(equality)]) ).
cnf(4269,plain,
( c(X1) = one
| multiplication(one,X1) != zero
| multiplication(X1,one) != zero
| ~ test(X1)
| zero != X1 ),
inference(spm,[status(thm)],[186,4047,theory(equality)]) ).
cnf(4291,plain,
( c(X1) = one
| X1 != zero
| multiplication(X1,one) != zero
| ~ test(X1)
| zero != X1 ),
inference(rw,[status(thm)],[4269,23,theory(equality)]) ).
cnf(4292,plain,
( c(X1) = one
| X1 != zero
| X1 != zero
| ~ test(X1)
| zero != X1 ),
inference(rw,[status(thm)],[4291,60,theory(equality)]) ).
cnf(4293,plain,
( c(X1) = one
| X1 != zero
| ~ test(X1) ),
inference(cn,[status(thm)],[4292,theory(equality)]) ).
cnf(4299,plain,
( c(X1) = one
| X1 != zero ),
inference(csr,[status(thm)],[4293,3863]) ).
cnf(5659,negated_conjecture,
( multiplication(one,esk1_1(esk2_0)) = multiplication(c(esk2_0),esk1_1(esk2_0))
| ~ test(esk2_0) ),
inference(spm,[status(thm)],[266,208,theory(equality)]) ).
cnf(5716,negated_conjecture,
( esk1_1(esk2_0) = multiplication(c(esk2_0),esk1_1(esk2_0))
| ~ test(esk2_0) ),
inference(rw,[status(thm)],[5659,23,theory(equality)]) ).
cnf(5717,negated_conjecture,
( esk1_1(esk2_0) = multiplication(c(esk2_0),esk1_1(esk2_0))
| $false ),
inference(rw,[status(thm)],[5716,71,theory(equality)]) ).
cnf(5718,negated_conjecture,
esk1_1(esk2_0) = multiplication(c(esk2_0),esk1_1(esk2_0)),
inference(cn,[status(thm)],[5717,theory(equality)]) ).
cnf(12385,negated_conjecture,
( one = addition(one,X1)
| zero = esk3_0
| esk3_0 != X1 ),
inference(spm,[status(thm)],[31,3861,theory(equality)]) ).
cnf(13495,negated_conjecture,
( one = multiplication(one,addition(one,X1))
| zero = esk3_0
| esk3_0 != multiplication(one,X1) ),
inference(spm,[status(thm)],[119,12385,theory(equality)]) ).
cnf(13568,negated_conjecture,
( one = addition(one,X1)
| zero = esk3_0
| esk3_0 != multiplication(one,X1) ),
inference(rw,[status(thm)],[13495,23,theory(equality)]) ).
cnf(13569,negated_conjecture,
( one = addition(one,X1)
| zero = esk3_0
| esk3_0 != X1 ),
inference(rw,[status(thm)],[13568,23,theory(equality)]) ).
cnf(14413,negated_conjecture,
c(esk2_0) = esk1_1(esk2_0),
inference(rw,[status(thm)],[5718,4029,theory(equality)]) ).
cnf(23895,negated_conjecture,
( multiplication(one,addition(esk3_0,X1)) = multiplication(one,X1)
| esk3_0 != zero ),
inference(spm,[status(thm)],[1116,4299,theory(equality)]) ).
cnf(23950,negated_conjecture,
( addition(esk3_0,X1) = multiplication(one,X1)
| esk3_0 != zero ),
inference(rw,[status(thm)],[23895,23,theory(equality)]) ).
cnf(23951,negated_conjecture,
( addition(esk3_0,X1) = X1
| esk3_0 != zero ),
inference(rw,[status(thm)],[23950,23,theory(equality)]) ).
cnf(24699,negated_conjecture,
( multiplication(esk2_0,c(esk2_0)) = multiplication(esk2_0,esk3_0)
| zero != esk3_0 ),
inference(spm,[status(thm)],[801,23951,theory(equality)]) ).
cnf(24804,negated_conjecture,
( zero = multiplication(esk2_0,esk3_0)
| zero != esk3_0 ),
inference(rw,[status(thm)],[24699,789,theory(equality)]) ).
cnf(25106,negated_conjecture,
( addition(one,zero) != one
| zero != esk3_0 ),
inference(spm,[status(thm)],[564,24804,theory(equality)]) ).
cnf(25150,negated_conjecture,
( $false
| zero != esk3_0 ),
inference(rw,[status(thm)],[25106,25,theory(equality)]) ).
cnf(25151,negated_conjecture,
zero != esk3_0,
inference(cn,[status(thm)],[25150,theory(equality)]) ).
cnf(27242,negated_conjecture,
( addition(one,X1) = one
| esk3_0 != X1 ),
inference(sr,[status(thm)],[13569,25151,theory(equality)]) ).
cnf(43078,negated_conjecture,
( multiplication(esk2_0,one) = multiplication(esk2_0,addition(esk2_0,X1))
| esk3_0 != X1 ),
inference(spm,[status(thm)],[1522,27242,theory(equality)]) ).
cnf(43226,negated_conjecture,
( esk2_0 = multiplication(esk2_0,addition(esk2_0,X1))
| esk3_0 != X1 ),
inference(rw,[status(thm)],[43078,60,theory(equality)]) ).
cnf(76977,negated_conjecture,
( multiplication(esk2_0,addition(X1,esk2_0)) = esk2_0
| esk3_0 != X1 ),
inference(spm,[status(thm)],[43226,31,theory(equality)]) ).
cnf(103097,negated_conjecture,
( addition(esk2_0,esk1_1(multiplication(esk2_0,esk2_0))) = addition(one,multiplication(esk2_0,X1))
| ~ test(multiplication(esk2_0,esk2_0))
| esk3_0 != X1 ),
inference(spm,[status(thm)],[1299,76977,theory(equality)]) ).
cnf(103253,negated_conjecture,
( one = addition(one,multiplication(esk2_0,X1))
| ~ test(multiplication(esk2_0,esk2_0))
| esk3_0 != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[103097,1505,theory(equality)]),14413,theory(equality)]),208,theory(equality)]) ).
cnf(103254,negated_conjecture,
( one = addition(one,multiplication(esk2_0,X1))
| $false
| esk3_0 != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[103253,1505,theory(equality)]),71,theory(equality)]) ).
cnf(103255,negated_conjecture,
( one = addition(one,multiplication(esk2_0,X1))
| esk3_0 != X1 ),
inference(cn,[status(thm)],[103254,theory(equality)]) ).
cnf(107027,negated_conjecture,
$false,
inference(spm,[status(thm)],[564,103255,theory(equality)]) ).
cnf(107170,negated_conjecture,
$false,
107027,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE010+2.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpEW3ZCw/sel_KLE010+2.p_1 with time limit 29
% -prover status Theorem
% Problem KLE010+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE010+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE010+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
%
%------------------------------------------------------------------------------