## TSTP Solution File: KLE011+1 by SInE---0.4

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE011+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 11:40:26 EST 2010

% Result   : Theorem 20.02s
% Output   : CNFRefutation 20.02s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  126 (  63 unt;   0 def)
%            Number of atoms       :  252 ( 148 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  226 ( 100   ~;  94   |;  26   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  165 (   3 sgn  67   !;   7   ?)

%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',multiplicative_left_identity) ).

fof(3,axiom,
! [X1] : addition(X1,zero) = X1,

fof(4,axiom,
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',left_distributivity) ).

fof(5,axiom,

fof(6,axiom,

fof(7,axiom,
! [X1] : addition(X1,X1) = X1,

fof(8,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',multiplicative_associativity) ).

fof(9,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',left_annihilation) ).

fof(11,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/tmp/tmpakaKV7/sel_KLE011+1.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/tmpakaKV7/sel_KLE011+1.p_1',test_2) ).

fof(13,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',test_1) ).

fof(14,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',multiplicative_right_identity) ).

fof(15,axiom,
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',right_distributivity) ).

fof(16,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
file('/tmp/tmpakaKV7/sel_KLE011+1.p_1',goals) ).

fof(17,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
inference(assume_negation,[status(cth)],[16]) ).

fof(21,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).

cnf(22,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[21]) ).

fof(23,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).

cnf(24,plain,
inference(split_conjunct,[status(thm)],[23]) ).

fof(25,plain,
inference(variable_rename,[status(thm)],[4]) ).

cnf(26,plain,
inference(split_conjunct,[status(thm)],[25]) ).

fof(27,plain,
inference(variable_rename,[status(thm)],[5]) ).

cnf(28,plain,
inference(split_conjunct,[status(thm)],[27]) ).

fof(29,plain,
inference(variable_rename,[status(thm)],[6]) ).

cnf(30,plain,
inference(split_conjunct,[status(thm)],[29]) ).

fof(31,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[7]) ).

cnf(32,plain,
inference(split_conjunct,[status(thm)],[31]) ).

fof(33,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[8]) ).

cnf(34,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[33]) ).

fof(35,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[9]) ).

cnf(36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[35]) ).

fof(40,plain,
! [X4,X5] :
( ~ test(X4)
| ( ( c(X4) != X5
| complement(X4,X5) )
& ( ~ complement(X4,X5)
| c(X4) = X5 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).

fof(41,plain,
! [X6,X7] :
( ~ test(X6)
| ( ( c(X6) != X7
| complement(X6,X7) )
& ( ~ complement(X6,X7)
| c(X6) = X7 ) ) ),
inference(variable_rename,[status(thm)],[40]) ).

fof(42,plain,
! [X6,X7] :
( ( c(X6) != X7
| complement(X6,X7)
| ~ test(X6) )
& ( ~ complement(X6,X7)
| c(X6) = X7
| ~ test(X6) ) ),
inference(distribute,[status(thm)],[41]) ).

cnf(43,plain,
( c(X1) = X2
| ~ test(X1)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[42]) ).

cnf(44,plain,
( complement(X1,X2)
| ~ test(X1)
| c(X1) != X2 ),
inference(split_conjunct,[status(thm)],[42]) ).

fof(45,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
| complement(X5,X4) ) ),
inference(fof_nnf,[status(thm)],[12]) ).

fof(46,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
| complement(X7,X6) ) ),
inference(variable_rename,[status(thm)],[45]) ).

fof(47,plain,
! [X6,X7] :
( ( multiplication(X6,X7) = zero
| ~ complement(X7,X6) )
& ( multiplication(X7,X6) = zero
| ~ complement(X7,X6) )
| ~ complement(X7,X6) )
& ( multiplication(X6,X7) != zero
| multiplication(X7,X6) != zero
| complement(X7,X6) ) ),
inference(distribute,[status(thm)],[46]) ).

cnf(48,plain,
( complement(X1,X2)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(split_conjunct,[status(thm)],[47]) ).

cnf(49,plain,
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).

cnf(50,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).

cnf(51,plain,
( multiplication(X2,X1) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).

fof(52,plain,
! [X4] :
( ( ~ test(X4)
| ? [X5] : complement(X5,X4) )
& ( ! [X5] : ~ complement(X5,X4)
| test(X4) ) ),
inference(fof_nnf,[status(thm)],[13]) ).

fof(53,plain,
! [X6] :
( ( ~ test(X6)
| ? [X7] : complement(X7,X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(variable_rename,[status(thm)],[52]) ).

fof(54,plain,
! [X6] :
( ( ~ test(X6)
| complement(esk1_1(X6),X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(skolemize,[status(esa)],[53]) ).

fof(55,plain,
! [X6,X8] :
( ( ~ complement(X8,X6)
| test(X6) )
& ( ~ test(X6)
| complement(esk1_1(X6),X6) ) ),
inference(shift_quantors,[status(thm)],[54]) ).

cnf(56,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[55]) ).

cnf(57,plain,
( test(X1)
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[55]) ).

fof(58,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[14]) ).

cnf(59,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[58]) ).

fof(60,plain,
inference(variable_rename,[status(thm)],[15]) ).

cnf(61,plain,
inference(split_conjunct,[status(thm)],[60]) ).

fof(62,negated_conjecture,
? [X4,X5] :
( test(X5)
& test(X4)
inference(fof_nnf,[status(thm)],[17]) ).

fof(63,negated_conjecture,
? [X6,X7] :
( test(X7)
& test(X6)
inference(variable_rename,[status(thm)],[62]) ).

fof(64,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
inference(skolemize,[status(esa)],[63]) ).

cnf(65,negated_conjecture,
inference(split_conjunct,[status(thm)],[64]) ).

cnf(66,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[64]) ).

cnf(67,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[64]) ).

cnf(75,plain,
| ~ test(X1) ),
inference(spm,[status(thm)],[49,56,theory(equality)]) ).

cnf(76,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[51,56,theory(equality)]) ).

cnf(77,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[50,56,theory(equality)]) ).

cnf(78,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[44,theory(equality)]) ).

cnf(101,plain,
inference(spm,[status(thm)],[28,32,theory(equality)]) ).

cnf(103,plain,
inference(spm,[status(thm)],[30,28,theory(equality)]) ).

cnf(105,plain,
inference(spm,[status(thm)],[28,30,theory(equality)]) ).

cnf(110,plain,
inference(rw,[status(thm)],[105,28,theory(equality)]) ).

cnf(112,plain,
inference(spm,[status(thm)],[61,59,theory(equality)]) ).

cnf(155,plain,
inference(spm,[status(thm)],[28,26,theory(equality)]) ).

cnf(175,plain,
( test(X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
inference(spm,[status(thm)],[57,48,theory(equality)]) ).

cnf(179,plain,
( c(X1) = X2
| ~ test(X1)
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
inference(spm,[status(thm)],[43,48,theory(equality)]) ).

cnf(180,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[65,30,theory(equality)]),28,theory(equality)]) ).

cnf(196,plain,
| ~ test(X1) ),
inference(spm,[status(thm)],[49,78,theory(equality)]) ).

cnf(199,plain,
| ~ test(X1) ),
inference(rw,[status(thm)],[196,30,theory(equality)]) ).

cnf(201,plain,
inference(spm,[status(thm)],[28,75,theory(equality)]) ).

cnf(208,negated_conjecture,
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[180,199,theory(equality)]) ).

cnf(213,negated_conjecture,
| ~ test(esk3_0) ),
inference(rw,[status(thm)],[208,22,theory(equality)]) ).

cnf(214,negated_conjecture,
| \$false ),
inference(rw,[status(thm)],[213,67,theory(equality)]) ).

cnf(215,negated_conjecture,
inference(cn,[status(thm)],[214,theory(equality)]) ).

cnf(244,plain,
( zero = multiplication(X1,multiplication(X2,esk1_1(multiplication(X1,X2))))
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[34,76,theory(equality)]) ).

cnf(246,plain,
| ~ test(X1) ),
inference(spm,[status(thm)],[61,76,theory(equality)]) ).

cnf(252,plain,
| ~ test(X1) ),
inference(rw,[status(thm)],[246,24,theory(equality)]) ).

cnf(296,plain,
( multiplication(zero,X2) = multiplication(esk1_1(X1),multiplication(X1,X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[34,77,theory(equality)]) ).

cnf(303,plain,
( zero = multiplication(esk1_1(X1),multiplication(X1,X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[296,36,theory(equality)]) ).

cnf(357,plain,
| ~ test(X1) ),
inference(spm,[status(thm)],[101,75,theory(equality)]) ).

cnf(370,negated_conjecture,
inference(spm,[status(thm)],[357,66,theory(equality)]) ).

cnf(371,negated_conjecture,
inference(spm,[status(thm)],[357,67,theory(equality)]) ).

cnf(374,negated_conjecture,
inference(rw,[status(thm)],[370,30,theory(equality)]) ).

cnf(375,negated_conjecture,
inference(rw,[status(thm)],[371,30,theory(equality)]) ).

cnf(378,negated_conjecture,
inference(spm,[status(thm)],[28,374,theory(equality)]) ).

cnf(587,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[215,103,theory(equality)]),30,theory(equality)]) ).

cnf(778,plain,
| ~ test(X2) ),
inference(spm,[status(thm)],[110,199,theory(equality)]) ).

cnf(877,negated_conjecture,
inference(spm,[status(thm)],[378,112,theory(equality)]) ).

cnf(2318,plain,
inference(spm,[status(thm)],[155,61,theory(equality)]) ).

cnf(2573,negated_conjecture,
inference(spm,[status(thm)],[877,375,theory(equality)]) ).

cnf(2615,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2573,59,theory(equality)]),374,theory(equality)]) ).

cnf(3555,plain,
( c(X1) = X2
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| ~ test(X1) ),
inference(spm,[status(thm)],[179,30,theory(equality)]) ).

cnf(4022,plain,
inference(spm,[status(thm)],[201,112,theory(equality)]) ).

cnf(5021,plain,
( multiplication(X1,one) = multiplication(X1,X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[252,75,theory(equality)]) ).

cnf(5061,plain,
( X1 = multiplication(X1,X1)
| ~ test(X1) ),
inference(rw,[status(thm)],[5021,59,theory(equality)]) ).

cnf(5064,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[5061,67,theory(equality)]) ).

cnf(5379,negated_conjecture,
multiplication(esk3_0,X1) = multiplication(esk3_0,multiplication(esk3_0,X1)),
inference(spm,[status(thm)],[34,5064,theory(equality)]) ).

cnf(5395,negated_conjecture,
( multiplication(esk1_1(esk3_0),esk3_0) = zero
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[303,5064,theory(equality)]) ).

cnf(5396,negated_conjecture,
( multiplication(esk3_0,multiplication(esk3_0,esk1_1(esk3_0))) = zero
| ~ test(esk3_0) ),
inference(spm,[status(thm)],[244,5064,theory(equality)]) ).

cnf(5413,negated_conjecture,
( multiplication(esk1_1(esk3_0),esk3_0) = zero
| \$false ),
inference(rw,[status(thm)],[5395,67,theory(equality)]) ).

cnf(5414,negated_conjecture,
multiplication(esk1_1(esk3_0),esk3_0) = zero,
inference(cn,[status(thm)],[5413,theory(equality)]) ).

cnf(5415,negated_conjecture,
( multiplication(esk3_0,multiplication(esk3_0,esk1_1(esk3_0))) = zero
| \$false ),
inference(rw,[status(thm)],[5396,67,theory(equality)]) ).

cnf(5416,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,esk1_1(esk3_0))) = zero,
inference(cn,[status(thm)],[5415,theory(equality)]) ).

cnf(12011,negated_conjecture,
multiplication(esk3_0,esk1_1(esk3_0)) = zero,
inference(rw,[status(thm)],[5416,5379,theory(equality)]) ).

cnf(253750,negated_conjecture,
inference(rw,[status(thm)],[587,2318,theory(equality)]) ).

cnf(429330,plain,
( c(X1) = X2
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
inference(csr,[status(thm)],[3555,175]) ).

cnf(478049,negated_conjecture,
inference(spm,[status(thm)],[4022,5064,theory(equality)]) ).

cnf(479284,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[478049,375,theory(equality)]),59,theory(equality)]),101,theory(equality)]) ).

cnf(479285,negated_conjecture,
| \$false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[479284,375,theory(equality)]),59,theory(equality)]),67,theory(equality)]) ).

cnf(479286,negated_conjecture,
inference(cn,[status(thm)],[479285,theory(equality)]) ).

cnf(487632,negated_conjecture,
( c(esk3_0) = esk1_1(esk3_0)
| multiplication(esk1_1(esk3_0),esk3_0) != zero
| multiplication(esk3_0,esk1_1(esk3_0)) != zero ),
inference(spm,[status(thm)],[429330,479286,theory(equality)]) ).

cnf(487907,negated_conjecture,
( c(esk3_0) = esk1_1(esk3_0)
| \$false
| multiplication(esk3_0,esk1_1(esk3_0)) != zero ),
inference(rw,[status(thm)],[487632,5414,theory(equality)]) ).

cnf(487908,negated_conjecture,
( c(esk3_0) = esk1_1(esk3_0)
| \$false
| \$false ),
inference(rw,[status(thm)],[487907,12011,theory(equality)]) ).

cnf(487909,negated_conjecture,
c(esk3_0) = esk1_1(esk3_0),
inference(cn,[status(thm)],[487908,theory(equality)]) ).

cnf(490304,negated_conjecture,
inference(rw,[status(thm)],[479286,487909,theory(equality)]) ).

cnf(492800,negated_conjecture,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[253750,490304,theory(equality)]),59,theory(equality)]) ).

cnf(493237,negated_conjecture,
| ~ test(esk2_0) ),
inference(spm,[status(thm)],[492800,778,theory(equality)]) ).

cnf(493251,negated_conjecture,
( \$false
| ~ test(esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[493237,30,theory(equality)]),2615,theory(equality)]) ).

cnf(493252,negated_conjecture,
( \$false
| \$false ),
inference(rw,[status(thm)],[493251,66,theory(equality)]) ).

cnf(493253,negated_conjecture,
\$false,
inference(cn,[status(thm)],[493252,theory(equality)]) ).

cnf(493254,negated_conjecture,
\$false,
493253,
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE011+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpakaKV7/sel_KLE011+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE011+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE011+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE011+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
%
%------------------------------------------------------------------------------
```