TSTP Solution File: KLE017+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE017+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 11:42:12 EST 2010
% Result : Theorem 2.54s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 14
% Syntax : Number of formulae : 170 ( 81 unt; 0 def)
% Number of atoms : 339 ( 166 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 269 ( 100 ~; 119 |; 43 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 180 ( 2 sgn 67 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',multiplicative_left_identity) ).
fof(3,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',additive_identity) ).
fof(4,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',left_distributivity) ).
fof(5,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',additive_idempotence) ).
fof(7,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',multiplicative_associativity) ).
fof(8,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',left_annihilation) ).
fof(9,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',additive_associativity) ).
fof(10,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',test_2) ).
fof(11,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',test_1) ).
fof(12,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',multiplicative_right_identity) ).
fof(13,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',right_distributivity) ).
fof(14,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',order) ).
fof(15,conjecture,
! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(X6,multiplication(X4,X5))
<=> ( leq(X6,X4)
& leq(X6,X5) ) ) ),
file('/tmp/tmpyQ9YuJ/sel_KLE017+1.p_1',goals) ).
fof(16,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X4)
& test(X5)
& test(X6) )
=> ( leq(X6,multiplication(X4,X5))
<=> ( leq(X6,X4)
& leq(X6,X5) ) ) ),
inference(assume_negation,[status(cth)],[15]) ).
fof(19,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[19]) ).
fof(21,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[3]) ).
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)],[4]) ).
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)],[5]) ).
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)],[6]) ).
cnf(28,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[7]) ).
cnf(30,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[8]) ).
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)],[9]) ).
cnf(34,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,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)],[10]) ).
fof(36,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)],[35]) ).
fof(37,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)],[36]) ).
cnf(39,plain,
( addition(X2,X1) = one
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(41,plain,
( multiplication(X2,X1) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(42,plain,
! [X4] :
( ( ~ test(X4)
| ? [X5] : complement(X5,X4) )
& ( ! [X5] : ~ complement(X5,X4)
| test(X4) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(43,plain,
! [X6] :
( ( ~ test(X6)
| ? [X7] : complement(X7,X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,plain,
! [X6] :
( ( ~ test(X6)
| complement(esk1_1(X6),X6) )
& ( ! [X8] : ~ complement(X8,X6)
| test(X6) ) ),
inference(skolemize,[status(esa)],[43]) ).
fof(45,plain,
! [X6,X8] :
( ( ~ complement(X8,X6)
| test(X6) )
& ( ~ test(X6)
| complement(esk1_1(X6),X6) ) ),
inference(shift_quantors,[status(thm)],[44]) ).
cnf(46,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(48,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[12]) ).
cnf(49,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(51,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(53,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[52]) ).
cnf(54,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(56,negated_conjecture,
? [X4,X5,X6] :
( test(X4)
& test(X5)
& test(X6)
& ( ~ leq(X6,multiplication(X4,X5))
| ~ leq(X6,X4)
| ~ leq(X6,X5) )
& ( leq(X6,multiplication(X4,X5))
| ( leq(X6,X4)
& leq(X6,X5) ) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(57,negated_conjecture,
? [X7,X8,X9] :
( test(X7)
& test(X8)
& test(X9)
& ( ~ leq(X9,multiplication(X7,X8))
| ~ leq(X9,X7)
| ~ leq(X9,X8) )
& ( leq(X9,multiplication(X7,X8))
| ( leq(X9,X7)
& leq(X9,X8) ) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,negated_conjecture,
( test(esk2_0)
& test(esk3_0)
& test(esk4_0)
& ( ~ leq(esk4_0,multiplication(esk2_0,esk3_0))
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) )
& ( leq(esk4_0,multiplication(esk2_0,esk3_0))
| ( leq(esk4_0,esk2_0)
& leq(esk4_0,esk3_0) ) ) ),
inference(skolemize,[status(esa)],[57]) ).
fof(59,negated_conjecture,
( test(esk2_0)
& test(esk3_0)
& test(esk4_0)
& ( ~ leq(esk4_0,multiplication(esk2_0,esk3_0))
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) )
& ( leq(esk4_0,esk2_0)
| leq(esk4_0,multiplication(esk2_0,esk3_0)) )
& ( leq(esk4_0,esk3_0)
| leq(esk4_0,multiplication(esk2_0,esk3_0)) ) ),
inference(distribute,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
( leq(esk4_0,multiplication(esk2_0,esk3_0))
| leq(esk4_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(61,negated_conjecture,
( leq(esk4_0,multiplication(esk2_0,esk3_0))
| leq(esk4_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(62,negated_conjecture,
( ~ leq(esk4_0,esk3_0)
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,multiplication(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(63,negated_conjecture,
test(esk4_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(64,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(65,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(66,negated_conjecture,
( addition(esk4_0,multiplication(esk2_0,esk3_0)) = multiplication(esk2_0,esk3_0)
| leq(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[55,61,theory(equality)]) ).
cnf(67,negated_conjecture,
( addition(esk4_0,multiplication(esk2_0,esk3_0)) = multiplication(esk2_0,esk3_0)
| leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[55,60,theory(equality)]) ).
cnf(70,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[41,46,theory(equality)]) ).
cnf(71,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[22,26,theory(equality)]) ).
cnf(77,plain,
( multiplication(esk1_1(X1),X1) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[40,46,theory(equality)]) ).
cnf(80,negated_conjecture,
( ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0)
| addition(esk4_0,multiplication(esk2_0,esk3_0)) != multiplication(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[62,54,theory(equality)]) ).
cnf(98,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[39,46,theory(equality)]) ).
cnf(102,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[34,28,theory(equality)]) ).
cnf(104,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[26,34,theory(equality)]) ).
cnf(106,plain,
addition(addition(X2,X1),X3) = addition(X1,addition(X2,X3)),
inference(spm,[status(thm)],[34,26,theory(equality)]) ).
cnf(111,plain,
addition(X2,addition(X1,X3)) = addition(X1,addition(X2,X3)),
inference(rw,[status(thm)],[106,34,theory(equality)]) ).
cnf(113,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[51,49,theory(equality)]) ).
cnf(151,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[24,20,theory(equality)]) ).
cnf(193,plain,
( zero = multiplication(X1,multiplication(X2,esk1_1(multiplication(X1,X2))))
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[30,70,theory(equality)]) ).
cnf(194,plain,
( addition(zero,multiplication(X1,X2)) = multiplication(X1,addition(esk1_1(X1),X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[51,70,theory(equality)]) ).
cnf(195,plain,
( addition(multiplication(X1,X2),zero) = multiplication(X1,addition(X2,esk1_1(X1)))
| ~ test(X1) ),
inference(spm,[status(thm)],[51,70,theory(equality)]) ).
cnf(196,plain,
( addition(zero,multiplication(X2,esk1_1(X1))) = multiplication(addition(X1,X2),esk1_1(X1))
| ~ test(X1) ),
inference(spm,[status(thm)],[24,70,theory(equality)]) ).
cnf(199,plain,
( multiplication(X1,X2) = multiplication(X1,addition(esk1_1(X1),X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[194,71,theory(equality)]) ).
cnf(200,plain,
( multiplication(X1,X2) = multiplication(X1,addition(X2,esk1_1(X1)))
| ~ test(X1) ),
inference(rw,[status(thm)],[195,22,theory(equality)]) ).
cnf(201,plain,
( multiplication(X2,esk1_1(X1)) = multiplication(addition(X1,X2),esk1_1(X1))
| ~ test(X1) ),
inference(rw,[status(thm)],[196,71,theory(equality)]) ).
cnf(207,plain,
( multiplication(zero,X2) = multiplication(esk1_1(X1),multiplication(X1,X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[30,77,theory(equality)]) ).
cnf(213,plain,
( zero = multiplication(esk1_1(X1),multiplication(X1,X2))
| ~ test(X1) ),
inference(rw,[status(thm)],[207,32,theory(equality)]) ).
cnf(219,plain,
( addition(one,X2) = addition(X1,addition(esk1_1(X1),X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[34,98,theory(equality)]) ).
cnf(320,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[102,26,theory(equality)]) ).
cnf(324,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[102,98,theory(equality)]) ).
cnf(336,negated_conjecture,
addition(esk2_0,one) = one,
inference(spm,[status(thm)],[324,65,theory(equality)]) ).
cnf(337,negated_conjecture,
addition(esk3_0,one) = one,
inference(spm,[status(thm)],[324,64,theory(equality)]) ).
cnf(338,negated_conjecture,
addition(esk4_0,one) = one,
inference(spm,[status(thm)],[324,63,theory(equality)]) ).
cnf(339,negated_conjecture,
addition(one,X1) = addition(esk2_0,addition(one,X1)),
inference(spm,[status(thm)],[34,336,theory(equality)]) ).
cnf(350,plain,
addition(addition(X2,X1),X3) = addition(X1,addition(addition(X2,X1),X3)),
inference(spm,[status(thm)],[34,320,theory(equality)]) ).
cnf(369,plain,
addition(X2,addition(X1,X3)) = addition(X1,addition(addition(X2,X1),X3)),
inference(rw,[status(thm)],[350,34,theory(equality)]) ).
cnf(370,plain,
addition(X2,addition(X1,X3)) = addition(X1,addition(X2,addition(X1,X3))),
inference(rw,[status(thm)],[369,34,theory(equality)]) ).
cnf(402,negated_conjecture,
addition(esk2_0,addition(X1,one)) = addition(X1,one),
inference(spm,[status(thm)],[339,320,theory(equality)]) ).
cnf(635,plain,
addition(X1,multiplication(X2,addition(one,X3))) = addition(X2,addition(X1,multiplication(X2,X3))),
inference(spm,[status(thm)],[111,113,theory(equality)]) ).
cnf(997,plain,
( addition(multiplication(X1,X2),multiplication(X3,addition(esk1_1(X1),X2))) = multiplication(addition(X1,X3),addition(esk1_1(X1),X2))
| ~ test(X1) ),
inference(spm,[status(thm)],[24,199,theory(equality)]) ).
cnf(1196,plain,
( multiplication(X1,one) = multiplication(X1,X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[200,98,theory(equality)]) ).
cnf(1221,plain,
( X1 = multiplication(X1,X1)
| ~ test(X1) ),
inference(rw,[status(thm)],[1196,49,theory(equality)]) ).
cnf(1227,negated_conjecture,
multiplication(esk4_0,esk4_0) = esk4_0,
inference(spm,[status(thm)],[1221,63,theory(equality)]) ).
cnf(1270,negated_conjecture,
multiplication(esk4_0,X1) = multiplication(esk4_0,multiplication(esk4_0,X1)),
inference(spm,[status(thm)],[30,1227,theory(equality)]) ).
cnf(1279,negated_conjecture,
( multiplication(esk1_1(esk4_0),esk4_0) = zero
| ~ test(esk4_0) ),
inference(spm,[status(thm)],[213,1227,theory(equality)]) ).
cnf(1289,negated_conjecture,
( multiplication(esk1_1(esk4_0),esk4_0) = zero
| $false ),
inference(rw,[status(thm)],[1279,63,theory(equality)]) ).
cnf(1290,negated_conjecture,
multiplication(esk1_1(esk4_0),esk4_0) = zero,
inference(cn,[status(thm)],[1289,theory(equality)]) ).
cnf(1474,negated_conjecture,
addition(multiplication(X1,esk4_0),zero) = multiplication(addition(X1,esk1_1(esk4_0)),esk4_0),
inference(spm,[status(thm)],[24,1290,theory(equality)]) ).
cnf(1487,negated_conjecture,
multiplication(X1,esk4_0) = multiplication(addition(X1,esk1_1(esk4_0)),esk4_0),
inference(rw,[status(thm)],[1474,22,theory(equality)]) ).
cnf(3437,negated_conjecture,
( multiplication(esk4_0,multiplication(esk4_0,esk1_1(esk4_0))) = zero
| ~ test(esk4_0) ),
inference(spm,[status(thm)],[193,1227,theory(equality)]) ).
cnf(3525,negated_conjecture,
( multiplication(esk4_0,esk1_1(esk4_0)) = zero
| ~ test(esk4_0) ),
inference(rw,[status(thm)],[3437,1270,theory(equality)]) ).
cnf(3526,negated_conjecture,
( multiplication(esk4_0,esk1_1(esk4_0)) = zero
| $false ),
inference(rw,[status(thm)],[3525,63,theory(equality)]) ).
cnf(3527,negated_conjecture,
multiplication(esk4_0,esk1_1(esk4_0)) = zero,
inference(cn,[status(thm)],[3526,theory(equality)]) ).
cnf(3695,negated_conjecture,
addition(multiplication(esk4_0,X1),zero) = multiplication(esk4_0,addition(X1,esk1_1(esk4_0))),
inference(spm,[status(thm)],[51,3527,theory(equality)]) ).
cnf(3714,negated_conjecture,
multiplication(esk4_0,X1) = multiplication(esk4_0,addition(X1,esk1_1(esk4_0))),
inference(rw,[status(thm)],[3695,22,theory(equality)]) ).
cnf(5144,negated_conjecture,
( addition(one,one) = addition(esk1_1(esk2_0),one)
| ~ test(esk2_0) ),
inference(spm,[status(thm)],[402,219,theory(equality)]) ).
cnf(5199,negated_conjecture,
( one = addition(esk1_1(esk2_0),one)
| ~ test(esk2_0) ),
inference(rw,[status(thm)],[5144,28,theory(equality)]) ).
cnf(5200,negated_conjecture,
( one = addition(one,esk1_1(esk2_0))
| ~ test(esk2_0) ),
inference(rw,[status(thm)],[5199,26,theory(equality)]) ).
cnf(5201,negated_conjecture,
( one = addition(one,esk1_1(esk2_0))
| $false ),
inference(rw,[status(thm)],[5200,65,theory(equality)]) ).
cnf(5202,negated_conjecture,
one = addition(one,esk1_1(esk2_0)),
inference(cn,[status(thm)],[5201,theory(equality)]) ).
cnf(25170,negated_conjecture,
( addition(esk4_0,multiplication(esk2_0,addition(one,esk3_0))) = addition(esk2_0,multiplication(esk2_0,esk3_0))
| leq(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[635,66,theory(equality)]) ).
cnf(25587,negated_conjecture,
( addition(esk4_0,esk2_0) = addition(esk2_0,multiplication(esk2_0,esk3_0))
| leq(esk4_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[25170,26,theory(equality)]),337,theory(equality)]),49,theory(equality)]) ).
cnf(25588,negated_conjecture,
( addition(esk4_0,esk2_0) = esk2_0
| leq(esk4_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[25587,113,theory(equality)]),26,theory(equality)]),337,theory(equality)]),49,theory(equality)]) ).
cnf(25852,negated_conjecture,
addition(esk4_0,esk2_0) = esk2_0,
inference(csr,[status(thm)],[25588,55]) ).
cnf(25856,negated_conjecture,
addition(esk4_0,addition(X1,esk2_0)) = addition(X1,esk2_0),
inference(spm,[status(thm)],[370,25852,theory(equality)]) ).
cnf(27269,negated_conjecture,
( addition(esk1_1(esk4_0),esk2_0) = addition(one,esk2_0)
| ~ test(esk4_0) ),
inference(spm,[status(thm)],[219,25856,theory(equality)]) ).
cnf(27309,negated_conjecture,
( addition(esk2_0,esk1_1(esk4_0)) = addition(one,esk2_0)
| ~ test(esk4_0) ),
inference(rw,[status(thm)],[27269,26,theory(equality)]) ).
cnf(27310,negated_conjecture,
( addition(esk2_0,esk1_1(esk4_0)) = one
| ~ test(esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[27309,26,theory(equality)]),336,theory(equality)]) ).
cnf(27311,negated_conjecture,
( addition(esk2_0,esk1_1(esk4_0)) = one
| $false ),
inference(rw,[status(thm)],[27310,63,theory(equality)]) ).
cnf(27312,negated_conjecture,
addition(esk2_0,esk1_1(esk4_0)) = one,
inference(cn,[status(thm)],[27311,theory(equality)]) ).
cnf(27331,negated_conjecture,
multiplication(one,esk4_0) = multiplication(esk2_0,esk4_0),
inference(spm,[status(thm)],[1487,27312,theory(equality)]) ).
cnf(27334,negated_conjecture,
multiplication(esk4_0,one) = multiplication(esk4_0,esk2_0),
inference(spm,[status(thm)],[3714,27312,theory(equality)]) ).
cnf(27347,negated_conjecture,
( multiplication(one,esk1_1(esk2_0)) = multiplication(esk1_1(esk4_0),esk1_1(esk2_0))
| ~ test(esk2_0) ),
inference(spm,[status(thm)],[201,27312,theory(equality)]) ).
cnf(27380,negated_conjecture,
esk4_0 = multiplication(esk2_0,esk4_0),
inference(rw,[status(thm)],[27331,20,theory(equality)]) ).
cnf(27383,negated_conjecture,
esk4_0 = multiplication(esk4_0,esk2_0),
inference(rw,[status(thm)],[27334,49,theory(equality)]) ).
cnf(27397,negated_conjecture,
( esk1_1(esk2_0) = multiplication(esk1_1(esk4_0),esk1_1(esk2_0))
| ~ test(esk2_0) ),
inference(rw,[status(thm)],[27347,20,theory(equality)]) ).
cnf(27398,negated_conjecture,
( esk1_1(esk2_0) = multiplication(esk1_1(esk4_0),esk1_1(esk2_0))
| $false ),
inference(rw,[status(thm)],[27397,65,theory(equality)]) ).
cnf(27399,negated_conjecture,
esk1_1(esk2_0) = multiplication(esk1_1(esk4_0),esk1_1(esk2_0)),
inference(cn,[status(thm)],[27398,theory(equality)]) ).
cnf(27457,negated_conjecture,
addition(esk4_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,addition(esk4_0,X1)),
inference(spm,[status(thm)],[51,27380,theory(equality)]) ).
cnf(27538,negated_conjecture,
multiplication(esk4_0,X1) = multiplication(esk4_0,multiplication(esk2_0,X1)),
inference(spm,[status(thm)],[30,27383,theory(equality)]) ).
cnf(28729,negated_conjecture,
addition(esk1_1(esk4_0),esk1_1(esk2_0)) = multiplication(esk1_1(esk4_0),addition(one,esk1_1(esk2_0))),
inference(spm,[status(thm)],[113,27399,theory(equality)]) ).
cnf(28769,negated_conjecture,
addition(esk1_1(esk4_0),esk1_1(esk2_0)) = esk1_1(esk4_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[28729,5202,theory(equality)]),49,theory(equality)]) ).
cnf(29029,negated_conjecture,
( addition(esk4_0,esk1_1(esk4_0)) = addition(one,esk1_1(esk2_0))
| ~ test(esk4_0) ),
inference(spm,[status(thm)],[219,28769,theory(equality)]) ).
cnf(29070,negated_conjecture,
( addition(esk4_0,esk1_1(esk4_0)) = one
| ~ test(esk4_0) ),
inference(rw,[status(thm)],[29029,5202,theory(equality)]) ).
cnf(29071,negated_conjecture,
( addition(esk4_0,esk1_1(esk4_0)) = one
| $false ),
inference(rw,[status(thm)],[29070,63,theory(equality)]) ).
cnf(29072,negated_conjecture,
addition(esk4_0,esk1_1(esk4_0)) = one,
inference(cn,[status(thm)],[29071,theory(equality)]) ).
cnf(30498,negated_conjecture,
( multiplication(esk2_0,addition(esk4_0,esk3_0)) = multiplication(esk2_0,esk3_0)
| leq(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[67,27457,theory(equality)]) ).
cnf(30499,negated_conjecture,
( multiplication(esk2_0,addition(esk4_0,esk3_0)) != multiplication(esk2_0,esk3_0)
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[80,27457,theory(equality)]) ).
cnf(30671,negated_conjecture,
( multiplication(esk4_0,multiplication(esk2_0,esk3_0)) = multiplication(esk4_0,addition(esk4_0,esk3_0))
| leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[27538,30498,theory(equality)]) ).
cnf(30709,negated_conjecture,
( multiplication(esk4_0,esk3_0) = multiplication(esk4_0,addition(esk4_0,esk3_0))
| leq(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[30671,27538,theory(equality)]) ).
cnf(66793,negated_conjecture,
( addition(multiplication(esk4_0,esk3_0),multiplication(X1,addition(esk1_1(esk4_0),addition(esk4_0,esk3_0)))) = multiplication(addition(esk4_0,X1),addition(esk1_1(esk4_0),addition(esk4_0,esk3_0)))
| leq(esk4_0,esk3_0)
| ~ test(esk4_0) ),
inference(spm,[status(thm)],[997,30709,theory(equality)]) ).
cnf(67452,negated_conjecture,
( addition(multiplication(esk4_0,esk3_0),X1) = multiplication(addition(esk4_0,X1),addition(esk1_1(esk4_0),addition(esk4_0,esk3_0)))
| leq(esk4_0,esk3_0)
| ~ test(esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[66793,104,theory(equality)]),26,theory(equality)]),29072,theory(equality)]),337,theory(equality)]),49,theory(equality)]) ).
cnf(67453,negated_conjecture,
( addition(multiplication(esk4_0,esk3_0),X1) = addition(esk4_0,X1)
| leq(esk4_0,esk3_0)
| ~ test(esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[67452,104,theory(equality)]),26,theory(equality)]),29072,theory(equality)]),337,theory(equality)]),49,theory(equality)]) ).
cnf(67454,negated_conjecture,
( addition(multiplication(esk4_0,esk3_0),X1) = addition(esk4_0,X1)
| leq(esk4_0,esk3_0)
| $false ),
inference(rw,[status(thm)],[67453,63,theory(equality)]) ).
cnf(67455,negated_conjecture,
( addition(multiplication(esk4_0,esk3_0),X1) = addition(esk4_0,X1)
| leq(esk4_0,esk3_0) ),
inference(cn,[status(thm)],[67454,theory(equality)]) ).
cnf(73969,negated_conjecture,
( addition(esk4_0,zero) = multiplication(esk4_0,esk3_0)
| leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[22,67455,theory(equality)]) ).
cnf(74164,negated_conjecture,
( esk4_0 = multiplication(esk4_0,esk3_0)
| leq(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[73969,22,theory(equality)]) ).
cnf(74330,negated_conjecture,
( addition(esk4_0,esk3_0) = esk3_0
| multiplication(esk4_0,esk3_0) = esk4_0 ),
inference(spm,[status(thm)],[55,74164,theory(equality)]) ).
cnf(74363,negated_conjecture,
( multiplication(esk4_0,esk3_0) = esk4_0
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[30499,74330,theory(equality)]) ).
cnf(74433,negated_conjecture,
( multiplication(esk4_0,esk3_0) = esk4_0
| ~ leq(esk4_0,esk2_0) ),
inference(csr,[status(thm)],[74363,74164]) ).
cnf(74434,negated_conjecture,
( multiplication(esk4_0,esk3_0) = esk4_0
| addition(esk4_0,esk2_0) != esk2_0 ),
inference(spm,[status(thm)],[74433,54,theory(equality)]) ).
cnf(74435,negated_conjecture,
( multiplication(esk4_0,esk3_0) = esk4_0
| $false ),
inference(rw,[status(thm)],[74434,25852,theory(equality)]) ).
cnf(74436,negated_conjecture,
multiplication(esk4_0,esk3_0) = esk4_0,
inference(cn,[status(thm)],[74435,theory(equality)]) ).
cnf(74443,negated_conjecture,
addition(esk3_0,esk4_0) = multiplication(addition(one,esk4_0),esk3_0),
inference(spm,[status(thm)],[151,74436,theory(equality)]) ).
cnf(74503,negated_conjecture,
addition(esk4_0,esk3_0) = multiplication(addition(one,esk4_0),esk3_0),
inference(rw,[status(thm)],[74443,26,theory(equality)]) ).
cnf(74504,negated_conjecture,
addition(esk4_0,esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[74503,26,theory(equality)]),338,theory(equality)]),20,theory(equality)]) ).
cnf(74616,negated_conjecture,
( $false
| ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[30499,74504,theory(equality)]) ).
cnf(74617,negated_conjecture,
( ~ leq(esk4_0,esk2_0)
| ~ leq(esk4_0,esk3_0) ),
inference(cn,[status(thm)],[74616,theory(equality)]) ).
cnf(75326,negated_conjecture,
( ~ leq(esk4_0,esk2_0)
| addition(esk4_0,esk3_0) != esk3_0 ),
inference(spm,[status(thm)],[74617,54,theory(equality)]) ).
cnf(75327,negated_conjecture,
( ~ leq(esk4_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[75326,74504,theory(equality)]) ).
cnf(75328,negated_conjecture,
~ leq(esk4_0,esk2_0),
inference(cn,[status(thm)],[75327,theory(equality)]) ).
cnf(75330,negated_conjecture,
addition(esk4_0,esk2_0) != esk2_0,
inference(spm,[status(thm)],[75328,54,theory(equality)]) ).
cnf(75335,negated_conjecture,
$false,
inference(rw,[status(thm)],[75330,25852,theory(equality)]) ).
cnf(75336,negated_conjecture,
$false,
inference(cn,[status(thm)],[75335,theory(equality)]) ).
cnf(75337,negated_conjecture,
$false,
75336,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE017+1.p
% --creating new selector for [KLE001+0.ax, KLE001+1.ax]
% -running prover on /tmp/tmpyQ9YuJ/sel_KLE017+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE017+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE017+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE017+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
%
%------------------------------------------------------------------------------