TSTP Solution File: KLE045+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE045+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 12:00:01 EST 2010
% Result : Theorem 7.91s
% Output : CNFRefutation 7.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 14
% Syntax : Number of formulae : 148 ( 115 unt; 0 def)
% Number of atoms : 185 ( 84 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 31 ~; 27 |; 5 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 217 ( 15 sgn 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',multiplicative_associativity) ).
fof(2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',left_distributivity) ).
fof(3,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',additive_associativity) ).
fof(4,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',additive_commutativity) ).
fof(5,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',additive_idempotence) ).
fof(6,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',star_induction_right) ).
fof(7,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',star_unfold_left) ).
fof(8,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',multiplicative_left_identity) ).
fof(9,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',multiplicative_right_identity) ).
fof(10,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',star_unfold_right) ).
fof(11,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',right_distributivity) ).
fof(12,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',star_induction_left) ).
fof(13,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',order) ).
fof(14,conjecture,
! [X4,X5,X6] :
( leq(multiplication(X4,X6),multiplication(X6,X5))
=> leq(multiplication(star(X4),X6),multiplication(X6,star(X5))) ),
file('/tmp/tmpAQADjx/sel_KLE045+1.p_1',goals) ).
fof(15,negated_conjecture,
~ ! [X4,X5,X6] :
( leq(multiplication(X4,X6),multiplication(X6,X5))
=> leq(multiplication(star(X4),X6),multiplication(X6,star(X5))) ),
inference(assume_negation,[status(cth)],[14]) ).
fof(16,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[1]) ).
cnf(17,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(19,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(23,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[5]) ).
cnf(25,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X1,X2,X3] :
( ~ leq(addition(multiplication(X1,X2),X3),X1)
| leq(multiplication(X3,star(X2)),X1) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(27,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X4,X5),X6),X4)
| leq(multiplication(X6,star(X5)),X4) ),
inference(variable_rename,[status(thm)],[26]) ).
cnf(28,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X2] : leq(addition(one,multiplication(star(X2),X2)),star(X2)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(30,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[8]) ).
cnf(32,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[9]) ).
cnf(34,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X2] : leq(addition(one,multiplication(X2,star(X2))),star(X2)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(36,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[11]) ).
cnf(38,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X1,X2,X3] :
( ~ leq(addition(multiplication(X1,X2),X3),X2)
| leq(multiplication(star(X1),X3),X2) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(40,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X4,X5),X6),X5)
| leq(multiplication(star(X4),X6),X5) ),
inference(variable_rename,[status(thm)],[39]) ).
cnf(41,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(multiplication(X1,X3),X2),X3) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| addition(X1,X2) = X2 )
& ( addition(X1,X2) != X2
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(43,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[42]) ).
cnf(44,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(46,negated_conjecture,
? [X4,X5,X6] :
( leq(multiplication(X4,X6),multiplication(X6,X5))
& ~ leq(multiplication(star(X4),X6),multiplication(X6,star(X5))) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(47,negated_conjecture,
? [X7,X8,X9] :
( leq(multiplication(X7,X9),multiplication(X9,X8))
& ~ leq(multiplication(star(X7),X9),multiplication(X9,star(X8))) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,negated_conjecture,
( leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,esk2_0))
& ~ leq(multiplication(star(esk1_0),esk3_0),multiplication(esk3_0,star(esk2_0))) ),
inference(skolemize,[status(esa)],[47]) ).
cnf(49,negated_conjecture,
~ leq(multiplication(star(esk1_0),esk3_0),multiplication(esk3_0,star(esk2_0))),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(55,plain,
leq(X1,X1),
inference(spm,[status(thm)],[44,25,theory(equality)]) ).
cnf(70,negated_conjecture,
addition(multiplication(esk1_0,esk3_0),multiplication(esk3_0,esk2_0)) = multiplication(esk3_0,esk2_0),
inference(spm,[status(thm)],[45,50,theory(equality)]) ).
cnf(71,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(spm,[status(thm)],[45,36,theory(equality)]) ).
cnf(72,plain,
addition(addition(one,multiplication(star(X1),X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[45,30,theory(equality)]) ).
cnf(73,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk1_0,esk3_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[70,23,theory(equality)]) ).
cnf(74,plain,
addition(star(X1),addition(one,multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[71,23,theory(equality)]) ).
cnf(75,plain,
addition(star(X1),addition(one,multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[72,23,theory(equality)]) ).
cnf(77,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[21,25,theory(equality)]) ).
cnf(79,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[23,21,theory(equality)]) ).
cnf(81,plain,
addition(addition(X2,X1),X3) = addition(X1,addition(X2,X3)),
inference(spm,[status(thm)],[21,23,theory(equality)]) ).
cnf(86,plain,
addition(X2,addition(X1,X3)) = addition(X1,addition(X2,X3)),
inference(rw,[status(thm)],[81,21,theory(equality)]) ).
cnf(97,plain,
( leq(multiplication(star(X1),multiplication(X1,X2)),X2)
| ~ leq(multiplication(X1,X2),X2) ),
inference(spm,[status(thm)],[41,25,theory(equality)]) ).
cnf(99,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[41,23,theory(equality)]) ).
cnf(101,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[38,34,theory(equality)]) ).
cnf(112,plain,
( leq(multiplication(multiplication(X1,X2),star(X3)),X1)
| ~ leq(multiplication(X1,addition(X3,X2)),X1) ),
inference(spm,[status(thm)],[28,38,theory(equality)]) ).
cnf(126,plain,
( leq(multiplication(X1,multiplication(X2,star(X3))),X1)
| ~ leq(multiplication(X1,addition(X3,X2)),X1) ),
inference(rw,[status(thm)],[112,17,theory(equality)]) ).
cnf(129,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[19,32,theory(equality)]) ).
cnf(132,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[19,17,theory(equality)]) ).
cnf(140,plain,
( leq(multiplication(star(X1),multiplication(X2,X3)),X3)
| ~ leq(multiplication(addition(X1,X2),X3),X3) ),
inference(spm,[status(thm)],[41,19,theory(equality)]) ).
cnf(178,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[77,23,theory(equality)]) ).
cnf(180,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[44,77,theory(equality)]) ).
cnf(197,plain,
leq(multiplication(X1,X2),multiplication(addition(X1,X3),X2)),
inference(spm,[status(thm)],[180,19,theory(equality)]) ).
cnf(200,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[180,23,theory(equality)]) ).
cnf(208,plain,
leq(X1,addition(X2,addition(X3,X1))),
inference(spm,[status(thm)],[200,21,theory(equality)]) ).
cnf(431,plain,
leq(X1,addition(X3,addition(X1,X2))),
inference(spm,[status(thm)],[180,79,theory(equality)]) ).
cnf(677,plain,
multiplication(addition(X1,X2),addition(one,X3)) = addition(X1,addition(X2,multiplication(addition(X1,X2),X3))),
inference(spm,[status(thm)],[21,101,theory(equality)]) ).
cnf(680,plain,
leq(X1,multiplication(X1,addition(one,X2))),
inference(spm,[status(thm)],[180,101,theory(equality)]) ).
cnf(1587,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),addition(X1,multiplication(esk3_0,esk2_0))),
inference(spm,[status(thm)],[208,73,theory(equality)]) ).
cnf(1656,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,addition(X1,esk2_0))),
inference(spm,[status(thm)],[1587,38,theory(equality)]) ).
cnf(1671,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[74,86,theory(equality)]),129,theory(equality)]) ).
cnf(1674,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[77,1671,theory(equality)]) ).
cnf(1680,plain,
leq(X1,multiplication(X1,star(X2))),
inference(spm,[status(thm)],[680,1671,theory(equality)]) ).
cnf(1685,plain,
addition(multiplication(addition(one,X1),star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[178,1671,theory(equality)]) ).
cnf(1719,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1685,23,theory(equality)]),129,theory(equality)]),77,theory(equality)]) ).
cnf(1727,plain,
addition(one,multiplication(star(X1),addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[75,86,theory(equality)]),101,theory(equality)]) ).
cnf(1741,plain,
addition(multiplication(star(X1),addition(one,X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[178,1727,theory(equality)]) ).
cnf(1777,plain,
multiplication(star(X1),addition(one,X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1741,23,theory(equality)]),101,theory(equality)]),77,theory(equality)]) ).
cnf(1917,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,addition(esk2_0,X1))),
inference(spm,[status(thm)],[1656,23,theory(equality)]) ).
cnf(2016,plain,
leq(addition(one,X1),star(X1)),
inference(spm,[status(thm)],[1680,1719,theory(equality)]) ).
cnf(2017,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(spm,[status(thm)],[1719,23,theory(equality)]) ).
cnf(2050,plain,
multiplication(star(addition(one,X1)),addition(one,X1)) = star(addition(one,X1)),
inference(spm,[status(thm)],[1777,77,theory(equality)]) ).
cnf(2061,plain,
multiplication(star(X1),addition(X1,one)) = star(X1),
inference(spm,[status(thm)],[1777,23,theory(equality)]) ).
cnf(2169,plain,
leq(addition(X1,one),star(X1)),
inference(spm,[status(thm)],[2016,23,theory(equality)]) ).
cnf(2190,plain,
addition(addition(X1,one),star(X1)) = star(X1),
inference(spm,[status(thm)],[45,2169,theory(equality)]) ).
cnf(2195,plain,
addition(X1,star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2190,21,theory(equality)]),1674,theory(equality)]) ).
cnf(2427,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(esk3_0,star(esk2_0))),
inference(spm,[status(thm)],[1917,2195,theory(equality)]) ).
cnf(2440,negated_conjecture,
addition(multiplication(esk1_0,esk3_0),multiplication(esk3_0,star(esk2_0))) = multiplication(esk3_0,star(esk2_0)),
inference(spm,[status(thm)],[45,2427,theory(equality)]) ).
cnf(2683,plain,
multiplication(star(X1),X2) = multiplication(addition(X1,one),multiplication(star(X1),X2)),
inference(spm,[status(thm)],[17,2017,theory(equality)]) ).
cnf(3045,negated_conjecture,
leq(multiplication(multiplication(esk1_0,esk3_0),X1),multiplication(multiplication(esk3_0,star(esk2_0)),X1)),
inference(spm,[status(thm)],[197,2440,theory(equality)]) ).
cnf(3073,negated_conjecture,
leq(multiplication(esk1_0,multiplication(esk3_0,X1)),multiplication(esk3_0,multiplication(star(esk2_0),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3045,17,theory(equality)]),17,theory(equality)]) ).
cnf(3157,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),addition(X1,multiplication(esk3_0,star(esk2_0)))),
inference(spm,[status(thm)],[431,2440,theory(equality)]) ).
cnf(3796,plain,
( leq(multiplication(star(addition(one,X1)),star(X1)),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(spm,[status(thm)],[97,1719,theory(equality)]) ).
cnf(3806,plain,
( leq(multiplication(star(addition(one,X1)),star(X1)),star(X1))
| $false ),
inference(rw,[status(thm)],[3796,55,theory(equality)]) ).
cnf(3807,plain,
leq(multiplication(star(addition(one,X1)),star(X1)),star(X1)),
inference(cn,[status(thm)],[3806,theory(equality)]) ).
cnf(4527,plain,
( leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(spm,[status(thm)],[126,2061,theory(equality)]) ).
cnf(4559,plain,
( leq(multiplication(star(X1),star(X1)),star(X1))
| ~ leq(star(X1),star(X1)) ),
inference(rw,[status(thm)],[4527,32,theory(equality)]) ).
cnf(4560,plain,
( leq(multiplication(star(X1),star(X1)),star(X1))
| $false ),
inference(rw,[status(thm)],[4559,55,theory(equality)]) ).
cnf(4561,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[4560,theory(equality)]) ).
cnf(4994,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(addition(X1,esk3_0),star(esk2_0))),
inference(spm,[status(thm)],[3157,19,theory(equality)]) ).
cnf(6053,plain,
addition(multiplication(star(X1),star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[45,4561,theory(equality)]) ).
cnf(6057,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6053,23,theory(equality)]),101,theory(equality)]),1674,theory(equality)]) ).
cnf(6068,plain,
addition(star(X1),multiplication(star(X1),X2)) = multiplication(star(X1),addition(star(X1),X2)),
inference(spm,[status(thm)],[38,6057,theory(equality)]) ).
cnf(6096,plain,
multiplication(star(X1),addition(one,X2)) = multiplication(star(X1),addition(star(X1),X2)),
inference(rw,[status(thm)],[6068,101,theory(equality)]) ).
cnf(6478,negated_conjecture,
leq(multiplication(esk1_0,esk3_0),multiplication(addition(esk3_0,X1),star(esk2_0))),
inference(spm,[status(thm)],[4994,23,theory(equality)]) ).
cnf(7653,negated_conjecture,
addition(multiplication(esk1_0,esk3_0),multiplication(addition(esk3_0,X1),star(esk2_0))) = multiplication(addition(esk3_0,X1),star(esk2_0)),
inference(spm,[status(thm)],[45,6478,theory(equality)]) ).
cnf(44252,plain,
multiplication(addition(addition(one,X1),one),star(addition(one,X1))) = star(addition(one,X1)),
inference(spm,[status(thm)],[2683,2050,theory(equality)]) ).
cnf(44359,plain,
multiplication(addition(X1,one),star(addition(one,X1))) = star(addition(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[44252,21,theory(equality)]),178,theory(equality)]) ).
cnf(44642,plain,
addition(multiplication(star(addition(one,X1)),star(X1)),star(X1)) = star(X1),
inference(spm,[status(thm)],[45,3807,theory(equality)]) ).
cnf(44680,plain,
multiplication(star(addition(one,X1)),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[44642,23,theory(equality)]),129,theory(equality)]),1674,theory(equality)]) ).
cnf(44853,plain,
addition(star(addition(one,X1)),star(X1)) = multiplication(star(addition(one,X1)),addition(one,star(X1))),
inference(spm,[status(thm)],[101,44680,theory(equality)]) ).
cnf(44998,plain,
addition(star(X1),star(addition(one,X1))) = multiplication(star(addition(one,X1)),addition(one,star(X1))),
inference(rw,[status(thm)],[44853,23,theory(equality)]) ).
cnf(44999,plain,
addition(star(X1),star(addition(one,X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[44998,1674,theory(equality)]),44680,theory(equality)]) ).
cnf(45234,plain,
multiplication(star(X1),star(X1)) = multiplication(star(X1),addition(one,star(addition(one,X1)))),
inference(spm,[status(thm)],[6096,44999,theory(equality)]) ).
cnf(45456,plain,
star(X1) = multiplication(star(X1),addition(one,star(addition(one,X1)))),
inference(rw,[status(thm)],[45234,6057,theory(equality)]) ).
cnf(45457,plain,
star(X1) = multiplication(star(X1),star(addition(one,X1))),
inference(rw,[status(thm)],[45456,1674,theory(equality)]) ).
cnf(47453,plain,
( leq(multiplication(star(X1),multiplication(one,star(addition(one,X1)))),star(addition(one,X1)))
| ~ leq(star(addition(one,X1)),star(addition(one,X1))) ),
inference(spm,[status(thm)],[140,44359,theory(equality)]) ).
cnf(47619,plain,
( leq(star(X1),star(addition(one,X1)))
| ~ leq(star(addition(one,X1)),star(addition(one,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[47453,32,theory(equality)]),45457,theory(equality)]) ).
cnf(47620,plain,
( leq(star(X1),star(addition(one,X1)))
| $false ),
inference(rw,[status(thm)],[47619,55,theory(equality)]) ).
cnf(47621,plain,
leq(star(X1),star(addition(one,X1))),
inference(cn,[status(thm)],[47620,theory(equality)]) ).
cnf(47691,plain,
addition(star(X1),star(addition(one,X1))) = star(addition(one,X1)),
inference(spm,[status(thm)],[45,47621,theory(equality)]) ).
cnf(47728,plain,
star(X1) = star(addition(one,X1)),
inference(rw,[status(thm)],[47691,44999,theory(equality)]) ).
cnf(78245,negated_conjecture,
addition(esk3_0,multiplication(addition(esk3_0,multiplication(esk1_0,esk3_0)),star(esk2_0))) = multiplication(addition(esk3_0,multiplication(esk1_0,esk3_0)),addition(one,star(esk2_0))),
inference(spm,[status(thm)],[677,7653,theory(equality)]) ).
cnf(78432,negated_conjecture,
addition(esk3_0,multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0)))) = multiplication(addition(esk3_0,multiplication(esk1_0,esk3_0)),addition(one,star(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[78245,129,theory(equality)]),17,theory(equality)]) ).
cnf(78433,negated_conjecture,
addition(esk3_0,multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0)))) = multiplication(addition(one,esk1_0),multiplication(esk3_0,addition(one,star(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[78432,129,theory(equality)]),17,theory(equality)]) ).
cnf(78528,negated_conjecture,
leq(esk3_0,multiplication(addition(one,esk1_0),multiplication(esk3_0,addition(one,star(esk2_0))))),
inference(spm,[status(thm)],[180,78433,theory(equality)]) ).
cnf(78606,negated_conjecture,
( leq(multiplication(star(addition(one,esk1_0)),esk3_0),multiplication(esk3_0,star(esk2_0)))
| ~ leq(multiplication(addition(one,esk1_0),multiplication(esk3_0,addition(one,star(esk2_0)))),multiplication(esk3_0,star(esk2_0))) ),
inference(spm,[status(thm)],[99,78433,theory(equality)]) ).
cnf(78717,negated_conjecture,
( leq(multiplication(star(esk1_0),esk3_0),multiplication(esk3_0,star(esk2_0)))
| ~ leq(multiplication(addition(one,esk1_0),multiplication(esk3_0,addition(one,star(esk2_0)))),multiplication(esk3_0,star(esk2_0))) ),
inference(rw,[status(thm)],[78606,47728,theory(equality)]) ).
cnf(78718,negated_conjecture,
~ leq(multiplication(addition(one,esk1_0),multiplication(esk3_0,addition(one,star(esk2_0)))),multiplication(esk3_0,star(esk2_0))),
inference(sr,[status(thm)],[78717,49,theory(equality)]) ).
cnf(79236,negated_conjecture,
leq(esk3_0,multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0)))),
inference(spm,[status(thm)],[78528,1674,theory(equality)]) ).
cnf(79238,negated_conjecture,
addition(esk3_0,multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0)))) = multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0))),
inference(spm,[status(thm)],[45,79236,theory(equality)]) ).
cnf(79239,negated_conjecture,
multiplication(addition(one,esk1_0),multiplication(esk3_0,addition(one,star(esk2_0)))) = multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0))),
inference(rw,[status(thm)],[79238,78433,theory(equality)]) ).
cnf(79444,negated_conjecture,
~ leq(multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0))),multiplication(esk3_0,star(esk2_0))),
inference(rw,[status(thm)],[78718,79239,theory(equality)]) ).
cnf(220115,negated_conjecture,
leq(multiplication(esk1_0,multiplication(esk3_0,star(esk2_0))),multiplication(esk3_0,star(esk2_0))),
inference(spm,[status(thm)],[3073,6057,theory(equality)]) ).
cnf(220352,negated_conjecture,
addition(multiplication(esk1_0,multiplication(esk3_0,star(esk2_0))),multiplication(esk3_0,star(esk2_0))) = multiplication(esk3_0,star(esk2_0)),
inference(spm,[status(thm)],[45,220115,theory(equality)]) ).
cnf(220354,negated_conjecture,
multiplication(addition(one,esk1_0),multiplication(esk3_0,star(esk2_0))) = multiplication(esk3_0,star(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[220352,132,theory(equality)]),23,theory(equality)]),129,theory(equality)]),17,theory(equality)]) ).
cnf(220508,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[79444,220354,theory(equality)]),55,theory(equality)]) ).
cnf(220509,negated_conjecture,
$false,
inference(cn,[status(thm)],[220508,theory(equality)]) ).
cnf(220510,negated_conjecture,
$false,
220509,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE045+1.p
% --creating new selector for [KLE002+0.ax]
% -running prover on /tmp/tmpAQADjx/sel_KLE045+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE045+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE045+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE045+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
%
%------------------------------------------------------------------------------