TSTP Solution File: LCL900+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LCL900+1 : TPTP v5.5.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2005MB
% OS : Linux 2.6.32.26-175.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Mon Oct 22 18:24:28 EDT 2012
% Result : Theorem 13.74s
% Output : CNFRefutation 13.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 13
% Syntax : Number of formulae : 196 ( 141 unt; 0 def)
% Number of atoms : 263 ( 118 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 118 ( 51 ~; 58 |; 4 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 387 ( 51 sgn 68 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : '>='(X1,'0'),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_08) ).
fof(3,axiom,
! [X1,X5] : equal('+'(X1,X5),'+'(X5,X1)),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_02) ).
fof(4,axiom,
! [X1] : equal('+'(X1,'0'),X1),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_03) ).
fof(5,axiom,
! [X1,X5] : equal('==>'('==>'(X1,X5),X5),'==>'('==>'(X5,X1),X1)),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_13) ).
fof(6,axiom,
! [X1,X5,X6] : equal('+'('+'(X1,X5),X6),'+'(X1,'+'(X5,X6))),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_01) ).
fof(7,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> equal(X7,X8) ),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_06) ).
fof(8,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_07) ).
fof(9,axiom,
! [X1] : '>='(X1,X1),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_04) ).
fof(10,axiom,
! [X12,X13,X14] :
( ( '>='(X12,X13)
& '>='(X13,X14) )
=> '>='(X12,X14) ),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_05) ).
fof(11,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X17,X15),'==>'(X17,X16)) ),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_11) ).
fof(12,conjecture,
! [X18,X19] : equal('+'(X18,'==>'(X18,X19)),'+'(X19,'==>'(X19,X18))),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',goals_14) ).
fof(13,axiom,
! [X20,X21,X22] :
( '>='(X20,X21)
=> '>='('==>'(X21,X22),'==>'(X20,X22)) ),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_10) ).
fof(14,axiom,
! [X1] : equal('+'(X1,'1'),'1'),
file('/tmp/tmpCWGjQb/sel_LCL900+1.p_1',sos_12) ).
fof(15,negated_conjecture,
~ ! [X18,X19] : equal('+'(X18,'==>'(X18,X19)),'+'(X19,'==>'(X19,X18))),
inference(assume_negation,[status(cth)],[12]) ).
fof(16,plain,
! [X2] : '>='(X2,'0'),
inference(variable_rename,[status(thm)],[1]) ).
cnf(17,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[16]) ).
fof(21,plain,
! [X6,X7] : equal('+'(X6,X7),'+'(X7,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(22,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,plain,
! [X2] : equal('+'(X2,'0'),X2),
inference(variable_rename,[status(thm)],[4]) ).
cnf(24,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X6,X7] : equal('==>'('==>'(X6,X7),X7),'==>'('==>'(X7,X6),X6)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(26,plain,
'==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X7,X8,X9] : equal('+'('+'(X7,X8),X9),'+'(X7,'+'(X8,X9))),
inference(variable_rename,[status(thm)],[6]) ).
cnf(28,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X7,X8] :
( ~ '>='(X7,X8)
| ~ '>='(X8,X7)
| equal(X7,X8) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(30,plain,
! [X9,X10] :
( ~ '>='(X9,X10)
| ~ '>='(X10,X9)
| equal(X9,X10) ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(31,plain,
( X1 = X2
| ~ '>='(X2,X1)
| ~ '>='(X1,X2) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X9,X10,X11] :
( ( ~ '>='('+'(X9,X10),X11)
| '>='(X10,'==>'(X9,X11)) )
& ( ~ '>='(X10,'==>'(X9,X11))
| '>='('+'(X9,X10),X11) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(33,plain,
! [X12,X13,X14] :
( ( ~ '>='('+'(X12,X13),X14)
| '>='(X13,'==>'(X12,X14)) )
& ( ~ '>='(X13,'==>'(X12,X14))
| '>='('+'(X12,X13),X14) ) ),
inference(variable_rename,[status(thm)],[32]) ).
cnf(34,plain,
( '>='('+'(X1,X2),X3)
| ~ '>='(X2,'==>'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X1),X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(36,plain,
! [X2] : '>='(X2,X2),
inference(variable_rename,[status(thm)],[9]) ).
cnf(37,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,plain,
! [X12,X13,X14] :
( ~ '>='(X12,X13)
| ~ '>='(X13,X14)
| '>='(X12,X14) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(39,plain,
! [X15,X16,X17] :
( ~ '>='(X15,X16)
| ~ '>='(X16,X17)
| '>='(X15,X17) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( '>='(X1,X2)
| ~ '>='(X3,X2)
| ~ '>='(X1,X3) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X15,X16,X17] :
( ~ '>='(X15,X16)
| '>='('==>'(X17,X15),'==>'(X17,X16)) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(42,plain,
! [X18,X19,X20] :
( ~ '>='(X18,X19)
| '>='('==>'(X20,X18),'==>'(X20,X19)) ),
inference(variable_rename,[status(thm)],[41]) ).
cnf(43,plain,
( '>='('==>'(X1,X2),'==>'(X1,X3))
| ~ '>='(X2,X3) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,negated_conjecture,
? [X18,X19] : ~ equal('+'(X18,'==>'(X18,X19)),'+'(X19,'==>'(X19,X18))),
inference(fof_nnf,[status(thm)],[15]) ).
fof(45,negated_conjecture,
? [X20,X21] : ~ equal('+'(X20,'==>'(X20,X21)),'+'(X21,'==>'(X21,X20))),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,negated_conjecture,
~ equal('+'(esk1_0,'==>'(esk1_0,esk2_0)),'+'(esk2_0,'==>'(esk2_0,esk1_0))),
inference(skolemize,[status(esa)],[45]) ).
cnf(47,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,plain,
! [X20,X21,X22] :
( ~ '>='(X20,X21)
| '>='('==>'(X21,X22),'==>'(X20,X22)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(49,plain,
! [X23,X24,X25] :
( ~ '>='(X23,X24)
| '>='('==>'(X24,X25),'==>'(X23,X25)) ),
inference(variable_rename,[status(thm)],[48]) ).
cnf(50,plain,
( '>='('==>'(X1,X2),'==>'(X3,X2))
| ~ '>='(X3,X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(51,plain,
! [X2] : equal('+'(X2,'1'),'1'),
inference(variable_rename,[status(thm)],[14]) ).
cnf(52,plain,
'+'(X1,'1') = '1',
inference(split_conjunct,[status(thm)],[51]) ).
cnf(53,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[52,22,theory(equality)]) ).
cnf(55,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[24,22,theory(equality)]) ).
cnf(62,plain,
'+'(X1,'+'(X2,X3)) = '+'(X3,'+'(X1,X2)),
inference(spm,[status(thm)],[22,28,theory(equality)]) ).
cnf(82,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[31,17,theory(equality)]) ).
cnf(88,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[35,37,theory(equality)]) ).
cnf(89,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[35,24,theory(equality)]) ).
cnf(91,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(spm,[status(thm)],[35,22,theory(equality)]) ).
cnf(93,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[34,37,theory(equality)]) ).
cnf(99,plain,
'>='('0','==>'(X1,'0')),
inference(spm,[status(thm)],[89,17,theory(equality)]) ).
cnf(100,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[89,37,theory(equality)]) ).
cnf(124,plain,
( '==>'(X1,'0') = '0'
| ~ '>='('==>'(X1,'0'),'0') ),
inference(spm,[status(thm)],[31,99,theory(equality)]) ).
cnf(132,plain,
( '==>'(X1,'0') = '0'
| $false ),
inference(rw,[status(thm)],[124,17,theory(equality)]) ).
cnf(133,plain,
'==>'(X1,'0') = '0',
inference(cn,[status(thm)],[132,theory(equality)]) ).
cnf(137,plain,
'==>'('0','0') = '==>'('==>'('0',X1),X1),
inference(spm,[status(thm)],[26,133,theory(equality)]) ).
cnf(143,plain,
'0' = '==>'('==>'('0',X1),X1),
inference(rw,[status(thm)],[137,133,theory(equality)]) ).
cnf(155,plain,
( '==>'(X1,X1) = '0'
| ~ '>='('==>'(X1,X1),'0') ),
inference(spm,[status(thm)],[31,100,theory(equality)]) ).
cnf(165,plain,
( '==>'(X1,X1) = '0'
| $false ),
inference(rw,[status(thm)],[155,17,theory(equality)]) ).
cnf(166,plain,
'==>'(X1,X1) = '0',
inference(cn,[status(thm)],[165,theory(equality)]) ).
cnf(179,plain,
( '>='('+'(X1,X2),X1)
| ~ '>='(X2,'0') ),
inference(spm,[status(thm)],[34,166,theory(equality)]) ).
cnf(180,plain,
( '==>'(X2,X2) = X1
| ~ '>='('==>'(X2,X2),X1) ),
inference(spm,[status(thm)],[82,166,theory(equality)]) ).
cnf(182,plain,
( '>='('+'(X1,X2),X1)
| $false ),
inference(rw,[status(thm)],[179,17,theory(equality)]) ).
cnf(183,plain,
'>='('+'(X1,X2),X1),
inference(cn,[status(thm)],[182,theory(equality)]) ).
cnf(208,plain,
( '>='('+'('==>'('0',X1),X2),X1)
| ~ '>='(X2,'0') ),
inference(spm,[status(thm)],[34,143,theory(equality)]) ).
cnf(213,plain,
( '>='('+'('==>'('0',X1),X2),X1)
| $false ),
inference(rw,[status(thm)],[208,17,theory(equality)]) ).
cnf(214,plain,
'>='('+'('==>'('0',X1),X2),X1),
inference(cn,[status(thm)],[213,theory(equality)]) ).
cnf(376,plain,
'>='('1',X1),
inference(spm,[status(thm)],[183,52,theory(equality)]) ).
cnf(392,plain,
'>='('==>'(X1,X2),'==>'('+'(X1,X3),X2)),
inference(spm,[status(thm)],[50,183,theory(equality)]) ).
cnf(395,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[91,183,theory(equality)]) ).
cnf(403,plain,
'>='('==>'(X1,'1'),'==>'(X1,X2)),
inference(spm,[status(thm)],[43,376,theory(equality)]) ).
cnf(404,plain,
( X1 = '1'
| ~ '>='(X1,'1') ),
inference(spm,[status(thm)],[31,376,theory(equality)]) ).
cnf(408,plain,
'>='('0','==>'('1',X1)),
inference(spm,[status(thm)],[89,376,theory(equality)]) ).
cnf(423,plain,
( '==>'('1',X1) = '0'
| ~ '>='('==>'('1',X1),'0') ),
inference(spm,[status(thm)],[31,408,theory(equality)]) ).
cnf(433,plain,
( '==>'('1',X1) = '0'
| $false ),
inference(rw,[status(thm)],[423,17,theory(equality)]) ).
cnf(434,plain,
'==>'('1',X1) = '0',
inference(cn,[status(thm)],[433,theory(equality)]) ).
cnf(439,plain,
'+'(X1,'==>'('1',X2)) = X1,
inference(spm,[status(thm)],[24,434,theory(equality)]) ).
cnf(440,plain,
'+'('==>'('1',X2),X1) = X1,
inference(spm,[status(thm)],[55,434,theory(equality)]) ).
cnf(663,plain,
'>='('==>'(X1,X2),'==>'(X1,'==>'(X3,X2))),
inference(spm,[status(thm)],[43,395,theory(equality)]) ).
cnf(665,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='(X1,X3) ),
inference(spm,[status(thm)],[40,395,theory(equality)]) ).
cnf(686,plain,
'>='('+'(X1,X2),'==>'(X3,X1)),
inference(spm,[status(thm)],[665,183,theory(equality)]) ).
cnf(1276,plain,
'>='('==>'('0',X1),X1),
inference(spm,[status(thm)],[214,24,theory(equality)]) ).
cnf(1462,plain,
( X1 = '==>'('0',X1)
| ~ '>='(X1,'==>'('0',X1)) ),
inference(spm,[status(thm)],[31,1276,theory(equality)]) ).
cnf(1485,plain,
( X1 = '==>'('0',X1)
| $false ),
inference(rw,[status(thm)],[1462,395,theory(equality)]) ).
cnf(1486,plain,
X1 = '==>'('0',X1),
inference(cn,[status(thm)],[1485,theory(equality)]) ).
cnf(1501,plain,
'==>'('==>'(X2,X2),X1) = X1,
inference(spm,[status(thm)],[1486,166,theory(equality)]) ).
cnf(1502,plain,
'==>'('==>'('1',X2),X1) = X1,
inference(spm,[status(thm)],[1486,434,theory(equality)]) ).
cnf(1537,plain,
X1 = '==>'('==>'(X1,'1'),'1'),
inference(spm,[status(thm)],[26,1502,theory(equality)]) ).
cnf(1589,plain,
( '>='('+'('==>'(X1,'1'),X2),'1')
| ~ '>='(X2,X1) ),
inference(spm,[status(thm)],[34,1537,theory(equality)]) ).
cnf(1785,plain,
'>='(X1,'==>'('+'(X2,X3),'+'(X2,'+'(X3,X1)))),
inference(spm,[status(thm)],[88,28,theory(equality)]) ).
cnf(1807,plain,
( '==>'(X1,'+'(X1,X2)) = X2
| ~ '>='('==>'(X1,'+'(X1,X2)),X2) ),
inference(spm,[status(thm)],[31,88,theory(equality)]) ).
cnf(1809,plain,
'>='(X1,'==>'(X2,'==>'(X3,'+'(X3,'+'(X2,X1))))),
inference(spm,[status(thm)],[35,88,theory(equality)]) ).
cnf(1813,plain,
'>='('0','==>'(X1,'==>'(X2,'+'(X2,X1)))),
inference(spm,[status(thm)],[89,88,theory(equality)]) ).
cnf(1958,plain,
'>='('0','==>'('==>'(X1,'1'),'==>'(X1,X2))),
inference(spm,[status(thm)],[89,403,theory(equality)]) ).
cnf(2135,plain,
'>='('==>'(X1,'+'(X2,'==>'(X2,X3))),'==>'(X1,X3)),
inference(spm,[status(thm)],[43,93,theory(equality)]) ).
cnf(2141,plain,
'>='('0','==>'('+'(X1,'==>'(X1,X2)),X2)),
inference(spm,[status(thm)],[89,93,theory(equality)]) ).
cnf(2143,plain,
'+'(X1,'==>'(X1,'1')) = '1',
inference(spm,[status(thm)],[404,93,theory(equality)]) ).
cnf(2178,plain,
'+'('1',X2) = '+'(X1,'+'('==>'(X1,'1'),X2)),
inference(spm,[status(thm)],[28,2143,theory(equality)]) ).
cnf(2179,plain,
'1' = '+'(X1,'+'(X2,'==>'('+'(X1,X2),'1'))),
inference(spm,[status(thm)],[28,2143,theory(equality)]) ).
cnf(2218,plain,
'1' = '+'(X1,'+'('==>'(X1,'1'),X2)),
inference(rw,[status(thm)],[2178,53,theory(equality)]) ).
cnf(2834,plain,
'>='('+'('==>'('==>'(X1,X2),'1'),X2),'1'),
inference(spm,[status(thm)],[1589,395,theory(equality)]) ).
cnf(2849,plain,
'>='('+'(X2,'==>'('==>'(X1,X2),'1')),'1'),
inference(rw,[status(thm)],[2834,22,theory(equality)]) ).
cnf(2932,plain,
'+'(X1,'1') = '+'('+'('==>'(X2,'1'),X3),'+'(X1,X2)),
inference(spm,[status(thm)],[62,2218,theory(equality)]) ).
cnf(2990,plain,
'1' = '+'('+'('==>'(X2,'1'),X3),'+'(X1,X2)),
inference(rw,[status(thm)],[2932,52,theory(equality)]) ).
cnf(2991,plain,
'1' = '+'('==>'(X2,'1'),'+'(X3,'+'(X1,X2))),
inference(rw,[status(thm)],[2990,28,theory(equality)]) ).
cnf(3575,plain,
'>='('0','==>'('+'(X1,X2),'==>'(X3,X1))),
inference(spm,[status(thm)],[89,686,theory(equality)]) ).
cnf(5591,plain,
( '==>'('==>'(X1,'1'),'==>'(X1,X2)) = '0'
| ~ '>='('==>'('==>'(X1,'1'),'==>'(X1,X2)),'0') ),
inference(spm,[status(thm)],[31,1958,theory(equality)]) ).
cnf(5663,plain,
( '==>'('==>'(X1,'1'),'==>'(X1,X2)) = '0'
| $false ),
inference(rw,[status(thm)],[5591,17,theory(equality)]) ).
cnf(5664,plain,
'==>'('==>'(X1,'1'),'==>'(X1,X2)) = '0',
inference(cn,[status(thm)],[5663,theory(equality)]) ).
cnf(5675,plain,
'+'('==>'('==>'(X2,'1'),'==>'(X2,X3)),X1) = X1,
inference(spm,[status(thm)],[55,5664,theory(equality)]) ).
cnf(9614,plain,
( '1' = '+'(X1,'==>'('==>'(X2,X1),'1'))
| ~ '>='('1','+'(X1,'==>'('==>'(X2,X1),'1'))) ),
inference(spm,[status(thm)],[31,2849,theory(equality)]) ).
cnf(9680,plain,
( '1' = '+'(X1,'==>'('==>'(X2,X1),'1'))
| $false ),
inference(rw,[status(thm)],[9614,376,theory(equality)]) ).
cnf(9681,plain,
'1' = '+'(X1,'==>'('==>'(X2,X1),'1')),
inference(cn,[status(thm)],[9680,theory(equality)]) ).
cnf(9740,plain,
'+'(X1,'==>'('==>'('==>'(X1,X2),X2),'1')) = '1',
inference(spm,[status(thm)],[9681,26,theory(equality)]) ).
cnf(11373,plain,
'==>'(X1,X1) = '==>'('+'(X1,X2),X1),
inference(spm,[status(thm)],[180,392,theory(equality)]) ).
cnf(11510,plain,
'==>'('+'(X2,X1),X1) = '==>'(X1,X1),
inference(spm,[status(thm)],[11373,22,theory(equality)]) ).
cnf(11744,plain,
'==>'('==>'(X2,X2),X2) = '==>'('==>'(X2,'+'(X1,X2)),'+'(X1,X2)),
inference(spm,[status(thm)],[26,11510,theory(equality)]) ).
cnf(11829,plain,
X2 = '==>'('==>'(X2,'+'(X1,X2)),'+'(X1,X2)),
inference(rw,[status(thm)],[11744,1501,theory(equality)]) ).
cnf(13442,plain,
( '==>'(X1,'==>'(X2,'+'(X2,X1))) = '0'
| ~ '>='('==>'(X1,'==>'(X2,'+'(X2,X1))),'0') ),
inference(spm,[status(thm)],[31,1813,theory(equality)]) ).
cnf(13493,plain,
( '==>'(X1,'==>'(X2,'+'(X2,X1))) = '0'
| $false ),
inference(rw,[status(thm)],[13442,17,theory(equality)]) ).
cnf(13494,plain,
'==>'(X1,'==>'(X2,'+'(X2,X1))) = '0',
inference(cn,[status(thm)],[13493,theory(equality)]) ).
cnf(14025,plain,
( '==>'('+'(X1,'==>'(X1,X2)),X2) = '0'
| ~ '>='('==>'('+'(X1,'==>'(X1,X2)),X2),'0') ),
inference(spm,[status(thm)],[31,2141,theory(equality)]) ).
cnf(14084,plain,
( '==>'('+'(X1,'==>'(X1,X2)),X2) = '0'
| $false ),
inference(rw,[status(thm)],[14025,17,theory(equality)]) ).
cnf(14085,plain,
'==>'('+'(X1,'==>'(X1,X2)),X2) = '0',
inference(cn,[status(thm)],[14084,theory(equality)]) ).
cnf(14163,plain,
'+'(X1,'+'(X2,'==>'('+'(X2,X1),'1'))) = '1',
inference(spm,[status(thm)],[2179,22,theory(equality)]) ).
cnf(14906,plain,
'==>'(X1,X1) = '==>'(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[180,663,theory(equality)]) ).
cnf(15038,plain,
'==>'(X1,'==>'('==>'(X1,X2),X2)) = '==>'(X1,X1),
inference(spm,[status(thm)],[14906,26,theory(equality)]) ).
cnf(16111,plain,
'==>'(X1,'==>'('0','==>'(X2,'+'(X2,X1)))) = '==>'(X1,X1),
inference(spm,[status(thm)],[15038,13494,theory(equality)]) ).
cnf(16196,plain,
'==>'(X1,'==>'(X2,'+'(X2,X1))) = '==>'(X1,X1),
inference(rw,[status(thm)],[16111,1486,theory(equality)]) ).
cnf(16579,plain,
'==>'(X1,'==>'(X2,'+'(X1,X2))) = '==>'(X1,X1),
inference(spm,[status(thm)],[16196,22,theory(equality)]) ).
cnf(18942,plain,
( '==>'('+'(X1,X2),'==>'(X3,X1)) = '0'
| ~ '>='('==>'('+'(X1,X2),'==>'(X3,X1)),'0') ),
inference(spm,[status(thm)],[31,3575,theory(equality)]) ).
cnf(19011,plain,
( '==>'('+'(X1,X2),'==>'(X3,X1)) = '0'
| $false ),
inference(rw,[status(thm)],[18942,17,theory(equality)]) ).
cnf(19012,plain,
'==>'('+'(X1,X2),'==>'(X3,X1)) = '0',
inference(cn,[status(thm)],[19011,theory(equality)]) ).
cnf(19027,plain,
'+'('==>'('+'(X2,X3),'==>'(X4,X2)),X1) = X1,
inference(spm,[status(thm)],[55,19012,theory(equality)]) ).
cnf(23907,plain,
'==>'('==>'('==>'(X1,'1'),'==>'(X1,X2)),'1') = '1',
inference(spm,[status(thm)],[2143,5675,theory(equality)]) ).
cnf(24428,plain,
'==>'('1','1') = '==>'('==>'(X1,'1'),'==>'(X1,X2)),
inference(spm,[status(thm)],[1537,23907,theory(equality)]) ).
cnf(26359,plain,
'+'('+'(X1,'==>'(X1,X2)),'==>'('==>'('0',X2),'1')) = '1',
inference(spm,[status(thm)],[9740,14085,theory(equality)]) ).
cnf(26511,plain,
'+'(X1,'+'('==>'(X1,X2),'==>'(X2,'1'))) = '1',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[26359,1486,theory(equality)]),28,theory(equality)]) ).
cnf(31891,plain,
'+'(X1,'+'('==>'(X1,'==>'(X2,'1')),X2)) = '1',
inference(spm,[status(thm)],[26511,1537,theory(equality)]) ).
cnf(32112,plain,
'+'(X1,'+'(X2,'==>'(X1,'==>'(X2,'1')))) = '1',
inference(rw,[status(thm)],[31891,22,theory(equality)]) ).
cnf(35649,plain,
'>='('==>'(X1,'==>'(X2,'1')),'==>'('+'(X1,X2),'1')),
inference(spm,[status(thm)],[1785,32112,theory(equality)]) ).
cnf(37589,plain,
'>='('==>'('+'(X1,X2),'1'),'==>'(X1,'==>'(X2,'1'))),
inference(spm,[status(thm)],[1809,14163,theory(equality)]) ).
cnf(37597,plain,
'>='('==>'(X1,'==>'(X2,'1')),'==>'(X2,'==>'(X1,'1'))),
inference(spm,[status(thm)],[1809,32112,theory(equality)]) ).
cnf(49889,plain,
'==>'('==>'('+'(X1,'+'(X2,X3)),'1'),'1') = '+'(X1,'+'(X2,X3)),
inference(spm,[status(thm)],[11829,2991,theory(equality)]) ).
cnf(50324,plain,
'==>'('==>'('+'(X1,X3),'1'),'1') = '+'(X1,X3),
inference(spm,[status(thm)],[49889,440,theory(equality)]) ).
cnf(60289,plain,
'==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
inference(spm,[status(thm)],[1807,2135,theory(equality)]) ).
cnf(64713,plain,
'==>'('==>'(X4,'1'),'1') = X4,
inference(spm,[status(thm)],[50324,19027,theory(equality)]) ).
cnf(248853,plain,
( '==>'(X1,'==>'(X2,'1')) = '==>'('+'(X1,X2),'1')
| ~ '>='('==>'(X1,'==>'(X2,'1')),'==>'('+'(X1,X2),'1')) ),
inference(spm,[status(thm)],[31,37589,theory(equality)]) ).
cnf(249038,plain,
( '==>'(X1,'==>'(X2,'1')) = '==>'('+'(X1,X2),'1')
| $false ),
inference(rw,[status(thm)],[248853,35649,theory(equality)]) ).
cnf(249039,plain,
'==>'(X1,'==>'(X2,'1')) = '==>'('+'(X1,X2),'1'),
inference(cn,[status(thm)],[249038,theory(equality)]) ).
cnf(249049,plain,
'==>'('+'(X1,'+'(X2,X3)),'1') = '==>'('+'(X1,X2),'==>'(X3,'1')),
inference(spm,[status(thm)],[249039,28,theory(equality)]) ).
cnf(249210,plain,
'==>'('==>'(X1,'==>'(X2,'1')),'1') = '+'(X1,X2),
inference(spm,[status(thm)],[64713,249039,theory(equality)]) ).
cnf(249539,plain,
'==>'(X1,'==>'(X2,'==>'(X3,'1'))) = '==>'('+'(X1,X2),'==>'(X3,'1')),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[249049,249039,theory(equality)]),249039,theory(equality)]) ).
cnf(250012,plain,
'==>'('==>'(X1,X2),'1') = '+'(X1,'==>'(X2,'1')),
inference(spm,[status(thm)],[249210,64713,theory(equality)]) ).
cnf(250961,plain,
'==>'('==>'(X1,X2),'1') = '+'(X1,'==>'('+'(X1,'==>'(X1,X2)),'1')),
inference(spm,[status(thm)],[250012,60289,theory(equality)]) ).
cnf(251482,plain,
'+'(X1,'==>'(X2,'1')) = '+'(X1,'==>'('+'(X1,'==>'(X1,X2)),'1')),
inference(rw,[status(thm)],[250961,250012,theory(equality)]) ).
cnf(251483,plain,
'+'(X1,'==>'(X2,'1')) = '+'(X1,'==>'(X1,'+'(X1,'==>'(X2,'1')))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[251482,249039,theory(equality)]),250012,theory(equality)]) ).
cnf(252448,plain,
'==>'('+'(X1,X2),'==>'('==>'('1',X3),X3)) = '==>'(X1,'==>'(X2,'==>'('==>'('1',X3),X3))),
inference(spm,[status(thm)],[249539,26,theory(equality)]) ).
cnf(252744,plain,
'==>'('+'(X1,X2),X3) = '==>'(X1,'==>'(X2,'==>'('==>'('1',X3),X3))),
inference(rw,[status(thm)],[252448,1502,theory(equality)]) ).
cnf(252745,plain,
'==>'('+'(X1,X2),X3) = '==>'(X1,'==>'(X2,X3)),
inference(rw,[status(thm)],[252744,1502,theory(equality)]) ).
cnf(254415,plain,
'+'(X1,'==>'(X1,'+'(X1,'==>'('==>'('1',X2),X2)))) = '+'(X1,'==>'('==>'('1',X2),X2)),
inference(spm,[status(thm)],[251483,26,theory(equality)]) ).
cnf(254810,plain,
'+'(X1,'==>'(X1,'+'(X1,X2))) = '+'(X1,'==>'('==>'('1',X2),X2)),
inference(rw,[status(thm)],[254415,1502,theory(equality)]) ).
cnf(254811,plain,
'+'(X1,'==>'(X1,'+'(X1,X2))) = '+'(X1,X2),
inference(rw,[status(thm)],[254810,1502,theory(equality)]) ).
cnf(256943,plain,
( '==>'(X1,'==>'(X2,'1')) = '==>'(X2,'==>'(X1,'1'))
| ~ '>='('==>'(X1,'==>'(X2,'1')),'==>'(X2,'==>'(X1,'1'))) ),
inference(spm,[status(thm)],[31,37597,theory(equality)]) ).
cnf(257049,plain,
( '==>'(X1,'==>'(X2,'1')) = '==>'(X2,'==>'(X1,'1'))
| $false ),
inference(rw,[status(thm)],[256943,37597,theory(equality)]) ).
cnf(257050,plain,
'==>'(X1,'==>'(X2,'1')) = '==>'(X2,'==>'(X1,'1')),
inference(cn,[status(thm)],[257049,theory(equality)]) ).
cnf(257627,plain,
'==>'('==>'(X2,'==>'(X1,'1')),'==>'(X2,'1')) = '==>'('==>'('==>'(X2,'1'),X1),X1),
inference(spm,[status(thm)],[26,257050,theory(equality)]) ).
cnf(257635,plain,
'==>'(X1,'==>'('==>'('1',X2),X2)) = '==>'('==>'(X2,'1'),'==>'(X1,'1')),
inference(spm,[status(thm)],[257050,26,theory(equality)]) ).
cnf(258147,plain,
'==>'(X2,'+'(X2,X1)) = '==>'('==>'('==>'(X2,'1'),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[257627,257050,theory(equality)]),250012,theory(equality)]),250012,theory(equality)]),439,theory(equality)]) ).
cnf(258155,plain,
'==>'(X1,X2) = '==>'('==>'(X2,'1'),'==>'(X1,'1')),
inference(rw,[status(thm)],[257635,1502,theory(equality)]) ).
cnf(258585,plain,
'==>'('==>'('==>'(X1,'1'),'==>'(X1,'1')),'==>'(X2,'+'('==>'(X1,'1'),X2))) = '==>'(X1,'+'(X1,'==>'(X2,'+'('==>'(X1,'1'),X2)))),
inference(spm,[status(thm)],[258147,16579,theory(equality)]) ).
cnf(259068,plain,
'==>'(X2,'+'('==>'(X1,'1'),X2)) = '==>'(X1,'+'(X1,'==>'(X2,'+'('==>'(X1,'1'),X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[258585,24428,theory(equality)]),1502,theory(equality)]) ).
cnf(260584,plain,
'==>'('==>'('==>'(X2,'1'),'==>'('==>'(X1,'1'),'1')),X2) = '==>'(X1,'+'(X1,X2)),
inference(spm,[status(thm)],[258147,258155,theory(equality)]) ).
cnf(260596,plain,
'==>'('==>'('==>'(X2,'1'),'==>'(X1,'1')),X2) = '==>'('==>'(X2,X1),X1),
inference(spm,[status(thm)],[26,258155,theory(equality)]) ).
cnf(260697,negated_conjecture,
'+'(esk1_0,'==>'('==>'(esk2_0,'1'),'==>'(esk1_0,'1'))) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
inference(rw,[status(thm)],[47,258155,theory(equality)]) ).
cnf(261096,plain,
'==>'('==>'('==>'(X2,'1'),X1),X2) = '==>'(X1,'+'(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[260584,250012,theory(equality)]),439,theory(equality)]) ).
cnf(262479,plain,
'==>'('==>'(X1,'1'),'+'('==>'(X1,'1'),X2)) = '==>'('==>'(X2,X1),X1),
inference(rw,[status(thm)],[260596,261096,theory(equality)]) ).
cnf(263127,plain,
'+'('==>'(X1,'1'),'==>'('==>'(X2,X1),X1)) = '+'('==>'(X1,'1'),X2),
inference(spm,[status(thm)],[254811,262479,theory(equality)]) ).
cnf(267782,plain,
'+'('==>'(X1,'1'),'==>'('==>'(X1,X2),X2)) = '+'('==>'(X1,'1'),X2),
inference(spm,[status(thm)],[263127,26,theory(equality)]) ).
cnf(269093,plain,
'+'('==>'('==>'(X1,'1'),'1'),'==>'('==>'(X2,X1),'==>'(X2,'1'))) = '+'('==>'('==>'(X1,'1'),'1'),'==>'(X2,'1')),
inference(spm,[status(thm)],[267782,258155,theory(equality)]) ).
cnf(269499,plain,
'+'(X1,'==>'(X2,'+'(X2,'==>'(X1,'1')))) = '+'('==>'('==>'(X1,'1'),'1'),'==>'(X2,'1')),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[269093,250012,theory(equality)]),439,theory(equality)]),257050,theory(equality)]),250012,theory(equality)]) ).
cnf(269500,plain,
'+'(X1,'==>'(X2,'+'(X2,'==>'(X1,'1')))) = '+'(X1,'==>'(X2,'1')),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[269499,250012,theory(equality)]),439,theory(equality)]) ).
cnf(269876,plain,
'+'(X1,'==>'(X2,'+'('==>'(X1,'1'),X2))) = '+'(X1,'==>'(X2,'1')),
inference(spm,[status(thm)],[269500,22,theory(equality)]) ).
cnf(519803,plain,
'==>'(X1,'+'(X1,'==>'(X2,'1'))) = '==>'(X2,'+'('==>'(X1,'1'),X2)),
inference(rw,[status(thm)],[259068,269876,theory(equality)]) ).
cnf(520363,plain,
'==>'('==>'(X2,'+'('==>'(X1,'1'),X2)),'1') = '+'(X1,'==>'('+'(X1,'==>'(X2,'1')),'1')),
inference(spm,[status(thm)],[250012,519803,theory(equality)]) ).
cnf(521781,plain,
'+'(X2,'==>'('==>'(X1,'1'),'==>'(X2,'1'))) = '+'(X1,'==>'('+'(X1,'==>'(X2,'1')),'1')),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[520363,250012,theory(equality)]),252745,theory(equality)]) ).
cnf(521782,plain,
'+'(X2,'==>'('==>'(X1,'1'),'==>'(X2,'1'))) = '+'(X1,'==>'(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[521781,249039,theory(equality)]),1537,theory(equality)]) ).
cnf(524809,negated_conjecture,
$false,
inference(rw,[status(thm)],[260697,521782,theory(equality)]) ).
cnf(524810,negated_conjecture,
$false,
inference(cn,[status(thm)],[524809,theory(equality)]) ).
cnf(524811,negated_conjecture,
$false,
524810,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LCL/LCL900+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCWGjQb/sel_LCL900+1.p_1 with time limit 29
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/tmp/tmpCWGjQb/sel_LCL900+1.p_1']
% -prover status Theorem
% Problem LCL900+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LCL/LCL900+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LCL/LCL900+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
%
%------------------------------------------------------------------------------