TSTP Solution File: SWV487+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV487+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 : Sun Dec 26 13:03:49 EST 2010
% Result : Theorem 0.98s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 11 unt; 0 def)
% Number of atoms : 310 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 393 ( 164 ~; 158 |; 53 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 93 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( int_less(X1,X2)
| X1 = X2 ) ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',int_leq) ).
fof(2,axiom,
! [X1,X2] :
( int_less(X1,X2)
<=> ? [X3] :
( plus(X1,X3) = X2
& int_less(int_zero,X3) ) ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',plus_and_inverse) ).
fof(3,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',ut) ).
fof(7,axiom,
! [X1,X2,X3] :
( ( int_less(X1,X2)
& int_less(X2,X3) )
=> int_less(X1,X3) ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',int_less_transitive) ).
fof(8,axiom,
! [X1] :
( int_less(int_zero,X1)
<=> int_leq(int_one,X1) ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',one_successor_of_zero) ).
fof(9,axiom,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ! [X4] :
( ( int_less(int_zero,X4)
& X1 = plus(X2,X4) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X4),X3) = real_zero ) )
& ! [X4] :
( ( int_leq(int_zero,X4)
& X2 = plus(X1,X4) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X4)) = lu(X3,plus(X3,X4)) ) ) ) ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',qiu) ).
fof(11,axiom,
! [X1,X2] :
( int_less(X1,X2)
=> X1 != X2 ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',int_less_irreflexive) ).
fof(12,axiom,
! [X1,X2] :
( int_less(X1,X2)
| int_leq(X2,X1) ),
file('/tmp/tmpdE-0Yz/sel_SWV487+1.p_1',int_less_total) ).
fof(14,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
inference(assume_negation,[status(cth)],[3]) ).
fof(15,plain,
! [X2,X1] :
( epred1_2(X1,X2)
=> ( ! [X4] :
( ( int_less(int_zero,X4)
& X1 = plus(X2,X4) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X4),X3) = real_zero ) )
& ! [X4] :
( ( int_leq(int_zero,X4)
& X2 = plus(X1,X4) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X4)) = lu(X3,plus(X3,X4)) ) ) ) ),
introduced(definition) ).
fof(16,plain,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> epred1_2(X1,X2) ),
inference(apply_def,[status(esa)],[9,15,theory(equality)]) ).
fof(17,plain,
! [X1,X2] :
( ( ~ int_leq(X1,X2)
| int_less(X1,X2)
| X1 = X2 )
& ( ( ~ int_less(X1,X2)
& X1 != X2 )
| int_leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(18,plain,
! [X3,X4] :
( ( ~ int_leq(X3,X4)
| int_less(X3,X4)
| X3 = X4 )
& ( ( ~ int_less(X3,X4)
& X3 != X4 )
| int_leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X3,X4] :
( ( ~ int_leq(X3,X4)
| int_less(X3,X4)
| X3 = X4 )
& ( ~ int_less(X3,X4)
| int_leq(X3,X4) )
& ( X3 != X4
| int_leq(X3,X4) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(20,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( int_leq(X1,X2)
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(22,plain,
( X1 = X2
| int_less(X1,X2)
| ~ int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,plain,
! [X1,X2] :
( ( ~ int_less(X1,X2)
| ? [X3] :
( plus(X1,X3) = X2
& int_less(int_zero,X3) ) )
& ( ! [X3] :
( plus(X1,X3) != X2
| ~ int_less(int_zero,X3) )
| int_less(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(24,plain,
! [X4,X5] :
( ( ~ int_less(X4,X5)
| ? [X6] :
( plus(X4,X6) = X5
& int_less(int_zero,X6) ) )
& ( ! [X7] :
( plus(X4,X7) != X5
| ~ int_less(int_zero,X7) )
| int_less(X4,X5) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5] :
( ( ~ int_less(X4,X5)
| ( plus(X4,esk1_2(X4,X5)) = X5
& int_less(int_zero,esk1_2(X4,X5)) ) )
& ( ! [X7] :
( plus(X4,X7) != X5
| ~ int_less(int_zero,X7) )
| int_less(X4,X5) ) ),
inference(skolemize,[status(esa)],[24]) ).
fof(26,plain,
! [X4,X5,X7] :
( ( plus(X4,X7) != X5
| ~ int_less(int_zero,X7)
| int_less(X4,X5) )
& ( ~ int_less(X4,X5)
| ( plus(X4,esk1_2(X4,X5)) = X5
& int_less(int_zero,esk1_2(X4,X5)) ) ) ),
inference(shift_quantors,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X7] :
( ( plus(X4,X7) != X5
| ~ int_less(int_zero,X7)
| int_less(X4,X5) )
& ( plus(X4,esk1_2(X4,X5)) = X5
| ~ int_less(X4,X5) )
& ( int_less(int_zero,esk1_2(X4,X5))
| ~ int_less(X4,X5) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( int_less(int_zero,esk1_2(X1,X2))
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,plain,
( plus(X1,esk1_2(X1,X2)) = X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(31,negated_conjecture,
? [X1,X2] :
( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n)
& a(X1,X2) != real_zero ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(32,negated_conjecture,
? [X3,X4] :
( int_leq(int_one,X4)
& int_less(X4,X3)
& int_leq(X3,n)
& a(X3,X4) != real_zero ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( int_leq(int_one,esk3_0)
& int_less(esk3_0,esk2_0)
& int_leq(esk2_0,n)
& a(esk2_0,esk3_0) != real_zero ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
a(esk2_0,esk3_0) != real_zero,
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,negated_conjecture,
int_leq(esk2_0,n),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,negated_conjecture,
int_less(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(37,negated_conjecture,
int_leq(int_one,esk3_0),
inference(split_conjunct,[status(thm)],[33]) ).
fof(43,plain,
! [X1,X2,X3] :
( ~ int_less(X1,X2)
| ~ int_less(X2,X3)
| int_less(X1,X3) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(44,plain,
! [X4,X5,X6] :
( ~ int_less(X4,X5)
| ~ int_less(X5,X6)
| int_less(X4,X6) ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(45,plain,
( int_less(X1,X2)
| ~ int_less(X3,X2)
| ~ int_less(X1,X3) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,plain,
! [X1] :
( ( ~ int_less(int_zero,X1)
| int_leq(int_one,X1) )
& ( ~ int_leq(int_one,X1)
| int_less(int_zero,X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(47,plain,
! [X2] :
( ( ~ int_less(int_zero,X2)
| int_leq(int_one,X2) )
& ( ~ int_leq(int_one,X2)
| int_less(int_zero,X2) ) ),
inference(variable_rename,[status(thm)],[46]) ).
cnf(48,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(50,plain,
! [X1,X2] :
( ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| epred1_2(X1,X2) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(51,plain,
! [X3,X4] :
( ~ int_leq(int_one,X3)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,n)
| epred1_2(X3,X4) ),
inference(variable_rename,[status(thm)],[50]) ).
cnf(52,plain,
( epred1_2(X1,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(54,plain,
! [X1,X2] :
( ~ int_less(X1,X2)
| X1 != X2 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(55,plain,
! [X3,X4] :
( ~ int_less(X3,X4)
| X3 != X4 ),
inference(variable_rename,[status(thm)],[54]) ).
cnf(56,plain,
( X1 != X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,plain,
! [X3,X4] :
( int_less(X3,X4)
| int_leq(X4,X3) ),
inference(variable_rename,[status(thm)],[12]) ).
cnf(58,plain,
( int_leq(X1,X2)
| int_less(X2,X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(62,plain,
! [X2,X1] :
( ~ epred1_2(X1,X2)
| ( ! [X4] :
( ~ int_less(int_zero,X4)
| X1 != plus(X2,X4)
| ! [X3] :
( ~ int_leq(int_one,X3)
| ~ int_leq(X3,X2)
| a(plus(X3,X4),X3) = real_zero ) )
& ! [X4] :
( ~ int_leq(int_zero,X4)
| X2 != plus(X1,X4)
| ! [X3] :
( ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1)
| a(X3,plus(X3,X4)) = lu(X3,plus(X3,X4)) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(63,plain,
! [X5,X6] :
( ~ epred1_2(X6,X5)
| ( ! [X7] :
( ~ int_less(int_zero,X7)
| X6 != plus(X5,X7)
| ! [X8] :
( ~ int_leq(int_one,X8)
| ~ int_leq(X8,X5)
| a(plus(X8,X7),X8) = real_zero ) )
& ! [X9] :
( ~ int_leq(int_zero,X9)
| X5 != plus(X6,X9)
| ! [X10] :
( ~ int_leq(int_one,X10)
| ~ int_leq(X10,X6)
| a(X10,plus(X10,X9)) = lu(X10,plus(X10,X9)) ) ) ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ( ~ int_leq(int_one,X10)
| ~ int_leq(X10,X6)
| a(X10,plus(X10,X9)) = lu(X10,plus(X10,X9))
| ~ int_leq(int_zero,X9)
| X5 != plus(X6,X9) )
& ( ~ int_leq(int_one,X8)
| ~ int_leq(X8,X5)
| a(plus(X8,X7),X8) = real_zero
| ~ int_less(int_zero,X7)
| X6 != plus(X5,X7) ) )
| ~ epred1_2(X6,X5) ),
inference(shift_quantors,[status(thm)],[63]) ).
fof(65,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ~ int_leq(int_one,X10)
| ~ int_leq(X10,X6)
| a(X10,plus(X10,X9)) = lu(X10,plus(X10,X9))
| ~ int_leq(int_zero,X9)
| X5 != plus(X6,X9)
| ~ epred1_2(X6,X5) )
& ( ~ int_leq(int_one,X8)
| ~ int_leq(X8,X5)
| a(plus(X8,X7),X8) = real_zero
| ~ int_less(int_zero,X7)
| X6 != plus(X5,X7)
| ~ epred1_2(X6,X5) ) ),
inference(distribute,[status(thm)],[64]) ).
cnf(66,plain,
( a(plus(X4,X3),X4) = real_zero
| ~ epred1_2(X1,X2)
| X1 != plus(X2,X3)
| ~ int_less(int_zero,X3)
| ~ int_leq(X4,X2)
| ~ int_leq(int_one,X4) ),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(70,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[20,theory(equality)]) ).
cnf(71,plain,
~ int_less(X1,X1),
inference(er,[status(thm)],[56,theory(equality)]) ).
cnf(73,negated_conjecture,
int_leq(esk3_0,esk2_0),
inference(spm,[status(thm)],[21,36,theory(equality)]) ).
cnf(79,negated_conjecture,
( int_less(X1,esk2_0)
| ~ int_less(X1,esk3_0) ),
inference(spm,[status(thm)],[45,36,theory(equality)]) ).
cnf(83,plain,
( int_less(X1,X2)
| X3 = X2
| ~ int_less(X1,X3)
| ~ int_leq(X3,X2) ),
inference(spm,[status(thm)],[45,22,theory(equality)]) ).
cnf(108,plain,
( a(plus(X1,esk1_2(X2,X3)),X1) = real_zero
| X3 != X4
| ~ epred1_2(X4,X2)
| ~ int_less(int_zero,esk1_2(X2,X3))
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_less(X2,X3) ),
inference(spm,[status(thm)],[66,29,theory(equality)]) ).
cnf(111,plain,
( a(plus(X1,esk1_2(X2,X3)),X1) = real_zero
| ~ epred1_2(X3,X2)
| ~ int_less(int_zero,esk1_2(X2,X3))
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_less(X2,X3) ),
inference(er,[status(thm)],[108,theory(equality)]) ).
cnf(135,negated_conjecture,
( int_leq(int_one,esk2_0)
| ~ int_less(int_zero,esk3_0) ),
inference(spm,[status(thm)],[49,79,theory(equality)]) ).
cnf(138,negated_conjecture,
( int_leq(int_one,esk2_0)
| ~ int_leq(int_one,esk3_0) ),
inference(spm,[status(thm)],[135,48,theory(equality)]) ).
cnf(270,negated_conjecture,
( esk2_0 = n
| int_less(X1,n)
| ~ int_less(X1,esk2_0) ),
inference(spm,[status(thm)],[83,35,theory(equality)]) ).
cnf(513,negated_conjecture,
( n = esk2_0
| ~ int_less(n,esk2_0) ),
inference(spm,[status(thm)],[71,270,theory(equality)]) ).
cnf(520,negated_conjecture,
( n = esk2_0
| ~ int_less(n,esk3_0) ),
inference(spm,[status(thm)],[513,79,theory(equality)]) ).
cnf(542,negated_conjecture,
( n = esk2_0
| int_leq(esk3_0,n) ),
inference(spm,[status(thm)],[520,58,theory(equality)]) ).
cnf(724,plain,
( a(plus(X1,esk1_2(X2,X3)),X1) = real_zero
| ~ epred1_2(X3,X2)
| ~ int_less(X2,X3)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2) ),
inference(csr,[status(thm)],[111,28]) ).
cnf(728,plain,
( a(X2,X1) = real_zero
| ~ epred1_2(X2,X1)
| ~ int_less(X1,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X1) ),
inference(spm,[status(thm)],[724,29,theory(equality)]) ).
cnf(730,plain,
( a(X2,X1) = real_zero
| ~ epred1_2(X2,X1)
| ~ int_less(X1,X2)
| ~ int_leq(int_one,X1)
| $false ),
inference(rw,[status(thm)],[728,70,theory(equality)]) ).
cnf(731,plain,
( a(X2,X1) = real_zero
| ~ epred1_2(X2,X1)
| ~ int_less(X1,X2)
| ~ int_leq(int_one,X1) ),
inference(cn,[status(thm)],[730,theory(equality)]) ).
cnf(15938,plain,
( ~ epred1_2(esk2_0,esk3_0)
| ~ int_less(esk3_0,esk2_0)
| ~ int_leq(int_one,esk3_0) ),
inference(spm,[status(thm)],[34,731,theory(equality)]) ).
cnf(15939,plain,
( ~ epred1_2(esk2_0,esk3_0)
| $false
| ~ int_leq(int_one,esk3_0) ),
inference(rw,[status(thm)],[15938,36,theory(equality)]) ).
cnf(15940,plain,
( ~ epred1_2(esk2_0,esk3_0)
| ~ int_leq(int_one,esk3_0) ),
inference(cn,[status(thm)],[15939,theory(equality)]) ).
cnf(15941,plain,
( ~ int_leq(int_one,esk3_0)
| ~ int_leq(esk3_0,n)
| ~ int_leq(esk2_0,n)
| ~ int_leq(int_one,esk2_0) ),
inference(spm,[status(thm)],[15940,52,theory(equality)]) ).
cnf(15942,plain,
( ~ int_leq(int_one,esk3_0)
| ~ int_leq(esk3_0,n)
| $false
| ~ int_leq(int_one,esk2_0) ),
inference(rw,[status(thm)],[15941,35,theory(equality)]) ).
cnf(15943,plain,
( ~ int_leq(int_one,esk3_0)
| ~ int_leq(esk3_0,n)
| ~ int_leq(int_one,esk2_0) ),
inference(cn,[status(thm)],[15942,theory(equality)]) ).
cnf(15944,plain,
( ~ int_leq(int_one,esk3_0)
| ~ int_leq(esk3_0,n) ),
inference(csr,[status(thm)],[15943,138]) ).
cnf(15945,negated_conjecture,
( n = esk2_0
| ~ int_leq(int_one,esk3_0) ),
inference(spm,[status(thm)],[15944,542,theory(equality)]) ).
cnf(15961,negated_conjecture,
n = esk2_0,
inference(spm,[status(thm)],[15945,37,theory(equality)]) ).
cnf(15971,plain,
( ~ int_leq(int_one,esk3_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[15944,15961,theory(equality)]),73,theory(equality)]) ).
cnf(15972,plain,
~ int_leq(int_one,esk3_0),
inference(cn,[status(thm)],[15971,theory(equality)]) ).
cnf(16211,negated_conjecture,
$false,
inference(sr,[status(thm)],[37,15972,theory(equality)]) ).
cnf(16212,negated_conjecture,
$false,
16211,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV487+1.p
% --creating new selector for []
% -running prover on /tmp/tmpdE-0Yz/sel_SWV487+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV487+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV487+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV487+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
%
%------------------------------------------------------------------------------