TSTP Solution File: SWV488+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV488+3 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 13:06:12 EST 2010
% Result : Theorem 0.48s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 14 unt; 0 def)
% Number of atoms : 319 ( 91 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 387 ( 147 ~; 166 |; 53 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 134 ( 1 sgn 82 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( int_less(X1,X2)
| X1 = X2 ) ),
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',int_leq) ).
fof(2,axiom,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ! [X3] :
( ( int_less(int_zero,X3)
& X1 = plus(X2,X3) )
=> ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X2) )
=> a(plus(X4,X3),X4) = real_zero ) )
& ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X2) )
=> a(X4,X4) = real_one )
& ! [X3] :
( ( int_less(int_zero,X3)
& X2 = plus(X1,X3) )
=> ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X1) )
=> a(X4,plus(X4,X3)) = real_zero ) ) ) ),
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',qii) ).
fof(3,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X2)
& int_leq(X2,X1)
& int_leq(X1,n) )
=> ( X1 = X2
=> a(X1,X2) != real_zero ) ),
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',uti) ).
fof(6,axiom,
real_zero != real_one,
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',real_constants) ).
fof(8,axiom,
! [X1,X2,X4] :
( ( int_less(X1,X2)
& int_less(X2,X4) )
=> int_less(X1,X4) ),
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',int_less_transitive) ).
fof(9,axiom,
! [X1] :
( int_less(int_zero,X1)
<=> int_leq(int_one,X1) ),
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',one_successor_of_zero) ).
fof(11,axiom,
! [X1,X2] :
( int_less(X1,X2)
=> X1 != X2 ),
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',int_less_irreflexive) ).
fof(12,axiom,
! [X1,X2] :
( int_less(X1,X2)
| int_leq(X2,X1) ),
file('/tmp/tmp4LrDs6/sel_SWV488+3.p_1',int_less_total) ).
fof(14,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X2)
& int_leq(X2,X1)
& int_leq(X1,n) )
=> ( X1 = X2
=> a(X1,X2) != real_zero ) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(15,plain,
! [X2,X1] :
( epred1_2(X1,X2)
=> ( ! [X3] :
( ( int_less(int_zero,X3)
& X1 = plus(X2,X3) )
=> ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X2) )
=> a(plus(X4,X3),X4) = real_zero ) )
& ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X2) )
=> a(X4,X4) = real_one )
& ! [X3] :
( ( int_less(int_zero,X3)
& X2 = plus(X1,X3) )
=> ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X1) )
=> a(X4,plus(X4,X3)) = real_zero ) ) ) ),
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)],[2,15,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(22,plain,
( X1 = X2
| int_less(X1,X2)
| ~ int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,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(24,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)],[23]) ).
cnf(25,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)],[24]) ).
fof(26,negated_conjecture,
? [X1,X2] :
( int_leq(int_one,X2)
& int_leq(X2,X1)
& int_leq(X1,n)
& X1 = X2
& a(X1,X2) = real_zero ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(27,negated_conjecture,
? [X3,X4] :
( int_leq(int_one,X4)
& int_leq(X4,X3)
& int_leq(X3,n)
& X3 = X4
& a(X3,X4) = real_zero ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,negated_conjecture,
( int_leq(int_one,esk2_0)
& int_leq(esk2_0,esk1_0)
& int_leq(esk1_0,n)
& esk1_0 = esk2_0
& a(esk1_0,esk2_0) = real_zero ),
inference(skolemize,[status(esa)],[27]) ).
cnf(29,negated_conjecture,
a(esk1_0,esk2_0) = real_zero,
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,negated_conjecture,
esk1_0 = esk2_0,
inference(split_conjunct,[status(thm)],[28]) ).
cnf(31,negated_conjecture,
int_leq(esk1_0,n),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(33,negated_conjecture,
int_leq(int_one,esk2_0),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(44,plain,
real_zero != real_one,
inference(split_conjunct,[status(thm)],[6]) ).
fof(47,plain,
! [X1,X2,X4] :
( ~ int_less(X1,X2)
| ~ int_less(X2,X4)
| int_less(X1,X4) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(48,plain,
! [X5,X6,X7] :
( ~ int_less(X5,X6)
| ~ int_less(X6,X7)
| int_less(X5,X7) ),
inference(variable_rename,[status(thm)],[47]) ).
cnf(49,plain,
( int_less(X1,X2)
| ~ int_less(X3,X2)
| ~ int_less(X1,X3) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,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)],[9]) ).
fof(51,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)],[50]) ).
cnf(52,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(53,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
fof(55,plain,
! [X1,X2] :
( ~ int_less(X1,X2)
| X1 != X2 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(56,plain,
! [X3,X4] :
( ~ int_less(X3,X4)
| X3 != X4 ),
inference(variable_rename,[status(thm)],[55]) ).
cnf(57,plain,
( X1 != X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(58,plain,
! [X3,X4] :
( int_less(X3,X4)
| int_leq(X4,X3) ),
inference(variable_rename,[status(thm)],[12]) ).
cnf(59,plain,
( int_leq(X1,X2)
| int_less(X2,X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(63,plain,
! [X2,X1] :
( ~ epred1_2(X1,X2)
| ( ! [X3] :
( ~ int_less(int_zero,X3)
| X1 != plus(X2,X3)
| ! [X4] :
( ~ int_leq(int_one,X4)
| ~ int_leq(X4,X2)
| a(plus(X4,X3),X4) = real_zero ) )
& ! [X4] :
( ~ int_leq(int_one,X4)
| ~ int_leq(X4,X2)
| a(X4,X4) = real_one )
& ! [X3] :
( ~ int_less(int_zero,X3)
| X2 != plus(X1,X3)
| ! [X4] :
( ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| a(X4,plus(X4,X3)) = real_zero ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(64,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_one,X9)
| ~ int_leq(X9,X5)
| a(X9,X9) = real_one )
& ! [X10] :
( ~ int_less(int_zero,X10)
| X5 != plus(X6,X10)
| ! [X11] :
( ~ int_leq(int_one,X11)
| ~ int_leq(X11,X6)
| a(X11,plus(X11,X10)) = real_zero ) ) ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X5,X6,X7,X8,X9,X10,X11] :
( ( ( ~ int_leq(int_one,X11)
| ~ int_leq(X11,X6)
| a(X11,plus(X11,X10)) = real_zero
| ~ int_less(int_zero,X10)
| X5 != plus(X6,X10) )
& ( ~ int_leq(int_one,X9)
| ~ int_leq(X9,X5)
| a(X9,X9) = real_one )
& ( ~ 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)],[64]) ).
fof(66,plain,
! [X5,X6,X7,X8,X9,X10,X11] :
( ( ~ int_leq(int_one,X11)
| ~ int_leq(X11,X6)
| a(X11,plus(X11,X10)) = real_zero
| ~ int_less(int_zero,X10)
| X5 != plus(X6,X10)
| ~ epred1_2(X6,X5) )
& ( ~ int_leq(int_one,X9)
| ~ int_leq(X9,X5)
| a(X9,X9) = real_one
| ~ 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)],[65]) ).
cnf(68,plain,
( a(X3,X3) = real_one
| ~ epred1_2(X1,X2)
| ~ int_leq(X3,X2)
| ~ int_leq(int_one,X3) ),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(70,negated_conjecture,
int_leq(int_one,esk1_0),
inference(rw,[status(thm)],[33,30,theory(equality)]) ).
cnf(72,negated_conjecture,
a(esk1_0,esk1_0) = real_zero,
inference(rw,[status(thm)],[29,30,theory(equality)]) ).
cnf(73,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[20,theory(equality)]) ).
cnf(74,plain,
~ int_less(X1,X1),
inference(er,[status(thm)],[57,theory(equality)]) ).
cnf(95,plain,
( int_less(X1,X2)
| int_leq(X2,X3)
| ~ int_less(X1,X3) ),
inference(spm,[status(thm)],[49,59,theory(equality)]) ).
cnf(97,plain,
( int_less(X1,X2)
| X3 = X2
| ~ int_less(X1,X3)
| ~ int_leq(X3,X2) ),
inference(spm,[status(thm)],[49,22,theory(equality)]) ).
cnf(99,plain,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X3)
| ~ int_leq(X3,n)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X3)
| ~ int_leq(int_one,X2) ),
inference(spm,[status(thm)],[68,25,theory(equality)]) ).
cnf(365,plain,
( int_less(int_zero,X1)
| int_leq(X1,X2)
| ~ int_leq(int_one,X2) ),
inference(spm,[status(thm)],[95,52,theory(equality)]) ).
cnf(426,negated_conjecture,
( esk1_0 = n
| int_less(X1,n)
| ~ int_less(X1,esk1_0) ),
inference(spm,[status(thm)],[97,31,theory(equality)]) ).
cnf(537,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,esk1_0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,esk1_0) ),
inference(spm,[status(thm)],[99,31,theory(equality)]) ).
cnf(546,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| $false
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,esk1_0) ),
inference(rw,[status(thm)],[537,70,theory(equality)]) ).
cnf(547,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,esk1_0) ),
inference(cn,[status(thm)],[546,theory(equality)]) ).
cnf(863,negated_conjecture,
( int_less(int_zero,X1)
| int_leq(X1,esk1_0) ),
inference(spm,[status(thm)],[365,70,theory(equality)]) ).
cnf(934,negated_conjecture,
( int_leq(int_one,X1)
| int_leq(X1,esk1_0) ),
inference(spm,[status(thm)],[53,863,theory(equality)]) ).
cnf(1484,negated_conjecture,
( n = esk1_0
| ~ int_less(n,esk1_0) ),
inference(spm,[status(thm)],[74,426,theory(equality)]) ).
cnf(1492,negated_conjecture,
( n = esk1_0
| ~ int_leq(n,esk1_0) ),
inference(spm,[status(thm)],[1484,22,theory(equality)]) ).
cnf(1513,negated_conjecture,
( n = esk1_0
| int_leq(int_one,n) ),
inference(spm,[status(thm)],[1492,934,theory(equality)]) ).
cnf(6812,negated_conjecture,
( a(X1,X1) = real_one
| n = esk1_0
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,int_one)
| ~ int_leq(X1,esk1_0) ),
inference(spm,[status(thm)],[547,1513,theory(equality)]) ).
cnf(6855,negated_conjecture,
( a(X1,X1) = real_one
| n = esk1_0
| ~ int_leq(int_one,X1)
| $false
| ~ int_leq(X1,esk1_0) ),
inference(rw,[status(thm)],[6812,73,theory(equality)]) ).
cnf(6856,negated_conjecture,
( a(X1,X1) = real_one
| n = esk1_0
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,esk1_0) ),
inference(cn,[status(thm)],[6855,theory(equality)]) ).
cnf(6864,negated_conjecture,
( real_one = real_zero
| n = esk1_0
| ~ int_leq(int_one,esk1_0)
| ~ int_leq(esk1_0,esk1_0) ),
inference(spm,[status(thm)],[72,6856,theory(equality)]) ).
cnf(6865,negated_conjecture,
( real_one = real_zero
| n = esk1_0
| $false
| ~ int_leq(esk1_0,esk1_0) ),
inference(rw,[status(thm)],[6864,70,theory(equality)]) ).
cnf(6866,negated_conjecture,
( real_one = real_zero
| n = esk1_0
| $false
| $false ),
inference(rw,[status(thm)],[6865,73,theory(equality)]) ).
cnf(6867,negated_conjecture,
( real_one = real_zero
| n = esk1_0 ),
inference(cn,[status(thm)],[6866,theory(equality)]) ).
cnf(6868,negated_conjecture,
n = esk1_0,
inference(sr,[status(thm)],[6867,44,theory(equality)]) ).
cnf(6871,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,esk1_0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,esk1_0) ),
inference(rw,[status(thm)],[547,6868,theory(equality)]) ).
cnf(7078,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,int_one)
| ~ int_leq(X1,esk1_0) ),
inference(spm,[status(thm)],[6871,70,theory(equality)]) ).
cnf(7120,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| $false
| ~ int_leq(X1,esk1_0) ),
inference(rw,[status(thm)],[7078,73,theory(equality)]) ).
cnf(7121,negated_conjecture,
( a(X1,X1) = real_one
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,esk1_0) ),
inference(cn,[status(thm)],[7120,theory(equality)]) ).
cnf(7131,negated_conjecture,
( real_one = real_zero
| ~ int_leq(int_one,esk1_0)
| ~ int_leq(esk1_0,esk1_0) ),
inference(spm,[status(thm)],[72,7121,theory(equality)]) ).
cnf(7132,negated_conjecture,
( real_one = real_zero
| $false
| ~ int_leq(esk1_0,esk1_0) ),
inference(rw,[status(thm)],[7131,70,theory(equality)]) ).
cnf(7133,negated_conjecture,
( real_one = real_zero
| $false
| $false ),
inference(rw,[status(thm)],[7132,73,theory(equality)]) ).
cnf(7134,negated_conjecture,
real_one = real_zero,
inference(cn,[status(thm)],[7133,theory(equality)]) ).
cnf(7135,negated_conjecture,
$false,
inference(sr,[status(thm)],[7134,44,theory(equality)]) ).
cnf(7136,negated_conjecture,
$false,
7135,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV488+3.p
% --creating new selector for []
% -running prover on /tmp/tmp4LrDs6/sel_SWV488+3.p_1 with time limit 29
% -prover status Theorem
% Problem SWV488+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV488+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV488+3.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
%
%------------------------------------------------------------------------------