TSTP Solution File: SWV142+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV142+1 : TPTP v5.0.0. Bugfixed v3.3.0.
% 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 12:18:30 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 29 unt; 0 def)
% Number of atoms : 274 ( 19 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 302 ( 91 ~; 71 |; 83 &)
% ( 1 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2,X3] :
( ( leq(X1,X2)
& leq(X2,X3) )
=> leq(X1,X3) ),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',transitivity_leq) ).
fof(4,axiom,
! [X1,X2] :
( ( leq(X1,X2)
& X1 != X2 )
=> gt(X2,X1) ),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',leq_gt2) ).
fof(5,axiom,
! [X1,X2] :
( gt(X2,X1)
=> leq(X1,X2) ),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',leq_gt1) ).
fof(6,axiom,
! [X1] : plus(n1,X1) = succ(X1),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',succ_plus_1_l) ).
fof(14,axiom,
! [X1] : plus(X1,n1) = succ(X1),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',succ_plus_1_r) ).
fof(15,axiom,
! [X1] : ~ gt(X1,X1),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',irreflexivity_gt) ).
fof(21,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> gt(succ(X2),X1) ),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',leq_succ_gt_equiv) ).
fof(35,axiom,
gt(n1,n0),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',gt_1_0) ).
fof(39,conjecture,
( ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) )
=> leq(s_best7,n3) ),
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',gauss_array_0012) ).
fof(52,axiom,
succ(n0) = n1,
file('/tmp/tmpp6CN33/sel_SWV142+1.p_1',successor_1) ).
fof(57,negated_conjecture,
~ ( ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) )
=> leq(s_best7,n3) ),
inference(assume_negation,[status(cth)],[39]) ).
fof(58,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(59,negated_conjecture,
~ ( ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) )
=> leq(s_best7,n3) ),
inference(fof_simplification,[status(thm)],[57,theory(equality)]) ).
fof(60,plain,
( epred1_0
=> ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) ) ),
introduced(definition) ).
fof(61,negated_conjecture,
~ ( epred1_0
=> leq(s_best7,n3) ),
inference(apply_def,[status(esa)],[59,60,theory(equality)]) ).
fof(67,plain,
! [X1,X2,X3] :
( ~ leq(X1,X2)
| ~ leq(X2,X3)
| leq(X1,X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(68,plain,
! [X4,X5,X6] :
( ~ leq(X4,X5)
| ~ leq(X5,X6)
| leq(X4,X6) ),
inference(variable_rename,[status(thm)],[67]) ).
cnf(69,plain,
( leq(X1,X2)
| ~ leq(X3,X2)
| ~ leq(X1,X3) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(70,plain,
! [X1,X2] :
( ~ leq(X1,X2)
| X1 = X2
| gt(X2,X1) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(71,plain,
! [X3,X4] :
( ~ leq(X3,X4)
| X3 = X4
| gt(X4,X3) ),
inference(variable_rename,[status(thm)],[70]) ).
cnf(72,plain,
( gt(X1,X2)
| X2 = X1
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(73,plain,
! [X1,X2] :
( ~ gt(X2,X1)
| leq(X1,X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(74,plain,
! [X3,X4] :
( ~ gt(X4,X3)
| leq(X3,X4) ),
inference(variable_rename,[status(thm)],[73]) ).
cnf(75,plain,
( leq(X1,X2)
| ~ gt(X2,X1) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(76,plain,
! [X2] : plus(n1,X2) = succ(X2),
inference(variable_rename,[status(thm)],[6]) ).
cnf(77,plain,
plus(n1,X1) = succ(X1),
inference(split_conjunct,[status(thm)],[76]) ).
fof(93,plain,
! [X2] : plus(X2,n1) = succ(X2),
inference(variable_rename,[status(thm)],[14]) ).
cnf(94,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[93]) ).
fof(95,plain,
! [X2] : ~ gt(X2,X2),
inference(variable_rename,[status(thm)],[58]) ).
cnf(96,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[95]) ).
fof(107,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| gt(succ(X2),X1) )
& ( ~ gt(succ(X2),X1)
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(108,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| gt(succ(X4),X3) )
& ( ~ gt(succ(X4),X3)
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[107]) ).
cnf(110,plain,
( gt(succ(X1),X2)
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[108]) ).
cnf(128,plain,
gt(n1,n0),
inference(split_conjunct,[status(thm)],[35]) ).
fof(132,negated_conjecture,
( epred1_0
& ~ leq(s_best7,n3) ),
inference(fof_nnf,[status(thm)],[61]) ).
cnf(133,negated_conjecture,
~ leq(s_best7,n3),
inference(split_conjunct,[status(thm)],[132]) ).
cnf(134,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[132]) ).
cnf(159,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[52]) ).
fof(164,plain,
( ~ epred1_0
| ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_best7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7) )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3) ) ) ),
inference(fof_nnf,[status(thm)],[60]) ).
fof(165,plain,
( ( leq(tptp_float_0_001,pv1341)
| ~ epred1_0 )
& ( leq(n1,loopcounter)
| ~ epred1_0 )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_best7)
| ~ epred1_0 )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7)
| ~ epred1_0 )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7)
| ~ epred1_0 )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3)
| ~ epred1_0 )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3)
| ~ epred1_0 )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3)
| ~ epred1_0 )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7)
| ~ epred1_0 )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7)
| ~ epred1_0 )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7)
| ~ epred1_0 )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3)
| ~ epred1_0 )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3)
| ~ epred1_0 )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3)
| ~ epred1_0 ) ),
inference(distribute,[status(thm)],[164]) ).
cnf(168,plain,
( leq(s_best7,n3)
| ~ epred1_0
| ~ gt(loopcounter,n0) ),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(178,plain,
( leq(n1,loopcounter)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(181,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[159,94,theory(equality)]),
[unfolding] ).
cnf(182,plain,
plus(n1,X1) = plus(X1,n1),
inference(rw,[status(thm)],[77,94,theory(equality)]),
[unfolding] ).
cnf(199,plain,
( gt(plus(X1,n1),X2)
| ~ leq(X2,X1) ),
inference(rw,[status(thm)],[110,94,theory(equality)]),
[unfolding] ).
cnf(202,plain,
( leq(n1,loopcounter)
| $false ),
inference(rw,[status(thm)],[178,134,theory(equality)]) ).
cnf(203,plain,
leq(n1,loopcounter),
inference(cn,[status(thm)],[202,theory(equality)]) ).
cnf(239,plain,
leq(n0,n1),
inference(spm,[status(thm)],[75,128,theory(equality)]) ).
cnf(251,plain,
( leq(X1,loopcounter)
| ~ leq(X1,n1) ),
inference(spm,[status(thm)],[69,203,theory(equality)]) ).
cnf(260,plain,
( leq(s_best7,n3)
| $false
| ~ gt(loopcounter,n0) ),
inference(rw,[status(thm)],[168,134,theory(equality)]) ).
cnf(261,plain,
( leq(s_best7,n3)
| ~ gt(loopcounter,n0) ),
inference(cn,[status(thm)],[260,theory(equality)]) ).
cnf(262,plain,
~ gt(loopcounter,n0),
inference(sr,[status(thm)],[261,133,theory(equality)]) ).
cnf(263,plain,
( loopcounter = n0
| ~ leq(n0,loopcounter) ),
inference(spm,[status(thm)],[262,72,theory(equality)]) ).
cnf(272,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[181,182,theory(equality)]) ).
cnf(286,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[96,199,theory(equality)]) ).
cnf(431,plain,
~ leq(plus(n1,X1),X1),
inference(spm,[status(thm)],[286,182,theory(equality)]) ).
cnf(453,plain,
~ leq(n1,n0),
inference(spm,[status(thm)],[431,272,theory(equality)]) ).
cnf(568,plain,
( loopcounter = n0
| ~ leq(n0,n1) ),
inference(spm,[status(thm)],[263,251,theory(equality)]) ).
cnf(571,plain,
( loopcounter = n0
| $false ),
inference(rw,[status(thm)],[568,239,theory(equality)]) ).
cnf(572,plain,
loopcounter = n0,
inference(cn,[status(thm)],[571,theory(equality)]) ).
cnf(573,plain,
leq(n1,n0),
inference(rw,[status(thm)],[203,572,theory(equality)]) ).
cnf(574,plain,
$false,
inference(sr,[status(thm)],[573,453,theory(equality)]) ).
cnf(575,plain,
$false,
574,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV142+1.p
% --creating new selector for [SWV003+0.ax]
% -running prover on /tmp/tmpp6CN33/sel_SWV142+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV142+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV142+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV142+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
%
%------------------------------------------------------------------------------