TSTP Solution File: SWV409+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV409+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 12:39:50 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 9 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 207 ( 88 ~; 79 |; 33 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 112 ( 0 sgn 64 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/tmp/tmpOAq1m7/sel_SWV409+1.p_1',totality) ).
fof(7,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/tmp/tmpOAq1m7/sel_SWV409+1.p_1',stricly_smaller_definition) ).
fof(12,conjecture,
! [X1,X2,X3] :
( ( contains_slb(X1,X2)
& strictly_less_than(X2,X3) )
=> ( pair_in_list(update_slb(X1,X3),X2,X3)
| ? [X4] :
( pair_in_list(update_slb(X1,X3),X2,X4)
& less_than(X3,X4) ) ) ),
file('/tmp/tmpOAq1m7/sel_SWV409+1.p_1',l45_co) ).
fof(13,axiom,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X4)
& less_than(X4,X3) )
=> ? [X5] :
( pair_in_list(update_slb(X1,X4),X2,X5)
& less_than(X4,X5) ) ),
file('/tmp/tmpOAq1m7/sel_SWV409+1.p_1',l45_l49) ).
fof(14,axiom,
! [X1,X2] :
( contains_slb(X1,X2)
=> ? [X3] : pair_in_list(X1,X2,X3) ),
file('/tmp/tmpOAq1m7/sel_SWV409+1.p_1',l45_li4647) ).
fof(15,axiom,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X2,X4)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/tmp/tmpOAq1m7/sel_SWV409+1.p_1',l45_l48) ).
fof(16,negated_conjecture,
~ ! [X1,X2,X3] :
( ( contains_slb(X1,X2)
& strictly_less_than(X2,X3) )
=> ( pair_in_list(update_slb(X1,X3),X2,X3)
| ? [X4] :
( pair_in_list(update_slb(X1,X3),X2,X4)
& less_than(X3,X4) ) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(17,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(33,plain,
! [X3,X4] :
( less_than(X3,X4)
| less_than(X4,X3) ),
inference(variable_rename,[status(thm)],[6]) ).
cnf(34,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X1,X2] :
( ( ~ strictly_less_than(X1,X2)
| ( less_than(X1,X2)
& ~ less_than(X2,X1) ) )
& ( ~ less_than(X1,X2)
| less_than(X2,X1)
| strictly_less_than(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(36,plain,
! [X3,X4] :
( ( ~ strictly_less_than(X3,X4)
| ( less_than(X3,X4)
& ~ less_than(X4,X3) ) )
& ( ~ less_than(X3,X4)
| less_than(X4,X3)
| strictly_less_than(X3,X4) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] :
( ( less_than(X3,X4)
| ~ strictly_less_than(X3,X4) )
& ( ~ less_than(X4,X3)
| ~ strictly_less_than(X3,X4) )
& ( ~ less_than(X3,X4)
| less_than(X4,X3)
| strictly_less_than(X3,X4) ) ),
inference(distribute,[status(thm)],[36]) ).
cnf(38,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(58,negated_conjecture,
? [X1,X2,X3] :
( contains_slb(X1,X2)
& strictly_less_than(X2,X3)
& ~ pair_in_list(update_slb(X1,X3),X2,X3)
& ! [X4] :
( ~ pair_in_list(update_slb(X1,X3),X2,X4)
| ~ less_than(X3,X4) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(59,negated_conjecture,
? [X5,X6,X7] :
( contains_slb(X5,X6)
& strictly_less_than(X6,X7)
& ~ pair_in_list(update_slb(X5,X7),X6,X7)
& ! [X8] :
( ~ pair_in_list(update_slb(X5,X7),X6,X8)
| ~ less_than(X7,X8) ) ),
inference(variable_rename,[status(thm)],[58]) ).
fof(60,negated_conjecture,
( contains_slb(esk1_0,esk2_0)
& strictly_less_than(esk2_0,esk3_0)
& ~ pair_in_list(update_slb(esk1_0,esk3_0),esk2_0,esk3_0)
& ! [X8] :
( ~ pair_in_list(update_slb(esk1_0,esk3_0),esk2_0,X8)
| ~ less_than(esk3_0,X8) ) ),
inference(skolemize,[status(esa)],[59]) ).
fof(61,negated_conjecture,
! [X8] :
( ( ~ pair_in_list(update_slb(esk1_0,esk3_0),esk2_0,X8)
| ~ less_than(esk3_0,X8) )
& ~ pair_in_list(update_slb(esk1_0,esk3_0),esk2_0,esk3_0)
& contains_slb(esk1_0,esk2_0)
& strictly_less_than(esk2_0,esk3_0) ),
inference(shift_quantors,[status(thm)],[60]) ).
cnf(62,negated_conjecture,
strictly_less_than(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(63,negated_conjecture,
contains_slb(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(64,negated_conjecture,
~ pair_in_list(update_slb(esk1_0,esk3_0),esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(65,negated_conjecture,
( ~ less_than(esk3_0,X1)
| ~ pair_in_list(update_slb(esk1_0,esk3_0),esk2_0,X1) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(66,plain,
! [X1,X2,X3,X4] :
( ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X2,X4)
| ~ less_than(X4,X3)
| ? [X5] :
( pair_in_list(update_slb(X1,X4),X2,X5)
& less_than(X4,X5) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(67,plain,
! [X6,X7,X8,X9] :
( ~ pair_in_list(X6,X7,X8)
| ~ strictly_less_than(X7,X9)
| ~ less_than(X9,X8)
| ? [X10] :
( pair_in_list(update_slb(X6,X9),X7,X10)
& less_than(X9,X10) ) ),
inference(variable_rename,[status(thm)],[66]) ).
fof(68,plain,
! [X6,X7,X8,X9] :
( ~ pair_in_list(X6,X7,X8)
| ~ strictly_less_than(X7,X9)
| ~ less_than(X9,X8)
| ( pair_in_list(update_slb(X6,X9),X7,esk4_4(X6,X7,X8,X9))
& less_than(X9,esk4_4(X6,X7,X8,X9)) ) ),
inference(skolemize,[status(esa)],[67]) ).
fof(69,plain,
! [X6,X7,X8,X9] :
( ( pair_in_list(update_slb(X6,X9),X7,esk4_4(X6,X7,X8,X9))
| ~ pair_in_list(X6,X7,X8)
| ~ strictly_less_than(X7,X9)
| ~ less_than(X9,X8) )
& ( less_than(X9,esk4_4(X6,X7,X8,X9))
| ~ pair_in_list(X6,X7,X8)
| ~ strictly_less_than(X7,X9)
| ~ less_than(X9,X8) ) ),
inference(distribute,[status(thm)],[68]) ).
cnf(70,plain,
( less_than(X1,esk4_4(X4,X3,X2,X1))
| ~ less_than(X1,X2)
| ~ strictly_less_than(X3,X1)
| ~ pair_in_list(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(71,plain,
( pair_in_list(update_slb(X4,X1),X3,esk4_4(X4,X3,X2,X1))
| ~ less_than(X1,X2)
| ~ strictly_less_than(X3,X1)
| ~ pair_in_list(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(72,plain,
! [X1,X2] :
( ~ contains_slb(X1,X2)
| ? [X3] : pair_in_list(X1,X2,X3) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(73,plain,
! [X4,X5] :
( ~ contains_slb(X4,X5)
| ? [X6] : pair_in_list(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,plain,
! [X4,X5] :
( ~ contains_slb(X4,X5)
| pair_in_list(X4,X5,esk5_2(X4,X5)) ),
inference(skolemize,[status(esa)],[73]) ).
cnf(75,plain,
( pair_in_list(X1,X2,esk5_2(X1,X2))
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(76,plain,
! [X1,X2,X3,X4] :
( ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X2,X4)
| ~ strictly_less_than(X3,X4)
| pair_in_list(update_slb(X1,X4),X2,X4) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(77,plain,
! [X5,X6,X7,X8] :
( ~ pair_in_list(X5,X6,X7)
| ~ strictly_less_than(X6,X8)
| ~ strictly_less_than(X7,X8)
| pair_in_list(update_slb(X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[76]) ).
cnf(78,plain,
( pair_in_list(update_slb(X1,X2),X3,X2)
| ~ strictly_less_than(X4,X2)
| ~ strictly_less_than(X3,X2)
| ~ pair_in_list(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(85,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[38,34]) ).
cnf(97,plain,
( pair_in_list(update_slb(X1,X2),X3,X2)
| ~ strictly_less_than(esk5_2(X1,X3),X2)
| ~ strictly_less_than(X3,X2)
| ~ contains_slb(X1,X3) ),
inference(spm,[status(thm)],[78,75,theory(equality)]) ).
cnf(105,plain,
( ~ less_than(esk3_0,esk4_4(esk1_0,esk2_0,X1,esk3_0))
| ~ pair_in_list(esk1_0,esk2_0,X1)
| ~ strictly_less_than(esk2_0,esk3_0)
| ~ less_than(esk3_0,X1) ),
inference(spm,[status(thm)],[65,71,theory(equality)]) ).
cnf(108,plain,
( ~ less_than(esk3_0,esk4_4(esk1_0,esk2_0,X1,esk3_0))
| ~ pair_in_list(esk1_0,esk2_0,X1)
| $false
| ~ less_than(esk3_0,X1) ),
inference(rw,[status(thm)],[105,62,theory(equality)]) ).
cnf(109,plain,
( ~ less_than(esk3_0,esk4_4(esk1_0,esk2_0,X1,esk3_0))
| ~ pair_in_list(esk1_0,esk2_0,X1)
| ~ less_than(esk3_0,X1) ),
inference(cn,[status(thm)],[108,theory(equality)]) ).
cnf(142,plain,
( ~ pair_in_list(esk1_0,esk2_0,X1)
| ~ less_than(esk3_0,X1)
| ~ strictly_less_than(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[109,70,theory(equality)]) ).
cnf(143,plain,
( ~ pair_in_list(esk1_0,esk2_0,X1)
| ~ less_than(esk3_0,X1)
| $false ),
inference(rw,[status(thm)],[142,62,theory(equality)]) ).
cnf(144,plain,
( ~ pair_in_list(esk1_0,esk2_0,X1)
| ~ less_than(esk3_0,X1) ),
inference(cn,[status(thm)],[143,theory(equality)]) ).
cnf(263,plain,
( pair_in_list(update_slb(X1,X2),X3,X2)
| less_than(X2,esk5_2(X1,X3))
| ~ contains_slb(X1,X3)
| ~ strictly_less_than(X3,X2) ),
inference(spm,[status(thm)],[97,85,theory(equality)]) ).
cnf(1430,negated_conjecture,
( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| less_than(X1,esk5_2(esk1_0,esk2_0))
| ~ strictly_less_than(esk2_0,X1) ),
inference(spm,[status(thm)],[263,63,theory(equality)]) ).
cnf(1488,negated_conjecture,
( pair_in_list(update_slb(esk1_0,esk3_0),esk2_0,esk3_0)
| less_than(esk3_0,esk5_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[1430,62,theory(equality)]) ).
cnf(1490,negated_conjecture,
less_than(esk3_0,esk5_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[1488,64,theory(equality)]) ).
cnf(1494,negated_conjecture,
~ pair_in_list(esk1_0,esk2_0,esk5_2(esk1_0,esk2_0)),
inference(spm,[status(thm)],[144,1490,theory(equality)]) ).
cnf(1525,plain,
~ contains_slb(esk1_0,esk2_0),
inference(spm,[status(thm)],[1494,75,theory(equality)]) ).
cnf(1526,plain,
$false,
inference(rw,[status(thm)],[1525,63,theory(equality)]) ).
cnf(1527,plain,
$false,
inference(cn,[status(thm)],[1526,theory(equality)]) ).
cnf(1528,plain,
$false,
1527,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV409+1.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax]
% -running prover on /tmp/tmpOAq1m7/sel_SWV409+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV409+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV409+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV409+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
%
%------------------------------------------------------------------------------