TSTP Solution File: SWV408+2 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV408+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 12:39:45 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 7 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 132 ( 53 ~; 46 |; 26 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 58 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',totality) ).
fof(11,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',stricly_smaller_definition) ).
fof(19,axiom,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',l48_li3839) ).
fof(20,axiom,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& less_than(X4,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X3) ),
file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',l49_li3637) ).
fof(21,axiom,
! [X1,X2] :
( contains_slb(X1,X2)
=> ? [X3] : pair_in_list(X1,X2,X3) ),
file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',l45_li4647) ).
fof(22,conjecture,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
| ? [X5] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
& less_than(findmin_pqp_res(X1),X5) ) ) ),
file('/tmp/tmpz3GHNm/sel_SWV408+2.p_1',l44_co) ).
fof(23,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
| ? [X5] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
& less_than(findmin_pqp_res(X1),X5) ) ) ),
inference(assume_negation,[status(cth)],[22]) ).
fof(25,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(55,plain,
! [X3,X4] :
( less_than(X3,X4)
| less_than(X4,X3) ),
inference(variable_rename,[status(thm)],[10]) ).
cnf(56,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(57,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)],[25]) ).
fof(58,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)],[57]) ).
fof(59,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)],[58]) ).
cnf(60,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(85,plain,
! [X1,X2,X3,X4] :
( ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X3,X4)
| pair_in_list(update_slb(X1,X4),X2,X4) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(86,plain,
! [X5,X6,X7,X8] :
( ~ pair_in_list(X5,X6,X7)
| ~ strictly_less_than(X7,X8)
| pair_in_list(update_slb(X5,X8),X6,X8) ),
inference(variable_rename,[status(thm)],[85]) ).
cnf(87,plain,
( pair_in_list(update_slb(X1,X2),X3,X2)
| ~ strictly_less_than(X4,X2)
| ~ pair_in_list(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[86]) ).
fof(88,plain,
! [X1,X2,X3,X4] :
( ~ pair_in_list(X1,X2,X3)
| ~ less_than(X4,X3)
| pair_in_list(update_slb(X1,X4),X2,X3) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(89,plain,
! [X5,X6,X7,X8] :
( ~ pair_in_list(X5,X6,X7)
| ~ less_than(X8,X7)
| pair_in_list(update_slb(X5,X8),X6,X7) ),
inference(variable_rename,[status(thm)],[88]) ).
cnf(90,plain,
( pair_in_list(update_slb(X1,X2),X3,X4)
| ~ less_than(X2,X4)
| ~ pair_in_list(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[89]) ).
fof(91,plain,
! [X1,X2] :
( ~ contains_slb(X1,X2)
| ? [X3] : pair_in_list(X1,X2,X3) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(92,plain,
! [X4,X5] :
( ~ contains_slb(X4,X5)
| ? [X6] : pair_in_list(X4,X5,X6) ),
inference(variable_rename,[status(thm)],[91]) ).
fof(93,plain,
! [X4,X5] :
( ~ contains_slb(X4,X5)
| pair_in_list(X4,X5,esk1_2(X4,X5)) ),
inference(skolemize,[status(esa)],[92]) ).
cnf(94,plain,
( pair_in_list(X1,X2,esk1_2(X1,X2))
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(95,negated_conjecture,
? [X1,X2,X3,X4] :
( contains_slb(X2,X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3)))
& ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
& ! [X5] :
( ~ pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
| ~ less_than(findmin_pqp_res(X1),X5) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(96,negated_conjecture,
? [X6,X7,X8,X9] :
( contains_slb(X7,X9)
& strictly_less_than(X9,findmin_cpq_res(triple(X6,X7,X8)))
& ~ pair_in_list(update_slb(X7,findmin_pqp_res(X6)),X9,findmin_pqp_res(X6))
& ! [X10] :
( ~ pair_in_list(update_slb(X7,findmin_pqp_res(X6)),X9,X10)
| ~ less_than(findmin_pqp_res(X6),X10) ) ),
inference(variable_rename,[status(thm)],[95]) ).
fof(97,negated_conjecture,
( contains_slb(esk3_0,esk5_0)
& strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0)))
& ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
& ! [X10] :
( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X10)
| ~ less_than(findmin_pqp_res(esk2_0),X10) ) ),
inference(skolemize,[status(esa)],[96]) ).
fof(98,negated_conjecture,
! [X10] :
( ( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X10)
| ~ less_than(findmin_pqp_res(esk2_0),X10) )
& ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
& contains_slb(esk3_0,esk5_0)
& strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0))) ),
inference(shift_quantors,[status(thm)],[97]) ).
cnf(100,negated_conjecture,
contains_slb(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[98]) ).
cnf(101,negated_conjecture,
~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0)),
inference(split_conjunct,[status(thm)],[98]) ).
cnf(102,negated_conjecture,
( ~ less_than(findmin_pqp_res(esk2_0),X1)
| ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X1) ),
inference(split_conjunct,[status(thm)],[98]) ).
cnf(109,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[60,56]) ).
cnf(123,plain,
( ~ less_than(findmin_pqp_res(esk2_0),X1)
| ~ pair_in_list(esk3_0,esk5_0,X1) ),
inference(spm,[status(thm)],[102,90,theory(equality)]) ).
cnf(124,plain,
( pair_in_list(update_slb(X1,X2),X3,X2)
| ~ strictly_less_than(esk1_2(X1,X3),X2)
| ~ contains_slb(X1,X3) ),
inference(spm,[status(thm)],[87,94,theory(equality)]) ).
cnf(254,plain,
( pair_in_list(update_slb(X1,X2),X3,X2)
| less_than(X2,esk1_2(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(spm,[status(thm)],[124,109,theory(equality)]) ).
cnf(1304,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk5_0,X1)
| less_than(X1,esk1_2(esk3_0,esk5_0)) ),
inference(spm,[status(thm)],[254,100,theory(equality)]) ).
cnf(1395,negated_conjecture,
( pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
| ~ pair_in_list(esk3_0,esk5_0,esk1_2(esk3_0,esk5_0)) ),
inference(spm,[status(thm)],[123,1304,theory(equality)]) ).
cnf(1404,negated_conjecture,
~ pair_in_list(esk3_0,esk5_0,esk1_2(esk3_0,esk5_0)),
inference(sr,[status(thm)],[1395,101,theory(equality)]) ).
cnf(1429,plain,
~ contains_slb(esk3_0,esk5_0),
inference(spm,[status(thm)],[1404,94,theory(equality)]) ).
cnf(1430,plain,
$false,
inference(rw,[status(thm)],[1429,100,theory(equality)]) ).
cnf(1431,plain,
$false,
inference(cn,[status(thm)],[1430,theory(equality)]) ).
cnf(1432,plain,
$false,
1431,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV408+2.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax, SWV007+3.ax]
% -running prover on /tmp/tmpz3GHNm/sel_SWV408+2.p_1 with time limit 29
% -prover status Theorem
% Problem SWV408+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV408+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV408+2.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
%
%------------------------------------------------------------------------------