TSTP Solution File: SET988+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET988+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:59:38 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 190 ( 57 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 220 ( 85 ~; 85 |; 43 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 143 ( 4 sgn 86 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpK26gKb/sel_SET988+1.p_1',commutativity_k2_tarski) ).
fof(5,conjecture,
! [X1] :
( ( ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : ordered_pair(X3,X4) != X2 )
& ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) )
=> ( relation(X1)
& function(X1) ) ),
file('/tmp/tmpK26gKb/sel_SET988+1.p_1',t2_funct_1) ).
fof(19,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('/tmp/tmpK26gKb/sel_SET988+1.p_1',d1_relat_1) ).
fof(26,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpK26gKb/sel_SET988+1.p_1',d5_tarski) ).
fof(31,axiom,
! [X1] :
( function(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) ),
file('/tmp/tmpK26gKb/sel_SET988+1.p_1',d1_funct_1) ).
fof(34,negated_conjecture,
~ ! [X1] :
( ( ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : ordered_pair(X3,X4) != X2 )
& ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) )
=> ( relation(X1)
& function(X1) ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(47,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(48,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[47]) ).
fof(55,negated_conjecture,
? [X1] :
( ! [X2] :
( ~ in(X2,X1)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X2,X3,X4] :
( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| X3 = X4 )
& ( ~ relation(X1)
| ~ function(X1) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(56,negated_conjecture,
? [X5] :
( ! [X6] :
( ~ in(X6,X5)
| ? [X7,X8] : ordered_pair(X7,X8) = X6 )
& ! [X9,X10,X11] :
( ~ in(ordered_pair(X9,X10),X5)
| ~ in(ordered_pair(X9,X11),X5)
| X10 = X11 )
& ( ~ relation(X5)
| ~ function(X5) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,negated_conjecture,
( ! [X6] :
( ~ in(X6,esk3_0)
| ordered_pair(esk4_1(X6),esk5_1(X6)) = X6 )
& ! [X9,X10,X11] :
( ~ in(ordered_pair(X9,X10),esk3_0)
| ~ in(ordered_pair(X9,X11),esk3_0)
| X10 = X11 )
& ( ~ relation(esk3_0)
| ~ function(esk3_0) ) ),
inference(skolemize,[status(esa)],[56]) ).
fof(58,negated_conjecture,
! [X6,X9,X10,X11] :
( ( ~ in(ordered_pair(X9,X10),esk3_0)
| ~ in(ordered_pair(X9,X11),esk3_0)
| X10 = X11 )
& ( ~ in(X6,esk3_0)
| ordered_pair(esk4_1(X6),esk5_1(X6)) = X6 )
& ( ~ relation(esk3_0)
| ~ function(esk3_0) ) ),
inference(shift_quantors,[status(thm)],[57]) ).
cnf(59,negated_conjecture,
( ~ function(esk3_0)
| ~ relation(esk3_0) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
( ordered_pair(esk4_1(X1),esk5_1(X1)) = X1
| ~ in(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(61,negated_conjecture,
( X1 = X2
| ~ in(ordered_pair(X3,X2),esk3_0)
| ~ in(ordered_pair(X3,X1),esk3_0) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(98,plain,
! [X1] :
( ( ~ relation(X1)
| ! [X2] :
( ~ in(X2,X1)
| ? [X3,X4] : X2 = ordered_pair(X3,X4) ) )
& ( ? [X2] :
( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
| relation(X1) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(99,plain,
! [X5] :
( ( ~ relation(X5)
| ! [X6] :
( ~ in(X6,X5)
| ? [X7,X8] : X6 = ordered_pair(X7,X8) ) )
& ( ? [X9] :
( in(X9,X5)
& ! [X10,X11] : X9 != ordered_pair(X10,X11) )
| relation(X5) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X5] :
( ( ~ relation(X5)
| ! [X6] :
( ~ in(X6,X5)
| X6 = ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6)) ) )
& ( ( in(esk10_1(X5),X5)
& ! [X10,X11] : esk10_1(X5) != ordered_pair(X10,X11) )
| relation(X5) ) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,plain,
! [X5,X6,X10,X11] :
( ( ( esk10_1(X5) != ordered_pair(X10,X11)
& in(esk10_1(X5),X5) )
| relation(X5) )
& ( ~ in(X6,X5)
| X6 = ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6))
| ~ relation(X5) ) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X5,X6,X10,X11] :
( ( esk10_1(X5) != ordered_pair(X10,X11)
| relation(X5) )
& ( in(esk10_1(X5),X5)
| relation(X5) )
& ( ~ in(X6,X5)
| X6 = ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6))
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(104,plain,
( relation(X1)
| in(esk10_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(105,plain,
( relation(X1)
| esk10_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(124,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[26]) ).
cnf(125,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[124]) ).
fof(140,plain,
! [X1] :
( ( ~ function(X1)
| ! [X2,X3,X4] :
( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X4),X1)
| X3 = X4 ) )
& ( ? [X2,X3,X4] :
( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1)
& X3 != X4 )
| function(X1) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(141,plain,
! [X5] :
( ( ~ function(X5)
| ! [X6,X7,X8] :
( ~ in(ordered_pair(X6,X7),X5)
| ~ in(ordered_pair(X6,X8),X5)
| X7 = X8 ) )
& ( ? [X9,X10,X11] :
( in(ordered_pair(X9,X10),X5)
& in(ordered_pair(X9,X11),X5)
& X10 != X11 )
| function(X5) ) ),
inference(variable_rename,[status(thm)],[140]) ).
fof(142,plain,
! [X5] :
( ( ~ function(X5)
| ! [X6,X7,X8] :
( ~ in(ordered_pair(X6,X7),X5)
| ~ in(ordered_pair(X6,X8),X5)
| X7 = X8 ) )
& ( ( in(ordered_pair(esk14_1(X5),esk15_1(X5)),X5)
& in(ordered_pair(esk14_1(X5),esk16_1(X5)),X5)
& esk15_1(X5) != esk16_1(X5) )
| function(X5) ) ),
inference(skolemize,[status(esa)],[141]) ).
fof(143,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X6,X7),X5)
| ~ in(ordered_pair(X6,X8),X5)
| X7 = X8
| ~ function(X5) )
& ( ( in(ordered_pair(esk14_1(X5),esk15_1(X5)),X5)
& in(ordered_pair(esk14_1(X5),esk16_1(X5)),X5)
& esk15_1(X5) != esk16_1(X5) )
| function(X5) ) ),
inference(shift_quantors,[status(thm)],[142]) ).
fof(144,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X6,X7),X5)
| ~ in(ordered_pair(X6,X8),X5)
| X7 = X8
| ~ function(X5) )
& ( in(ordered_pair(esk14_1(X5),esk15_1(X5)),X5)
| function(X5) )
& ( in(ordered_pair(esk14_1(X5),esk16_1(X5)),X5)
| function(X5) )
& ( esk15_1(X5) != esk16_1(X5)
| function(X5) ) ),
inference(distribute,[status(thm)],[143]) ).
cnf(145,plain,
( function(X1)
| esk15_1(X1) != esk16_1(X1) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(146,plain,
( function(X1)
| in(ordered_pair(esk14_1(X1),esk16_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(147,plain,
( function(X1)
| in(ordered_pair(esk14_1(X1),esk15_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(156,plain,
( function(X1)
| in(unordered_pair(unordered_pair(esk14_1(X1),esk15_1(X1)),singleton(esk14_1(X1))),X1) ),
inference(rw,[status(thm)],[147,125,theory(equality)]),
[unfolding] ).
cnf(157,plain,
( function(X1)
| in(unordered_pair(unordered_pair(esk14_1(X1),esk16_1(X1)),singleton(esk14_1(X1))),X1) ),
inference(rw,[status(thm)],[146,125,theory(equality)]),
[unfolding] ).
cnf(158,plain,
( relation(X1)
| unordered_pair(unordered_pair(X2,X3),singleton(X2)) != esk10_1(X1) ),
inference(rw,[status(thm)],[105,125,theory(equality)]),
[unfolding] ).
cnf(159,negated_conjecture,
( unordered_pair(unordered_pair(esk4_1(X1),esk5_1(X1)),singleton(esk4_1(X1))) = X1
| ~ in(X1,esk3_0) ),
inference(rw,[status(thm)],[60,125,theory(equality)]),
[unfolding] ).
cnf(160,negated_conjecture,
( X1 = X2
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),esk3_0)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[61,125,theory(equality)]),125,theory(equality)]),
[unfolding] ).
cnf(193,plain,
( relation(X1)
| unordered_pair(singleton(X2),unordered_pair(X2,X3)) != esk10_1(X1) ),
inference(spm,[status(thm)],[158,48,theory(equality)]) ).
cnf(196,negated_conjecture,
( unordered_pair(singleton(esk4_1(X1)),unordered_pair(esk4_1(X1),esk5_1(X1))) = X1
| ~ in(X1,esk3_0) ),
inference(rw,[status(thm)],[159,48,theory(equality)]) ).
cnf(209,plain,
( function(X1)
| in(unordered_pair(singleton(esk14_1(X1)),unordered_pair(esk14_1(X1),esk15_1(X1))),X1) ),
inference(rw,[status(thm)],[156,48,theory(equality)]) ).
cnf(212,plain,
( function(X1)
| in(unordered_pair(singleton(esk14_1(X1)),unordered_pair(esk14_1(X1),esk16_1(X1))),X1) ),
inference(rw,[status(thm)],[157,48,theory(equality)]) ).
cnf(216,negated_conjecture,
( X1 = X2
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),esk3_0)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),esk3_0) ),
inference(spm,[status(thm)],[160,48,theory(equality)]) ).
cnf(332,negated_conjecture,
( relation(X1)
| X2 != esk10_1(X1)
| ~ in(X2,esk3_0) ),
inference(spm,[status(thm)],[193,196,theory(equality)]) ).
cnf(341,negated_conjecture,
( relation(X1)
| relation(esk3_0)
| esk10_1(esk3_0) != esk10_1(X1) ),
inference(spm,[status(thm)],[332,104,theory(equality)]) ).
cnf(346,negated_conjecture,
relation(esk3_0),
inference(er,[status(thm)],[341,theory(equality)]) ).
cnf(349,negated_conjecture,
( ~ function(esk3_0)
| $false ),
inference(rw,[status(thm)],[59,346,theory(equality)]) ).
cnf(350,negated_conjecture,
~ function(esk3_0),
inference(cn,[status(thm)],[349,theory(equality)]) ).
cnf(544,negated_conjecture,
( X1 = esk15_1(esk3_0)
| function(esk3_0)
| ~ in(unordered_pair(unordered_pair(esk14_1(esk3_0),X1),singleton(esk14_1(esk3_0))),esk3_0) ),
inference(spm,[status(thm)],[216,209,theory(equality)]) ).
cnf(549,negated_conjecture,
( X1 = esk15_1(esk3_0)
| ~ in(unordered_pair(unordered_pair(esk14_1(esk3_0),X1),singleton(esk14_1(esk3_0))),esk3_0) ),
inference(sr,[status(thm)],[544,350,theory(equality)]) ).
cnf(959,negated_conjecture,
( X1 = esk15_1(esk3_0)
| ~ in(unordered_pair(singleton(esk14_1(esk3_0)),unordered_pair(esk14_1(esk3_0),X1)),esk3_0) ),
inference(spm,[status(thm)],[549,48,theory(equality)]) ).
cnf(975,negated_conjecture,
( esk16_1(esk3_0) = esk15_1(esk3_0)
| function(esk3_0) ),
inference(spm,[status(thm)],[959,212,theory(equality)]) ).
cnf(976,negated_conjecture,
esk16_1(esk3_0) = esk15_1(esk3_0),
inference(sr,[status(thm)],[975,350,theory(equality)]) ).
cnf(977,negated_conjecture,
function(esk3_0),
inference(spm,[status(thm)],[145,976,theory(equality)]) ).
cnf(981,negated_conjecture,
$false,
inference(sr,[status(thm)],[977,350,theory(equality)]) ).
cnf(982,negated_conjecture,
$false,
981,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET988+1.p
% --creating new selector for []
% -running prover on /tmp/tmpK26gKb/sel_SET988+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET988+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET988+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET988+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
%
%------------------------------------------------------------------------------