TSTP Solution File: SET763+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET763+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% 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 03:34:33 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 17 unt; 0 def)
% Number of atoms : 305 ( 12 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 387 ( 139 ~; 142 |; 96 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 164 ( 6 sgn 107 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpWsQJRP/sel_SET763+4.p_1',subset) ).
fof(2,axiom,
! [X4,X1,X2] :
( maps(X4,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X5] :
( member(X5,X2)
& apply(X4,X3,X5) ) )
& ! [X3,X6,X7] :
( ( member(X3,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X4,X3,X6)
& apply(X4,X3,X7) )
=> X6 = X7 ) ) ) ),
file('/tmp/tmpWsQJRP/sel_SET763+4.p_1',maps) ).
fof(3,axiom,
! [X4,X1,X5] :
( member(X5,image2(X4,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X4,X3,X5) ) ),
file('/tmp/tmpWsQJRP/sel_SET763+4.p_1',image2) ).
fof(4,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpWsQJRP/sel_SET763+4.p_1',equal_set) ).
fof(5,axiom,
! [X3] : ~ member(X3,empty_set),
file('/tmp/tmpWsQJRP/sel_SET763+4.p_1',empty_set) ).
fof(6,conjecture,
! [X4,X1,X2,X3] :
( ( maps(X4,X1,X2)
& subset(X3,X1)
& equal_set(image2(X4,X3),empty_set) )
=> equal_set(X3,empty_set) ),
file('/tmp/tmpWsQJRP/sel_SET763+4.p_1',thIIa13) ).
fof(7,negated_conjecture,
~ ! [X4,X1,X2,X3] :
( ( maps(X4,X1,X2)
& subset(X3,X1)
& equal_set(image2(X4,X3),empty_set) )
=> equal_set(X3,empty_set) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(8,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(9,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(10,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[9]) ).
fof(11,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[10]) ).
fof(12,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[11]) ).
fof(13,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[12]) ).
cnf(15,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(16,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,plain,
! [X4,X1,X2] :
( ( ~ maps(X4,X1,X2)
| ( ! [X3] :
( ~ member(X3,X1)
| ? [X5] :
( member(X5,X2)
& apply(X4,X3,X5) ) )
& ! [X3,X6,X7] :
( ~ member(X3,X1)
| ~ member(X6,X2)
| ~ member(X7,X2)
| ~ apply(X4,X3,X6)
| ~ apply(X4,X3,X7)
| X6 = X7 ) ) )
& ( ? [X3] :
( member(X3,X1)
& ! [X5] :
( ~ member(X5,X2)
| ~ apply(X4,X3,X5) ) )
| ? [X3,X6,X7] :
( member(X3,X1)
& member(X6,X2)
& member(X7,X2)
& apply(X4,X3,X6)
& apply(X4,X3,X7)
& X6 != X7 )
| maps(X4,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(18,plain,
! [X8,X9,X10] :
( ( ~ maps(X8,X9,X10)
| ( ! [X11] :
( ~ member(X11,X9)
| ? [X12] :
( member(X12,X10)
& apply(X8,X11,X12) ) )
& ! [X13,X14,X15] :
( ~ member(X13,X9)
| ~ member(X14,X10)
| ~ member(X15,X10)
| ~ apply(X8,X13,X14)
| ~ apply(X8,X13,X15)
| X14 = X15 ) ) )
& ( ? [X16] :
( member(X16,X9)
& ! [X17] :
( ~ member(X17,X10)
| ~ apply(X8,X16,X17) ) )
| ? [X18,X19,X20] :
( member(X18,X9)
& member(X19,X10)
& member(X20,X10)
& apply(X8,X18,X19)
& apply(X8,X18,X20)
& X19 != X20 )
| maps(X8,X9,X10) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X8,X9,X10] :
( ( ~ maps(X8,X9,X10)
| ( ! [X11] :
( ~ member(X11,X9)
| ( member(esk2_4(X8,X9,X10,X11),X10)
& apply(X8,X11,esk2_4(X8,X9,X10,X11)) ) )
& ! [X13,X14,X15] :
( ~ member(X13,X9)
| ~ member(X14,X10)
| ~ member(X15,X10)
| ~ apply(X8,X13,X14)
| ~ apply(X8,X13,X15)
| X14 = X15 ) ) )
& ( ( member(esk3_3(X8,X9,X10),X9)
& ! [X17] :
( ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17) ) )
| ( member(esk4_3(X8,X9,X10),X9)
& member(esk5_3(X8,X9,X10),X10)
& member(esk6_3(X8,X9,X10),X10)
& apply(X8,esk4_3(X8,X9,X10),esk5_3(X8,X9,X10))
& apply(X8,esk4_3(X8,X9,X10),esk6_3(X8,X9,X10))
& esk5_3(X8,X9,X10) != esk6_3(X8,X9,X10) )
| maps(X8,X9,X10) ) ),
inference(skolemize,[status(esa)],[18]) ).
fof(20,plain,
! [X8,X9,X10,X11,X13,X14,X15,X17] :
( ( ( ( ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17) )
& member(esk3_3(X8,X9,X10),X9) )
| ( member(esk4_3(X8,X9,X10),X9)
& member(esk5_3(X8,X9,X10),X10)
& member(esk6_3(X8,X9,X10),X10)
& apply(X8,esk4_3(X8,X9,X10),esk5_3(X8,X9,X10))
& apply(X8,esk4_3(X8,X9,X10),esk6_3(X8,X9,X10))
& esk5_3(X8,X9,X10) != esk6_3(X8,X9,X10) )
| maps(X8,X9,X10) )
& ( ( ( ~ member(X13,X9)
| ~ member(X14,X10)
| ~ member(X15,X10)
| ~ apply(X8,X13,X14)
| ~ apply(X8,X13,X15)
| X14 = X15 )
& ( ~ member(X11,X9)
| ( member(esk2_4(X8,X9,X10,X11),X10)
& apply(X8,X11,esk2_4(X8,X9,X10,X11)) ) ) )
| ~ maps(X8,X9,X10) ) ),
inference(shift_quantors,[status(thm)],[19]) ).
fof(21,plain,
! [X8,X9,X10,X11,X13,X14,X15,X17] :
( ( member(esk4_3(X8,X9,X10),X9)
| ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17)
| maps(X8,X9,X10) )
& ( member(esk5_3(X8,X9,X10),X10)
| ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17)
| maps(X8,X9,X10) )
& ( member(esk6_3(X8,X9,X10),X10)
| ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17)
| maps(X8,X9,X10) )
& ( apply(X8,esk4_3(X8,X9,X10),esk5_3(X8,X9,X10))
| ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17)
| maps(X8,X9,X10) )
& ( apply(X8,esk4_3(X8,X9,X10),esk6_3(X8,X9,X10))
| ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17)
| maps(X8,X9,X10) )
& ( esk5_3(X8,X9,X10) != esk6_3(X8,X9,X10)
| ~ member(X17,X10)
| ~ apply(X8,esk3_3(X8,X9,X10),X17)
| maps(X8,X9,X10) )
& ( member(esk4_3(X8,X9,X10),X9)
| member(esk3_3(X8,X9,X10),X9)
| maps(X8,X9,X10) )
& ( member(esk5_3(X8,X9,X10),X10)
| member(esk3_3(X8,X9,X10),X9)
| maps(X8,X9,X10) )
& ( member(esk6_3(X8,X9,X10),X10)
| member(esk3_3(X8,X9,X10),X9)
| maps(X8,X9,X10) )
& ( apply(X8,esk4_3(X8,X9,X10),esk5_3(X8,X9,X10))
| member(esk3_3(X8,X9,X10),X9)
| maps(X8,X9,X10) )
& ( apply(X8,esk4_3(X8,X9,X10),esk6_3(X8,X9,X10))
| member(esk3_3(X8,X9,X10),X9)
| maps(X8,X9,X10) )
& ( esk5_3(X8,X9,X10) != esk6_3(X8,X9,X10)
| member(esk3_3(X8,X9,X10),X9)
| maps(X8,X9,X10) )
& ( ~ member(X13,X9)
| ~ member(X14,X10)
| ~ member(X15,X10)
| ~ apply(X8,X13,X14)
| ~ apply(X8,X13,X15)
| X14 = X15
| ~ maps(X8,X9,X10) )
& ( member(esk2_4(X8,X9,X10,X11),X10)
| ~ member(X11,X9)
| ~ maps(X8,X9,X10) )
& ( apply(X8,X11,esk2_4(X8,X9,X10,X11))
| ~ member(X11,X9)
| ~ maps(X8,X9,X10) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(22,plain,
( apply(X1,X4,esk2_4(X1,X2,X3,X4))
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(37,plain,
! [X4,X1,X5] :
( ( ~ member(X5,image2(X4,X1))
| ? [X3] :
( member(X3,X1)
& apply(X4,X3,X5) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ apply(X4,X3,X5) )
| member(X5,image2(X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(38,plain,
! [X6,X7,X8] :
( ( ~ member(X8,image2(X6,X7))
| ? [X9] :
( member(X9,X7)
& apply(X6,X9,X8) ) )
& ( ! [X10] :
( ~ member(X10,X7)
| ~ apply(X6,X10,X8) )
| member(X8,image2(X6,X7)) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X6,X7,X8] :
( ( ~ member(X8,image2(X6,X7))
| ( member(esk7_3(X6,X7,X8),X7)
& apply(X6,esk7_3(X6,X7,X8),X8) ) )
& ( ! [X10] :
( ~ member(X10,X7)
| ~ apply(X6,X10,X8) )
| member(X8,image2(X6,X7)) ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,plain,
! [X6,X7,X8,X10] :
( ( ~ member(X10,X7)
| ~ apply(X6,X10,X8)
| member(X8,image2(X6,X7)) )
& ( ~ member(X8,image2(X6,X7))
| ( member(esk7_3(X6,X7,X8),X7)
& apply(X6,esk7_3(X6,X7,X8),X8) ) ) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,plain,
! [X6,X7,X8,X10] :
( ( ~ member(X10,X7)
| ~ apply(X6,X10,X8)
| member(X8,image2(X6,X7)) )
& ( member(esk7_3(X6,X7,X8),X7)
| ~ member(X8,image2(X6,X7)) )
& ( apply(X6,esk7_3(X6,X7,X8),X8)
| ~ member(X8,image2(X6,X7)) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(44,plain,
( member(X1,image2(X2,X3))
| ~ apply(X2,X4,X1)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(45,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(46,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(48,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(50,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(51,plain,
! [X4] : ~ member(X4,empty_set),
inference(variable_rename,[status(thm)],[8]) ).
cnf(52,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[51]) ).
fof(53,negated_conjecture,
? [X4,X1,X2,X3] :
( maps(X4,X1,X2)
& subset(X3,X1)
& equal_set(image2(X4,X3),empty_set)
& ~ equal_set(X3,empty_set) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(54,negated_conjecture,
? [X5,X6,X7,X8] :
( maps(X5,X6,X7)
& subset(X8,X6)
& equal_set(image2(X5,X8),empty_set)
& ~ equal_set(X8,empty_set) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,negated_conjecture,
( maps(esk8_0,esk9_0,esk10_0)
& subset(esk11_0,esk9_0)
& equal_set(image2(esk8_0,esk11_0),empty_set)
& ~ equal_set(esk11_0,empty_set) ),
inference(skolemize,[status(esa)],[54]) ).
cnf(56,negated_conjecture,
~ equal_set(esk11_0,empty_set),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(57,negated_conjecture,
equal_set(image2(esk8_0,esk11_0),empty_set),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(58,negated_conjecture,
subset(esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(59,negated_conjecture,
maps(esk8_0,esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(61,negated_conjecture,
subset(image2(esk8_0,esk11_0),empty_set),
inference(spm,[status(thm)],[50,57,theory(equality)]) ).
cnf(62,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[52,15,theory(equality)]) ).
cnf(63,negated_conjecture,
( member(X1,esk9_0)
| ~ member(X1,esk11_0) ),
inference(spm,[status(thm)],[16,58,theory(equality)]) ).
cnf(64,negated_conjecture,
( ~ subset(empty_set,esk11_0)
| ~ subset(esk11_0,empty_set) ),
inference(spm,[status(thm)],[56,48,theory(equality)]) ).
cnf(71,plain,
( member(esk2_4(X1,X2,X3,X4),image2(X1,X5))
| ~ member(X4,X5)
| ~ maps(X1,X2,X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[44,22,theory(equality)]) ).
cnf(90,negated_conjecture,
( member(X1,empty_set)
| ~ member(X1,image2(esk8_0,esk11_0)) ),
inference(spm,[status(thm)],[16,61,theory(equality)]) ).
cnf(91,negated_conjecture,
~ member(X1,image2(esk8_0,esk11_0)),
inference(sr,[status(thm)],[90,52,theory(equality)]) ).
cnf(104,negated_conjecture,
( $false
| ~ subset(esk11_0,empty_set) ),
inference(rw,[status(thm)],[64,62,theory(equality)]) ).
cnf(105,negated_conjecture,
~ subset(esk11_0,empty_set),
inference(cn,[status(thm)],[104,theory(equality)]) ).
cnf(141,negated_conjecture,
( ~ maps(esk8_0,X1,X2)
| ~ member(X3,esk11_0)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[91,71,theory(equality)]) ).
cnf(332,negated_conjecture,
( ~ member(X1,esk11_0)
| ~ member(X1,esk9_0) ),
inference(spm,[status(thm)],[141,59,theory(equality)]) ).
cnf(351,negated_conjecture,
~ member(X1,esk11_0),
inference(csr,[status(thm)],[332,63]) ).
cnf(352,negated_conjecture,
subset(esk11_0,X1),
inference(spm,[status(thm)],[351,15,theory(equality)]) ).
cnf(373,negated_conjecture,
$false,
inference(rw,[status(thm)],[105,352,theory(equality)]) ).
cnf(374,negated_conjecture,
$false,
inference(cn,[status(thm)],[373,theory(equality)]) ).
cnf(375,negated_conjecture,
$false,
374,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET763+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpWsQJRP/sel_SET763+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET763+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET763+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET763+4.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
%
%------------------------------------------------------------------------------