TSTP Solution File: SET997+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET997+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 04:01:26 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 5 unt; 0 def)
% Number of atoms : 236 ( 58 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 323 ( 124 ~; 127 |; 63 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn 59 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
~ ( in(X4,relation_dom(X2))
& X3 = apply(X2,X4) ) )
=> subset(X1,relation_rng(X2)) ) ),
file('/tmp/tmp0PHIYn/sel_SET997+1.p_1',t19_funct_1) ).
fof(11,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/tmp/tmp0PHIYn/sel_SET997+1.p_1',d5_funct_1) ).
fof(31,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmp0PHIYn/sel_SET997+1.p_1',d3_tarski) ).
fof(33,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] :
~ ( in(X4,relation_dom(X2))
& X3 = apply(X2,X4) ) )
=> subset(X1,relation_rng(X2)) ) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(45,negated_conjecture,
? [X1,X2] :
( relation(X2)
& function(X2)
& ! [X3] :
( ~ in(X3,X1)
| ? [X4] :
( in(X4,relation_dom(X2))
& X3 = apply(X2,X4) ) )
& ~ subset(X1,relation_rng(X2)) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(46,negated_conjecture,
? [X5,X6] :
( relation(X6)
& function(X6)
& ! [X7] :
( ~ in(X7,X5)
| ? [X8] :
( in(X8,relation_dom(X6))
& X7 = apply(X6,X8) ) )
& ~ subset(X5,relation_rng(X6)) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,negated_conjecture,
( relation(esk3_0)
& function(esk3_0)
& ! [X7] :
( ~ in(X7,esk2_0)
| ( in(esk4_1(X7),relation_dom(esk3_0))
& X7 = apply(esk3_0,esk4_1(X7)) ) )
& ~ subset(esk2_0,relation_rng(esk3_0)) ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,negated_conjecture,
! [X7] :
( ( ~ in(X7,esk2_0)
| ( in(esk4_1(X7),relation_dom(esk3_0))
& X7 = apply(esk3_0,esk4_1(X7)) ) )
& ~ subset(esk2_0,relation_rng(esk3_0))
& relation(esk3_0)
& function(esk3_0) ),
inference(shift_quantors,[status(thm)],[47]) ).
fof(49,negated_conjecture,
! [X7] :
( ( in(esk4_1(X7),relation_dom(esk3_0))
| ~ in(X7,esk2_0) )
& ( X7 = apply(esk3_0,esk4_1(X7))
| ~ in(X7,esk2_0) )
& ~ subset(esk2_0,relation_rng(esk3_0))
& relation(esk3_0)
& function(esk3_0) ),
inference(distribute,[status(thm)],[48]) ).
cnf(50,negated_conjecture,
function(esk3_0),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(51,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(52,negated_conjecture,
~ subset(esk2_0,relation_rng(esk3_0)),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(53,negated_conjecture,
( X1 = apply(esk3_0,esk4_1(X1))
| ~ in(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(54,negated_conjecture,
( in(esk4_1(X1),relation_dom(esk3_0))
| ~ in(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(83,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2] :
( ( X2 != relation_rng(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| X3 != apply(X1,X4) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X1))
| X3 != apply(X1,X4) ) )
& ( in(X3,X2)
| ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) )
| X2 = relation_rng(X1) ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(84,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] :
( in(X8,relation_dom(X5))
& X7 = apply(X5,X8) ) )
& ( ! [X9] :
( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9) )
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] :
( ~ in(X11,relation_dom(X5))
| X10 != apply(X5,X11) ) )
& ( in(X10,X6)
| ? [X12] :
( in(X12,relation_dom(X5))
& X10 = apply(X5,X12) ) ) )
| X6 = relation_rng(X5) ) ) ),
inference(variable_rename,[status(thm)],[83]) ).
fof(85,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ( in(esk8_3(X5,X6,X7),relation_dom(X5))
& X7 = apply(X5,esk8_3(X5,X6,X7)) ) )
& ( ! [X9] :
( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9) )
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk9_2(X5,X6),X6)
| ! [X11] :
( ~ in(X11,relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,X11) ) )
& ( in(esk9_2(X5,X6),X6)
| ( in(esk10_2(X5,X6),relation_dom(X5))
& esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6)) ) ) )
| X6 = relation_rng(X5) ) ) ),
inference(skolemize,[status(esa)],[84]) ).
fof(86,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(X11,relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,X11)
| ~ in(esk9_2(X5,X6),X6) )
& ( in(esk9_2(X5,X6),X6)
| ( in(esk10_2(X5,X6),relation_dom(X5))
& esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6)) ) ) )
| X6 = relation_rng(X5) )
& ( ( ( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9)
| in(X7,X6) )
& ( ~ in(X7,X6)
| ( in(esk8_3(X5,X6,X7),relation_dom(X5))
& X7 = apply(X5,esk8_3(X5,X6,X7)) ) ) )
| X6 != relation_rng(X5) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[85]) ).
fof(87,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(X11,relation_dom(X5))
| esk9_2(X5,X6) != apply(X5,X11)
| ~ in(esk9_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk10_2(X5,X6),relation_dom(X5))
| in(esk9_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk9_2(X5,X6) = apply(X5,esk10_2(X5,X6))
| in(esk9_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk8_3(X5,X6,X7),relation_dom(X5))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,esk8_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[86]) ).
cnf(90,plain,
( in(X3,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| X3 != apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[87]) ).
fof(153,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(154,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[153]) ).
fof(155,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk15_2(X4,X5),X4)
& ~ in(esk15_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[154]) ).
fof(156,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk15_2(X4,X5),X4)
& ~ in(esk15_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[155]) ).
fof(157,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk15_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk15_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[156]) ).
cnf(158,plain,
( subset(X1,X2)
| ~ in(esk15_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(159,plain,
( subset(X1,X2)
| in(esk15_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[157]) ).
cnf(212,negated_conjecture,
( in(X1,X2)
| X3 != X1
| relation_rng(esk3_0) != X2
| ~ in(esk4_1(X3),relation_dom(esk3_0))
| ~ function(esk3_0)
| ~ relation(esk3_0)
| ~ in(X3,esk2_0) ),
inference(spm,[status(thm)],[90,53,theory(equality)]) ).
cnf(213,negated_conjecture,
( in(X1,X2)
| X3 != X1
| relation_rng(esk3_0) != X2
| ~ in(esk4_1(X3),relation_dom(esk3_0))
| $false
| ~ relation(esk3_0)
| ~ in(X3,esk2_0) ),
inference(rw,[status(thm)],[212,50,theory(equality)]) ).
cnf(214,negated_conjecture,
( in(X1,X2)
| X3 != X1
| relation_rng(esk3_0) != X2
| ~ in(esk4_1(X3),relation_dom(esk3_0))
| $false
| $false
| ~ in(X3,esk2_0) ),
inference(rw,[status(thm)],[213,51,theory(equality)]) ).
cnf(215,negated_conjecture,
( in(X1,X2)
| X3 != X1
| relation_rng(esk3_0) != X2
| ~ in(esk4_1(X3),relation_dom(esk3_0))
| ~ in(X3,esk2_0) ),
inference(cn,[status(thm)],[214,theory(equality)]) ).
cnf(216,negated_conjecture,
( in(X1,X2)
| relation_rng(esk3_0) != X2
| ~ in(esk4_1(X1),relation_dom(esk3_0))
| ~ in(X1,esk2_0) ),
inference(er,[status(thm)],[215,theory(equality)]) ).
cnf(552,negated_conjecture,
( in(X1,X2)
| relation_rng(esk3_0) != X2
| ~ in(X1,esk2_0) ),
inference(csr,[status(thm)],[216,54]) ).
cnf(553,negated_conjecture,
( in(esk15_2(esk2_0,X1),X2)
| subset(esk2_0,X1)
| relation_rng(esk3_0) != X2 ),
inference(spm,[status(thm)],[552,159,theory(equality)]) ).
cnf(617,negated_conjecture,
( subset(esk2_0,X1)
| relation_rng(esk3_0) != X1 ),
inference(spm,[status(thm)],[158,553,theory(equality)]) ).
cnf(631,negated_conjecture,
$false,
inference(spm,[status(thm)],[52,617,theory(equality)]) ).
cnf(635,negated_conjecture,
$false,
631,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET997+1.p
% --creating new selector for []
% -running prover on /tmp/tmp0PHIYn/sel_SET997+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET997+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET997+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET997+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
%
%------------------------------------------------------------------------------