TSTP Solution File: SEU046+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU046+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 04:16:13 EST 2010
% Result : Theorem 0.57s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 5 unt; 0 def)
% Number of atoms : 321 ( 34 equ)
% Maximal formula atoms : 79 ( 6 avg)
% Number of connectives : 452 ( 180 ~; 194 |; 66 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 111 ( 6 sgn 72 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/tmp/tmpI_vPJa/sel_SEU046+1.p_1',dt_k8_relat_1) ).
fof(5,axiom,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('/tmp/tmpI_vPJa/sel_SEU046+1.p_1',t118_relat_1) ).
fof(6,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
file('/tmp/tmpI_vPJa/sel_SEU046+1.p_1',fc5_funct_1) ).
fof(12,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_rng_restriction(X1,X3)
<=> ( ! [X4] :
( in(X4,relation_dom(X2))
<=> ( in(X4,relation_dom(X3))
& in(apply(X3,X4),X1) ) )
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/tmp/tmpI_vPJa/sel_SEU046+1.p_1',t85_funct_1) ).
fof(23,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
& subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ) ),
file('/tmp/tmpI_vPJa/sel_SEU046+1.p_1',t89_funct_1) ).
fof(36,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpI_vPJa/sel_SEU046+1.p_1',d3_tarski) ).
fof(39,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
& subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(47,plain,
! [X1,X2] :
( ~ relation(X2)
| relation(relation_rng_restriction(X1,X2)) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(48,plain,
! [X3,X4] :
( ~ relation(X4)
| relation(relation_rng_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[47]) ).
cnf(49,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(60,plain,
! [X1,X2] :
( ~ relation(X2)
| subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(61,plain,
! [X3,X4] :
( ~ relation(X4)
| subset(relation_rng(relation_rng_restriction(X3,X4)),relation_rng(X4)) ),
inference(variable_rename,[status(thm)],[60]) ).
cnf(62,plain,
( subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(63,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(64,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| ( relation(relation_rng_restriction(X3,X4))
& function(relation_rng_restriction(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ( relation(relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(X4) )
& ( function(relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[64]) ).
cnf(66,plain,
( function(relation_rng_restriction(X2,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(87,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ! [X3] :
( ~ relation(X3)
| ~ function(X3)
| ( ( X2 != relation_rng_restriction(X1,X3)
| ( ! [X4] :
( ( ~ in(X4,relation_dom(X2))
| ( in(X4,relation_dom(X3))
& in(apply(X3,X4),X1) ) )
& ( ~ in(X4,relation_dom(X3))
| ~ in(apply(X3,X4),X1)
| in(X4,relation_dom(X2)) ) )
& ! [X4] :
( ~ in(X4,relation_dom(X2))
| apply(X2,X4) = apply(X3,X4) ) ) )
& ( ? [X4] :
( ( ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X3))
| ~ in(apply(X3,X4),X1) )
& ( in(X4,relation_dom(X2))
| ( in(X4,relation_dom(X3))
& in(apply(X3,X4),X1) ) ) )
| ? [X4] :
( in(X4,relation_dom(X2))
& apply(X2,X4) != apply(X3,X4) )
| X2 = relation_rng_restriction(X1,X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(88,plain,
! [X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ! [X7] :
( ~ relation(X7)
| ~ function(X7)
| ( ( X6 != relation_rng_restriction(X5,X7)
| ( ! [X8] :
( ( ~ in(X8,relation_dom(X6))
| ( in(X8,relation_dom(X7))
& in(apply(X7,X8),X5) ) )
& ( ~ in(X8,relation_dom(X7))
| ~ in(apply(X7,X8),X5)
| in(X8,relation_dom(X6)) ) )
& ! [X9] :
( ~ in(X9,relation_dom(X6))
| apply(X6,X9) = apply(X7,X9) ) ) )
& ( ? [X10] :
( ( ~ in(X10,relation_dom(X6))
| ~ in(X10,relation_dom(X7))
| ~ in(apply(X7,X10),X5) )
& ( in(X10,relation_dom(X6))
| ( in(X10,relation_dom(X7))
& in(apply(X7,X10),X5) ) ) )
| ? [X11] :
( in(X11,relation_dom(X6))
& apply(X6,X11) != apply(X7,X11) )
| X6 = relation_rng_restriction(X5,X7) ) ) ) ),
inference(variable_rename,[status(thm)],[87]) ).
fof(89,plain,
! [X5,X6] :
( ~ relation(X6)
| ~ function(X6)
| ! [X7] :
( ~ relation(X7)
| ~ function(X7)
| ( ( X6 != relation_rng_restriction(X5,X7)
| ( ! [X8] :
( ( ~ in(X8,relation_dom(X6))
| ( in(X8,relation_dom(X7))
& in(apply(X7,X8),X5) ) )
& ( ~ in(X8,relation_dom(X7))
| ~ in(apply(X7,X8),X5)
| in(X8,relation_dom(X6)) ) )
& ! [X9] :
( ~ in(X9,relation_dom(X6))
| apply(X6,X9) = apply(X7,X9) ) ) )
& ( ( ( ~ in(esk5_3(X5,X6,X7),relation_dom(X6))
| ~ in(esk5_3(X5,X6,X7),relation_dom(X7))
| ~ in(apply(X7,esk5_3(X5,X6,X7)),X5) )
& ( in(esk5_3(X5,X6,X7),relation_dom(X6))
| ( in(esk5_3(X5,X6,X7),relation_dom(X7))
& in(apply(X7,esk5_3(X5,X6,X7)),X5) ) ) )
| ( in(esk6_3(X5,X6,X7),relation_dom(X6))
& apply(X6,esk6_3(X5,X6,X7)) != apply(X7,esk6_3(X5,X6,X7)) )
| X6 = relation_rng_restriction(X5,X7) ) ) ) ),
inference(skolemize,[status(esa)],[88]) ).
fof(90,plain,
! [X5,X6,X7,X8,X9] :
( ( ( ( ( ~ in(X9,relation_dom(X6))
| apply(X6,X9) = apply(X7,X9) )
& ( ~ in(X8,relation_dom(X6))
| ( in(X8,relation_dom(X7))
& in(apply(X7,X8),X5) ) )
& ( ~ in(X8,relation_dom(X7))
| ~ in(apply(X7,X8),X5)
| in(X8,relation_dom(X6)) ) )
| X6 != relation_rng_restriction(X5,X7) )
& ( ( ( ~ in(esk5_3(X5,X6,X7),relation_dom(X6))
| ~ in(esk5_3(X5,X6,X7),relation_dom(X7))
| ~ in(apply(X7,esk5_3(X5,X6,X7)),X5) )
& ( in(esk5_3(X5,X6,X7),relation_dom(X6))
| ( in(esk5_3(X5,X6,X7),relation_dom(X7))
& in(apply(X7,esk5_3(X5,X6,X7)),X5) ) ) )
| ( in(esk6_3(X5,X6,X7),relation_dom(X6))
& apply(X6,esk6_3(X5,X6,X7)) != apply(X7,esk6_3(X5,X6,X7)) )
| X6 = relation_rng_restriction(X5,X7) ) )
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) ),
inference(shift_quantors,[status(thm)],[89]) ).
fof(91,plain,
! [X5,X6,X7,X8,X9] :
( ( ~ in(X9,relation_dom(X6))
| apply(X6,X9) = apply(X7,X9)
| X6 != relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(X8,relation_dom(X7))
| ~ in(X8,relation_dom(X6))
| X6 != relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(apply(X7,X8),X5)
| ~ in(X8,relation_dom(X6))
| X6 != relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( ~ in(X8,relation_dom(X7))
| ~ in(apply(X7,X8),X5)
| in(X8,relation_dom(X6))
| X6 != relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk6_3(X5,X6,X7),relation_dom(X6))
| ~ in(esk5_3(X5,X6,X7),relation_dom(X6))
| ~ in(esk5_3(X5,X6,X7),relation_dom(X7))
| ~ in(apply(X7,esk5_3(X5,X6,X7)),X5)
| X6 = relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( apply(X6,esk6_3(X5,X6,X7)) != apply(X7,esk6_3(X5,X6,X7))
| ~ in(esk5_3(X5,X6,X7),relation_dom(X6))
| ~ in(esk5_3(X5,X6,X7),relation_dom(X7))
| ~ in(apply(X7,esk5_3(X5,X6,X7)),X5)
| X6 = relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk6_3(X5,X6,X7),relation_dom(X6))
| in(esk5_3(X5,X6,X7),relation_dom(X7))
| in(esk5_3(X5,X6,X7),relation_dom(X6))
| X6 = relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( apply(X6,esk6_3(X5,X6,X7)) != apply(X7,esk6_3(X5,X6,X7))
| in(esk5_3(X5,X6,X7),relation_dom(X7))
| in(esk5_3(X5,X6,X7),relation_dom(X6))
| X6 = relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( in(esk6_3(X5,X6,X7),relation_dom(X6))
| in(apply(X7,esk5_3(X5,X6,X7)),X5)
| in(esk5_3(X5,X6,X7),relation_dom(X6))
| X6 = relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) )
& ( apply(X6,esk6_3(X5,X6,X7)) != apply(X7,esk6_3(X5,X6,X7))
| in(apply(X7,esk5_3(X5,X6,X7)),X5)
| in(esk5_3(X5,X6,X7),relation_dom(X6))
| X6 = relation_rng_restriction(X5,X7)
| ~ relation(X7)
| ~ function(X7)
| ~ relation(X6)
| ~ function(X6) ) ),
inference(distribute,[status(thm)],[90]) ).
cnf(100,plain,
( in(X4,relation_dom(X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| X1 != relation_rng_restriction(X3,X2)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[91]) ).
fof(137,negated_conjecture,
? [X1,X2] :
( relation(X2)
& function(X2)
& ( ~ subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(138,negated_conjecture,
? [X3,X4] :
( relation(X4)
& function(X4)
& ( ~ subset(relation_dom(relation_rng_restriction(X3,X4)),relation_dom(X4))
| ~ subset(relation_rng(relation_rng_restriction(X3,X4)),relation_rng(X4)) ) ),
inference(variable_rename,[status(thm)],[137]) ).
fof(139,negated_conjecture,
( relation(esk10_0)
& function(esk10_0)
& ( ~ subset(relation_dom(relation_rng_restriction(esk9_0,esk10_0)),relation_dom(esk10_0))
| ~ subset(relation_rng(relation_rng_restriction(esk9_0,esk10_0)),relation_rng(esk10_0)) ) ),
inference(skolemize,[status(esa)],[138]) ).
cnf(140,negated_conjecture,
( ~ subset(relation_rng(relation_rng_restriction(esk9_0,esk10_0)),relation_rng(esk10_0))
| ~ subset(relation_dom(relation_rng_restriction(esk9_0,esk10_0)),relation_dom(esk10_0)) ),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(141,negated_conjecture,
function(esk10_0),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(142,negated_conjecture,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[139]) ).
fof(182,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)],[36]) ).
fof(183,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)],[182]) ).
fof(184,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)],[183]) ).
fof(185,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)],[184]) ).
fof(186,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)],[185]) ).
cnf(187,plain,
( subset(X1,X2)
| ~ in(esk15_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[186]) ).
cnf(188,plain,
( subset(X1,X2)
| in(esk15_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[186]) ).
cnf(248,negated_conjecture,
( ~ subset(relation_dom(relation_rng_restriction(esk9_0,esk10_0)),relation_dom(esk10_0))
| ~ relation(esk10_0) ),
inference(spm,[status(thm)],[140,62,theory(equality)]) ).
cnf(249,negated_conjecture,
( ~ subset(relation_dom(relation_rng_restriction(esk9_0,esk10_0)),relation_dom(esk10_0))
| $false ),
inference(rw,[status(thm)],[248,142,theory(equality)]) ).
cnf(250,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(esk9_0,esk10_0)),relation_dom(esk10_0)),
inference(cn,[status(thm)],[249,theory(equality)]) ).
cnf(261,plain,
( in(esk15_2(relation_dom(X1),X2),relation_dom(X3))
| subset(relation_dom(X1),X2)
| relation_rng_restriction(X4,X3) != X1
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1) ),
inference(spm,[status(thm)],[100,188,theory(equality)]) ).
cnf(728,plain,
( subset(relation_dom(relation_rng_restriction(X1,X2)),X3)
| in(esk15_2(relation_dom(relation_rng_restriction(X1,X2)),X3),relation_dom(X2))
| ~ function(X2)
| ~ function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2)) ),
inference(er,[status(thm)],[261,theory(equality)]) ).
cnf(6860,plain,
( subset(relation_dom(relation_rng_restriction(X1,X2)),X3)
| in(esk15_2(relation_dom(relation_rng_restriction(X1,X2)),X3),relation_dom(X2))
| ~ function(relation_rng_restriction(X1,X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(csr,[status(thm)],[728,49]) ).
cnf(6861,plain,
( subset(relation_dom(relation_rng_restriction(X1,X2)),X3)
| in(esk15_2(relation_dom(relation_rng_restriction(X1,X2)),X3),relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(csr,[status(thm)],[6860,66]) ).
cnf(6866,plain,
( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ function(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[187,6861,theory(equality)]) ).
cnf(7147,negated_conjecture,
( ~ function(esk10_0)
| ~ relation(esk10_0) ),
inference(spm,[status(thm)],[250,6866,theory(equality)]) ).
cnf(7203,negated_conjecture,
( $false
| ~ relation(esk10_0) ),
inference(rw,[status(thm)],[7147,141,theory(equality)]) ).
cnf(7204,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[7203,142,theory(equality)]) ).
cnf(7205,negated_conjecture,
$false,
inference(cn,[status(thm)],[7204,theory(equality)]) ).
cnf(7206,negated_conjecture,
$false,
7205,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU046+1.p
% --creating new selector for []
% -running prover on /tmp/tmpI_vPJa/sel_SEU046+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU046+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU046+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU046+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
%
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