TSTP Solution File: SEU307+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU307+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 07:05:03 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 12 unt; 0 def)
% Number of atoms : 84 ( 27 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 35 ~; 27 |; 9 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 50 ( 2 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(21,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/tmp/tmpRRtJq5/sel_SEU307+1.p_1',t3_subset) ).
fof(25,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpRRtJq5/sel_SEU307+1.p_1',reflexivity_r1_tarski) ).
fof(33,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/tmp/tmpRRtJq5/sel_SEU307+1.p_1',t28_xboole_1) ).
fof(34,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
file('/tmp/tmpRRtJq5/sel_SEU307+1.p_1',t15_pre_topc) ).
fof(42,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/tmp/tmpRRtJq5/sel_SEU307+1.p_1',d3_pre_topc) ).
fof(56,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/tmp/tmpRRtJq5/sel_SEU307+1.p_1',redefinition_k5_subset_1) ).
fof(60,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) = X2 ) ),
inference(assume_negation,[status(cth)],[34]) ).
fof(139,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(140,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[139]) ).
cnf(141,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[140]) ).
cnf(142,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[140]) ).
fof(151,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[25]) ).
cnf(152,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[151]) ).
fof(191,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(192,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[191]) ).
cnf(193,plain,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[192]) ).
fof(194,negated_conjecture,
? [X1] :
( one_sorted_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& subset_intersection2(the_carrier(X1),X2,cast_as_carrier_subset(X1)) != X2 ) ),
inference(fof_nnf,[status(thm)],[60]) ).
fof(195,negated_conjecture,
? [X3] :
( one_sorted_str(X3)
& ? [X4] :
( element(X4,powerset(the_carrier(X3)))
& subset_intersection2(the_carrier(X3),X4,cast_as_carrier_subset(X3)) != X4 ) ),
inference(variable_rename,[status(thm)],[194]) ).
fof(196,negated_conjecture,
( one_sorted_str(esk4_0)
& element(esk5_0,powerset(the_carrier(esk4_0)))
& subset_intersection2(the_carrier(esk4_0),esk5_0,cast_as_carrier_subset(esk4_0)) != esk5_0 ),
inference(skolemize,[status(esa)],[195]) ).
cnf(197,negated_conjecture,
subset_intersection2(the_carrier(esk4_0),esk5_0,cast_as_carrier_subset(esk4_0)) != esk5_0,
inference(split_conjunct,[status(thm)],[196]) ).
cnf(198,negated_conjecture,
element(esk5_0,powerset(the_carrier(esk4_0))),
inference(split_conjunct,[status(thm)],[196]) ).
cnf(199,negated_conjecture,
one_sorted_str(esk4_0),
inference(split_conjunct,[status(thm)],[196]) ).
fof(227,plain,
! [X1] :
( ~ one_sorted_str(X1)
| cast_as_carrier_subset(X1) = the_carrier(X1) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(228,plain,
! [X2] :
( ~ one_sorted_str(X2)
| cast_as_carrier_subset(X2) = the_carrier(X2) ),
inference(variable_rename,[status(thm)],[227]) ).
cnf(229,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[228]) ).
fof(290,plain,
! [X1,X2,X3] :
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
inference(fof_nnf,[status(thm)],[56]) ).
fof(291,plain,
! [X4,X5,X6] :
( ~ element(X5,powerset(X4))
| ~ element(X6,powerset(X4))
| subset_intersection2(X4,X5,X6) = set_intersection2(X5,X6) ),
inference(variable_rename,[status(thm)],[290]) ).
cnf(292,plain,
( subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[291]) ).
cnf(335,negated_conjecture,
( subset_intersection2(the_carrier(esk4_0),esk5_0,the_carrier(esk4_0)) != esk5_0
| ~ one_sorted_str(esk4_0) ),
inference(spm,[status(thm)],[197,229,theory(equality)]) ).
cnf(336,negated_conjecture,
( subset_intersection2(the_carrier(esk4_0),esk5_0,the_carrier(esk4_0)) != esk5_0
| $false ),
inference(rw,[status(thm)],[335,199,theory(equality)]) ).
cnf(337,negated_conjecture,
subset_intersection2(the_carrier(esk4_0),esk5_0,the_carrier(esk4_0)) != esk5_0,
inference(cn,[status(thm)],[336,theory(equality)]) ).
cnf(338,plain,
element(X1,powerset(X1)),
inference(spm,[status(thm)],[141,152,theory(equality)]) ).
cnf(446,plain,
( set_intersection2(X1,X2) = X1
| ~ element(X1,powerset(X2)) ),
inference(spm,[status(thm)],[193,142,theory(equality)]) ).
cnf(825,negated_conjecture,
( set_intersection2(esk5_0,the_carrier(esk4_0)) != esk5_0
| ~ element(the_carrier(esk4_0),powerset(the_carrier(esk4_0)))
| ~ element(esk5_0,powerset(the_carrier(esk4_0))) ),
inference(spm,[status(thm)],[337,292,theory(equality)]) ).
cnf(826,negated_conjecture,
( set_intersection2(esk5_0,the_carrier(esk4_0)) != esk5_0
| $false
| ~ element(esk5_0,powerset(the_carrier(esk4_0))) ),
inference(rw,[status(thm)],[825,338,theory(equality)]) ).
cnf(827,negated_conjecture,
( set_intersection2(esk5_0,the_carrier(esk4_0)) != esk5_0
| $false
| $false ),
inference(rw,[status(thm)],[826,198,theory(equality)]) ).
cnf(828,negated_conjecture,
set_intersection2(esk5_0,the_carrier(esk4_0)) != esk5_0,
inference(cn,[status(thm)],[827,theory(equality)]) ).
cnf(1166,negated_conjecture,
set_intersection2(esk5_0,the_carrier(esk4_0)) = esk5_0,
inference(spm,[status(thm)],[446,198,theory(equality)]) ).
cnf(1173,negated_conjecture,
$false,
inference(sr,[status(thm)],[1166,828,theory(equality)]) ).
cnf(1174,negated_conjecture,
$false,
1173,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU307+1.p
% --creating new selector for []
% -running prover on /tmp/tmpRRtJq5/sel_SEU307+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU307+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU307+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU307+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
%
%------------------------------------------------------------------------------