TSTP Solution File: SEU353+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU353+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 07:45:39 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 213 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 254 ( 114 ~; 93 |; 32 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-4 aty)
% Number of variables : 82 ( 0 sgn 56 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',redefinition_m2_relset_1) ).
fof(16,axiom,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',t35_funct_1) ).
fof(18,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',fc1_struct_0) ).
fof(27,axiom,
! [X1] :
( one_sorted_str(X1)
=> ( function(identity_on_carrier(X1))
& quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1)) ) ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',dt_k7_grcat_1) ).
fof(32,axiom,
! [X1] : identity_as_relation_of(X1) = identity_relation(X1),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',redefinition_k6_partfun1) ).
fof(33,axiom,
! [X1] :
( one_sorted_str(X1)
=> identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1)) ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',d11_grcat_1) ).
fof(36,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',t91_tmap_1) ).
fof(38,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',t2_subset) ).
fof(40,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
file('/tmp/tmpJcM505/sel_SEU353+1.p_1',redefinition_k8_funct_2) ).
fof(58,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
inference(assume_negation,[status(cth)],[36]) ).
fof(62,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[18,theory(equality)]) ).
fof(67,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[58,theory(equality)]) ).
fof(68,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2)
& element(X4,X1) )
=> apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
inference(fof_simplification,[status(thm)],[40,theory(equality)]) ).
fof(94,plain,
! [X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X1,X2)
| relation_of2(X3,X1,X2) )
& ( ~ relation_of2(X3,X1,X2)
| relation_of2_as_subset(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(95,plain,
! [X4,X5,X6] :
( ( ~ relation_of2_as_subset(X6,X4,X5)
| relation_of2(X6,X4,X5) )
& ( ~ relation_of2(X6,X4,X5)
| relation_of2_as_subset(X6,X4,X5) ) ),
inference(variable_rename,[status(thm)],[94]) ).
cnf(97,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[95]) ).
fof(130,plain,
! [X1,X2] :
( ~ in(X2,X1)
| apply(identity_relation(X1),X2) = X2 ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(131,plain,
! [X3,X4] :
( ~ in(X4,X3)
| apply(identity_relation(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[130]) ).
cnf(132,plain,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[131]) ).
fof(142,plain,
! [X1] :
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[62]) ).
fof(143,plain,
! [X2] :
( empty_carrier(X2)
| ~ one_sorted_str(X2)
| ~ empty(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[142]) ).
cnf(144,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[143]) ).
fof(177,plain,
! [X1] :
( ~ one_sorted_str(X1)
| ( function(identity_on_carrier(X1))
& quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
& relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1)) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(178,plain,
! [X2] :
( ~ one_sorted_str(X2)
| ( function(identity_on_carrier(X2))
& quasi_total(identity_on_carrier(X2),the_carrier(X2),the_carrier(X2))
& relation_of2_as_subset(identity_on_carrier(X2),the_carrier(X2),the_carrier(X2)) ) ),
inference(variable_rename,[status(thm)],[177]) ).
fof(179,plain,
! [X2] :
( ( function(identity_on_carrier(X2))
| ~ one_sorted_str(X2) )
& ( quasi_total(identity_on_carrier(X2),the_carrier(X2),the_carrier(X2))
| ~ one_sorted_str(X2) )
& ( relation_of2_as_subset(identity_on_carrier(X2),the_carrier(X2),the_carrier(X2))
| ~ one_sorted_str(X2) ) ),
inference(distribute,[status(thm)],[178]) ).
cnf(180,plain,
( relation_of2_as_subset(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[179]) ).
cnf(181,plain,
( quasi_total(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[179]) ).
cnf(182,plain,
( function(identity_on_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[179]) ).
fof(199,plain,
! [X2] : identity_as_relation_of(X2) = identity_relation(X2),
inference(variable_rename,[status(thm)],[32]) ).
cnf(200,plain,
identity_as_relation_of(X1) = identity_relation(X1),
inference(split_conjunct,[status(thm)],[199]) ).
fof(201,plain,
! [X1] :
( ~ one_sorted_str(X1)
| identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1)) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(202,plain,
! [X2] :
( ~ one_sorted_str(X2)
| identity_on_carrier(X2) = identity_as_relation_of(the_carrier(X2)) ),
inference(variable_rename,[status(thm)],[201]) ).
cnf(203,plain,
( identity_on_carrier(X1) = identity_as_relation_of(the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[202]) ).
fof(208,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& one_sorted_str(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& apply_as_element(the_carrier(X1),the_carrier(X1),identity_on_carrier(X1),X2) != X2 ) ),
inference(fof_nnf,[status(thm)],[67]) ).
fof(209,negated_conjecture,
? [X3] :
( ~ empty_carrier(X3)
& one_sorted_str(X3)
& ? [X4] :
( element(X4,the_carrier(X3))
& apply_as_element(the_carrier(X3),the_carrier(X3),identity_on_carrier(X3),X4) != X4 ) ),
inference(variable_rename,[status(thm)],[208]) ).
fof(210,negated_conjecture,
( ~ empty_carrier(esk11_0)
& one_sorted_str(esk11_0)
& element(esk12_0,the_carrier(esk11_0))
& apply_as_element(the_carrier(esk11_0),the_carrier(esk11_0),identity_on_carrier(esk11_0),esk12_0) != esk12_0 ),
inference(skolemize,[status(esa)],[209]) ).
cnf(211,negated_conjecture,
apply_as_element(the_carrier(esk11_0),the_carrier(esk11_0),identity_on_carrier(esk11_0),esk12_0) != esk12_0,
inference(split_conjunct,[status(thm)],[210]) ).
cnf(212,negated_conjecture,
element(esk12_0,the_carrier(esk11_0)),
inference(split_conjunct,[status(thm)],[210]) ).
cnf(213,negated_conjecture,
one_sorted_str(esk11_0),
inference(split_conjunct,[status(thm)],[210]) ).
cnf(214,negated_conjecture,
~ empty_carrier(esk11_0),
inference(split_conjunct,[status(thm)],[210]) ).
fof(218,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(219,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[218]) ).
cnf(220,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[219]) ).
fof(222,plain,
! [X1,X2,X3,X4] :
( empty(X1)
| ~ function(X3)
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2(X3,X1,X2)
| ~ element(X4,X1)
| apply_as_element(X1,X2,X3,X4) = apply(X3,X4) ),
inference(fof_nnf,[status(thm)],[68]) ).
fof(223,plain,
! [X5,X6,X7,X8] :
( empty(X5)
| ~ function(X7)
| ~ quasi_total(X7,X5,X6)
| ~ relation_of2(X7,X5,X6)
| ~ element(X8,X5)
| apply_as_element(X5,X6,X7,X8) = apply(X7,X8) ),
inference(variable_rename,[status(thm)],[222]) ).
cnf(224,plain,
( apply_as_element(X1,X2,X3,X4) = apply(X3,X4)
| empty(X1)
| ~ element(X4,X1)
| ~ relation_of2(X3,X1,X2)
| ~ quasi_total(X3,X1,X2)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[223]) ).
cnf(294,plain,
( apply(identity_as_relation_of(X1),X2) = X2
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[132,200,theory(equality)]),
[unfolding] ).
cnf(299,negated_conjecture,
( ~ one_sorted_str(esk11_0)
| ~ empty(the_carrier(esk11_0)) ),
inference(spm,[status(thm)],[214,144,theory(equality)]) ).
cnf(301,negated_conjecture,
( $false
| ~ empty(the_carrier(esk11_0)) ),
inference(rw,[status(thm)],[299,213,theory(equality)]) ).
cnf(302,negated_conjecture,
~ empty(the_carrier(esk11_0)),
inference(cn,[status(thm)],[301,theory(equality)]) ).
cnf(332,plain,
( apply(identity_on_carrier(X1),X2) = X2
| ~ in(X2,the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[294,203,theory(equality)]) ).
cnf(335,plain,
( relation_of2(identity_on_carrier(X1),the_carrier(X1),the_carrier(X1))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[97,180,theory(equality)]) ).
cnf(399,negated_conjecture,
( empty(the_carrier(esk11_0))
| apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ quasi_total(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| ~ function(identity_on_carrier(esk11_0))
| ~ relation_of2(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| ~ element(esk12_0,the_carrier(esk11_0)) ),
inference(spm,[status(thm)],[211,224,theory(equality)]) ).
cnf(401,negated_conjecture,
( empty(the_carrier(esk11_0))
| apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ quasi_total(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| ~ function(identity_on_carrier(esk11_0))
| ~ relation_of2(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| $false ),
inference(rw,[status(thm)],[399,212,theory(equality)]) ).
cnf(402,negated_conjecture,
( empty(the_carrier(esk11_0))
| apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ quasi_total(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| ~ function(identity_on_carrier(esk11_0))
| ~ relation_of2(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0)) ),
inference(cn,[status(thm)],[401,theory(equality)]) ).
cnf(821,negated_conjecture,
( apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ quasi_total(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| ~ function(identity_on_carrier(esk11_0))
| ~ relation_of2(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0)) ),
inference(sr,[status(thm)],[402,302,theory(equality)]) ).
cnf(822,negated_conjecture,
( apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ function(identity_on_carrier(esk11_0))
| ~ relation_of2(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| ~ one_sorted_str(esk11_0) ),
inference(spm,[status(thm)],[821,181,theory(equality)]) ).
cnf(823,negated_conjecture,
( apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ function(identity_on_carrier(esk11_0))
| ~ relation_of2(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0))
| $false ),
inference(rw,[status(thm)],[822,213,theory(equality)]) ).
cnf(824,negated_conjecture,
( apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ function(identity_on_carrier(esk11_0))
| ~ relation_of2(identity_on_carrier(esk11_0),the_carrier(esk11_0),the_carrier(esk11_0)) ),
inference(cn,[status(thm)],[823,theory(equality)]) ).
cnf(835,negated_conjecture,
( apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ function(identity_on_carrier(esk11_0))
| ~ one_sorted_str(esk11_0) ),
inference(spm,[status(thm)],[824,335,theory(equality)]) ).
cnf(836,negated_conjecture,
( apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ function(identity_on_carrier(esk11_0))
| $false ),
inference(rw,[status(thm)],[835,213,theory(equality)]) ).
cnf(837,negated_conjecture,
( apply(identity_on_carrier(esk11_0),esk12_0) != esk12_0
| ~ function(identity_on_carrier(esk11_0)) ),
inference(cn,[status(thm)],[836,theory(equality)]) ).
cnf(838,negated_conjecture,
( ~ function(identity_on_carrier(esk11_0))
| ~ one_sorted_str(esk11_0)
| ~ in(esk12_0,the_carrier(esk11_0)) ),
inference(spm,[status(thm)],[837,332,theory(equality)]) ).
cnf(839,negated_conjecture,
( ~ function(identity_on_carrier(esk11_0))
| $false
| ~ in(esk12_0,the_carrier(esk11_0)) ),
inference(rw,[status(thm)],[838,213,theory(equality)]) ).
cnf(840,negated_conjecture,
( ~ function(identity_on_carrier(esk11_0))
| ~ in(esk12_0,the_carrier(esk11_0)) ),
inference(cn,[status(thm)],[839,theory(equality)]) ).
cnf(858,negated_conjecture,
( empty(the_carrier(esk11_0))
| ~ function(identity_on_carrier(esk11_0))
| ~ element(esk12_0,the_carrier(esk11_0)) ),
inference(spm,[status(thm)],[840,220,theory(equality)]) ).
cnf(859,negated_conjecture,
( empty(the_carrier(esk11_0))
| ~ function(identity_on_carrier(esk11_0))
| $false ),
inference(rw,[status(thm)],[858,212,theory(equality)]) ).
cnf(860,negated_conjecture,
( empty(the_carrier(esk11_0))
| ~ function(identity_on_carrier(esk11_0)) ),
inference(cn,[status(thm)],[859,theory(equality)]) ).
cnf(861,negated_conjecture,
~ function(identity_on_carrier(esk11_0)),
inference(sr,[status(thm)],[860,302,theory(equality)]) ).
cnf(878,negated_conjecture,
~ one_sorted_str(esk11_0),
inference(spm,[status(thm)],[861,182,theory(equality)]) ).
cnf(879,negated_conjecture,
$false,
inference(rw,[status(thm)],[878,213,theory(equality)]) ).
cnf(880,negated_conjecture,
$false,
inference(cn,[status(thm)],[879,theory(equality)]) ).
cnf(881,negated_conjecture,
$false,
880,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU353+1.p
% --creating new selector for []
% -running prover on /tmp/tmpJcM505/sel_SEU353+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU353+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU353+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU353+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
%
%------------------------------------------------------------------------------