TSTP Solution File: SEU293+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU293+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 06:54:38 EST 2010
% Result : Theorem 0.47s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 105 ( 14 unt; 0 def)
% Number of atoms : 447 ( 86 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 558 ( 216 ~; 243 |; 76 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 208 ( 10 sgn 121 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',cc1_relset_1) ).
fof(8,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',d13_funct_1) ).
fof(13,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',redefinition_k4_relset_1) ).
fof(15,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t4_subset) ).
fof(27,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',redefinition_m2_relset_1) ).
fof(28,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t5_subset) ).
fof(32,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',dt_m2_relset_1) ).
fof(33,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t2_subset) ).
fof(37,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t1_subset) ).
fof(50,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',dt_k4_relset_1) ).
fof(51,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',d1_funct_2) ).
fof(53,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( X2 != empty_set
=> ! [X5] :
( in(X5,relation_inverse_image(X4,X3))
<=> ( in(X5,X1)
& in(apply(X4,X5),X3) ) ) ) ),
file('/tmp/tmpFx5MoK/sel_SEU293+1.p_1',t46_funct_2) ).
fof(54,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( X2 != empty_set
=> ! [X5] :
( in(X5,relation_inverse_image(X4,X3))
<=> ( in(X5,X1)
& in(apply(X4,X5),X3) ) ) ) ),
inference(assume_negation,[status(cth)],[53]) ).
fof(76,plain,
! [X1,X2,X3] :
( ~ element(X3,powerset(cartesian_product2(X1,X2)))
| relation(X3) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(77,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(cartesian_product2(X4,X5)))
| relation(X6) ),
inference(variable_rename,[status(thm)],[76]) ).
cnf(78,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(90,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| ! [X2,X3] :
( ( X3 != relation_inverse_image(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) )
& ( ~ in(X4,relation_dom(X1))
| ~ in(apply(X1,X4),X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,relation_dom(X1))
| ~ in(apply(X1,X4),X2) )
& ( in(X4,X3)
| ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) )
| X3 = relation_inverse_image(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(91,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6,X7] :
( ( X7 != relation_inverse_image(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,relation_dom(X5))
& in(apply(X5,X8),X6) ) )
& ( ~ in(X8,relation_dom(X5))
| ~ in(apply(X5,X8),X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,relation_dom(X5))
| ~ in(apply(X5,X9),X6) )
& ( in(X9,X7)
| ( in(X9,relation_dom(X5))
& in(apply(X5,X9),X6) ) ) )
| X7 = relation_inverse_image(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,plain,
! [X5] :
( ~ relation(X5)
| ~ function(X5)
| ! [X6,X7] :
( ( X7 != relation_inverse_image(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,relation_dom(X5))
& in(apply(X5,X8),X6) ) )
& ( ~ in(X8,relation_dom(X5))
| ~ in(apply(X5,X8),X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
| ~ in(esk5_3(X5,X6,X7),relation_dom(X5))
| ~ in(apply(X5,esk5_3(X5,X6,X7)),X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| ( in(esk5_3(X5,X6,X7),relation_dom(X5))
& in(apply(X5,esk5_3(X5,X6,X7)),X6) ) ) )
| X7 = relation_inverse_image(X5,X6) ) ) ),
inference(skolemize,[status(esa)],[91]) ).
fof(93,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ in(X8,X7)
| ( in(X8,relation_dom(X5))
& in(apply(X5,X8),X6) ) )
& ( ~ in(X8,relation_dom(X5))
| ~ in(apply(X5,X8),X6)
| in(X8,X7) ) )
| X7 != relation_inverse_image(X5,X6) )
& ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
| ~ in(esk5_3(X5,X6,X7),relation_dom(X5))
| ~ in(apply(X5,esk5_3(X5,X6,X7)),X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| ( in(esk5_3(X5,X6,X7),relation_dom(X5))
& in(apply(X5,esk5_3(X5,X6,X7)),X6) ) ) )
| X7 = relation_inverse_image(X5,X6) ) )
| ~ relation(X5)
| ~ function(X5) ),
inference(shift_quantors,[status(thm)],[92]) ).
fof(94,plain,
! [X5,X6,X7,X8] :
( ( in(X8,relation_dom(X5))
| ~ in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X5,X8),X6)
| ~ in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X8,relation_dom(X5))
| ~ in(apply(X5,X8),X6)
| in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk5_3(X5,X6,X7),X7)
| ~ in(esk5_3(X5,X6,X7),relation_dom(X5))
| ~ in(apply(X5,esk5_3(X5,X6,X7)),X6)
| X7 = relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk5_3(X5,X6,X7),relation_dom(X5))
| in(esk5_3(X5,X6,X7),X7)
| X7 = relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X5,esk5_3(X5,X6,X7)),X6)
| in(esk5_3(X5,X6,X7),X7)
| X7 = relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[93]) ).
cnf(98,plain,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[94]) ).
cnf(99,plain,
( in(apply(X1,X4),X3)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[94]) ).
cnf(100,plain,
( in(X4,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(119,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(120,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| relation_dom_as_subset(X4,X5,X6) = relation_dom(X6) ),
inference(variable_rename,[status(thm)],[119]) ).
cnf(121,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[120]) ).
fof(124,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(125,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[124]) ).
cnf(126,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[125]) ).
fof(163,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)],[27]) ).
fof(164,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)],[163]) ).
cnf(165,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[164]) ).
cnf(166,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[164]) ).
fof(167,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(168,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[167]) ).
cnf(169,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[168]) ).
fof(177,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| element(X3,powerset(cartesian_product2(X1,X2))) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(178,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| element(X6,powerset(cartesian_product2(X4,X5))) ),
inference(variable_rename,[status(thm)],[177]) ).
cnf(179,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[178]) ).
fof(180,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(181,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[180]) ).
cnf(182,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[181]) ).
fof(191,plain,
! [X1,X2] :
( ~ in(X1,X2)
| element(X1,X2) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(192,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[191]) ).
cnf(193,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[192]) ).
fof(223,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[50]) ).
fof(224,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| element(relation_dom_as_subset(X4,X5,X6),powerset(X4)) ),
inference(variable_rename,[status(thm)],[223]) ).
cnf(225,plain,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[224]) ).
fof(226,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ( ( ( X2 = empty_set
& X1 != empty_set )
| ( ( ~ quasi_total(X3,X1,X2)
| X1 = relation_dom_as_subset(X1,X2,X3) )
& ( X1 != relation_dom_as_subset(X1,X2,X3)
| quasi_total(X3,X1,X2) ) ) )
& ( X2 != empty_set
| X1 = empty_set
| ( ( ~ quasi_total(X3,X1,X2)
| X3 = empty_set )
& ( X3 != empty_set
| quasi_total(X3,X1,X2) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[51]) ).
fof(227,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| ( ( ( X5 = empty_set
& X4 != empty_set )
| ( ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5) ) ) )
& ( X5 != empty_set
| X4 = empty_set
| ( ( ~ quasi_total(X6,X4,X5)
| X6 = empty_set )
& ( X6 != empty_set
| quasi_total(X6,X4,X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[226]) ).
fof(228,plain,
! [X4,X5,X6] :
( ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6)
| X5 = empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5)
| X5 = empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( ~ quasi_total(X6,X4,X5)
| X4 = relation_dom_as_subset(X4,X5,X6)
| X4 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X4 != relation_dom_as_subset(X4,X5,X6)
| quasi_total(X6,X4,X5)
| X4 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( ~ quasi_total(X6,X4,X5)
| X6 = empty_set
| X4 = empty_set
| X5 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( X6 != empty_set
| quasi_total(X6,X4,X5)
| X4 = empty_set
| X5 != empty_set
| ~ relation_of2_as_subset(X6,X4,X5) ) ),
inference(distribute,[status(thm)],[227]) ).
cnf(234,plain,
( X3 = empty_set
| X2 = relation_dom_as_subset(X2,X3,X1)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[228]) ).
fof(240,negated_conjecture,
? [X1,X2,X3,X4] :
( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2)
& X2 != empty_set
& ? [X5] :
( ( ~ in(X5,relation_inverse_image(X4,X3))
| ~ in(X5,X1)
| ~ in(apply(X4,X5),X3) )
& ( in(X5,relation_inverse_image(X4,X3))
| ( in(X5,X1)
& in(apply(X4,X5),X3) ) ) ) ),
inference(fof_nnf,[status(thm)],[54]) ).
fof(241,negated_conjecture,
? [X6,X7,X8,X9] :
( function(X9)
& quasi_total(X9,X6,X7)
& relation_of2_as_subset(X9,X6,X7)
& X7 != empty_set
& ? [X10] :
( ( ~ in(X10,relation_inverse_image(X9,X8))
| ~ in(X10,X6)
| ~ in(apply(X9,X10),X8) )
& ( in(X10,relation_inverse_image(X9,X8))
| ( in(X10,X6)
& in(apply(X9,X10),X8) ) ) ) ),
inference(variable_rename,[status(thm)],[240]) ).
fof(242,negated_conjecture,
( function(esk22_0)
& quasi_total(esk22_0,esk19_0,esk20_0)
& relation_of2_as_subset(esk22_0,esk19_0,esk20_0)
& esk20_0 != empty_set
& ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0)
| ~ in(apply(esk22_0,esk23_0),esk21_0) )
& ( in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ( in(esk23_0,esk19_0)
& in(apply(esk22_0,esk23_0),esk21_0) ) ) ),
inference(skolemize,[status(esa)],[241]) ).
fof(243,negated_conjecture,
( function(esk22_0)
& quasi_total(esk22_0,esk19_0,esk20_0)
& relation_of2_as_subset(esk22_0,esk19_0,esk20_0)
& esk20_0 != empty_set
& ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0)
| ~ in(apply(esk22_0,esk23_0),esk21_0) )
& ( in(esk23_0,esk19_0)
| in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) )
& ( in(apply(esk22_0,esk23_0),esk21_0)
| in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) ) ),
inference(distribute,[status(thm)],[242]) ).
cnf(244,negated_conjecture,
( in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| in(apply(esk22_0,esk23_0),esk21_0) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(245,negated_conjecture,
( in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| in(esk23_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(246,negated_conjecture,
( ~ in(apply(esk22_0,esk23_0),esk21_0)
| ~ in(esk23_0,esk19_0)
| ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) ),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(247,negated_conjecture,
esk20_0 != empty_set,
inference(split_conjunct,[status(thm)],[243]) ).
cnf(248,negated_conjecture,
relation_of2_as_subset(esk22_0,esk19_0,esk20_0),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(249,negated_conjecture,
quasi_total(esk22_0,esk19_0,esk20_0),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(250,negated_conjecture,
function(esk22_0),
inference(split_conjunct,[status(thm)],[243]) ).
cnf(302,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[78,179,theory(equality)]) ).
cnf(309,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_inverse_image(X1,X3))
| ~ function(X1)
| ~ relation(X1) ),
inference(er,[status(thm)],[99,theory(equality)]) ).
cnf(310,plain,
( X1 = relation_dom(X3)
| empty_set = X2
| ~ relation_of2(X3,X1,X2)
| ~ relation_of2_as_subset(X3,X1,X2)
| ~ quasi_total(X3,X1,X2) ),
inference(spm,[status(thm)],[121,234,theory(equality)]) ).
cnf(317,plain,
( element(relation_dom(X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(spm,[status(thm)],[225,121,theory(equality)]) ).
cnf(320,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_inverse_image(X2,X3))
| ~ function(X2)
| ~ relation(X2) ),
inference(er,[status(thm)],[100,theory(equality)]) ).
cnf(468,negated_conjecture,
relation(esk22_0),
inference(spm,[status(thm)],[302,248,theory(equality)]) ).
cnf(563,negated_conjecture,
( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0)
| ~ function(esk22_0)
| ~ relation(esk22_0) ),
inference(spm,[status(thm)],[246,309,theory(equality)]) ).
cnf(576,negated_conjecture,
( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0)
| $false
| ~ relation(esk22_0) ),
inference(rw,[status(thm)],[563,250,theory(equality)]) ).
cnf(577,negated_conjecture,
( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0)
| $false
| $false ),
inference(rw,[status(thm)],[576,468,theory(equality)]) ).
cnf(578,negated_conjecture,
( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0) ),
inference(cn,[status(thm)],[577,theory(equality)]) ).
cnf(658,plain,
( element(relation_dom(X1),powerset(X2))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[317,166,theory(equality)]) ).
cnf(713,plain,
( X1 = relation_dom(X3)
| empty_set = X2
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2(X3,X1,X2) ),
inference(csr,[status(thm)],[310,165]) ).
cnf(717,plain,
( X1 = relation_dom(X2)
| empty_set = X3
| ~ quasi_total(X2,X1,X3)
| ~ relation_of2_as_subset(X2,X1,X3) ),
inference(spm,[status(thm)],[713,166,theory(equality)]) ).
cnf(1063,negated_conjecture,
( in(esk23_0,relation_dom(esk22_0))
| in(esk23_0,esk19_0)
| ~ function(esk22_0)
| ~ relation(esk22_0) ),
inference(spm,[status(thm)],[320,245,theory(equality)]) ).
cnf(1068,negated_conjecture,
( in(esk23_0,relation_dom(esk22_0))
| in(esk23_0,esk19_0)
| $false
| ~ relation(esk22_0) ),
inference(rw,[status(thm)],[1063,250,theory(equality)]) ).
cnf(1069,negated_conjecture,
( in(esk23_0,relation_dom(esk22_0))
| in(esk23_0,esk19_0)
| $false
| $false ),
inference(rw,[status(thm)],[1068,468,theory(equality)]) ).
cnf(1070,negated_conjecture,
( in(esk23_0,relation_dom(esk22_0))
| in(esk23_0,esk19_0) ),
inference(cn,[status(thm)],[1069,theory(equality)]) ).
cnf(4076,negated_conjecture,
element(relation_dom(esk22_0),powerset(esk19_0)),
inference(spm,[status(thm)],[658,248,theory(equality)]) ).
cnf(4091,negated_conjecture,
( ~ in(X1,relation_dom(esk22_0))
| ~ empty(esk19_0) ),
inference(spm,[status(thm)],[169,4076,theory(equality)]) ).
cnf(4092,negated_conjecture,
( element(X1,esk19_0)
| ~ in(X1,relation_dom(esk22_0)) ),
inference(spm,[status(thm)],[126,4076,theory(equality)]) ).
cnf(4112,negated_conjecture,
( element(esk23_0,esk19_0)
| in(esk23_0,esk19_0) ),
inference(spm,[status(thm)],[4092,1070,theory(equality)]) ).
cnf(4138,negated_conjecture,
( in(esk23_0,esk19_0)
| ~ empty(esk19_0) ),
inference(spm,[status(thm)],[4091,1070,theory(equality)]) ).
cnf(4156,negated_conjecture,
element(esk23_0,esk19_0),
inference(csr,[status(thm)],[4112,193]) ).
cnf(4157,negated_conjecture,
( in(esk23_0,esk19_0)
| empty(esk19_0) ),
inference(spm,[status(thm)],[182,4156,theory(equality)]) ).
cnf(4163,negated_conjecture,
in(esk23_0,esk19_0),
inference(csr,[status(thm)],[4138,4157]) ).
cnf(4178,negated_conjecture,
( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| $false ),
inference(rw,[status(thm)],[578,4163,theory(equality)]) ).
cnf(4179,negated_conjecture,
~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0)),
inference(cn,[status(thm)],[4178,theory(equality)]) ).
cnf(4188,negated_conjecture,
in(apply(esk22_0,esk23_0),esk21_0),
inference(sr,[status(thm)],[244,4179,theory(equality)]) ).
cnf(4197,negated_conjecture,
( in(esk23_0,X1)
| relation_inverse_image(esk22_0,esk21_0) != X1
| ~ in(esk23_0,relation_dom(esk22_0))
| ~ function(esk22_0)
| ~ relation(esk22_0) ),
inference(spm,[status(thm)],[98,4188,theory(equality)]) ).
cnf(4199,negated_conjecture,
( in(esk23_0,X1)
| relation_inverse_image(esk22_0,esk21_0) != X1
| ~ in(esk23_0,relation_dom(esk22_0))
| $false
| ~ relation(esk22_0) ),
inference(rw,[status(thm)],[4197,250,theory(equality)]) ).
cnf(4200,negated_conjecture,
( in(esk23_0,X1)
| relation_inverse_image(esk22_0,esk21_0) != X1
| ~ in(esk23_0,relation_dom(esk22_0))
| $false
| $false ),
inference(rw,[status(thm)],[4199,468,theory(equality)]) ).
cnf(4201,negated_conjecture,
( in(esk23_0,X1)
| relation_inverse_image(esk22_0,esk21_0) != X1
| ~ in(esk23_0,relation_dom(esk22_0)) ),
inference(cn,[status(thm)],[4200,theory(equality)]) ).
cnf(4494,negated_conjecture,
( esk19_0 = relation_dom(esk22_0)
| empty_set = esk20_0
| ~ relation_of2_as_subset(esk22_0,esk19_0,esk20_0) ),
inference(spm,[status(thm)],[717,249,theory(equality)]) ).
cnf(4502,negated_conjecture,
( esk19_0 = relation_dom(esk22_0)
| empty_set = esk20_0
| $false ),
inference(rw,[status(thm)],[4494,248,theory(equality)]) ).
cnf(4503,negated_conjecture,
( esk19_0 = relation_dom(esk22_0)
| empty_set = esk20_0 ),
inference(cn,[status(thm)],[4502,theory(equality)]) ).
cnf(4504,negated_conjecture,
relation_dom(esk22_0) = esk19_0,
inference(sr,[status(thm)],[4503,247,theory(equality)]) ).
cnf(4557,negated_conjecture,
( in(esk23_0,X1)
| relation_inverse_image(esk22_0,esk21_0) != X1
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[4201,4504,theory(equality)]),4163,theory(equality)]) ).
cnf(4558,negated_conjecture,
( in(esk23_0,X1)
| relation_inverse_image(esk22_0,esk21_0) != X1 ),
inference(cn,[status(thm)],[4557,theory(equality)]) ).
cnf(4584,negated_conjecture,
in(esk23_0,relation_inverse_image(esk22_0,esk21_0)),
inference(er,[status(thm)],[4558,theory(equality)]) ).
cnf(4587,negated_conjecture,
$false,
inference(sr,[status(thm)],[4584,4179,theory(equality)]) ).
cnf(4588,negated_conjecture,
$false,
4587,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU293+1.p
% --creating new selector for []
% -running prover on /tmp/tmpFx5MoK/sel_SEU293+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU293+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU293+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU293+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
%
%------------------------------------------------------------------------------