TSTP Solution File: SEU265+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU265+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 06:28:39 EST 2010
% Result : Theorem 0.54s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 20
% Syntax : Number of formulae : 152 ( 23 unt; 0 def)
% Number of atoms : 453 ( 107 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 526 ( 225 ~; 231 |; 47 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 295 ( 23 sgn 167 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',cc1_relset_1) ).
fof(2,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t5_subset) ).
fof(4,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',dt_k4_relset_1) ).
fof(6,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',redefinition_k4_relset_1) ).
fof(8,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t4_subset) ).
fof(9,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t7_boole) ).
fof(10,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t2_tarski) ).
fof(16,axiom,
empty(empty_set),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',fc1_xboole_0) ).
fof(17,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',redefinition_m2_relset_1) ).
fof(20,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',dt_m2_relset_1) ).
fof(21,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',d4_relat_1) ).
fof(22,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t2_subset) ).
fof(26,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',commutativity_k2_tarski) ).
fof(29,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',d5_tarski) ).
fof(30,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t20_relat_1) ).
fof(31,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',existence_m1_subset_1) ).
fof(37,conjecture,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
<=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t22_relset_1) ).
fof(38,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmpa2En-d/sel_SEU265+1.p_1',t6_boole) ).
fof(39,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
<=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
inference(assume_negation,[status(cth)],[37]) ).
fof(43,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
<=> relation_dom_as_subset(X2,X1,X3) = X2 ) ),
inference(fof_simplification,[status(thm)],[39,theory(equality)]) ).
fof(44,plain,
! [X1,X2,X3] :
( ~ element(X3,powerset(cartesian_product2(X1,X2)))
| relation(X3) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(45,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(cartesian_product2(X4,X5)))
| relation(X6) ),
inference(variable_rename,[status(thm)],[44]) ).
cnf(46,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(47,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(48,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[47]) ).
cnf(49,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(53,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(54,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| element(relation_dom_as_subset(X4,X5,X6),powerset(X4)) ),
inference(variable_rename,[status(thm)],[53]) ).
cnf(55,plain,
( element(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(59,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(60,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| relation_dom_as_subset(X4,X5,X6) = relation_dom(X6) ),
inference(variable_rename,[status(thm)],[59]) ).
cnf(61,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom(X3)
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(64,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(65,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[64]) ).
cnf(66,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(67,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(68,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[67]) ).
cnf(69,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(70,plain,
! [X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X2) ) )
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(71,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,plain,
! [X4,X5] :
( ( ( ~ in(esk2_2(X4,X5),X4)
| ~ in(esk2_2(X4,X5),X5) )
& ( in(esk2_2(X4,X5),X4)
| in(esk2_2(X4,X5),X5) ) )
| X4 = X5 ),
inference(skolemize,[status(esa)],[71]) ).
fof(73,plain,
! [X4,X5] :
( ( ~ in(esk2_2(X4,X5),X4)
| ~ in(esk2_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk2_2(X4,X5),X4)
| in(esk2_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[72]) ).
cnf(74,plain,
( X1 = X2
| in(esk2_2(X1,X2),X2)
| in(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[73]) ).
cnf(75,plain,
( X1 = X2
| ~ in(esk2_2(X1,X2),X2)
| ~ in(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[73]) ).
cnf(88,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[16]) ).
fof(89,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)],[17]) ).
fof(90,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)],[89]) ).
cnf(92,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[90]) ).
fof(95,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| element(X3,powerset(cartesian_product2(X1,X2))) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(96,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| element(X6,powerset(cartesian_product2(X4,X5))) ),
inference(variable_rename,[status(thm)],[95]) ).
cnf(97,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(98,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_dom(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) )
& ( ! [X4] : ~ in(ordered_pair(X3,X4),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X3,X4),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) ) )
| X2 = relation_dom(X1) ) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(99,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X7,X8),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X10,X11),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X10,X12),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk5_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk6_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk6_2(X5,X6),X11),X5) )
& ( in(esk6_2(X5,X6),X6)
| in(ordered_pair(esk6_2(X5,X6),esk7_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk6_2(X5,X6),X11),X5)
| ~ in(esk6_2(X5,X6),X6) )
& ( in(esk6_2(X5,X6),X6)
| in(ordered_pair(esk6_2(X5,X6),esk7_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk5_3(X5,X6,X7)),X5) ) )
| X6 != relation_dom(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk6_2(X5,X6),X11),X5)
| ~ in(esk6_2(X5,X6),X6)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk6_2(X5,X6),X6)
| in(ordered_pair(esk6_2(X5,X6),esk7_2(X5,X6)),X5)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk5_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(103,plain,
( in(ordered_pair(X3,esk5_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(107,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(108,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[107]) ).
cnf(109,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[108]) ).
fof(116,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[26]) ).
cnf(117,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[116]) ).
fof(120,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[29]) ).
cnf(121,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[120]) ).
fof(122,plain,
! [X1,X2,X3] :
( ~ relation(X3)
| ~ in(ordered_pair(X1,X2),X3)
| ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(123,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ in(ordered_pair(X4,X5),X6)
| ( in(X4,relation_dom(X6))
& in(X5,relation_rng(X6)) ) ),
inference(variable_rename,[status(thm)],[122]) ).
fof(124,plain,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_rng(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[123]) ).
cnf(126,plain,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[124]) ).
fof(127,plain,
! [X3] :
? [X4] : element(X4,X3),
inference(variable_rename,[status(thm)],[31]) ).
fof(128,plain,
! [X3] : element(esk8_1(X3),X3),
inference(skolemize,[status(esa)],[127]) ).
cnf(129,plain,
element(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[128]) ).
fof(139,negated_conjecture,
? [X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X1)
& ( ? [X4] :
( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X4,X5),X3) )
| relation_dom_as_subset(X2,X1,X3) != X2 )
& ( ! [X4] :
( ~ in(X4,X2)
| ? [X5] : in(ordered_pair(X4,X5),X3) )
| relation_dom_as_subset(X2,X1,X3) = X2 ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(140,negated_conjecture,
? [X6,X7,X8] :
( relation_of2_as_subset(X8,X7,X6)
& ( ? [X9] :
( in(X9,X7)
& ! [X10] : ~ in(ordered_pair(X9,X10),X8) )
| relation_dom_as_subset(X7,X6,X8) != X7 )
& ( ! [X11] :
( ~ in(X11,X7)
| ? [X12] : in(ordered_pair(X11,X12),X8) )
| relation_dom_as_subset(X7,X6,X8) = X7 ) ),
inference(variable_rename,[status(thm)],[139]) ).
fof(141,negated_conjecture,
( relation_of2_as_subset(esk12_0,esk11_0,esk10_0)
& ( ( in(esk13_0,esk11_0)
& ! [X10] : ~ in(ordered_pair(esk13_0,X10),esk12_0) )
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0 )
& ( ! [X11] :
( ~ in(X11,esk11_0)
| in(ordered_pair(X11,esk14_1(X11)),esk12_0) )
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0 ) ),
inference(skolemize,[status(esa)],[140]) ).
fof(142,negated_conjecture,
! [X10,X11] :
( ( ~ in(X11,esk11_0)
| in(ordered_pair(X11,esk14_1(X11)),esk12_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0 )
& ( ( ~ in(ordered_pair(esk13_0,X10),esk12_0)
& in(esk13_0,esk11_0) )
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0 )
& relation_of2_as_subset(esk12_0,esk11_0,esk10_0) ),
inference(shift_quantors,[status(thm)],[141]) ).
fof(143,negated_conjecture,
! [X10,X11] :
( ( ~ in(X11,esk11_0)
| in(ordered_pair(X11,esk14_1(X11)),esk12_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0 )
& ( ~ in(ordered_pair(esk13_0,X10),esk12_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0 )
& ( in(esk13_0,esk11_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0 )
& relation_of2_as_subset(esk12_0,esk11_0,esk10_0) ),
inference(distribute,[status(thm)],[142]) ).
cnf(144,negated_conjecture,
relation_of2_as_subset(esk12_0,esk11_0,esk10_0),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(145,negated_conjecture,
( in(esk13_0,esk11_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0 ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(146,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0
| ~ in(ordered_pair(esk13_0,X1),esk12_0) ),
inference(split_conjunct,[status(thm)],[143]) ).
cnf(147,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| in(ordered_pair(X1,esk14_1(X1)),esk12_0)
| ~ in(X1,esk11_0) ),
inference(split_conjunct,[status(thm)],[143]) ).
fof(148,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(149,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[148]) ).
cnf(150,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[149]) ).
cnf(151,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| in(unordered_pair(unordered_pair(X1,esk14_1(X1)),singleton(X1)),esk12_0)
| ~ in(X1,esk11_0) ),
inference(rw,[status(thm)],[147,121,theory(equality)]),
[unfolding] ).
cnf(154,plain,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(rw,[status(thm)],[126,121,theory(equality)]),
[unfolding] ).
cnf(156,plain,
( in(unordered_pair(unordered_pair(X3,esk5_3(X1,X2,X3)),singleton(X3)),X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(rw,[status(thm)],[103,121,theory(equality)]),
[unfolding] ).
cnf(159,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0
| ~ in(unordered_pair(unordered_pair(esk13_0,X1),singleton(esk13_0)),esk12_0) ),
inference(rw,[status(thm)],[146,121,theory(equality)]),
[unfolding] ).
cnf(164,plain,
( empty(X1)
| in(esk8_1(X1),X1) ),
inference(spm,[status(thm)],[109,129,theory(equality)]) ).
cnf(173,plain,
( ~ empty(X1)
| ~ in(X2,esk8_1(powerset(X1))) ),
inference(spm,[status(thm)],[49,129,theory(equality)]) ).
cnf(175,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk14_1(X1))),esk12_0)
| ~ in(X1,esk11_0) ),
inference(rw,[status(thm)],[151,117,theory(equality)]) ).
cnf(178,negated_conjecture,
( in(esk13_0,esk11_0)
| relation_dom(esk12_0) != esk11_0
| ~ relation_of2(esk12_0,esk11_0,esk10_0) ),
inference(spm,[status(thm)],[145,61,theory(equality)]) ).
cnf(190,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0
| ~ in(unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,X1)),esk12_0) ),
inference(spm,[status(thm)],[159,117,theory(equality)]) ).
cnf(195,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[46,97,theory(equality)]) ).
cnf(199,plain,
( ~ empty(X1)
| ~ in(X2,relation_dom_as_subset(X1,X3,X4))
| ~ relation_of2(X4,X1,X3) ),
inference(spm,[status(thm)],[49,55,theory(equality)]) ).
cnf(200,plain,
( element(relation_dom(X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(spm,[status(thm)],[55,61,theory(equality)]) ).
cnf(208,plain,
( in(X1,relation_dom(X2))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[154,117,theory(equality)]) ).
cnf(215,plain,
( in(unordered_pair(singleton(X3),unordered_pair(X3,esk5_3(X1,X2,X3))),X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(rw,[status(thm)],[156,117,theory(equality)]) ).
cnf(241,negated_conjecture,
relation(esk12_0),
inference(spm,[status(thm)],[195,144,theory(equality)]) ).
cnf(248,plain,
( empty(esk8_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[173,164,theory(equality)]) ).
cnf(275,plain,
( empty_set = esk8_1(powerset(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[150,248,theory(equality)]) ).
cnf(281,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[173,275,theory(equality)]) ).
cnf(284,negated_conjecture,
( in(esk13_0,esk11_0)
| relation_dom(esk12_0) != esk11_0
| ~ relation_of2_as_subset(esk12_0,esk11_0,esk10_0) ),
inference(spm,[status(thm)],[178,92,theory(equality)]) ).
cnf(285,negated_conjecture,
( in(esk13_0,esk11_0)
| relation_dom(esk12_0) != esk11_0
| $false ),
inference(rw,[status(thm)],[284,144,theory(equality)]) ).
cnf(286,negated_conjecture,
( in(esk13_0,esk11_0)
| relation_dom(esk12_0) != esk11_0 ),
inference(cn,[status(thm)],[285,theory(equality)]) ).
fof(293,plain,
( ~ epred1_0
<=> ! [X1] : ~ empty(X1) ),
introduced(definition),
[split] ).
cnf(294,plain,
( epred1_0
| ~ empty(X1) ),
inference(split_equiv,[status(thm)],[293]) ).
fof(295,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition),
[split] ).
cnf(296,plain,
( epred2_0
| ~ in(X2,empty_set) ),
inference(split_equiv,[status(thm)],[295]) ).
cnf(297,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[281,293,theory(equality)]),295,theory(equality)]),
[split] ).
cnf(308,plain,
epred1_0,
inference(spm,[status(thm)],[294,88,theory(equality)]) ).
cnf(312,plain,
( ~ epred2_0
| $false ),
inference(rw,[status(thm)],[297,308,theory(equality)]) ).
cnf(313,plain,
~ epred2_0,
inference(cn,[status(thm)],[312,theory(equality)]) ).
cnf(314,plain,
~ in(X2,empty_set),
inference(sr,[status(thm)],[296,313,theory(equality)]) ).
cnf(315,plain,
( empty_set = X1
| in(esk2_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[314,74,theory(equality)]) ).
cnf(413,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0
| relation_dom(esk12_0) != X1
| ~ in(esk13_0,X1)
| ~ relation(esk12_0) ),
inference(spm,[status(thm)],[190,215,theory(equality)]) ).
cnf(414,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0
| relation_dom(esk12_0) != X1
| ~ in(esk13_0,X1)
| $false ),
inference(rw,[status(thm)],[413,241,theory(equality)]) ).
cnf(415,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0
| relation_dom(esk12_0) != X1
| ~ in(esk13_0,X1) ),
inference(cn,[status(thm)],[414,theory(equality)]) ).
cnf(465,plain,
( element(relation_dom(X1),powerset(X2))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[200,92,theory(equality)]) ).
cnf(525,plain,
( empty_set = relation_dom_as_subset(X2,X3,X1)
| ~ relation_of2(X1,X2,X3)
| ~ empty(X2) ),
inference(spm,[status(thm)],[199,315,theory(equality)]) ).
cnf(633,plain,
( empty_set = relation_dom(X3)
| ~ relation_of2(X3,X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[61,525,theory(equality)]) ).
cnf(642,plain,
( relation_dom(X1) = empty_set
| ~ empty(X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[633,92,theory(equality)]) ).
cnf(643,negated_conjecture,
( relation_dom(esk12_0) = empty_set
| ~ empty(esk11_0) ),
inference(spm,[status(thm)],[642,144,theory(equality)]) ).
cnf(646,negated_conjecture,
( in(esk13_0,esk11_0)
| empty_set != esk11_0
| ~ empty(esk11_0) ),
inference(spm,[status(thm)],[286,643,theory(equality)]) ).
cnf(651,negated_conjecture,
( in(esk13_0,esk11_0)
| ~ empty(esk11_0) ),
inference(csr,[status(thm)],[646,150]) ).
cnf(652,negated_conjecture,
~ empty(esk11_0),
inference(csr,[status(thm)],[651,69]) ).
cnf(780,negated_conjecture,
( in(X1,relation_dom(esk12_0))
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| ~ relation(esk12_0)
| ~ in(X1,esk11_0) ),
inference(spm,[status(thm)],[208,175,theory(equality)]) ).
cnf(785,negated_conjecture,
( in(X1,relation_dom(esk12_0))
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| $false
| ~ in(X1,esk11_0) ),
inference(rw,[status(thm)],[780,241,theory(equality)]) ).
cnf(786,negated_conjecture,
( in(X1,relation_dom(esk12_0))
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| ~ in(X1,esk11_0) ),
inference(cn,[status(thm)],[785,theory(equality)]) ).
cnf(795,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| in(esk2_2(esk11_0,X1),relation_dom(esk12_0))
| esk11_0 = X1
| in(esk2_2(esk11_0,X1),X1) ),
inference(spm,[status(thm)],[786,74,theory(equality)]) ).
cnf(842,negated_conjecture,
element(relation_dom(esk12_0),powerset(esk11_0)),
inference(spm,[status(thm)],[465,144,theory(equality)]) ).
cnf(856,negated_conjecture,
( element(X1,esk11_0)
| ~ in(X1,relation_dom(esk12_0)) ),
inference(spm,[status(thm)],[66,842,theory(equality)]) ).
cnf(4796,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| esk11_0 = relation_dom(esk12_0)
| in(esk2_2(esk11_0,relation_dom(esk12_0)),relation_dom(esk12_0)) ),
inference(ef,[status(thm)],[795,theory(equality)]) ).
cnf(5184,negated_conjecture,
( esk11_0 = relation_dom(esk12_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| ~ in(esk2_2(esk11_0,relation_dom(esk12_0)),esk11_0) ),
inference(spm,[status(thm)],[75,4796,theory(equality)]) ).
cnf(5188,negated_conjecture,
( element(esk2_2(esk11_0,relation_dom(esk12_0)),esk11_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| relation_dom(esk12_0) = esk11_0 ),
inference(spm,[status(thm)],[856,4796,theory(equality)]) ).
cnf(5263,negated_conjecture,
( empty(esk11_0)
| in(esk2_2(esk11_0,relation_dom(esk12_0)),esk11_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| relation_dom(esk12_0) = esk11_0 ),
inference(spm,[status(thm)],[109,5188,theory(equality)]) ).
cnf(5266,negated_conjecture,
( in(esk2_2(esk11_0,relation_dom(esk12_0)),esk11_0)
| relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| relation_dom(esk12_0) = esk11_0 ),
inference(sr,[status(thm)],[5263,652,theory(equality)]) ).
cnf(5370,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) = esk11_0
| relation_dom(esk12_0) = esk11_0 ),
inference(csr,[status(thm)],[5184,5266]) ).
cnf(5371,negated_conjecture,
( in(esk13_0,esk11_0)
| relation_dom(esk12_0) = esk11_0 ),
inference(spm,[status(thm)],[145,5370,theory(equality)]) ).
cnf(5372,negated_conjecture,
( esk11_0 = relation_dom(esk12_0)
| ~ relation_of2(esk12_0,esk11_0,esk10_0) ),
inference(spm,[status(thm)],[61,5370,theory(equality)]) ).
cnf(5385,negated_conjecture,
in(esk13_0,esk11_0),
inference(csr,[status(thm)],[5371,286]) ).
cnf(5466,negated_conjecture,
( relation_dom(esk12_0) = esk11_0
| ~ relation_of2_as_subset(esk12_0,esk11_0,esk10_0) ),
inference(spm,[status(thm)],[5372,92,theory(equality)]) ).
cnf(5467,negated_conjecture,
( relation_dom(esk12_0) = esk11_0
| $false ),
inference(rw,[status(thm)],[5466,144,theory(equality)]) ).
cnf(5468,negated_conjecture,
relation_dom(esk12_0) = esk11_0,
inference(cn,[status(thm)],[5467,theory(equality)]) ).
cnf(5580,negated_conjecture,
( relation_dom_as_subset(esk11_0,esk10_0,esk12_0) != esk11_0
| esk11_0 != X1
| ~ in(esk13_0,X1) ),
inference(rw,[status(thm)],[415,5468,theory(equality)]) ).
cnf(5776,negated_conjecture,
( relation_dom(esk12_0) != esk11_0
| esk11_0 != X1
| ~ in(esk13_0,X1)
| ~ relation_of2(esk12_0,esk11_0,esk10_0) ),
inference(spm,[status(thm)],[5580,61,theory(equality)]) ).
cnf(5781,negated_conjecture,
( $false
| esk11_0 != X1
| ~ in(esk13_0,X1)
| ~ relation_of2(esk12_0,esk11_0,esk10_0) ),
inference(rw,[status(thm)],[5776,5468,theory(equality)]) ).
cnf(5782,negated_conjecture,
( esk11_0 != X1
| ~ in(esk13_0,X1)
| ~ relation_of2(esk12_0,esk11_0,esk10_0) ),
inference(cn,[status(thm)],[5781,theory(equality)]) ).
cnf(5812,negated_conjecture,
( esk11_0 != X1
| ~ in(esk13_0,X1)
| ~ relation_of2_as_subset(esk12_0,esk11_0,esk10_0) ),
inference(spm,[status(thm)],[5782,92,theory(equality)]) ).
cnf(5813,negated_conjecture,
( esk11_0 != X1
| ~ in(esk13_0,X1)
| $false ),
inference(rw,[status(thm)],[5812,144,theory(equality)]) ).
cnf(5814,negated_conjecture,
( esk11_0 != X1
| ~ in(esk13_0,X1) ),
inference(cn,[status(thm)],[5813,theory(equality)]) ).
cnf(5815,negated_conjecture,
$false,
inference(spm,[status(thm)],[5814,5385,theory(equality)]) ).
cnf(5824,negated_conjecture,
$false,
5815,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU265+1.p
% --creating new selector for []
% -running prover on /tmp/tmpa2En-d/sel_SEU265+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU265+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU265+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU265+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
%
%------------------------------------------------------------------------------