TSTP Solution File: SEU266+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU266+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 06:29:14 EST 2010
% Result : Theorem 0.53s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 20
% Syntax : Number of formulae : 152 ( 23 unt; 0 def)
% Number of atoms : 453 ( 104 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 528 ( 227 ~; 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 : 289 ( 17 sgn 167 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',d5_relat_1) ).
fof(2,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',cc1_relset_1) ).
fof(3,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',t5_subset) ).
fof(7,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',t4_subset) ).
fof(8,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',t7_boole) ).
fof(9,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',t2_tarski) ).
fof(15,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',dt_k5_relset_1) ).
fof(16,axiom,
empty(empty_set),
file('/tmp/tmpSeZFvs/sel_SEU266+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/tmpSeZFvs/sel_SEU266+1.p_1',redefinition_m2_relset_1) ).
fof(18,conjecture,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X5,X4),X3) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',t23_relset_1) ).
fof(21,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',dt_m2_relset_1) ).
fof(22,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',t2_subset) ).
fof(26,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpSeZFvs/sel_SEU266+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/tmpSeZFvs/sel_SEU266+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/tmpSeZFvs/sel_SEU266+1.p_1',t20_relat_1) ).
fof(31,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',existence_m1_subset_1) ).
fof(36,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',redefinition_k5_relset_1) ).
fof(38,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmpSeZFvs/sel_SEU266+1.p_1',t6_boole) ).
fof(39,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X5,X4),X3) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
inference(assume_negation,[status(cth)],[18]) ).
fof(43,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X5,X4),X3) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
inference(fof_simplification,[status(thm)],[39,theory(equality)]) ).
fof(44,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_rng(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) )
& ( ! [X4] : ~ in(ordered_pair(X4,X3),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X4,X3),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) ) )
| X2 = relation_rng(X1) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(45,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X8,X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X11,X10),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X12,X10),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk2_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(skolemize,[status(esa)],[45]) ).
fof(47,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) )
& ( ( ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) ) )
| X6 != relation_rng(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5)
| X6 != relation_rng(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(49,plain,
( in(ordered_pair(esk1_3(X1,X2,X3),X3),X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(53,plain,
! [X1,X2,X3] :
( ~ element(X3,powerset(cartesian_product2(X1,X2)))
| relation(X3) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(54,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(cartesian_product2(X4,X5)))
| relation(X6) ),
inference(variable_rename,[status(thm)],[53]) ).
cnf(55,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(56,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(57,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[56]) ).
cnf(58,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(67,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(68,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[67]) ).
cnf(69,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(70,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(71,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[70]) ).
cnf(72,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(73,plain,
! [X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X2) ) )
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(74,plain,
! [X4,X5] :
( ? [X6] :
( ( ~ in(X6,X4)
| ~ in(X6,X5) )
& ( in(X6,X4)
| in(X6,X5) ) )
| X4 = X5 ),
inference(variable_rename,[status(thm)],[73]) ).
fof(75,plain,
! [X4,X5] :
( ( ( ~ in(esk5_2(X4,X5),X4)
| ~ in(esk5_2(X4,X5),X5) )
& ( in(esk5_2(X4,X5),X4)
| in(esk5_2(X4,X5),X5) ) )
| X4 = X5 ),
inference(skolemize,[status(esa)],[74]) ).
fof(76,plain,
! [X4,X5] :
( ( ~ in(esk5_2(X4,X5),X4)
| ~ in(esk5_2(X4,X5),X5)
| X4 = X5 )
& ( in(esk5_2(X4,X5),X4)
| in(esk5_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[75]) ).
cnf(77,plain,
( X1 = X2
| in(esk5_2(X1,X2),X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(78,plain,
( X1 = X2
| ~ in(esk5_2(X1,X2),X2)
| ~ in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
fof(91,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(92,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| element(relation_rng_as_subset(X4,X5,X6),powerset(X5)) ),
inference(variable_rename,[status(thm)],[91]) ).
cnf(93,plain,
( element(relation_rng_as_subset(X1,X2,X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[92]) ).
cnf(94,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[16]) ).
fof(95,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(96,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)],[95]) ).
cnf(98,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(99,negated_conjecture,
? [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
& ( ? [X4] :
( in(X4,X2)
& ! [X5] : ~ in(ordered_pair(X5,X4),X3) )
| relation_rng_as_subset(X1,X2,X3) != X2 )
& ( ! [X4] :
( ~ in(X4,X2)
| ? [X5] : in(ordered_pair(X5,X4),X3) )
| relation_rng_as_subset(X1,X2,X3) = X2 ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(100,negated_conjecture,
? [X6,X7,X8] :
( relation_of2_as_subset(X8,X6,X7)
& ( ? [X9] :
( in(X9,X7)
& ! [X10] : ~ in(ordered_pair(X10,X9),X8) )
| relation_rng_as_subset(X6,X7,X8) != X7 )
& ( ! [X11] :
( ~ in(X11,X7)
| ? [X12] : in(ordered_pair(X12,X11),X8) )
| relation_rng_as_subset(X6,X7,X8) = X7 ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,negated_conjecture,
( relation_of2_as_subset(esk10_0,esk8_0,esk9_0)
& ( ( in(esk11_0,esk9_0)
& ! [X10] : ~ in(ordered_pair(X10,esk11_0),esk10_0) )
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0 )
& ( ! [X11] :
( ~ in(X11,esk9_0)
| in(ordered_pair(esk12_1(X11),X11),esk10_0) )
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0 ) ),
inference(skolemize,[status(esa)],[100]) ).
fof(102,negated_conjecture,
! [X10,X11] :
( ( ~ in(X11,esk9_0)
| in(ordered_pair(esk12_1(X11),X11),esk10_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0 )
& ( ( ~ in(ordered_pair(X10,esk11_0),esk10_0)
& in(esk11_0,esk9_0) )
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0 )
& relation_of2_as_subset(esk10_0,esk8_0,esk9_0) ),
inference(shift_quantors,[status(thm)],[101]) ).
fof(103,negated_conjecture,
! [X10,X11] :
( ( ~ in(X11,esk9_0)
| in(ordered_pair(esk12_1(X11),X11),esk10_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0 )
& ( ~ in(ordered_pair(X10,esk11_0),esk10_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0 )
& ( in(esk11_0,esk9_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0 )
& relation_of2_as_subset(esk10_0,esk8_0,esk9_0) ),
inference(distribute,[status(thm)],[102]) ).
cnf(104,negated_conjecture,
relation_of2_as_subset(esk10_0,esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(105,negated_conjecture,
( in(esk11_0,esk9_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0 ),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(106,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0
| ~ in(ordered_pair(X1,esk11_0),esk10_0) ),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(107,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| in(ordered_pair(esk12_1(X1),X1),esk10_0)
| ~ in(X1,esk9_0) ),
inference(split_conjunct,[status(thm)],[103]) ).
fof(110,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| element(X3,powerset(cartesian_product2(X1,X2))) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(111,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| element(X6,powerset(cartesian_product2(X4,X5))) ),
inference(variable_rename,[status(thm)],[110]) ).
cnf(112,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(113,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(114,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[113]) ).
cnf(115,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[114]) ).
fof(122,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[26]) ).
cnf(123,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[122]) ).
fof(126,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[29]) ).
cnf(127,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[126]) ).
fof(128,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(129,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)],[128]) ).
fof(130,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)],[129]) ).
cnf(131,plain,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[130]) ).
fof(133,plain,
! [X3] :
? [X4] : element(X4,X3),
inference(variable_rename,[status(thm)],[31]) ).
fof(134,plain,
! [X3] : element(esk13_1(X3),X3),
inference(skolemize,[status(esa)],[133]) ).
cnf(135,plain,
element(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[134]) ).
fof(142,plain,
! [X1,X2,X3] :
( ~ relation_of2(X3,X1,X2)
| relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(143,plain,
! [X4,X5,X6] :
( ~ relation_of2(X6,X4,X5)
| relation_rng_as_subset(X4,X5,X6) = relation_rng(X6) ),
inference(variable_rename,[status(thm)],[142]) ).
cnf(144,plain,
( relation_rng_as_subset(X1,X2,X3) = relation_rng(X3)
| ~ relation_of2(X3,X1,X2) ),
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_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| in(unordered_pair(unordered_pair(esk12_1(X1),X1),singleton(esk12_1(X1))),esk10_0)
| ~ in(X1,esk9_0) ),
inference(rw,[status(thm)],[107,127,theory(equality)]),
[unfolding] ).
cnf(153,plain,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(rw,[status(thm)],[131,127,theory(equality)]),
[unfolding] ).
cnf(156,plain,
( in(unordered_pair(unordered_pair(esk1_3(X1,X2,X3),X3),singleton(esk1_3(X1,X2,X3))),X1)
| relation_rng(X1) != X2
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(rw,[status(thm)],[49,127,theory(equality)]),
[unfolding] ).
cnf(159,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0
| ~ in(unordered_pair(unordered_pair(X1,esk11_0),singleton(X1)),esk10_0) ),
inference(rw,[status(thm)],[106,127,theory(equality)]),
[unfolding] ).
cnf(165,plain,
( empty(X1)
| in(esk13_1(X1),X1) ),
inference(spm,[status(thm)],[115,135,theory(equality)]) ).
cnf(173,plain,
( ~ empty(X1)
| ~ in(X2,esk13_1(powerset(X1))) ),
inference(spm,[status(thm)],[58,135,theory(equality)]) ).
cnf(175,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| in(unordered_pair(unordered_pair(X1,esk12_1(X1)),singleton(esk12_1(X1))),esk10_0)
| ~ in(X1,esk9_0) ),
inference(rw,[status(thm)],[151,123,theory(equality)]) ).
cnf(180,negated_conjecture,
( in(esk11_0,esk9_0)
| relation_rng(esk10_0) != esk9_0
| ~ relation_of2(esk10_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[105,144,theory(equality)]) ).
cnf(191,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0
| ~ in(unordered_pair(unordered_pair(esk11_0,X1),singleton(X1)),esk10_0) ),
inference(spm,[status(thm)],[159,123,theory(equality)]) ).
cnf(195,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[55,112,theory(equality)]) ).
cnf(199,plain,
( ~ empty(X1)
| ~ in(X4,relation_rng_as_subset(X2,X1,X3))
| ~ relation_of2(X3,X2,X1) ),
inference(spm,[status(thm)],[58,93,theory(equality)]) ).
cnf(200,plain,
( element(relation_rng(X3),powerset(X2))
| ~ relation_of2(X3,X1,X2) ),
inference(spm,[status(thm)],[93,144,theory(equality)]) ).
cnf(203,plain,
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[153,123,theory(equality)]) ).
cnf(221,plain,
( in(unordered_pair(unordered_pair(X3,esk1_3(X1,X2,X3)),singleton(esk1_3(X1,X2,X3))),X1)
| relation_rng(X1) != X2
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(rw,[status(thm)],[156,123,theory(equality)]) ).
cnf(246,negated_conjecture,
relation(esk10_0),
inference(spm,[status(thm)],[195,104,theory(equality)]) ).
cnf(253,plain,
( empty(esk13_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[173,165,theory(equality)]) ).
cnf(276,plain,
( empty_set = esk13_1(powerset(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[150,253,theory(equality)]) ).
cnf(285,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[173,276,theory(equality)]) ).
cnf(289,negated_conjecture,
( in(esk11_0,esk9_0)
| relation_rng(esk10_0) != esk9_0
| ~ relation_of2_as_subset(esk10_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[180,98,theory(equality)]) ).
cnf(290,negated_conjecture,
( in(esk11_0,esk9_0)
| relation_rng(esk10_0) != esk9_0
| $false ),
inference(rw,[status(thm)],[289,104,theory(equality)]) ).
cnf(291,negated_conjecture,
( in(esk11_0,esk9_0)
| relation_rng(esk10_0) != esk9_0 ),
inference(cn,[status(thm)],[290,theory(equality)]) ).
fof(292,plain,
( ~ epred1_0
<=> ! [X1] : ~ empty(X1) ),
introduced(definition),
[split] ).
cnf(293,plain,
( epred1_0
| ~ empty(X1) ),
inference(split_equiv,[status(thm)],[292]) ).
fof(294,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition),
[split] ).
cnf(295,plain,
( epred2_0
| ~ in(X2,empty_set) ),
inference(split_equiv,[status(thm)],[294]) ).
cnf(296,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[285,292,theory(equality)]),294,theory(equality)]),
[split] ).
cnf(297,plain,
epred1_0,
inference(spm,[status(thm)],[293,94,theory(equality)]) ).
cnf(301,plain,
( ~ epred2_0
| $false ),
inference(rw,[status(thm)],[296,297,theory(equality)]) ).
cnf(302,plain,
~ epred2_0,
inference(cn,[status(thm)],[301,theory(equality)]) ).
cnf(303,plain,
~ in(X2,empty_set),
inference(sr,[status(thm)],[295,302,theory(equality)]) ).
cnf(304,plain,
( empty_set = X1
| in(esk5_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[303,77,theory(equality)]) ).
cnf(400,plain,
( element(relation_rng(X1),powerset(X2))
| ~ relation_of2_as_subset(X1,X3,X2) ),
inference(spm,[status(thm)],[200,98,theory(equality)]) ).
cnf(425,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0
| relation_rng(esk10_0) != X1
| ~ in(esk11_0,X1)
| ~ relation(esk10_0) ),
inference(spm,[status(thm)],[191,221,theory(equality)]) ).
cnf(426,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0
| relation_rng(esk10_0) != X1
| ~ in(esk11_0,X1)
| $false ),
inference(rw,[status(thm)],[425,246,theory(equality)]) ).
cnf(427,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0
| relation_rng(esk10_0) != X1
| ~ in(esk11_0,X1) ),
inference(cn,[status(thm)],[426,theory(equality)]) ).
cnf(564,plain,
( empty_set = relation_rng_as_subset(X2,X3,X1)
| ~ relation_of2(X1,X2,X3)
| ~ empty(X3) ),
inference(spm,[status(thm)],[199,304,theory(equality)]) ).
cnf(582,negated_conjecture,
( in(esk11_0,esk9_0)
| empty_set != esk9_0
| ~ relation_of2(esk10_0,esk8_0,esk9_0)
| ~ empty(esk9_0) ),
inference(spm,[status(thm)],[105,564,theory(equality)]) ).
cnf(592,negated_conjecture,
( in(esk11_0,esk9_0)
| ~ relation_of2(esk10_0,esk8_0,esk9_0)
| ~ empty(esk9_0) ),
inference(csr,[status(thm)],[582,150]) ).
cnf(593,negated_conjecture,
( ~ relation_of2(esk10_0,esk8_0,esk9_0)
| ~ empty(esk9_0) ),
inference(csr,[status(thm)],[592,72]) ).
cnf(594,negated_conjecture,
( ~ empty(esk9_0)
| ~ relation_of2_as_subset(esk10_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[593,98,theory(equality)]) ).
cnf(595,negated_conjecture,
( ~ empty(esk9_0)
| $false ),
inference(rw,[status(thm)],[594,104,theory(equality)]) ).
cnf(596,negated_conjecture,
~ empty(esk9_0),
inference(cn,[status(thm)],[595,theory(equality)]) ).
cnf(644,negated_conjecture,
( in(X1,relation_rng(esk10_0))
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| ~ relation(esk10_0)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[203,175,theory(equality)]) ).
cnf(648,negated_conjecture,
( in(X1,relation_rng(esk10_0))
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| $false
| ~ in(X1,esk9_0) ),
inference(rw,[status(thm)],[644,246,theory(equality)]) ).
cnf(649,negated_conjecture,
( in(X1,relation_rng(esk10_0))
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| ~ in(X1,esk9_0) ),
inference(cn,[status(thm)],[648,theory(equality)]) ).
cnf(656,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| in(esk5_2(esk9_0,X1),relation_rng(esk10_0))
| esk9_0 = X1
| in(esk5_2(esk9_0,X1),X1) ),
inference(spm,[status(thm)],[649,77,theory(equality)]) ).
cnf(887,negated_conjecture,
element(relation_rng(esk10_0),powerset(esk9_0)),
inference(spm,[status(thm)],[400,104,theory(equality)]) ).
cnf(917,negated_conjecture,
( element(X1,esk9_0)
| ~ in(X1,relation_rng(esk10_0)) ),
inference(spm,[status(thm)],[69,887,theory(equality)]) ).
cnf(4748,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| esk9_0 = relation_rng(esk10_0)
| in(esk5_2(esk9_0,relation_rng(esk10_0)),relation_rng(esk10_0)) ),
inference(ef,[status(thm)],[656,theory(equality)]) ).
cnf(4814,negated_conjecture,
( esk9_0 = relation_rng(esk10_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| ~ in(esk5_2(esk9_0,relation_rng(esk10_0)),esk9_0) ),
inference(spm,[status(thm)],[78,4748,theory(equality)]) ).
cnf(4819,negated_conjecture,
( element(esk5_2(esk9_0,relation_rng(esk10_0)),esk9_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| relation_rng(esk10_0) = esk9_0 ),
inference(spm,[status(thm)],[917,4748,theory(equality)]) ).
cnf(4843,negated_conjecture,
( empty(esk9_0)
| in(esk5_2(esk9_0,relation_rng(esk10_0)),esk9_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| relation_rng(esk10_0) = esk9_0 ),
inference(spm,[status(thm)],[115,4819,theory(equality)]) ).
cnf(4846,negated_conjecture,
( in(esk5_2(esk9_0,relation_rng(esk10_0)),esk9_0)
| relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| relation_rng(esk10_0) = esk9_0 ),
inference(sr,[status(thm)],[4843,596,theory(equality)]) ).
cnf(5326,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) = esk9_0
| relation_rng(esk10_0) = esk9_0 ),
inference(csr,[status(thm)],[4814,4846]) ).
cnf(5327,negated_conjecture,
( in(esk11_0,esk9_0)
| relation_rng(esk10_0) = esk9_0 ),
inference(spm,[status(thm)],[105,5326,theory(equality)]) ).
cnf(5328,negated_conjecture,
( esk9_0 = relation_rng(esk10_0)
| ~ relation_of2(esk10_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[144,5326,theory(equality)]) ).
cnf(5341,negated_conjecture,
in(esk11_0,esk9_0),
inference(csr,[status(thm)],[5327,291]) ).
cnf(5378,negated_conjecture,
( relation_rng(esk10_0) = esk9_0
| ~ relation_of2_as_subset(esk10_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[5328,98,theory(equality)]) ).
cnf(5379,negated_conjecture,
( relation_rng(esk10_0) = esk9_0
| $false ),
inference(rw,[status(thm)],[5378,104,theory(equality)]) ).
cnf(5380,negated_conjecture,
relation_rng(esk10_0) = esk9_0,
inference(cn,[status(thm)],[5379,theory(equality)]) ).
cnf(5493,negated_conjecture,
( relation_rng_as_subset(esk8_0,esk9_0,esk10_0) != esk9_0
| esk9_0 != X1
| ~ in(esk11_0,X1) ),
inference(rw,[status(thm)],[427,5380,theory(equality)]) ).
cnf(5700,negated_conjecture,
( relation_rng(esk10_0) != esk9_0
| esk9_0 != X1
| ~ in(esk11_0,X1)
| ~ relation_of2(esk10_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[5493,144,theory(equality)]) ).
cnf(5704,negated_conjecture,
( $false
| esk9_0 != X1
| ~ in(esk11_0,X1)
| ~ relation_of2(esk10_0,esk8_0,esk9_0) ),
inference(rw,[status(thm)],[5700,5380,theory(equality)]) ).
cnf(5705,negated_conjecture,
( esk9_0 != X1
| ~ in(esk11_0,X1)
| ~ relation_of2(esk10_0,esk8_0,esk9_0) ),
inference(cn,[status(thm)],[5704,theory(equality)]) ).
cnf(5711,negated_conjecture,
( esk9_0 != X1
| ~ in(esk11_0,X1)
| ~ relation_of2_as_subset(esk10_0,esk8_0,esk9_0) ),
inference(spm,[status(thm)],[5705,98,theory(equality)]) ).
cnf(5712,negated_conjecture,
( esk9_0 != X1
| ~ in(esk11_0,X1)
| $false ),
inference(rw,[status(thm)],[5711,104,theory(equality)]) ).
cnf(5713,negated_conjecture,
( esk9_0 != X1
| ~ in(esk11_0,X1) ),
inference(cn,[status(thm)],[5712,theory(equality)]) ).
cnf(5714,negated_conjecture,
$false,
inference(spm,[status(thm)],[5713,5341,theory(equality)]) ).
cnf(5723,negated_conjecture,
$false,
5714,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU266+1.p
% --creating new selector for []
% -running prover on /tmp/tmpSeZFvs/sel_SEU266+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU266+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU266+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU266+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
%
%------------------------------------------------------------------------------