TSTP Solution File: NUM409+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM409+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n042.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 15:21:15 EST 2018
% Result : Theorem 0.07s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 102 ( 32 unt; 0 def)
% Number of atoms : 320 ( 14 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 376 ( 158 ~; 165 |; 41 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 170 ( 23 sgn 83 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t5_subset) ).
fof(10,axiom,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ( relation(X2)
& function(X2)
& transfinite_sequence(X2) ) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',dt_m1_ordinal1) ).
fof(12,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',fc2_ordinal1) ).
fof(20,axiom,
! [X1,X2] : equal(unordered_pair(X1,X2),unordered_pair(X2,X1)),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',commutativity_k2_tarski) ).
fof(21,axiom,
! [X1] :
? [X2] : transfinite_sequence_of(X2,X1),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',existence_m1_ordinal1) ).
fof(30,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( equal(X2,relation_dom(X1))
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',d4_relat_1) ).
fof(33,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',fc6_relat_1) ).
fof(34,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t3_subset) ).
fof(36,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',d8_ordinal1) ).
fof(38,axiom,
! [X1,X2] : equal(ordered_pair(X1,X2),unordered_pair(unordered_pair(X1,X2),singleton(X1))),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',d5_tarski) ).
fof(39,axiom,
! [X1] :
( empty(X1)
=> equal(X1,empty_set) ),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t6_boole) ).
fof(44,conjecture,
! [X1] : transfinite_sequence_of(empty_set,X1),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t45_ordinal1) ).
fof(51,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1',t2_xboole_1) ).
fof(52,negated_conjecture,
~ ! [X1] : transfinite_sequence_of(empty_set,X1),
inference(assume_negation,[status(cth)],[44]) ).
fof(58,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[33,theory(equality)]) ).
fof(73,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(74,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[73]) ).
cnf(75,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(100,plain,
! [X1,X2] :
( ~ transfinite_sequence_of(X2,X1)
| ( relation(X2)
& function(X2)
& transfinite_sequence(X2) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(101,plain,
! [X3,X4] :
( ~ transfinite_sequence_of(X4,X3)
| ( relation(X4)
& function(X4)
& transfinite_sequence(X4) ) ),
inference(variable_rename,[status(thm)],[100]) ).
fof(102,plain,
! [X3,X4] :
( ( relation(X4)
| ~ transfinite_sequence_of(X4,X3) )
& ( function(X4)
| ~ transfinite_sequence_of(X4,X3) )
& ( transfinite_sequence(X4)
| ~ transfinite_sequence_of(X4,X3) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(103,plain,
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(104,plain,
( function(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(105,plain,
( relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(112,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(116,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[12]) ).
fof(143,plain,
! [X3,X4] : equal(unordered_pair(X3,X4),unordered_pair(X4,X3)),
inference(variable_rename,[status(thm)],[20]) ).
cnf(144,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[143]) ).
fof(145,plain,
! [X3] :
? [X4] : transfinite_sequence_of(X4,X3),
inference(variable_rename,[status(thm)],[21]) ).
fof(146,plain,
! [X3] : transfinite_sequence_of(esk8_1(X3),X3),
inference(skolemize,[status(esa)],[145]) ).
cnf(147,plain,
transfinite_sequence_of(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[146]) ).
fof(177,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( ~ equal(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) ) )
| equal(X2,relation_dom(X1)) ) ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(178,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( ~ equal(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) ) )
| equal(X6,relation_dom(X5)) ) ) ),
inference(variable_rename,[status(thm)],[177]) ).
fof(179,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( ~ equal(X6,relation_dom(X5))
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk9_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk10_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk10_2(X5,X6),X11),X5) )
& ( in(esk10_2(X5,X6),X6)
| in(ordered_pair(esk10_2(X5,X6),esk11_2(X5,X6)),X5) ) )
| equal(X6,relation_dom(X5)) ) ) ),
inference(skolemize,[status(esa)],[178]) ).
fof(180,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk10_2(X5,X6),X11),X5)
| ~ in(esk10_2(X5,X6),X6) )
& ( in(esk10_2(X5,X6),X6)
| in(ordered_pair(esk10_2(X5,X6),esk11_2(X5,X6)),X5) ) )
| equal(X6,relation_dom(X5)) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk9_3(X5,X6,X7)),X5) ) )
| ~ equal(X6,relation_dom(X5)) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[179]) ).
fof(181,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk10_2(X5,X6),X11),X5)
| ~ in(esk10_2(X5,X6),X6)
| equal(X6,relation_dom(X5))
| ~ relation(X5) )
& ( in(esk10_2(X5,X6),X6)
| in(ordered_pair(esk10_2(X5,X6),esk11_2(X5,X6)),X5)
| equal(X6,relation_dom(X5))
| ~ relation(X5) )
& ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6)
| ~ equal(X6,relation_dom(X5))
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk9_3(X5,X6,X7)),X5)
| ~ equal(X6,relation_dom(X5))
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[180]) ).
cnf(184,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk10_2(X1,X2),esk11_2(X1,X2)),X1)
| in(esk10_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[181]) ).
fof(194,plain,
! [X1] :
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ),
inference(fof_nnf,[status(thm)],[58]) ).
fof(195,plain,
! [X2] :
( empty(X2)
| ~ relation(X2)
| ~ empty(relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[194]) ).
cnf(196,plain,
( empty(X1)
| ~ empty(relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[195]) ).
fof(197,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(198,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[197]) ).
cnf(199,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[198]) ).
fof(204,plain,
! [X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| ~ transfinite_sequence(X2)
| ( ( ~ transfinite_sequence_of(X2,X1)
| subset(relation_rng(X2),X1) )
& ( ~ subset(relation_rng(X2),X1)
| transfinite_sequence_of(X2,X1) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(205,plain,
! [X3,X4] :
( ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4)
| ( ( ~ transfinite_sequence_of(X4,X3)
| subset(relation_rng(X4),X3) )
& ( ~ subset(relation_rng(X4),X3)
| transfinite_sequence_of(X4,X3) ) ) ),
inference(variable_rename,[status(thm)],[204]) ).
fof(206,plain,
! [X3,X4] :
( ( ~ transfinite_sequence_of(X4,X3)
| subset(relation_rng(X4),X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) )
& ( ~ subset(relation_rng(X4),X3)
| transfinite_sequence_of(X4,X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) ) ),
inference(distribute,[status(thm)],[205]) ).
cnf(207,plain,
( transfinite_sequence_of(X1,X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[206]) ).
cnf(208,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[206]) ).
fof(212,plain,
! [X3,X4] : equal(ordered_pair(X3,X4),unordered_pair(unordered_pair(X3,X4),singleton(X3))),
inference(variable_rename,[status(thm)],[38]) ).
cnf(213,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[212]) ).
fof(214,plain,
! [X1] :
( ~ empty(X1)
| equal(X1,empty_set) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(215,plain,
! [X2] :
( ~ empty(X2)
| equal(X2,empty_set) ),
inference(variable_rename,[status(thm)],[214]) ).
cnf(216,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[215]) ).
fof(233,negated_conjecture,
? [X1] : ~ transfinite_sequence_of(empty_set,X1),
inference(fof_nnf,[status(thm)],[52]) ).
fof(234,negated_conjecture,
? [X2] : ~ transfinite_sequence_of(empty_set,X2),
inference(variable_rename,[status(thm)],[233]) ).
fof(235,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk15_0),
inference(skolemize,[status(esa)],[234]) ).
cnf(236,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk15_0),
inference(split_conjunct,[status(thm)],[235]) ).
fof(262,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[51]) ).
cnf(263,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[262]) ).
cnf(264,plain,
( relation_dom(X1) = X2
| in(esk10_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk10_2(X1,X2),esk11_2(X1,X2)),singleton(esk10_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[184,213,theory(equality)]),
[unfolding] ).
cnf(279,plain,
relation(esk8_1(X1)),
inference(spm,[status(thm)],[105,147,theory(equality)]) ).
cnf(280,plain,
function(esk8_1(X1)),
inference(spm,[status(thm)],[104,147,theory(equality)]) ).
cnf(281,plain,
transfinite_sequence(esk8_1(X1)),
inference(spm,[status(thm)],[103,147,theory(equality)]) ).
cnf(334,plain,
( ~ empty(X2)
| ~ in(X3,X1)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[75,199,theory(equality)]) ).
cnf(340,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[208,103]) ).
cnf(341,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[340,104]) ).
cnf(342,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2) ),
inference(csr,[status(thm)],[341,105]) ).
cnf(361,plain,
( relation_dom(X1) = X2
| in(esk10_2(X1,X2),X2)
| in(unordered_pair(singleton(esk10_2(X1,X2)),unordered_pair(esk10_2(X1,X2),esk11_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[264,144,theory(equality)]) ).
cnf(366,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[334,263,theory(equality)]) ).
cnf(368,plain,
( ~ empty(X2)
| ~ in(X3,relation_rng(X1))
| ~ transfinite_sequence_of(X1,X2) ),
inference(spm,[status(thm)],[334,342,theory(equality)]) ).
fof(369,plain,
( ~ epred1_0
<=> ! [X1] : ~ empty(X1) ),
introduced(definition),
[split] ).
cnf(370,plain,
( epred1_0
| ~ empty(X1) ),
inference(split_equiv,[status(thm)],[369]) ).
fof(371,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition),
[split] ).
cnf(372,plain,
( epred2_0
| ~ in(X2,empty_set) ),
inference(split_equiv,[status(thm)],[371]) ).
cnf(373,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[366,369,theory(equality)]),371,theory(equality)]),
[split] ).
cnf(400,plain,
epred1_0,
inference(spm,[status(thm)],[370,112,theory(equality)]) ).
cnf(404,plain,
( ~ epred2_0
| $false ),
inference(rw,[status(thm)],[373,400,theory(equality)]) ).
cnf(405,plain,
~ epred2_0,
inference(cn,[status(thm)],[404,theory(equality)]) ).
cnf(406,plain,
~ in(X2,empty_set),
inference(sr,[status(thm)],[372,405,theory(equality)]) ).
cnf(408,plain,
( relation_dom(empty_set) = X1
| in(esk10_2(empty_set,X1),X1)
| ~ relation(empty_set) ),
inference(spm,[status(thm)],[406,361,theory(equality)]) ).
cnf(411,plain,
( relation_dom(empty_set) = X1
| in(esk10_2(empty_set,X1),X1)
| $false ),
inference(rw,[status(thm)],[408,116,theory(equality)]) ).
cnf(412,plain,
( relation_dom(empty_set) = X1
| in(esk10_2(empty_set,X1),X1) ),
inference(cn,[status(thm)],[411,theory(equality)]) ).
cnf(425,plain,
relation_dom(empty_set) = empty_set,
inference(spm,[status(thm)],[406,412,theory(equality)]) ).
cnf(434,plain,
( empty_set = X1
| in(esk10_2(empty_set,X1),X1) ),
inference(rw,[status(thm)],[412,425,theory(equality)]) ).
cnf(677,plain,
( empty_set = relation_rng(X1)
| ~ transfinite_sequence_of(X1,X2)
| ~ empty(X2) ),
inference(spm,[status(thm)],[368,434,theory(equality)]) ).
cnf(681,plain,
( relation_rng(esk8_1(X1)) = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[677,147,theory(equality)]) ).
cnf(685,plain,
( empty(esk8_1(X1))
| ~ relation(esk8_1(X1))
| ~ empty(empty_set)
| ~ empty(X1) ),
inference(spm,[status(thm)],[196,681,theory(equality)]) ).
cnf(688,plain,
( transfinite_sequence_of(esk8_1(X1),X2)
| ~ subset(empty_set,X2)
| ~ transfinite_sequence(esk8_1(X1))
| ~ function(esk8_1(X1))
| ~ relation(esk8_1(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[207,681,theory(equality)]) ).
cnf(698,plain,
( empty(esk8_1(X1))
| $false
| ~ empty(empty_set)
| ~ empty(X1) ),
inference(rw,[status(thm)],[685,279,theory(equality)]) ).
cnf(699,plain,
( empty(esk8_1(X1))
| $false
| $false
| ~ empty(X1) ),
inference(rw,[status(thm)],[698,112,theory(equality)]) ).
cnf(700,plain,
( empty(esk8_1(X1))
| ~ empty(X1) ),
inference(cn,[status(thm)],[699,theory(equality)]) ).
cnf(705,plain,
( transfinite_sequence_of(esk8_1(X1),X2)
| $false
| ~ transfinite_sequence(esk8_1(X1))
| ~ function(esk8_1(X1))
| ~ relation(esk8_1(X1))
| ~ empty(X1) ),
inference(rw,[status(thm)],[688,263,theory(equality)]) ).
cnf(706,plain,
( transfinite_sequence_of(esk8_1(X1),X2)
| $false
| $false
| ~ function(esk8_1(X1))
| ~ relation(esk8_1(X1))
| ~ empty(X1) ),
inference(rw,[status(thm)],[705,281,theory(equality)]) ).
cnf(707,plain,
( transfinite_sequence_of(esk8_1(X1),X2)
| $false
| $false
| $false
| ~ relation(esk8_1(X1))
| ~ empty(X1) ),
inference(rw,[status(thm)],[706,280,theory(equality)]) ).
cnf(708,plain,
( transfinite_sequence_of(esk8_1(X1),X2)
| $false
| $false
| $false
| $false
| ~ empty(X1) ),
inference(rw,[status(thm)],[707,279,theory(equality)]) ).
cnf(709,plain,
( transfinite_sequence_of(esk8_1(X1),X2)
| ~ empty(X1) ),
inference(cn,[status(thm)],[708,theory(equality)]) ).
cnf(719,plain,
( empty_set = esk8_1(X1)
| ~ empty(X1) ),
inference(spm,[status(thm)],[216,700,theory(equality)]) ).
cnf(729,plain,
( transfinite_sequence_of(empty_set,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[709,719,theory(equality)]) ).
cnf(749,plain,
transfinite_sequence_of(empty_set,X1),
inference(spm,[status(thm)],[729,112,theory(equality)]) ).
cnf(759,negated_conjecture,
$false,
inference(rw,[status(thm)],[236,749,theory(equality)]) ).
cnf(760,negated_conjecture,
$false,
inference(cn,[status(thm)],[759,theory(equality)]) ).
cnf(761,negated_conjecture,
$false,
760,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM409+1 : TPTP v7.0.0. Released v3.2.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.03/0.23 % Computer : n042.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 02:47:30 CST 2018
% 0.03/0.23 % CPUTime :
% 0.03/0.28 % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.28 --creating new selector for []
% 0.07/0.36 -running prover on /export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1 with time limit 29
% 0.07/0.36 -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpyMnON0/sel_theBenchmark.p_1']
% 0.07/0.36 -prover status Theorem
% 0.07/0.36 Problem theBenchmark.p solved in phase 0.
% 0.07/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 Solved 1 out of 1.
% 0.07/0.36 # Problem is unsatisfiable (or provable), constructing proof object
% 0.07/0.36 # SZS status Theorem
% 0.07/0.36 # SZS output start CNFRefutation.
% See solution above
% 0.07/0.36 # SZS output end CNFRefutation
%------------------------------------------------------------------------------