TSTP Solution File: NUM390+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM390+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n138.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 15:21:14 EST 2018
% Result : Theorem 0.06s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 16 unt; 0 def)
% Number of atoms : 258 ( 7 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 286 ( 112 ~; 110 |; 45 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 135 ( 4 sgn 87 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',cc1_ordinal1) ).
fof(3,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t1_xboole_1) ).
fof(4,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t5_subset) ).
fof(9,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',reflexivity_r1_tarski) ).
fof(12,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t4_subset) ).
fof(15,conjecture,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( subset(X1,X2)
& in(X2,X3) )
=> in(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t22_ordinal1) ).
fof(17,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',d2_ordinal1) ).
fof(23,axiom,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t21_ordinal1) ).
fof(24,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t2_subset) ).
fof(25,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t3_subset) ).
fof(26,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& ~ equal(X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',d8_xboole_0) ).
fof(38,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& subset(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t7_ordinal1) ).
fof(39,negated_conjecture,
~ ! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( subset(X1,X2)
& in(X2,X3) )
=> in(X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[15]) ).
fof(50,plain,
! [X1] :
( ~ ordinal(X1)
| ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(51,plain,
! [X2] :
( ~ ordinal(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(54,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(55,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X2,X3)
| subset(X1,X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(56,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[55]) ).
cnf(57,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(58,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(59,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[58]) ).
cnf(60,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(74,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[9]) ).
cnf(75,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[74]) ).
fof(83,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(84,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[83]) ).
cnf(85,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[84]) ).
fof(94,negated_conjecture,
? [X1] :
( epsilon_transitive(X1)
& ? [X2] :
( ordinal(X2)
& ? [X3] :
( ordinal(X3)
& subset(X1,X2)
& in(X2,X3)
& ~ in(X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(95,negated_conjecture,
? [X4] :
( epsilon_transitive(X4)
& ? [X5] :
( ordinal(X5)
& ? [X6] :
( ordinal(X6)
& subset(X4,X5)
& in(X5,X6)
& ~ in(X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[94]) ).
fof(96,negated_conjecture,
( epsilon_transitive(esk6_0)
& ordinal(esk7_0)
& ordinal(esk8_0)
& subset(esk6_0,esk7_0)
& in(esk7_0,esk8_0)
& ~ in(esk6_0,esk8_0) ),
inference(skolemize,[status(esa)],[95]) ).
cnf(97,negated_conjecture,
~ in(esk6_0,esk8_0),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(98,negated_conjecture,
in(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(99,negated_conjecture,
subset(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(100,negated_conjecture,
ordinal(esk8_0),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(102,negated_conjecture,
epsilon_transitive(esk6_0),
inference(split_conjunct,[status(thm)],[96]) ).
fof(106,plain,
! [X1] :
( ( ~ epsilon_transitive(X1)
| ! [X2] :
( ~ in(X2,X1)
| subset(X2,X1) ) )
& ( ? [X2] :
( in(X2,X1)
& ~ subset(X2,X1) )
| epsilon_transitive(X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(107,plain,
! [X3] :
( ( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ in(X4,X3)
| subset(X4,X3) ) )
& ( ? [X5] :
( in(X5,X3)
& ~ subset(X5,X3) )
| epsilon_transitive(X3) ) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,plain,
! [X3] :
( ( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ in(X4,X3)
| subset(X4,X3) ) )
& ( ( in(esk9_1(X3),X3)
& ~ subset(esk9_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(skolemize,[status(esa)],[107]) ).
fof(109,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( ( in(esk9_1(X3),X3)
& ~ subset(esk9_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(shift_quantors,[status(thm)],[108]) ).
fof(110,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( in(esk9_1(X3),X3)
| epsilon_transitive(X3) )
& ( ~ subset(esk9_1(X3),X3)
| epsilon_transitive(X3) ) ),
inference(distribute,[status(thm)],[109]) ).
cnf(113,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[110]) ).
fof(132,plain,
! [X1] :
( ~ epsilon_transitive(X1)
| ! [X2] :
( ~ ordinal(X2)
| ~ proper_subset(X1,X2)
| in(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(133,plain,
! [X3] :
( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ ordinal(X4)
| ~ proper_subset(X3,X4)
| in(X3,X4) ) ),
inference(variable_rename,[status(thm)],[132]) ).
fof(134,plain,
! [X3,X4] :
( ~ ordinal(X4)
| ~ proper_subset(X3,X4)
| in(X3,X4)
| ~ epsilon_transitive(X3) ),
inference(shift_quantors,[status(thm)],[133]) ).
cnf(135,plain,
( in(X1,X2)
| ~ epsilon_transitive(X1)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[134]) ).
fof(136,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(137,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[136]) ).
cnf(138,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[137]) ).
fof(139,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(140,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[139]) ).
cnf(141,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[140]) ).
fof(143,plain,
! [X1,X2] :
( ( ~ proper_subset(X1,X2)
| ( subset(X1,X2)
& ~ equal(X1,X2) ) )
& ( ~ subset(X1,X2)
| equal(X1,X2)
| proper_subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(144,plain,
! [X3,X4] :
( ( ~ proper_subset(X3,X4)
| ( subset(X3,X4)
& ~ equal(X3,X4) ) )
& ( ~ subset(X3,X4)
| equal(X3,X4)
| proper_subset(X3,X4) ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ proper_subset(X3,X4) )
& ( ~ equal(X3,X4)
| ~ proper_subset(X3,X4) )
& ( ~ subset(X3,X4)
| equal(X3,X4)
| proper_subset(X3,X4) ) ),
inference(distribute,[status(thm)],[144]) ).
cnf(146,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(186,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ subset(X2,X1) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(187,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ subset(X4,X3) ),
inference(variable_rename,[status(thm)],[186]) ).
cnf(188,plain,
( ~ subset(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(190,negated_conjecture,
epsilon_transitive(esk8_0),
inference(spm,[status(thm)],[54,100,theory(equality)]) ).
cnf(200,plain,
~ in(X1,X1),
inference(spm,[status(thm)],[188,75,theory(equality)]) ).
cnf(217,negated_conjecture,
( subset(X1,esk7_0)
| ~ subset(X1,esk6_0) ),
inference(spm,[status(thm)],[57,99,theory(equality)]) ).
cnf(232,plain,
( in(X1,X2)
| X1 = X2
| ~ ordinal(X2)
| ~ epsilon_transitive(X1)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[135,146,theory(equality)]) ).
cnf(235,plain,
( ~ empty(X1)
| ~ in(X3,X2)
| ~ subset(X2,X1) ),
inference(spm,[status(thm)],[60,141,theory(equality)]) ).
cnf(238,plain,
( element(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(spm,[status(thm)],[85,141,theory(equality)]) ).
cnf(240,negated_conjecture,
( subset(X1,esk8_0)
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[113,190,theory(equality)]) ).
cnf(270,negated_conjecture,
( subset(X1,esk8_0)
| ~ subset(X1,X2)
| ~ in(X2,esk8_0) ),
inference(spm,[status(thm)],[57,240,theory(equality)]) ).
cnf(321,negated_conjecture,
( ~ empty(X1)
| ~ subset(esk8_0,X1) ),
inference(spm,[status(thm)],[235,98,theory(equality)]) ).
cnf(441,negated_conjecture,
( element(esk7_0,X1)
| ~ subset(esk8_0,X1) ),
inference(spm,[status(thm)],[238,98,theory(equality)]) ).
cnf(457,negated_conjecture,
( empty(X1)
| in(esk7_0,X1)
| ~ subset(esk8_0,X1) ),
inference(spm,[status(thm)],[138,441,theory(equality)]) ).
cnf(460,negated_conjecture,
( in(esk7_0,X1)
| ~ subset(esk8_0,X1) ),
inference(csr,[status(thm)],[457,321]) ).
cnf(463,negated_conjecture,
( in(esk7_0,esk7_0)
| ~ subset(esk8_0,esk6_0) ),
inference(spm,[status(thm)],[460,217,theory(equality)]) ).
cnf(470,negated_conjecture,
~ subset(esk8_0,esk6_0),
inference(sr,[status(thm)],[463,200,theory(equality)]) ).
cnf(492,negated_conjecture,
( subset(esk6_0,esk8_0)
| ~ in(esk7_0,esk8_0) ),
inference(spm,[status(thm)],[270,99,theory(equality)]) ).
cnf(501,negated_conjecture,
( subset(esk6_0,esk8_0)
| $false ),
inference(rw,[status(thm)],[492,98,theory(equality)]) ).
cnf(502,negated_conjecture,
subset(esk6_0,esk8_0),
inference(cn,[status(thm)],[501,theory(equality)]) ).
cnf(516,negated_conjecture,
( esk6_0 = esk8_0
| in(esk6_0,esk8_0)
| ~ ordinal(esk8_0)
| ~ epsilon_transitive(esk6_0) ),
inference(spm,[status(thm)],[232,502,theory(equality)]) ).
cnf(522,negated_conjecture,
( esk6_0 = esk8_0
| in(esk6_0,esk8_0)
| $false
| ~ epsilon_transitive(esk6_0) ),
inference(rw,[status(thm)],[516,100,theory(equality)]) ).
cnf(523,negated_conjecture,
( esk6_0 = esk8_0
| in(esk6_0,esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[522,102,theory(equality)]) ).
cnf(524,negated_conjecture,
( esk6_0 = esk8_0
| in(esk6_0,esk8_0) ),
inference(cn,[status(thm)],[523,theory(equality)]) ).
cnf(525,negated_conjecture,
esk8_0 = esk6_0,
inference(sr,[status(thm)],[524,97,theory(equality)]) ).
cnf(535,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[470,525,theory(equality)]),75,theory(equality)]) ).
cnf(536,negated_conjecture,
$false,
inference(cn,[status(thm)],[535,theory(equality)]) ).
cnf(537,negated_conjecture,
$false,
536,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM390+1 : TPTP v7.0.0. Released v3.2.0.
% 0.00/0.03 % Command : Source/sine.py -e eprover -t %d %s
% 0.02/0.22 % Computer : n138.star.cs.uiowa.edu
% 0.02/0.22 % Model : x86_64 x86_64
% 0.02/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.22 % Memory : 32218.625MB
% 0.02/0.22 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.22 % CPULimit : 300
% 0.02/0.22 % DateTime : Fri Jan 5 02:37:15 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.27 % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.27 --creating new selector for []
% 0.06/0.34 -running prover on /export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1 with time limit 29
% 0.06/0.34 -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/tmp8vNz0_/sel_theBenchmark.p_1']
% 0.06/0.34 -prover status Theorem
% 0.06/0.34 Problem theBenchmark.p solved in phase 0.
% 0.06/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.34 % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.34 Solved 1 out of 1.
% 0.06/0.34 # Problem is unsatisfiable (or provable), constructing proof object
% 0.06/0.34 # SZS status Theorem
% 0.06/0.34 # SZS output start CNFRefutation.
% See solution above
% 0.06/0.34 # SZS output end CNFRefutation
%------------------------------------------------------------------------------