TSTP Solution File: NUM404+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM404+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n100.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 91.73s
% Output : CNFRefutation 91.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 8 unt; 0 def)
% Number of atoms : 307 ( 8 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 368 ( 137 ~; 147 |; 67 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 86 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& ~ equal(X2,X3)
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',d3_ordinal1) ).
fof(3,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',t23_ordinal1) ).
fof(11,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',d4_ordinal1) ).
fof(19,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',d2_ordinal1) ).
fof(21,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',antisymmetry_r2_hidden) ).
fof(27,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& ~ equal(X1,X2)
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',t24_ordinal1) ).
fof(32,conjecture,
! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',t37_ordinal1) ).
fof(40,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2',d3_tarski) ).
fof(42,negated_conjecture,
~ ! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
inference(assume_negation,[status(cth)],[32]) ).
fof(43,plain,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& ~ equal(X2,X3)
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(46,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[21,theory(equality)]) ).
fof(47,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& ~ equal(X1,X2)
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).
fof(49,plain,
! [X1] :
( ( ~ epsilon_connected(X1)
| ! [X2,X3] :
( ~ in(X2,X1)
| ~ in(X3,X1)
| in(X2,X3)
| equal(X2,X3)
| in(X3,X2) ) )
& ( ? [X2,X3] :
( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& ~ equal(X2,X3)
& ~ in(X3,X2) )
| epsilon_connected(X1) ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(50,plain,
! [X4] :
( ( ~ epsilon_connected(X4)
| ! [X5,X6] :
( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| equal(X5,X6)
| in(X6,X5) ) )
& ( ? [X7,X8] :
( in(X7,X4)
& in(X8,X4)
& ~ in(X7,X8)
& ~ equal(X7,X8)
& ~ in(X8,X7) )
| epsilon_connected(X4) ) ),
inference(variable_rename,[status(thm)],[49]) ).
fof(51,plain,
! [X4] :
( ( ~ epsilon_connected(X4)
| ! [X5,X6] :
( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| equal(X5,X6)
| in(X6,X5) ) )
& ( ( in(esk1_1(X4),X4)
& in(esk2_1(X4),X4)
& ~ in(esk1_1(X4),esk2_1(X4))
& ~ equal(esk1_1(X4),esk2_1(X4))
& ~ in(esk2_1(X4),esk1_1(X4)) )
| epsilon_connected(X4) ) ),
inference(skolemize,[status(esa)],[50]) ).
fof(52,plain,
! [X4,X5,X6] :
( ( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| equal(X5,X6)
| in(X6,X5)
| ~ epsilon_connected(X4) )
& ( ( in(esk1_1(X4),X4)
& in(esk2_1(X4),X4)
& ~ in(esk1_1(X4),esk2_1(X4))
& ~ equal(esk1_1(X4),esk2_1(X4))
& ~ in(esk2_1(X4),esk1_1(X4)) )
| epsilon_connected(X4) ) ),
inference(shift_quantors,[status(thm)],[51]) ).
fof(53,plain,
! [X4,X5,X6] :
( ( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| equal(X5,X6)
| in(X6,X5)
| ~ epsilon_connected(X4) )
& ( in(esk1_1(X4),X4)
| epsilon_connected(X4) )
& ( in(esk2_1(X4),X4)
| epsilon_connected(X4) )
& ( ~ in(esk1_1(X4),esk2_1(X4))
| epsilon_connected(X4) )
& ( ~ equal(esk1_1(X4),esk2_1(X4))
| epsilon_connected(X4) )
& ( ~ in(esk2_1(X4),esk1_1(X4))
| epsilon_connected(X4) ) ),
inference(distribute,[status(thm)],[52]) ).
cnf(54,plain,
( epsilon_connected(X1)
| ~ in(esk2_1(X1),esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,plain,
( epsilon_connected(X1)
| esk1_1(X1) != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,plain,
( epsilon_connected(X1)
| ~ in(esk1_1(X1),esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(57,plain,
( epsilon_connected(X1)
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(58,plain,
( epsilon_connected(X1)
| in(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(63,plain,
! [X1,X2] :
( ~ ordinal(X2)
| ~ in(X1,X2)
| ordinal(X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(64,plain,
! [X3,X4] :
( ~ ordinal(X4)
| ~ in(X3,X4)
| ordinal(X3) ),
inference(variable_rename,[status(thm)],[63]) ).
cnf(65,plain,
( ordinal(X1)
| ~ in(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(99,plain,
! [X1] :
( ( ~ ordinal(X1)
| ( epsilon_transitive(X1)
& epsilon_connected(X1) ) )
& ( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(100,plain,
! [X2] :
( ( ~ ordinal(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) )
& ( ~ epsilon_transitive(X2)
| ~ epsilon_connected(X2)
| ordinal(X2) ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ ordinal(X2) )
& ( ~ epsilon_transitive(X2)
| ~ epsilon_connected(X2)
| ordinal(X2) ) ),
inference(distribute,[status(thm)],[100]) ).
cnf(102,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(137,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)],[19]) ).
fof(138,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)],[137]) ).
fof(139,plain,
! [X3] :
( ( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ in(X4,X3)
| subset(X4,X3) ) )
& ( ( in(esk11_1(X3),X3)
& ~ subset(esk11_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(skolemize,[status(esa)],[138]) ).
fof(140,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( ( in(esk11_1(X3),X3)
& ~ subset(esk11_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(shift_quantors,[status(thm)],[139]) ).
fof(141,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( in(esk11_1(X3),X3)
| epsilon_transitive(X3) )
& ( ~ subset(esk11_1(X3),X3)
| epsilon_transitive(X3) ) ),
inference(distribute,[status(thm)],[140]) ).
cnf(142,plain,
( epsilon_transitive(X1)
| ~ subset(esk11_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(143,plain,
( epsilon_transitive(X1)
| in(esk11_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[141]) ).
fof(147,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(148,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[147]) ).
cnf(149,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[148]) ).
fof(169,plain,
! [X1] :
( ~ ordinal(X1)
| ! [X2] :
( ~ ordinal(X2)
| in(X1,X2)
| equal(X1,X2)
| in(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(170,plain,
! [X3] :
( ~ ordinal(X3)
| ! [X4] :
( ~ ordinal(X4)
| in(X3,X4)
| equal(X3,X4)
| in(X4,X3) ) ),
inference(variable_rename,[status(thm)],[169]) ).
fof(171,plain,
! [X3,X4] :
( ~ ordinal(X4)
| in(X3,X4)
| equal(X3,X4)
| in(X4,X3)
| ~ ordinal(X3) ),
inference(shift_quantors,[status(thm)],[170]) ).
cnf(172,plain,
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[171]) ).
fof(188,negated_conjecture,
? [X1] :
! [X2] :
( ( ~ in(X2,X1)
| ordinal(X2) )
& ( ~ ordinal(X2)
| in(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(189,negated_conjecture,
? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ordinal(X4) )
& ( ~ ordinal(X4)
| in(X4,X3) ) ),
inference(variable_rename,[status(thm)],[188]) ).
fof(190,negated_conjecture,
! [X4] :
( ( ~ in(X4,esk13_0)
| ordinal(X4) )
& ( ~ ordinal(X4)
| in(X4,esk13_0) ) ),
inference(skolemize,[status(esa)],[189]) ).
cnf(191,negated_conjecture,
( in(X1,esk13_0)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(192,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[190]) ).
fof(216,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(217,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[216]) ).
fof(218,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk18_2(X4,X5),X4)
& ~ in(esk18_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[217]) ).
fof(219,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk18_2(X4,X5),X4)
& ~ in(esk18_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[218]) ).
fof(220,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk18_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk18_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[219]) ).
cnf(221,plain,
( subset(X1,X2)
| ~ in(esk18_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[220]) ).
cnf(222,plain,
( subset(X1,X2)
| in(esk18_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[220]) ).
cnf(282,negated_conjecture,
( X1 = X2
| in(X1,X2)
| in(X2,X1)
| ~ ordinal(X1)
| ~ in(X2,esk13_0) ),
inference(spm,[status(thm)],[172,192,theory(equality)]) ).
cnf(286,plain,
( ordinal(esk18_2(X1,X2))
| subset(X1,X2)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[65,222,theory(equality)]) ).
cnf(516,negated_conjecture,
( X1 = esk1_1(esk13_0)
| in(esk1_1(esk13_0),X1)
| in(X1,esk1_1(esk13_0))
| epsilon_connected(esk13_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[282,58,theory(equality)]) ).
cnf(560,negated_conjecture,
( in(esk18_2(X1,X2),esk13_0)
| subset(X1,X2)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[191,286,theory(equality)]) ).
cnf(1415,negated_conjecture,
( X1 = esk1_1(esk13_0)
| in(X1,esk1_1(esk13_0))
| in(esk1_1(esk13_0),X1)
| epsilon_connected(esk13_0)
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[516,192,theory(equality)]) ).
cnf(1611,negated_conjecture,
( subset(X1,esk13_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[221,560,theory(equality)]) ).
cnf(1629,negated_conjecture,
( epsilon_transitive(esk13_0)
| ~ ordinal(esk11_1(esk13_0)) ),
inference(spm,[status(thm)],[142,1611,theory(equality)]) ).
cnf(1633,negated_conjecture,
( epsilon_transitive(esk13_0)
| ~ in(esk11_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[1629,192,theory(equality)]) ).
cnf(1713,negated_conjecture,
epsilon_transitive(esk13_0),
inference(csr,[status(thm)],[1633,143]) ).
cnf(1714,negated_conjecture,
( ordinal(esk13_0)
| ~ epsilon_connected(esk13_0) ),
inference(spm,[status(thm)],[102,1713,theory(equality)]) ).
cnf(20281,negated_conjecture,
( esk2_1(esk13_0) = esk1_1(esk13_0)
| in(esk1_1(esk13_0),esk2_1(esk13_0))
| in(esk2_1(esk13_0),esk1_1(esk13_0))
| epsilon_connected(esk13_0) ),
inference(spm,[status(thm)],[1415,57,theory(equality)]) ).
cnf(2035404,negated_conjecture,
( esk2_1(esk13_0) = esk1_1(esk13_0)
| in(esk1_1(esk13_0),esk2_1(esk13_0))
| epsilon_connected(esk13_0) ),
inference(csr,[status(thm)],[20281,54]) ).
cnf(2035405,negated_conjecture,
( esk2_1(esk13_0) = esk1_1(esk13_0)
| epsilon_connected(esk13_0) ),
inference(csr,[status(thm)],[2035404,56]) ).
cnf(2035406,negated_conjecture,
epsilon_connected(esk13_0),
inference(csr,[status(thm)],[2035405,55]) ).
cnf(2035706,negated_conjecture,
( ordinal(esk13_0)
| $false ),
inference(rw,[status(thm)],[1714,2035406,theory(equality)]) ).
cnf(2035707,negated_conjecture,
ordinal(esk13_0),
inference(cn,[status(thm)],[2035706,theory(equality)]) ).
cnf(2036185,negated_conjecture,
in(esk13_0,esk13_0),
inference(spm,[status(thm)],[191,2035707,theory(equality)]) ).
cnf(2036602,negated_conjecture,
~ in(esk13_0,esk13_0),
inference(spm,[status(thm)],[149,2036185,theory(equality)]) ).
cnf(2036803,negated_conjecture,
$false,
inference(rw,[status(thm)],[2036602,2036185,theory(equality)]) ).
cnf(2036804,negated_conjecture,
$false,
inference(cn,[status(thm)],[2036803,theory(equality)]) ).
cnf(2036805,negated_conjecture,
$false,
2036804,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM404+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 : n100.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 02:51:45 CST 2018
% 0.03/0.23 % CPUTime :
% 0.06/0.28 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.28 --creating new selector for []
% 29.08/29.41 eprover: CPU time limit exceeded, terminating
% 91.73/94.12 -running prover on /export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_1 with time limit 29
% 91.73/94.12 -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_1']
% 91.73/94.12 -prover status ResourceOut
% 91.73/94.12 -running prover on /export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2 with time limit 80
% 91.73/94.12 -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=80', '/export/starexec/sandbox/tmp/tmpN3YMPi/sel_theBenchmark.p_2']
% 91.73/94.12 -prover status Theorem
% 91.73/94.12 Problem theBenchmark.p solved in phase 1.
% 91.73/94.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 91.73/94.12 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 91.73/94.12 Solved 1 out of 1.
% 91.73/94.12 # Problem is unsatisfiable (or provable), constructing proof object
% 91.73/94.12 # SZS status Theorem
% 91.73/94.12 # SZS output start CNFRefutation.
% See solution above
% 91.79/94.15 # SZS output end CNFRefutation
%------------------------------------------------------------------------------