TSTP Solution File: NUM385+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM385+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n058.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 15:21:13 EST 2018
% Result : Theorem 0.07s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 17 unt; 0 def)
% Number of atoms : 196 ( 13 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 234 ( 86 ~; 97 |; 43 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 58 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/tmp/tmpBJxrCc/sel_theBenchmark.p_1',t10_ordinal1) ).
fof(9,conjecture,
! [X1,X2] :
( equal(succ(X1),succ(X2))
=> equal(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmpBJxrCc/sel_theBenchmark.p_1',t12_ordinal1) ).
fof(15,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmpBJxrCc/sel_theBenchmark.p_1',antisymmetry_r2_hidden) ).
fof(19,axiom,
! [X1] : equal(succ(X1),set_union2(X1,singleton(X1))),
file('/export/starexec/sandbox/tmp/tmpBJxrCc/sel_theBenchmark.p_1',d1_ordinal1) ).
fof(21,axiom,
! [X1,X2,X3] :
( equal(X3,set_union2(X1,X2))
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmpBJxrCc/sel_theBenchmark.p_1',d2_xboole_0) ).
fof(31,axiom,
! [X1,X2] :
( equal(X2,singleton(X1))
<=> ! [X3] :
( in(X3,X2)
<=> equal(X3,X1) ) ),
file('/export/starexec/sandbox/tmp/tmpBJxrCc/sel_theBenchmark.p_1',d1_tarski) ).
fof(36,negated_conjecture,
~ ! [X1,X2] :
( equal(succ(X1),succ(X2))
=> equal(X1,X2) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(39,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(50,plain,
! [X2] : in(X2,succ(X2)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(51,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[50]) ).
fof(69,negated_conjecture,
? [X1,X2] :
( equal(succ(X1),succ(X2))
& ~ equal(X1,X2) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(70,negated_conjecture,
? [X3,X4] :
( equal(succ(X3),succ(X4))
& ~ equal(X3,X4) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,negated_conjecture,
( equal(succ(esk5_0),succ(esk6_0))
& ~ equal(esk5_0,esk6_0) ),
inference(skolemize,[status(esa)],[70]) ).
cnf(72,negated_conjecture,
esk5_0 != esk6_0,
inference(split_conjunct,[status(thm)],[71]) ).
cnf(73,negated_conjecture,
succ(esk5_0) = succ(esk6_0),
inference(split_conjunct,[status(thm)],[71]) ).
fof(87,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(88,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[87]) ).
cnf(89,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(103,plain,
! [X2] : equal(succ(X2),set_union2(X2,singleton(X2))),
inference(variable_rename,[status(thm)],[19]) ).
cnf(104,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[103]) ).
fof(107,plain,
! [X1,X2,X3] :
( ( ~ equal(X3,set_union2(X1,X2))
| ! [X4] :
( ( ~ in(X4,X3)
| in(X4,X1)
| in(X4,X2) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X2) )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) )
& ( in(X4,X3)
| in(X4,X1)
| in(X4,X2) ) )
| equal(X3,set_union2(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(108,plain,
! [X5,X6,X7] :
( ( ~ equal(X7,set_union2(X5,X6))
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( ~ in(X9,X5)
& ~ in(X9,X6) ) )
& ( in(X9,X7)
| in(X9,X5)
| in(X9,X6) ) )
| equal(X7,set_union2(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X5,X6,X7] :
( ( ~ equal(X7,set_union2(X5,X6))
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( ~ in(esk8_3(X5,X6,X7),X5)
& ~ in(esk8_3(X5,X6,X7),X6) ) )
& ( in(esk8_3(X5,X6,X7),X7)
| in(esk8_3(X5,X6,X7),X5)
| in(esk8_3(X5,X6,X7),X6) ) )
| equal(X7,set_union2(X5,X6)) ) ),
inference(skolemize,[status(esa)],[108]) ).
fof(110,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) )
| ~ equal(X7,set_union2(X5,X6)) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( ~ in(esk8_3(X5,X6,X7),X5)
& ~ in(esk8_3(X5,X6,X7),X6) ) )
& ( in(esk8_3(X5,X6,X7),X7)
| in(esk8_3(X5,X6,X7),X5)
| in(esk8_3(X5,X6,X7),X6) ) )
| equal(X7,set_union2(X5,X6)) ) ),
inference(shift_quantors,[status(thm)],[109]) ).
fof(111,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| ~ equal(X7,set_union2(X5,X6)) )
& ( ~ in(X8,X5)
| in(X8,X7)
| ~ equal(X7,set_union2(X5,X6)) )
& ( ~ in(X8,X6)
| in(X8,X7)
| ~ equal(X7,set_union2(X5,X6)) )
& ( ~ in(esk8_3(X5,X6,X7),X5)
| ~ in(esk8_3(X5,X6,X7),X7)
| equal(X7,set_union2(X5,X6)) )
& ( ~ in(esk8_3(X5,X6,X7),X6)
| ~ in(esk8_3(X5,X6,X7),X7)
| equal(X7,set_union2(X5,X6)) )
& ( in(esk8_3(X5,X6,X7),X7)
| in(esk8_3(X5,X6,X7),X5)
| in(esk8_3(X5,X6,X7),X6)
| equal(X7,set_union2(X5,X6)) ) ),
inference(distribute,[status(thm)],[110]) ).
cnf(117,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(143,plain,
! [X1,X2] :
( ( ~ equal(X2,singleton(X1))
| ! [X3] :
( ( ~ in(X3,X2)
| equal(X3,X1) )
& ( ~ equal(X3,X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ equal(X3,X1) )
& ( in(X3,X2)
| equal(X3,X1) ) )
| equal(X2,singleton(X1)) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(144,plain,
! [X4,X5] :
( ( ~ equal(X5,singleton(X4))
| ! [X6] :
( ( ~ in(X6,X5)
| equal(X6,X4) )
& ( ~ equal(X6,X4)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ equal(X7,X4) )
& ( in(X7,X5)
| equal(X7,X4) ) )
| equal(X5,singleton(X4)) ) ),
inference(variable_rename,[status(thm)],[143]) ).
fof(145,plain,
! [X4,X5] :
( ( ~ equal(X5,singleton(X4))
| ! [X6] :
( ( ~ in(X6,X5)
| equal(X6,X4) )
& ( ~ equal(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk11_2(X4,X5),X5)
| ~ equal(esk11_2(X4,X5),X4) )
& ( in(esk11_2(X4,X5),X5)
| equal(esk11_2(X4,X5),X4) ) )
| equal(X5,singleton(X4)) ) ),
inference(skolemize,[status(esa)],[144]) ).
fof(146,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| equal(X6,X4) )
& ( ~ equal(X6,X4)
| in(X6,X5) ) )
| ~ equal(X5,singleton(X4)) )
& ( ( ( ~ in(esk11_2(X4,X5),X5)
| ~ equal(esk11_2(X4,X5),X4) )
& ( in(esk11_2(X4,X5),X5)
| equal(esk11_2(X4,X5),X4) ) )
| equal(X5,singleton(X4)) ) ),
inference(shift_quantors,[status(thm)],[145]) ).
fof(147,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| equal(X6,X4)
| ~ equal(X5,singleton(X4)) )
& ( ~ equal(X6,X4)
| in(X6,X5)
| ~ equal(X5,singleton(X4)) )
& ( ~ in(esk11_2(X4,X5),X5)
| ~ equal(esk11_2(X4,X5),X4)
| equal(X5,singleton(X4)) )
& ( in(esk11_2(X4,X5),X5)
| equal(esk11_2(X4,X5),X4)
| equal(X5,singleton(X4)) ) ),
inference(distribute,[status(thm)],[146]) ).
cnf(151,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[147]) ).
cnf(170,negated_conjecture,
set_union2(esk6_0,singleton(esk6_0)) = set_union2(esk5_0,singleton(esk5_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[73,104,theory(equality)]),104,theory(equality)]),
[unfolding] ).
cnf(171,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[51,104,theory(equality)]),
[unfolding] ).
cnf(186,negated_conjecture,
in(esk5_0,set_union2(esk6_0,singleton(esk6_0))),
inference(spm,[status(thm)],[171,170,theory(equality)]) ).
cnf(237,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[117,theory(equality)]) ).
cnf(700,negated_conjecture,
( in(X1,singleton(esk5_0))
| in(X1,esk5_0)
| ~ in(X1,set_union2(esk6_0,singleton(esk6_0))) ),
inference(spm,[status(thm)],[237,170,theory(equality)]) ).
cnf(703,negated_conjecture,
( in(esk5_0,singleton(esk6_0))
| in(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[237,186,theory(equality)]) ).
cnf(719,negated_conjecture,
( X1 = esk5_0
| in(esk5_0,esk6_0)
| singleton(X1) != singleton(esk6_0) ),
inference(spm,[status(thm)],[151,703,theory(equality)]) ).
cnf(724,negated_conjecture,
( esk6_0 = esk5_0
| in(esk5_0,esk6_0) ),
inference(er,[status(thm)],[719,theory(equality)]) ).
cnf(727,negated_conjecture,
in(esk5_0,esk6_0),
inference(sr,[status(thm)],[724,72,theory(equality)]) ).
cnf(730,negated_conjecture,
~ in(esk6_0,esk5_0),
inference(spm,[status(thm)],[89,727,theory(equality)]) ).
cnf(2488,negated_conjecture,
( in(esk6_0,singleton(esk5_0))
| in(esk6_0,esk5_0) ),
inference(spm,[status(thm)],[700,171,theory(equality)]) ).
cnf(2519,negated_conjecture,
in(esk6_0,singleton(esk5_0)),
inference(sr,[status(thm)],[2488,730,theory(equality)]) ).
cnf(2523,negated_conjecture,
( X1 = esk6_0
| singleton(X1) != singleton(esk5_0) ),
inference(spm,[status(thm)],[151,2519,theory(equality)]) ).
cnf(2532,negated_conjecture,
esk5_0 = esk6_0,
inference(er,[status(thm)],[2523,theory(equality)]) ).
cnf(2535,negated_conjecture,
$false,
inference(sr,[status(thm)],[2532,72,theory(equality)]) ).
cnf(2536,negated_conjecture,
$false,
2535,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM385+1 : TPTP v7.0.0. Released v3.2.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.02/0.24 % Computer : n058.star.cs.uiowa.edu
% 0.02/0.24 % Model : x86_64 x86_64
% 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24 % Memory : 32218.625MB
% 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24 % CPULimit : 300
% 0.02/0.24 % DateTime : Fri Jan 5 02:36:00 CST 2018
% 0.02/0.24 % CPUTime :
% 0.07/0.28 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.28 --creating new selector for []
% 0.07/0.40 -running prover on /export/starexec/sandbox/tmp/tmpBJxrCc/sel_theBenchmark.p_1 with time limit 29
% 0.07/0.40 -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/tmpBJxrCc/sel_theBenchmark.p_1']
% 0.07/0.40 -prover status Theorem
% 0.07/0.40 Problem theBenchmark.p solved in phase 0.
% 0.07/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.40 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.40 Solved 1 out of 1.
% 0.07/0.40 # Problem is unsatisfiable (or provable), constructing proof object
% 0.07/0.40 # SZS status Theorem
% 0.07/0.40 # SZS output start CNFRefutation.
% See solution above
% 0.07/0.40 # SZS output end CNFRefutation
%------------------------------------------------------------------------------