TSTP Solution File: SET960+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SET960+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %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 : Thu Dec 30 00:24:21 EST 2010
% Result : Theorem 0.95s
% Output : Solution 0.95s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP11582/SET960+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP11582/SET960+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP11582/SET960+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 11678
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Preprocessing time : 0.012 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(1, axiom,![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))),file('/tmp/SRASS.s.p', d1_xboole_0)).
% fof(3, axiom,![X1]:![X2]:![X3]:(X3=cartesian_product2(X1,X2)<=>![X4]:(in(X4,X3)<=>?[X5]:?[X6]:((in(X5,X1)&in(X6,X2))&X4=ordered_pair(X5,X6)))),file('/tmp/SRASS.s.p', d2_zfmisc_1)).
% fof(9, axiom,![X1]:![X2]:ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1)),file('/tmp/SRASS.s.p', d5_tarski)).
% fof(10, conjecture,![X1]:![X2]:(cartesian_product2(X1,X2)=empty_set<=>(X1=empty_set|X2=empty_set)),file('/tmp/SRASS.s.p', t113_zfmisc_1)).
% fof(11, negated_conjecture,~(![X1]:![X2]:(cartesian_product2(X1,X2)=empty_set<=>(X1=empty_set|X2=empty_set))),inference(assume_negation,[status(cth)],[10])).
% fof(12, plain,![X1]:(X1=empty_set<=>![X2]:~(in(X2,X1))),inference(fof_simplification,[status(thm)],[1,theory(equality)])).
% fof(16, plain,![X1]:((~(X1=empty_set)|![X2]:~(in(X2,X1)))&(?[X2]:in(X2,X1)|X1=empty_set)),inference(fof_nnf,[status(thm)],[12])).
% fof(17, plain,![X3]:((~(X3=empty_set)|![X4]:~(in(X4,X3)))&(?[X5]:in(X5,X3)|X3=empty_set)),inference(variable_rename,[status(thm)],[16])).
% fof(18, plain,![X3]:((~(X3=empty_set)|![X4]:~(in(X4,X3)))&(in(esk1_1(X3),X3)|X3=empty_set)),inference(skolemize,[status(esa)],[17])).
% fof(19, plain,![X3]:![X4]:((~(in(X4,X3))|~(X3=empty_set))&(in(esk1_1(X3),X3)|X3=empty_set)),inference(shift_quantors,[status(thm)],[18])).
% cnf(20,plain,(X1=empty_set|in(esk1_1(X1),X1)),inference(split_conjunct,[status(thm)],[19])).
% cnf(21,plain,(X1!=empty_set|~in(X2,X1)),inference(split_conjunct,[status(thm)],[19])).
% fof(23, plain,![X1]:![X2]:![X3]:((~(X3=cartesian_product2(X1,X2))|![X4]:((~(in(X4,X3))|?[X5]:?[X6]:((in(X5,X1)&in(X6,X2))&X4=ordered_pair(X5,X6)))&(![X5]:![X6]:((~(in(X5,X1))|~(in(X6,X2)))|~(X4=ordered_pair(X5,X6)))|in(X4,X3))))&(?[X4]:((~(in(X4,X3))|![X5]:![X6]:((~(in(X5,X1))|~(in(X6,X2)))|~(X4=ordered_pair(X5,X6))))&(in(X4,X3)|?[X5]:?[X6]:((in(X5,X1)&in(X6,X2))&X4=ordered_pair(X5,X6))))|X3=cartesian_product2(X1,X2))),inference(fof_nnf,[status(thm)],[3])).
% fof(24, plain,![X7]:![X8]:![X9]:((~(X9=cartesian_product2(X7,X8))|![X10]:((~(in(X10,X9))|?[X11]:?[X12]:((in(X11,X7)&in(X12,X8))&X10=ordered_pair(X11,X12)))&(![X13]:![X14]:((~(in(X13,X7))|~(in(X14,X8)))|~(X10=ordered_pair(X13,X14)))|in(X10,X9))))&(?[X15]:((~(in(X15,X9))|![X16]:![X17]:((~(in(X16,X7))|~(in(X17,X8)))|~(X15=ordered_pair(X16,X17))))&(in(X15,X9)|?[X18]:?[X19]:((in(X18,X7)&in(X19,X8))&X15=ordered_pair(X18,X19))))|X9=cartesian_product2(X7,X8))),inference(variable_rename,[status(thm)],[23])).
% fof(25, plain,![X7]:![X8]:![X9]:((~(X9=cartesian_product2(X7,X8))|![X10]:((~(in(X10,X9))|((in(esk2_4(X7,X8,X9,X10),X7)&in(esk3_4(X7,X8,X9,X10),X8))&X10=ordered_pair(esk2_4(X7,X8,X9,X10),esk3_4(X7,X8,X9,X10))))&(![X13]:![X14]:((~(in(X13,X7))|~(in(X14,X8)))|~(X10=ordered_pair(X13,X14)))|in(X10,X9))))&(((~(in(esk4_3(X7,X8,X9),X9))|![X16]:![X17]:((~(in(X16,X7))|~(in(X17,X8)))|~(esk4_3(X7,X8,X9)=ordered_pair(X16,X17))))&(in(esk4_3(X7,X8,X9),X9)|((in(esk5_3(X7,X8,X9),X7)&in(esk6_3(X7,X8,X9),X8))&esk4_3(X7,X8,X9)=ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)))))|X9=cartesian_product2(X7,X8))),inference(skolemize,[status(esa)],[24])).
% fof(26, plain,![X7]:![X8]:![X9]:![X10]:![X13]:![X14]:![X16]:![X17]:((((((~(in(X16,X7))|~(in(X17,X8)))|~(esk4_3(X7,X8,X9)=ordered_pair(X16,X17)))|~(in(esk4_3(X7,X8,X9),X9)))&(in(esk4_3(X7,X8,X9),X9)|((in(esk5_3(X7,X8,X9),X7)&in(esk6_3(X7,X8,X9),X8))&esk4_3(X7,X8,X9)=ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)))))|X9=cartesian_product2(X7,X8))&(((((~(in(X13,X7))|~(in(X14,X8)))|~(X10=ordered_pair(X13,X14)))|in(X10,X9))&(~(in(X10,X9))|((in(esk2_4(X7,X8,X9,X10),X7)&in(esk3_4(X7,X8,X9,X10),X8))&X10=ordered_pair(esk2_4(X7,X8,X9,X10),esk3_4(X7,X8,X9,X10)))))|~(X9=cartesian_product2(X7,X8)))),inference(shift_quantors,[status(thm)],[25])).
% fof(27, plain,![X7]:![X8]:![X9]:![X10]:![X13]:![X14]:![X16]:![X17]:((((((~(in(X16,X7))|~(in(X17,X8)))|~(esk4_3(X7,X8,X9)=ordered_pair(X16,X17)))|~(in(esk4_3(X7,X8,X9),X9)))|X9=cartesian_product2(X7,X8))&((((in(esk5_3(X7,X8,X9),X7)|in(esk4_3(X7,X8,X9),X9))|X9=cartesian_product2(X7,X8))&((in(esk6_3(X7,X8,X9),X8)|in(esk4_3(X7,X8,X9),X9))|X9=cartesian_product2(X7,X8)))&((esk4_3(X7,X8,X9)=ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9))|in(esk4_3(X7,X8,X9),X9))|X9=cartesian_product2(X7,X8))))&(((((~(in(X13,X7))|~(in(X14,X8)))|~(X10=ordered_pair(X13,X14)))|in(X10,X9))|~(X9=cartesian_product2(X7,X8)))&((((in(esk2_4(X7,X8,X9,X10),X7)|~(in(X10,X9)))|~(X9=cartesian_product2(X7,X8)))&((in(esk3_4(X7,X8,X9,X10),X8)|~(in(X10,X9)))|~(X9=cartesian_product2(X7,X8))))&((X10=ordered_pair(esk2_4(X7,X8,X9,X10),esk3_4(X7,X8,X9,X10))|~(in(X10,X9)))|~(X9=cartesian_product2(X7,X8)))))),inference(distribute,[status(thm)],[26])).
% cnf(29,plain,(in(esk3_4(X2,X3,X1,X4),X3)|X1!=cartesian_product2(X2,X3)|~in(X4,X1)),inference(split_conjunct,[status(thm)],[27])).
% cnf(30,plain,(in(esk2_4(X2,X3,X1,X4),X2)|X1!=cartesian_product2(X2,X3)|~in(X4,X1)),inference(split_conjunct,[status(thm)],[27])).
% cnf(31,plain,(in(X4,X1)|X1!=cartesian_product2(X2,X3)|X4!=ordered_pair(X5,X6)|~in(X6,X3)|~in(X5,X2)),inference(split_conjunct,[status(thm)],[27])).
% cnf(34,plain,(X1=cartesian_product2(X2,X3)|in(esk4_3(X2,X3,X1),X1)|in(esk5_3(X2,X3,X1),X2)),inference(split_conjunct,[status(thm)],[27])).
% fof(49, plain,![X3]:![X4]:ordered_pair(X3,X4)=unordered_pair(unordered_pair(X3,X4),singleton(X3)),inference(variable_rename,[status(thm)],[9])).
% cnf(50,plain,(ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1))),inference(split_conjunct,[status(thm)],[49])).
% fof(51, negated_conjecture,?[X1]:?[X2]:((~(cartesian_product2(X1,X2)=empty_set)|(~(X1=empty_set)&~(X2=empty_set)))&(cartesian_product2(X1,X2)=empty_set|(X1=empty_set|X2=empty_set))),inference(fof_nnf,[status(thm)],[11])).
% fof(52, negated_conjecture,?[X3]:?[X4]:((~(cartesian_product2(X3,X4)=empty_set)|(~(X3=empty_set)&~(X4=empty_set)))&(cartesian_product2(X3,X4)=empty_set|(X3=empty_set|X4=empty_set))),inference(variable_rename,[status(thm)],[51])).
% fof(53, negated_conjecture,((~(cartesian_product2(esk9_0,esk10_0)=empty_set)|(~(esk9_0=empty_set)&~(esk10_0=empty_set)))&(cartesian_product2(esk9_0,esk10_0)=empty_set|(esk9_0=empty_set|esk10_0=empty_set))),inference(skolemize,[status(esa)],[52])).
% fof(54, negated_conjecture,(((~(esk9_0=empty_set)|~(cartesian_product2(esk9_0,esk10_0)=empty_set))&(~(esk10_0=empty_set)|~(cartesian_product2(esk9_0,esk10_0)=empty_set)))&(cartesian_product2(esk9_0,esk10_0)=empty_set|(esk9_0=empty_set|esk10_0=empty_set))),inference(distribute,[status(thm)],[53])).
% cnf(55,negated_conjecture,(esk10_0=empty_set|esk9_0=empty_set|cartesian_product2(esk9_0,esk10_0)=empty_set),inference(split_conjunct,[status(thm)],[54])).
% cnf(56,negated_conjecture,(cartesian_product2(esk9_0,esk10_0)!=empty_set|esk10_0!=empty_set),inference(split_conjunct,[status(thm)],[54])).
% cnf(57,negated_conjecture,(cartesian_product2(esk9_0,esk10_0)!=empty_set|esk9_0!=empty_set),inference(split_conjunct,[status(thm)],[54])).
% cnf(60,plain,(in(X4,X1)|cartesian_product2(X2,X3)!=X1|unordered_pair(unordered_pair(X5,X6),singleton(X5))!=X4|~in(X6,X3)|~in(X5,X2)),inference(rw,[status(thm)],[31,50,theory(equality)]),['unfolding']).
% cnf(73,plain,(empty_set!=X1|cartesian_product2(X1,X2)!=X3|~in(X4,X3)),inference(spm,[status(thm)],[21,30,theory(equality)])).
% cnf(75,plain,(empty_set!=X1|cartesian_product2(X2,X1)!=X3|~in(X4,X3)),inference(spm,[status(thm)],[21,29,theory(equality)])).
% cnf(77,plain,(in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)|cartesian_product2(X4,X5)!=X3|~in(X2,X5)|~in(X1,X4)),inference(er,[status(thm)],[60,theory(equality)])).
% cnf(96,plain,(empty_set!=X1|~in(X2,cartesian_product2(X1,X3))),inference(er,[status(thm)],[73,theory(equality)])).
% cnf(105,plain,(empty_set=cartesian_product2(X1,X2)|empty_set!=X1),inference(spm,[status(thm)],[96,20,theory(equality)])).
% cnf(106,negated_conjecture,(esk9_0!=empty_set),inference(spm,[status(thm)],[57,105,theory(equality)])).
% cnf(109,plain,(empty_set!=X1|~in(X2,empty_set)),inference(spm,[status(thm)],[96,105,theory(equality)])).
% cnf(110,negated_conjecture,(cartesian_product2(esk9_0,esk10_0)=empty_set|esk10_0=empty_set),inference(sr,[status(thm)],[55,106,theory(equality)])).
% fof(123, plain,(~(epred1_0)<=>![X1]:~(empty_set=X1)),introduced(definition),['split']).
% cnf(124,plain,(epred1_0|empty_set!=X1),inference(split_equiv,[status(thm)],[123])).
% fof(125, plain,(~(epred2_0)<=>![X2]:~(in(X2,empty_set))),introduced(definition),['split']).
% cnf(126,plain,(epred2_0|~in(X2,empty_set)),inference(split_equiv,[status(thm)],[125])).
% cnf(127,plain,(~epred2_0|~epred1_0),inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[109,123,theory(equality)]),125,theory(equality)]),['split']).
% cnf(128,plain,(epred1_0),inference(er,[status(thm)],[124,theory(equality)])).
% cnf(130,plain,(~epred2_0|$false),inference(rw,[status(thm)],[127,128,theory(equality)])).
% cnf(131,plain,(~epred2_0),inference(cn,[status(thm)],[130,theory(equality)])).
% cnf(132,plain,(~in(X2,empty_set)),inference(sr,[status(thm)],[126,131,theory(equality)])).
% cnf(134,plain,(cartesian_product2(empty_set,X1)=X2|in(esk4_3(empty_set,X1,X2),X2)),inference(spm,[status(thm)],[132,34,theory(equality)])).
% cnf(136,plain,(cartesian_product2(empty_set,X1)!=X2|~in(X3,X2)),inference(spm,[status(thm)],[132,30,theory(equality)])).
% cnf(161,plain,(~in(X1,cartesian_product2(empty_set,X2))),inference(er,[status(thm)],[136,theory(equality)])).
% cnf(172,plain,(empty_set=cartesian_product2(empty_set,X1)),inference(spm,[status(thm)],[161,20,theory(equality)])).
% cnf(177,plain,(empty_set!=X1|~in(X2,cartesian_product2(X3,X1))),inference(er,[status(thm)],[75,theory(equality)])).
% cnf(192,plain,(empty_set=cartesian_product2(X2,X1)|empty_set!=X1),inference(spm,[status(thm)],[177,20,theory(equality)])).
% cnf(194,negated_conjecture,(esk10_0!=empty_set),inference(spm,[status(thm)],[56,192,theory(equality)])).
% cnf(199,negated_conjecture,(cartesian_product2(esk9_0,esk10_0)=empty_set),inference(sr,[status(thm)],[110,194,theory(equality)])).
% cnf(236,plain,(in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))|~in(X2,X4)|~in(X1,X3)),inference(er,[status(thm)],[77,theory(equality)])).
% cnf(1221,plain,(empty_set=X2|in(esk4_3(empty_set,X1,X2),X2)),inference(rw,[status(thm)],[134,172,theory(equality)])).
% cnf(1564,negated_conjecture,(in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),empty_set)|~in(X2,esk10_0)|~in(X1,esk9_0)),inference(spm,[status(thm)],[236,199,theory(equality)])).
% cnf(1585,negated_conjecture,(~in(X2,esk10_0)|~in(X1,esk9_0)),inference(sr,[status(thm)],[1564,132,theory(equality)])).
% fof(1594, plain,(~(epred7_0)<=>![X2]:~(in(X2,esk10_0))),introduced(definition),['split']).
% cnf(1595,plain,(epred7_0|~in(X2,esk10_0)),inference(split_equiv,[status(thm)],[1594])).
% fof(1596, plain,(~(epred8_0)<=>![X1]:~(in(X1,esk9_0))),introduced(definition),['split']).
% cnf(1597,plain,(epred8_0|~in(X1,esk9_0)),inference(split_equiv,[status(thm)],[1596])).
% cnf(1598,negated_conjecture,(~epred8_0|~epred7_0),inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[1585,1594,theory(equality)]),1596,theory(equality)]),['split']).
% cnf(1609,negated_conjecture,(epred7_0|empty_set=esk10_0),inference(spm,[status(thm)],[1595,1221,theory(equality)])).
% cnf(1618,negated_conjecture,(epred7_0),inference(sr,[status(thm)],[1609,194,theory(equality)])).
% cnf(1621,negated_conjecture,(~epred8_0|$false),inference(rw,[status(thm)],[1598,1618,theory(equality)])).
% cnf(1622,negated_conjecture,(~epred8_0),inference(cn,[status(thm)],[1621,theory(equality)])).
% cnf(1624,negated_conjecture,(~in(X1,esk9_0)),inference(sr,[status(thm)],[1597,1622,theory(equality)])).
% cnf(1635,negated_conjecture,(empty_set=esk9_0),inference(spm,[status(thm)],[1624,1221,theory(equality)])).
% cnf(1644,negated_conjecture,($false),inference(sr,[status(thm)],[1635,106,theory(equality)])).
% cnf(1645,negated_conjecture,($false),1644,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 523
% # ...of these trivial : 0
% # ...subsumed : 383
% # ...remaining for further processing: 140
% # Other redundant clauses eliminated : 1
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 2
% # Backward-rewritten : 11
% # Generated clauses : 1020
% # ...of the previous two non-trivial : 969
% # Contextual simplify-reflections : 355
% # Paramodulations : 980
% # Factorizations : 0
% # Equation resolutions : 26
% # Current number of processed clauses: 102
% # Positive orientable unit clauses: 9
% # Positive unorientable unit clauses: 1
% # Negative unit clauses : 13
% # Non-unit-clauses : 79
% # Current number of unprocessed clauses: 448
% # ...number of literals in the above : 1752
% # Clause-clause subsumption calls (NU) : 2822
% # Rec. Clause-clause subsumption calls : 2577
% # Unit Clause-clause subsumption calls : 248
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 17
% # Indexed BW rewrite successes : 17
% # Backwards rewriting index: 91 leaves, 1.66+/-1.811 terms/leaf
% # Paramod-from index: 26 leaves, 1.15+/-0.361 terms/leaf
% # Paramod-into index: 85 leaves, 1.48+/-1.058 terms/leaf
% # -------------------------------------------------
% # User time : 0.051 s
% # System time : 0.006 s
% # Total time : 0.057 s
% # Maximum resident set size: 0 pages
% PrfWatch: 0.16 CPU 0.24 WC
% FINAL PrfWatch: 0.16 CPU 0.24 WC
% SZS output end Solution for /tmp/SystemOnTPTP11582/SET960+1.tptp
%
%------------------------------------------------------------------------------