TSTP Solution File: SET894+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SET894+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art06.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 00:16:28 EST 2010
% Result : Theorem 0.97s
% Output : Solution 0.97s
% 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/SystemOnTPTP2036/SET894+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP2036/SET894+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP2036/SET894+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 2198
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 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]:![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(2, axiom,![X1]:![X2]:![X3]:![X4]:(in(ordered_pair(X1,X2),cartesian_product2(X3,X4))<=>(in(X1,X3)&in(X2,X4))),file('/tmp/SRASS.s.p', l55_zfmisc_1)).
% fof(3, axiom,![X1]:![X2]:(X2=singleton(X1)<=>![X3]:(in(X3,X2)<=>X3=X1)),file('/tmp/SRASS.s.p', d1_tarski)).
% fof(4, axiom,![X1]:![X2]:ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1)),file('/tmp/SRASS.s.p', d5_tarski)).
% fof(6, axiom,![X1]:![X2]:unordered_pair(X1,X2)=unordered_pair(X2,X1),file('/tmp/SRASS.s.p', commutativity_k2_tarski)).
% fof(11, conjecture,![X1]:![X2]:cartesian_product2(singleton(X1),singleton(X2))=singleton(ordered_pair(X1,X2)),file('/tmp/SRASS.s.p', t35_zfmisc_1)).
% fof(12, negated_conjecture,~(![X1]:![X2]:cartesian_product2(singleton(X1),singleton(X2))=singleton(ordered_pair(X1,X2))),inference(assume_negation,[status(cth)],[11])).
% fof(16, 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)],[1])).
% fof(17, 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)],[16])).
% fof(18, plain,![X7]:![X8]:![X9]:((~(X9=cartesian_product2(X7,X8))|![X10]:((~(in(X10,X9))|((in(esk1_4(X7,X8,X9,X10),X7)&in(esk2_4(X7,X8,X9,X10),X8))&X10=ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10))))&(![X13]:![X14]:((~(in(X13,X7))|~(in(X14,X8)))|~(X10=ordered_pair(X13,X14)))|in(X10,X9))))&(((~(in(esk3_3(X7,X8,X9),X9))|![X16]:![X17]:((~(in(X16,X7))|~(in(X17,X8)))|~(esk3_3(X7,X8,X9)=ordered_pair(X16,X17))))&(in(esk3_3(X7,X8,X9),X9)|((in(esk4_3(X7,X8,X9),X7)&in(esk5_3(X7,X8,X9),X8))&esk3_3(X7,X8,X9)=ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9)))))|X9=cartesian_product2(X7,X8))),inference(skolemize,[status(esa)],[17])).
% fof(19, plain,![X7]:![X8]:![X9]:![X10]:![X13]:![X14]:![X16]:![X17]:((((((~(in(X16,X7))|~(in(X17,X8)))|~(esk3_3(X7,X8,X9)=ordered_pair(X16,X17)))|~(in(esk3_3(X7,X8,X9),X9)))&(in(esk3_3(X7,X8,X9),X9)|((in(esk4_3(X7,X8,X9),X7)&in(esk5_3(X7,X8,X9),X8))&esk3_3(X7,X8,X9)=ordered_pair(esk4_3(X7,X8,X9),esk5_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(esk1_4(X7,X8,X9,X10),X7)&in(esk2_4(X7,X8,X9,X10),X8))&X10=ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10)))))|~(X9=cartesian_product2(X7,X8)))),inference(shift_quantors,[status(thm)],[18])).
% fof(20, plain,![X7]:![X8]:![X9]:![X10]:![X13]:![X14]:![X16]:![X17]:((((((~(in(X16,X7))|~(in(X17,X8)))|~(esk3_3(X7,X8,X9)=ordered_pair(X16,X17)))|~(in(esk3_3(X7,X8,X9),X9)))|X9=cartesian_product2(X7,X8))&((((in(esk4_3(X7,X8,X9),X7)|in(esk3_3(X7,X8,X9),X9))|X9=cartesian_product2(X7,X8))&((in(esk5_3(X7,X8,X9),X8)|in(esk3_3(X7,X8,X9),X9))|X9=cartesian_product2(X7,X8)))&((esk3_3(X7,X8,X9)=ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9))|in(esk3_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(esk1_4(X7,X8,X9,X10),X7)|~(in(X10,X9)))|~(X9=cartesian_product2(X7,X8)))&((in(esk2_4(X7,X8,X9,X10),X8)|~(in(X10,X9)))|~(X9=cartesian_product2(X7,X8))))&((X10=ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10))|~(in(X10,X9)))|~(X9=cartesian_product2(X7,X8)))))),inference(distribute,[status(thm)],[19])).
% cnf(21,plain,(X4=ordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4))|X1!=cartesian_product2(X2,X3)|~in(X4,X1)),inference(split_conjunct,[status(thm)],[20])).
% cnf(22,plain,(in(esk2_4(X2,X3,X1,X4),X3)|X1!=cartesian_product2(X2,X3)|~in(X4,X1)),inference(split_conjunct,[status(thm)],[20])).
% cnf(23,plain,(in(esk1_4(X2,X3,X1,X4),X2)|X1!=cartesian_product2(X2,X3)|~in(X4,X1)),inference(split_conjunct,[status(thm)],[20])).
% fof(29, plain,![X1]:![X2]:![X3]:![X4]:((~(in(ordered_pair(X1,X2),cartesian_product2(X3,X4)))|(in(X1,X3)&in(X2,X4)))&((~(in(X1,X3))|~(in(X2,X4)))|in(ordered_pair(X1,X2),cartesian_product2(X3,X4)))),inference(fof_nnf,[status(thm)],[2])).
% fof(30, plain,![X5]:![X6]:![X7]:![X8]:((~(in(ordered_pair(X5,X6),cartesian_product2(X7,X8)))|(in(X5,X7)&in(X6,X8)))&((~(in(X5,X7))|~(in(X6,X8)))|in(ordered_pair(X5,X6),cartesian_product2(X7,X8)))),inference(variable_rename,[status(thm)],[29])).
% fof(31, plain,![X5]:![X6]:![X7]:![X8]:(((in(X5,X7)|~(in(ordered_pair(X5,X6),cartesian_product2(X7,X8))))&(in(X6,X8)|~(in(ordered_pair(X5,X6),cartesian_product2(X7,X8)))))&((~(in(X5,X7))|~(in(X6,X8)))|in(ordered_pair(X5,X6),cartesian_product2(X7,X8)))),inference(distribute,[status(thm)],[30])).
% cnf(32,plain,(in(ordered_pair(X1,X2),cartesian_product2(X3,X4))|~in(X2,X4)|~in(X1,X3)),inference(split_conjunct,[status(thm)],[31])).
% fof(35, plain,![X1]:![X2]:((~(X2=singleton(X1))|![X3]:((~(in(X3,X2))|X3=X1)&(~(X3=X1)|in(X3,X2))))&(?[X3]:((~(in(X3,X2))|~(X3=X1))&(in(X3,X2)|X3=X1))|X2=singleton(X1))),inference(fof_nnf,[status(thm)],[3])).
% fof(36, plain,![X4]:![X5]:((~(X5=singleton(X4))|![X6]:((~(in(X6,X5))|X6=X4)&(~(X6=X4)|in(X6,X5))))&(?[X7]:((~(in(X7,X5))|~(X7=X4))&(in(X7,X5)|X7=X4))|X5=singleton(X4))),inference(variable_rename,[status(thm)],[35])).
% fof(37, plain,![X4]:![X5]:((~(X5=singleton(X4))|![X6]:((~(in(X6,X5))|X6=X4)&(~(X6=X4)|in(X6,X5))))&(((~(in(esk6_2(X4,X5),X5))|~(esk6_2(X4,X5)=X4))&(in(esk6_2(X4,X5),X5)|esk6_2(X4,X5)=X4))|X5=singleton(X4))),inference(skolemize,[status(esa)],[36])).
% fof(38, plain,![X4]:![X5]:![X6]:((((~(in(X6,X5))|X6=X4)&(~(X6=X4)|in(X6,X5)))|~(X5=singleton(X4)))&(((~(in(esk6_2(X4,X5),X5))|~(esk6_2(X4,X5)=X4))&(in(esk6_2(X4,X5),X5)|esk6_2(X4,X5)=X4))|X5=singleton(X4))),inference(shift_quantors,[status(thm)],[37])).
% fof(39, plain,![X4]:![X5]:![X6]:((((~(in(X6,X5))|X6=X4)|~(X5=singleton(X4)))&((~(X6=X4)|in(X6,X5))|~(X5=singleton(X4))))&(((~(in(esk6_2(X4,X5),X5))|~(esk6_2(X4,X5)=X4))|X5=singleton(X4))&((in(esk6_2(X4,X5),X5)|esk6_2(X4,X5)=X4)|X5=singleton(X4)))),inference(distribute,[status(thm)],[38])).
% cnf(40,plain,(X1=singleton(X2)|esk6_2(X2,X1)=X2|in(esk6_2(X2,X1),X1)),inference(split_conjunct,[status(thm)],[39])).
% cnf(41,plain,(X1=singleton(X2)|esk6_2(X2,X1)!=X2|~in(esk6_2(X2,X1),X1)),inference(split_conjunct,[status(thm)],[39])).
% cnf(42,plain,(in(X3,X1)|X1!=singleton(X2)|X3!=X2),inference(split_conjunct,[status(thm)],[39])).
% cnf(43,plain,(X3=X2|X1!=singleton(X2)|~in(X3,X1)),inference(split_conjunct,[status(thm)],[39])).
% fof(44, plain,![X3]:![X4]:ordered_pair(X3,X4)=unordered_pair(unordered_pair(X3,X4),singleton(X3)),inference(variable_rename,[status(thm)],[4])).
% cnf(45,plain,(ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1))),inference(split_conjunct,[status(thm)],[44])).
% fof(49, plain,![X3]:![X4]:unordered_pair(X3,X4)=unordered_pair(X4,X3),inference(variable_rename,[status(thm)],[6])).
% cnf(50,plain,(unordered_pair(X1,X2)=unordered_pair(X2,X1)),inference(split_conjunct,[status(thm)],[49])).
% fof(65, negated_conjecture,?[X1]:?[X2]:~(cartesian_product2(singleton(X1),singleton(X2))=singleton(ordered_pair(X1,X2))),inference(fof_nnf,[status(thm)],[12])).
% fof(66, negated_conjecture,?[X3]:?[X4]:~(cartesian_product2(singleton(X3),singleton(X4))=singleton(ordered_pair(X3,X4))),inference(variable_rename,[status(thm)],[65])).
% fof(67, negated_conjecture,~(cartesian_product2(singleton(esk10_0),singleton(esk11_0))=singleton(ordered_pair(esk10_0,esk11_0))),inference(skolemize,[status(esa)],[66])).
% cnf(68,negated_conjecture,(cartesian_product2(singleton(esk10_0),singleton(esk11_0))!=singleton(ordered_pair(esk10_0,esk11_0))),inference(split_conjunct,[status(thm)],[67])).
% cnf(72,plain,(in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))|~in(X2,X4)|~in(X1,X3)),inference(rw,[status(thm)],[32,45,theory(equality)]),['unfolding']).
% cnf(73,plain,(unordered_pair(unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4)),singleton(esk1_4(X2,X3,X1,X4)))=X4|cartesian_product2(X2,X3)!=X1|~in(X4,X1)),inference(rw,[status(thm)],[21,45,theory(equality)]),['unfolding']).
% cnf(77,negated_conjecture,(cartesian_product2(singleton(esk10_0),singleton(esk11_0))!=singleton(unordered_pair(unordered_pair(esk10_0,esk11_0),singleton(esk10_0)))),inference(rw,[status(thm)],[68,45,theory(equality)]),['unfolding']).
% cnf(78,plain,(in(X1,X2)|singleton(X1)!=X2),inference(er,[status(thm)],[42,theory(equality)])).
% cnf(79,plain,(unordered_pair(singleton(esk1_4(X2,X3,X1,X4)),unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4)))=X4|cartesian_product2(X2,X3)!=X1|~in(X4,X1)),inference(rw,[status(thm)],[73,50,theory(equality)])).
% cnf(85,plain,(in(X1,singleton(X1))),inference(er,[status(thm)],[78,theory(equality)])).
% cnf(104,plain,(X1=esk1_4(X2,X3,X4,X5)|singleton(X1)!=X2|cartesian_product2(X2,X3)!=X4|~in(X5,X4)),inference(spm,[status(thm)],[43,23,theory(equality)])).
% cnf(106,plain,(X1=esk2_4(X2,X3,X4,X5)|singleton(X1)!=X3|cartesian_product2(X2,X3)!=X4|~in(X5,X4)),inference(spm,[status(thm)],[43,22,theory(equality)])).
% cnf(113,plain,(in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))|~in(X2,X4)|~in(X1,X3)),inference(spm,[status(thm)],[72,50,theory(equality)])).
% cnf(256,plain,(X1=esk1_4(singleton(X1),X2,X3,X4)|cartesian_product2(singleton(X1),X2)!=X3|~in(X4,X3)),inference(er,[status(thm)],[104,theory(equality)])).
% cnf(266,plain,(unordered_pair(singleton(X1),unordered_pair(X1,esk2_4(singleton(X1),X2,X3,X4)))=X4|cartesian_product2(singleton(X1),X2)!=X3|~in(X4,X3)),inference(spm,[status(thm)],[79,256,theory(equality)])).
% cnf(269,plain,(X1=esk2_4(X2,singleton(X1),X3,X4)|cartesian_product2(X2,singleton(X1))!=X3|~in(X4,X3)),inference(er,[status(thm)],[106,theory(equality)])).
% cnf(547,plain,(unordered_pair(singleton(X1),unordered_pair(X1,X2))=X4|cartesian_product2(singleton(X1),singleton(X2))!=X3|~in(X4,X3)),inference(spm,[status(thm)],[266,269,theory(equality)])).
% cnf(548,plain,(unordered_pair(singleton(X1),unordered_pair(X1,X2))=X3|~in(X3,cartesian_product2(singleton(X1),singleton(X2)))),inference(er,[status(thm)],[547,theory(equality)])).
% cnf(553,plain,(unordered_pair(singleton(X1),unordered_pair(X1,X2))=esk6_2(X3,cartesian_product2(singleton(X1),singleton(X2)))|esk6_2(X3,cartesian_product2(singleton(X1),singleton(X2)))=X3|singleton(X3)=cartesian_product2(singleton(X1),singleton(X2))),inference(spm,[status(thm)],[548,40,theory(equality)])).
% cnf(576,plain,(esk6_2(X6,cartesian_product2(singleton(X4),singleton(X5)))=X6|singleton(X6)=cartesian_product2(singleton(X4),singleton(X5))|unordered_pair(singleton(X4),unordered_pair(X4,X5))!=X6),inference(ef,[status(thm)],[553,theory(equality)])).
% cnf(631,plain,(esk6_2(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(singleton(X1),singleton(X2)))=unordered_pair(singleton(X1),unordered_pair(X1,X2))|singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2)))=cartesian_product2(singleton(X1),singleton(X2))),inference(er,[status(thm)],[576,theory(equality)])).
% cnf(646,plain,(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2)))=cartesian_product2(singleton(X1),singleton(X2))|~in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(singleton(X1),singleton(X2)))),inference(spm,[status(thm)],[41,631,theory(equality)])).
% cnf(993,plain,(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2)))=cartesian_product2(singleton(X1),singleton(X2))|~in(X2,singleton(X2))|~in(X1,singleton(X1))),inference(spm,[status(thm)],[646,113,theory(equality)])).
% cnf(999,plain,(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2)))=cartesian_product2(singleton(X1),singleton(X2))|$false|~in(X1,singleton(X1))),inference(rw,[status(thm)],[993,85,theory(equality)])).
% cnf(1000,plain,(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2)))=cartesian_product2(singleton(X1),singleton(X2))|$false|$false),inference(rw,[status(thm)],[999,85,theory(equality)])).
% cnf(1001,plain,(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2)))=cartesian_product2(singleton(X1),singleton(X2))),inference(cn,[status(thm)],[1000,theory(equality)])).
% cnf(1128,plain,(singleton(unordered_pair(unordered_pair(X1,X2),singleton(X1)))=cartesian_product2(singleton(X1),singleton(X2))),inference(spm,[status(thm)],[1001,50,theory(equality)])).
% cnf(1494,negated_conjecture,($false),inference(rw,[status(thm)],[77,1128,theory(equality)])).
% cnf(1495,negated_conjecture,($false),inference(cn,[status(thm)],[1494,theory(equality)])).
% cnf(1496,negated_conjecture,($false),1495,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 321
% # ...of these trivial : 1
% # ...subsumed : 146
% # ...remaining for further processing: 174
% # Other redundant clauses eliminated : 11
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 0
% # Backward-rewritten : 5
% # Generated clauses : 1302
% # ...of the previous two non-trivial : 1098
% # Contextual simplify-reflections : 18
% # Paramodulations : 1254
% # Factorizations : 12
% # Equation resolutions : 36
% # Current number of processed clauses: 145
% # Positive orientable unit clauses: 6
% # Positive unorientable unit clauses: 1
% # Negative unit clauses : 8
% # Non-unit-clauses : 130
% # Current number of unprocessed clauses: 759
% # ...number of literals in the above : 2907
% # Clause-clause subsumption calls (NU) : 2506
% # Rec. Clause-clause subsumption calls : 1707
% # Unit Clause-clause subsumption calls : 44
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 7
% # Indexed BW rewrite successes : 4
% # Backwards rewriting index: 131 leaves, 2.18+/-2.346 terms/leaf
% # Paramod-from index: 34 leaves, 1.26+/-0.441 terms/leaf
% # Paramod-into index: 118 leaves, 1.86+/-1.785 terms/leaf
% # -------------------------------------------------
% # User time : 0.070 s
% # System time : 0.004 s
% # Total time : 0.074 s
% # Maximum resident set size: 0 pages
% PrfWatch: 0.17 CPU 0.26 WC
% FINAL PrfWatch: 0.17 CPU 0.27 WC
% SZS output end Solution for /tmp/SystemOnTPTP2036/SET894+1.tptp
%
%------------------------------------------------------------------------------