TSTP Solution File: GRA003+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : GRA003+1 : TPTP v5.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art05.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 : Wed Dec 29 05:40:29 EST 2010
% Result : Theorem 0.93s
% Output : Solution 0.93s
% 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/SystemOnTPTP30096/GRA003+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP30096/GRA003+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP30096/GRA003+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 30192
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Preprocessing time : 0.017 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(1, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:((shortest_path(X1,X2,X5)&precedes(X3,X4,X5))=>(~(?[X6]:(tail_of(X6)=tail_of(X3)&head_of(X6)=head_of(X4)))&~(precedes(X4,X3,X5)))),file('/tmp/SRASS.s.p', shortest_path_properties)).
% fof(3, axiom,![X1]:![X2]:![X8]:(shortest_path(X1,X2,X8)<=>((path(X1,X2,X8)&~(X1=X2))&![X5]:(path(X1,X2,X5)=>less_or_equal(length_of(X8),length_of(X5))))),file('/tmp/SRASS.s.p', shortest_path_defn)).
% fof(6, axiom,![X5]:![X1]:![X2]:(path(X1,X2,X5)=>![X3]:![X4]:(precedes(X3,X4,X5)=>((on_path(X3,X5)&on_path(X4,X5))&(sequential(X3,X4)<~>?[X6]:(sequential(X3,X6)&precedes(X6,X4,X5)))))),file('/tmp/SRASS.s.p', precedes_properties)).
% fof(9, axiom,![X1]:![X2]:![X5]:(path(X1,X2,X5)=>((vertex(X1)&vertex(X2))&?[X7]:((edge(X7)&X1=tail_of(X7))&((X2=head_of(X7)&X5=path_cons(X7,empty))<~>?[X9]:(path(head_of(X7),X2,X9)&X5=path_cons(X7,X9)))))),file('/tmp/SRASS.s.p', path_properties)).
% fof(12, axiom,![X1]:![X2]:![X5]:![X7]:((path(X1,X2,X5)&on_path(X7,X5))=>((edge(X7)&in_path(head_of(X7),X5))&in_path(tail_of(X7),X5))),file('/tmp/SRASS.s.p', on_path_properties)).
% fof(18, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((shortest_path(X1,X2,X5)&precedes(X3,X4,X5))=>((((((vertex(X1)&vertex(X2))&~(X1=X2))&edge(X3))&edge(X4))&~(X3=X4))&path(X1,X2,X5))),file('/tmp/SRASS.s.p', vertices_and_edges)).
% fof(19, negated_conjecture,~(![X1]:![X2]:![X3]:![X4]:![X5]:((shortest_path(X1,X2,X5)&precedes(X3,X4,X5))=>((((((vertex(X1)&vertex(X2))&~(X1=X2))&edge(X3))&edge(X4))&~(X3=X4))&path(X1,X2,X5)))),inference(assume_negation,[status(cth)],[18])).
% fof(20, plain,![X1]:![X2]:![X3]:![X4]:![X5]:((shortest_path(X1,X2,X5)&precedes(X3,X4,X5))=>(~(?[X6]:(tail_of(X6)=tail_of(X3)&head_of(X6)=head_of(X4)))&~(precedes(X4,X3,X5)))),inference(fof_simplification,[status(thm)],[1,theory(equality)])).
% fof(22, plain,![X5]:![X1]:![X2]:(path(X1,X2,X5)=>![X3]:![X4]:(precedes(X3,X4,X5)=>((on_path(X3,X5)&on_path(X4,X5))&~((sequential(X3,X4)<=>?[X6]:(sequential(X3,X6)&precedes(X6,X4,X5))))))),inference(fof_simplification,[status(thm)],[6,theory(equality)])).
% fof(25, plain,![X1]:![X2]:![X5]:(path(X1,X2,X5)=>((vertex(X1)&vertex(X2))&?[X7]:((edge(X7)&X1=tail_of(X7))&~(((X2=head_of(X7)&X5=path_cons(X7,empty))<=>?[X9]:(path(head_of(X7),X2,X9)&X5=path_cons(X7,X9))))))),inference(fof_simplification,[status(thm)],[9,theory(equality)])).
% fof(26, plain,![X1]:![X2]:![X3]:![X4]:![X5]:((~(shortest_path(X1,X2,X5))|~(precedes(X3,X4,X5)))|(![X6]:(~(tail_of(X6)=tail_of(X3))|~(head_of(X6)=head_of(X4)))&~(precedes(X4,X3,X5)))),inference(fof_nnf,[status(thm)],[20])).
% fof(27, plain,![X7]:![X8]:![X9]:![X10]:![X11]:((~(shortest_path(X7,X8,X11))|~(precedes(X9,X10,X11)))|(![X12]:(~(tail_of(X12)=tail_of(X9))|~(head_of(X12)=head_of(X10)))&~(precedes(X10,X9,X11)))),inference(variable_rename,[status(thm)],[26])).
% fof(28, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:(((~(tail_of(X12)=tail_of(X9))|~(head_of(X12)=head_of(X10)))&~(precedes(X10,X9,X11)))|(~(shortest_path(X7,X8,X11))|~(precedes(X9,X10,X11)))),inference(shift_quantors,[status(thm)],[27])).
% fof(29, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:(((~(tail_of(X12)=tail_of(X9))|~(head_of(X12)=head_of(X10)))|(~(shortest_path(X7,X8,X11))|~(precedes(X9,X10,X11))))&(~(precedes(X10,X9,X11))|(~(shortest_path(X7,X8,X11))|~(precedes(X9,X10,X11))))),inference(distribute,[status(thm)],[28])).
% cnf(31,plain,(~precedes(X1,X2,X3)|~shortest_path(X4,X5,X3)|head_of(X6)!=head_of(X2)|tail_of(X6)!=tail_of(X1)),inference(split_conjunct,[status(thm)],[29])).
% fof(37, plain,![X1]:![X2]:![X8]:((~(shortest_path(X1,X2,X8))|((path(X1,X2,X8)&~(X1=X2))&![X5]:(~(path(X1,X2,X5))|less_or_equal(length_of(X8),length_of(X5)))))&(((~(path(X1,X2,X8))|X1=X2)|?[X5]:(path(X1,X2,X5)&~(less_or_equal(length_of(X8),length_of(X5)))))|shortest_path(X1,X2,X8))),inference(fof_nnf,[status(thm)],[3])).
% fof(38, plain,![X9]:![X10]:![X11]:((~(shortest_path(X9,X10,X11))|((path(X9,X10,X11)&~(X9=X10))&![X12]:(~(path(X9,X10,X12))|less_or_equal(length_of(X11),length_of(X12)))))&(((~(path(X9,X10,X11))|X9=X10)|?[X13]:(path(X9,X10,X13)&~(less_or_equal(length_of(X11),length_of(X13)))))|shortest_path(X9,X10,X11))),inference(variable_rename,[status(thm)],[37])).
% fof(39, plain,![X9]:![X10]:![X11]:((~(shortest_path(X9,X10,X11))|((path(X9,X10,X11)&~(X9=X10))&![X12]:(~(path(X9,X10,X12))|less_or_equal(length_of(X11),length_of(X12)))))&(((~(path(X9,X10,X11))|X9=X10)|(path(X9,X10,esk1_3(X9,X10,X11))&~(less_or_equal(length_of(X11),length_of(esk1_3(X9,X10,X11))))))|shortest_path(X9,X10,X11))),inference(skolemize,[status(esa)],[38])).
% fof(40, plain,![X9]:![X10]:![X11]:![X12]:((((~(path(X9,X10,X12))|less_or_equal(length_of(X11),length_of(X12)))&(path(X9,X10,X11)&~(X9=X10)))|~(shortest_path(X9,X10,X11)))&(((~(path(X9,X10,X11))|X9=X10)|(path(X9,X10,esk1_3(X9,X10,X11))&~(less_or_equal(length_of(X11),length_of(esk1_3(X9,X10,X11))))))|shortest_path(X9,X10,X11))),inference(shift_quantors,[status(thm)],[39])).
% fof(41, plain,![X9]:![X10]:![X11]:![X12]:((((~(path(X9,X10,X12))|less_or_equal(length_of(X11),length_of(X12)))|~(shortest_path(X9,X10,X11)))&((path(X9,X10,X11)|~(shortest_path(X9,X10,X11)))&(~(X9=X10)|~(shortest_path(X9,X10,X11)))))&(((path(X9,X10,esk1_3(X9,X10,X11))|(~(path(X9,X10,X11))|X9=X10))|shortest_path(X9,X10,X11))&((~(less_or_equal(length_of(X11),length_of(esk1_3(X9,X10,X11))))|(~(path(X9,X10,X11))|X9=X10))|shortest_path(X9,X10,X11)))),inference(distribute,[status(thm)],[40])).
% cnf(44,plain,(~shortest_path(X1,X2,X3)|X1!=X2),inference(split_conjunct,[status(thm)],[41])).
% cnf(45,plain,(path(X1,X2,X3)|~shortest_path(X1,X2,X3)),inference(split_conjunct,[status(thm)],[41])).
% fof(56, plain,![X5]:![X1]:![X2]:(~(path(X1,X2,X5))|![X3]:![X4]:(~(precedes(X3,X4,X5))|((on_path(X3,X5)&on_path(X4,X5))&((~(sequential(X3,X4))|![X6]:(~(sequential(X3,X6))|~(precedes(X6,X4,X5))))&(sequential(X3,X4)|?[X6]:(sequential(X3,X6)&precedes(X6,X4,X5))))))),inference(fof_nnf,[status(thm)],[22])).
% fof(57, plain,![X7]:![X8]:![X9]:(~(path(X8,X9,X7))|![X10]:![X11]:(~(precedes(X10,X11,X7))|((on_path(X10,X7)&on_path(X11,X7))&((~(sequential(X10,X11))|![X12]:(~(sequential(X10,X12))|~(precedes(X12,X11,X7))))&(sequential(X10,X11)|?[X13]:(sequential(X10,X13)&precedes(X13,X11,X7))))))),inference(variable_rename,[status(thm)],[56])).
% fof(58, plain,![X7]:![X8]:![X9]:(~(path(X8,X9,X7))|![X10]:![X11]:(~(precedes(X10,X11,X7))|((on_path(X10,X7)&on_path(X11,X7))&((~(sequential(X10,X11))|![X12]:(~(sequential(X10,X12))|~(precedes(X12,X11,X7))))&(sequential(X10,X11)|(sequential(X10,esk2_5(X7,X8,X9,X10,X11))&precedes(esk2_5(X7,X8,X9,X10,X11),X11,X7))))))),inference(skolemize,[status(esa)],[57])).
% fof(59, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:((((((~(sequential(X10,X12))|~(precedes(X12,X11,X7)))|~(sequential(X10,X11)))&(sequential(X10,X11)|(sequential(X10,esk2_5(X7,X8,X9,X10,X11))&precedes(esk2_5(X7,X8,X9,X10,X11),X11,X7))))&(on_path(X10,X7)&on_path(X11,X7)))|~(precedes(X10,X11,X7)))|~(path(X8,X9,X7))),inference(shift_quantors,[status(thm)],[58])).
% fof(60, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:((((((~(sequential(X10,X12))|~(precedes(X12,X11,X7)))|~(sequential(X10,X11)))|~(precedes(X10,X11,X7)))|~(path(X8,X9,X7)))&((((sequential(X10,esk2_5(X7,X8,X9,X10,X11))|sequential(X10,X11))|~(precedes(X10,X11,X7)))|~(path(X8,X9,X7)))&(((precedes(esk2_5(X7,X8,X9,X10,X11),X11,X7)|sequential(X10,X11))|~(precedes(X10,X11,X7)))|~(path(X8,X9,X7)))))&(((on_path(X10,X7)|~(precedes(X10,X11,X7)))|~(path(X8,X9,X7)))&((on_path(X11,X7)|~(precedes(X10,X11,X7)))|~(path(X8,X9,X7))))),inference(distribute,[status(thm)],[59])).
% cnf(61,plain,(on_path(X5,X3)|~path(X1,X2,X3)|~precedes(X4,X5,X3)),inference(split_conjunct,[status(thm)],[60])).
% cnf(62,plain,(on_path(X4,X3)|~path(X1,X2,X3)|~precedes(X4,X5,X3)),inference(split_conjunct,[status(thm)],[60])).
% fof(83, plain,![X1]:![X2]:![X5]:(~(path(X1,X2,X5))|((vertex(X1)&vertex(X2))&?[X7]:((edge(X7)&X1=tail_of(X7))&(((~(X2=head_of(X7))|~(X5=path_cons(X7,empty)))|![X9]:(~(path(head_of(X7),X2,X9))|~(X5=path_cons(X7,X9))))&((X2=head_of(X7)&X5=path_cons(X7,empty))|?[X9]:(path(head_of(X7),X2,X9)&X5=path_cons(X7,X9))))))),inference(fof_nnf,[status(thm)],[25])).
% fof(84, plain,![X10]:![X11]:![X12]:(~(path(X10,X11,X12))|((vertex(X10)&vertex(X11))&?[X13]:((edge(X13)&X10=tail_of(X13))&(((~(X11=head_of(X13))|~(X12=path_cons(X13,empty)))|![X14]:(~(path(head_of(X13),X11,X14))|~(X12=path_cons(X13,X14))))&((X11=head_of(X13)&X12=path_cons(X13,empty))|?[X15]:(path(head_of(X13),X11,X15)&X12=path_cons(X13,X15))))))),inference(variable_rename,[status(thm)],[83])).
% fof(85, plain,![X10]:![X11]:![X12]:(~(path(X10,X11,X12))|((vertex(X10)&vertex(X11))&((edge(esk4_3(X10,X11,X12))&X10=tail_of(esk4_3(X10,X11,X12)))&(((~(X11=head_of(esk4_3(X10,X11,X12)))|~(X12=path_cons(esk4_3(X10,X11,X12),empty)))|![X14]:(~(path(head_of(esk4_3(X10,X11,X12)),X11,X14))|~(X12=path_cons(esk4_3(X10,X11,X12),X14))))&((X11=head_of(esk4_3(X10,X11,X12))&X12=path_cons(esk4_3(X10,X11,X12),empty))|(path(head_of(esk4_3(X10,X11,X12)),X11,esk5_3(X10,X11,X12))&X12=path_cons(esk4_3(X10,X11,X12),esk5_3(X10,X11,X12)))))))),inference(skolemize,[status(esa)],[84])).
% fof(86, plain,![X10]:![X11]:![X12]:![X14]:((((((~(path(head_of(esk4_3(X10,X11,X12)),X11,X14))|~(X12=path_cons(esk4_3(X10,X11,X12),X14)))|(~(X11=head_of(esk4_3(X10,X11,X12)))|~(X12=path_cons(esk4_3(X10,X11,X12),empty))))&((X11=head_of(esk4_3(X10,X11,X12))&X12=path_cons(esk4_3(X10,X11,X12),empty))|(path(head_of(esk4_3(X10,X11,X12)),X11,esk5_3(X10,X11,X12))&X12=path_cons(esk4_3(X10,X11,X12),esk5_3(X10,X11,X12)))))&(edge(esk4_3(X10,X11,X12))&X10=tail_of(esk4_3(X10,X11,X12))))&(vertex(X10)&vertex(X11)))|~(path(X10,X11,X12))),inference(shift_quantors,[status(thm)],[85])).
% fof(87, plain,![X10]:![X11]:![X12]:![X14]:((((((~(path(head_of(esk4_3(X10,X11,X12)),X11,X14))|~(X12=path_cons(esk4_3(X10,X11,X12),X14)))|(~(X11=head_of(esk4_3(X10,X11,X12)))|~(X12=path_cons(esk4_3(X10,X11,X12),empty))))|~(path(X10,X11,X12)))&((((path(head_of(esk4_3(X10,X11,X12)),X11,esk5_3(X10,X11,X12))|X11=head_of(esk4_3(X10,X11,X12)))|~(path(X10,X11,X12)))&((X12=path_cons(esk4_3(X10,X11,X12),esk5_3(X10,X11,X12))|X11=head_of(esk4_3(X10,X11,X12)))|~(path(X10,X11,X12))))&(((path(head_of(esk4_3(X10,X11,X12)),X11,esk5_3(X10,X11,X12))|X12=path_cons(esk4_3(X10,X11,X12),empty))|~(path(X10,X11,X12)))&((X12=path_cons(esk4_3(X10,X11,X12),esk5_3(X10,X11,X12))|X12=path_cons(esk4_3(X10,X11,X12),empty))|~(path(X10,X11,X12))))))&((edge(esk4_3(X10,X11,X12))|~(path(X10,X11,X12)))&(X10=tail_of(esk4_3(X10,X11,X12))|~(path(X10,X11,X12)))))&((vertex(X10)|~(path(X10,X11,X12)))&(vertex(X11)|~(path(X10,X11,X12))))),inference(distribute,[status(thm)],[86])).
% cnf(88,plain,(vertex(X2)|~path(X1,X2,X3)),inference(split_conjunct,[status(thm)],[87])).
% cnf(89,plain,(vertex(X1)|~path(X1,X2,X3)),inference(split_conjunct,[status(thm)],[87])).
% fof(112, plain,![X1]:![X2]:![X5]:![X7]:((~(path(X1,X2,X5))|~(on_path(X7,X5)))|((edge(X7)&in_path(head_of(X7),X5))&in_path(tail_of(X7),X5))),inference(fof_nnf,[status(thm)],[12])).
% fof(113, plain,![X8]:![X9]:![X10]:![X11]:((~(path(X8,X9,X10))|~(on_path(X11,X10)))|((edge(X11)&in_path(head_of(X11),X10))&in_path(tail_of(X11),X10))),inference(variable_rename,[status(thm)],[112])).
% fof(114, plain,![X8]:![X9]:![X10]:![X11]:(((edge(X11)|(~(path(X8,X9,X10))|~(on_path(X11,X10))))&(in_path(head_of(X11),X10)|(~(path(X8,X9,X10))|~(on_path(X11,X10)))))&(in_path(tail_of(X11),X10)|(~(path(X8,X9,X10))|~(on_path(X11,X10))))),inference(distribute,[status(thm)],[113])).
% cnf(117,plain,(edge(X1)|~on_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[114])).
% fof(145, negated_conjecture,?[X1]:?[X2]:?[X3]:?[X4]:?[X5]:((shortest_path(X1,X2,X5)&precedes(X3,X4,X5))&((((((~(vertex(X1))|~(vertex(X2)))|X1=X2)|~(edge(X3)))|~(edge(X4)))|X3=X4)|~(path(X1,X2,X5)))),inference(fof_nnf,[status(thm)],[19])).
% fof(146, negated_conjecture,?[X6]:?[X7]:?[X8]:?[X9]:?[X10]:((shortest_path(X6,X7,X10)&precedes(X8,X9,X10))&((((((~(vertex(X6))|~(vertex(X7)))|X6=X7)|~(edge(X8)))|~(edge(X9)))|X8=X9)|~(path(X6,X7,X10)))),inference(variable_rename,[status(thm)],[145])).
% fof(147, negated_conjecture,((shortest_path(esk9_0,esk10_0,esk13_0)&precedes(esk11_0,esk12_0,esk13_0))&((((((~(vertex(esk9_0))|~(vertex(esk10_0)))|esk9_0=esk10_0)|~(edge(esk11_0)))|~(edge(esk12_0)))|esk11_0=esk12_0)|~(path(esk9_0,esk10_0,esk13_0)))),inference(skolemize,[status(esa)],[146])).
% cnf(148,negated_conjecture,(esk11_0=esk12_0|esk9_0=esk10_0|~path(esk9_0,esk10_0,esk13_0)|~edge(esk12_0)|~edge(esk11_0)|~vertex(esk10_0)|~vertex(esk9_0)),inference(split_conjunct,[status(thm)],[147])).
% cnf(149,negated_conjecture,(precedes(esk11_0,esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[147])).
% cnf(150,negated_conjecture,(shortest_path(esk9_0,esk10_0,esk13_0)),inference(split_conjunct,[status(thm)],[147])).
% cnf(151,plain,(~shortest_path(X1,X1,X2)),inference(er,[status(thm)],[44,theory(equality)])).
% cnf(153,negated_conjecture,(esk9_0=esk10_0|esk12_0=esk11_0|~path(esk9_0,esk10_0,esk13_0)|~vertex(esk9_0)|~edge(esk11_0)|~edge(esk12_0)),inference(csr,[status(thm)],[148,88])).
% cnf(154,negated_conjecture,(esk9_0=esk10_0|esk12_0=esk11_0|~path(esk9_0,esk10_0,esk13_0)|~edge(esk11_0)|~edge(esk12_0)),inference(csr,[status(thm)],[153,89])).
% cnf(160,negated_conjecture,(path(esk9_0,esk10_0,esk13_0)),inference(spm,[status(thm)],[45,150,theory(equality)])).
% cnf(190,negated_conjecture,(tail_of(esk11_0)!=tail_of(X1)|head_of(esk12_0)!=head_of(X1)|~shortest_path(X2,X3,esk13_0)),inference(spm,[status(thm)],[31,149,theory(equality)])).
% cnf(243,negated_conjecture,(edge(X1)|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[117,160,theory(equality)])).
% cnf(247,negated_conjecture,(on_path(X1,esk13_0)|~precedes(X2,X1,esk13_0)),inference(spm,[status(thm)],[61,160,theory(equality)])).
% cnf(248,negated_conjecture,(on_path(X1,esk13_0)|~precedes(X1,X2,esk13_0)),inference(spm,[status(thm)],[62,160,theory(equality)])).
% cnf(254,negated_conjecture,(esk9_0=esk10_0|esk12_0=esk11_0|$false|~edge(esk11_0)|~edge(esk12_0)),inference(rw,[status(thm)],[154,160,theory(equality)])).
% cnf(255,negated_conjecture,(esk9_0=esk10_0|esk12_0=esk11_0|~edge(esk11_0)|~edge(esk12_0)),inference(cn,[status(thm)],[254,theory(equality)])).
% fof(257, plain,(~(epred1_0)<=>![X1]:(~(head_of(esk12_0)=head_of(X1))|~(tail_of(esk11_0)=tail_of(X1)))),introduced(definition),['split']).
% cnf(258,plain,(epred1_0|head_of(esk12_0)!=head_of(X1)|tail_of(esk11_0)!=tail_of(X1)),inference(split_equiv,[status(thm)],[257])).
% fof(259, plain,(~(epred2_0)<=>![X3]:![X2]:~(shortest_path(X2,X3,esk13_0))),introduced(definition),['split']).
% cnf(260,plain,(epred2_0|~shortest_path(X2,X3,esk13_0)),inference(split_equiv,[status(thm)],[259])).
% cnf(261,negated_conjecture,(~epred2_0|~epred1_0),inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[190,257,theory(equality)]),259,theory(equality)]),['split']).
% cnf(267,negated_conjecture,(epred2_0),inference(spm,[status(thm)],[260,150,theory(equality)])).
% cnf(268,negated_conjecture,($false|~epred1_0),inference(rw,[status(thm)],[261,267,theory(equality)])).
% cnf(269,negated_conjecture,(~epred1_0),inference(cn,[status(thm)],[268,theory(equality)])).
% cnf(271,negated_conjecture,(head_of(esk12_0)!=head_of(X1)|tail_of(esk11_0)!=tail_of(X1)),inference(sr,[status(thm)],[258,269,theory(equality)])).
% cnf(272,negated_conjecture,(head_of(esk12_0)!=head_of(esk11_0)),inference(er,[status(thm)],[271,theory(equality)])).
% cnf(277,negated_conjecture,(on_path(esk12_0,esk13_0)),inference(spm,[status(thm)],[247,149,theory(equality)])).
% cnf(279,negated_conjecture,(edge(esk12_0)),inference(spm,[status(thm)],[243,277,theory(equality)])).
% cnf(280,negated_conjecture,(esk12_0=esk11_0|esk9_0=esk10_0|~edge(esk11_0)|$false),inference(rw,[status(thm)],[255,279,theory(equality)])).
% cnf(281,negated_conjecture,(esk12_0=esk11_0|esk9_0=esk10_0|~edge(esk11_0)),inference(cn,[status(thm)],[280,theory(equality)])).
% cnf(285,negated_conjecture,(on_path(esk11_0,esk13_0)),inference(spm,[status(thm)],[248,149,theory(equality)])).
% cnf(287,negated_conjecture,(edge(esk11_0)),inference(spm,[status(thm)],[243,285,theory(equality)])).
% cnf(288,negated_conjecture,(esk9_0=esk10_0|esk12_0=esk11_0|$false),inference(rw,[status(thm)],[281,287,theory(equality)])).
% cnf(289,negated_conjecture,(esk9_0=esk10_0|esk12_0=esk11_0),inference(cn,[status(thm)],[288,theory(equality)])).
% cnf(291,negated_conjecture,(esk9_0=esk10_0),inference(spm,[status(thm)],[272,289,theory(equality)])).
% cnf(302,negated_conjecture,(shortest_path(esk10_0,esk10_0,esk13_0)),inference(rw,[status(thm)],[150,291,theory(equality)])).
% cnf(303,negated_conjecture,($false),inference(sr,[status(thm)],[302,151,theory(equality)])).
% cnf(304,negated_conjecture,($false),303,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 154
% # ...of these trivial : 0
% # ...subsumed : 2
% # ...remaining for further processing: 152
% # Other redundant clauses eliminated : 2
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 0
% # Backward-rewritten : 9
% # Generated clauses : 123
% # ...of the previous two non-trivial : 115
% # Contextual simplify-reflections : 11
% # Paramodulations : 116
% # Factorizations : 0
% # Equation resolutions : 4
% # Current number of processed clauses: 79
% # Positive orientable unit clauses: 10
% # Positive unorientable unit clauses: 0
% # Negative unit clauses : 5
% # Non-unit-clauses : 64
% # Current number of unprocessed clauses: 75
% # ...number of literals in the above : 356
% # Clause-clause subsumption calls (NU) : 116
% # Rec. Clause-clause subsumption calls : 81
% # Unit Clause-clause subsumption calls : 28
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 5
% # Indexed BW rewrite successes : 5
% # Backwards rewriting index: 85 leaves, 1.56+/-1.732 terms/leaf
% # Paramod-from index: 27 leaves, 1.00+/-0.000 terms/leaf
% # Paramod-into index: 62 leaves, 1.35+/-1.123 terms/leaf
% # -------------------------------------------------
% # User time : 0.028 s
% # System time : 0.004 s
% # Total time : 0.032 s
% # Maximum resident set size: 0 pages
% PrfWatch: 0.12 CPU 0.21 WC
% FINAL PrfWatch: 0.12 CPU 0.21 WC
% SZS output end Solution for /tmp/SystemOnTPTP30096/GRA003+1.tptp
%
%------------------------------------------------------------------------------