TSTP Solution File: GRA008+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : GRA008+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 : art02.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 05:40:57 EST 2010
% Result : Theorem 3.68s
% Output : Solution 3.68s
% 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/SystemOnTPTP18749/GRA008+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP18749/GRA008+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP18749/GRA008+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 18845
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% PrfWatch: 1.93 CPU 2.02 WC
% # Preprocessing time : 0.018 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(1, axiom,![X1]:![X2]:![X3]:(triangle(X1,X2,X3)<=>(((((edge(X1)&edge(X2))&edge(X3))&sequential(X1,X2))&sequential(X2,X3))&sequential(X3,X1))),file('/tmp/SRASS.s.p', triangle_defn)).
% fof(2, axiom,![X4]:![X5]:![X6]:(path(X5,X6,X4)=>![X1]:![X2]:(precedes(X1,X2,X4)<=((on_path(X1,X4)&on_path(X2,X4))&(sequential(X1,X2)|?[X3]:(sequential(X1,X3)&precedes(X3,X2,X4)))))),file('/tmp/SRASS.s.p', precedes_defn)).
% fof(3, axiom,![X4]:![X5]:![X6]:(path(X5,X6,X4)=>![X1]:![X2]:(precedes(X1,X2,X4)=>((on_path(X1,X4)&on_path(X2,X4))&(sequential(X1,X2)<~>?[X3]:(sequential(X1,X3)&precedes(X3,X2,X4)))))),file('/tmp/SRASS.s.p', precedes_properties)).
% fof(4, axiom,![X5]:![X6]:![X1]:![X2]:![X4]:((shortest_path(X5,X6,X4)&precedes(X1,X2,X4))=>(~(?[X3]:(tail_of(X3)=tail_of(X1)&head_of(X3)=head_of(X2)))&~(precedes(X2,X1,X4)))),file('/tmp/SRASS.s.p', shortest_path_properties)).
% fof(5, axiom,![X7]:(edge(X7)=>~(head_of(X7)=tail_of(X7))),file('/tmp/SRASS.s.p', no_loops)).
% fof(7, axiom,(complete=>![X5]:![X6]:(((vertex(X5)&vertex(X6))&~(X5=X6))=>?[X7]:(edge(X7)&((X5=head_of(X7)&X6=tail_of(X7))<~>(X6=head_of(X7)&X5=tail_of(X7)))))),file('/tmp/SRASS.s.p', complete_properties)).
% fof(8, axiom,![X1]:![X2]:(sequential(X1,X2)<=>(((edge(X1)&edge(X2))&~(X1=X2))&head_of(X1)=tail_of(X2))),file('/tmp/SRASS.s.p', sequential_defn)).
% fof(9, axiom,![X5]:![X6]:![X8]:(shortest_path(X5,X6,X8)<=>((path(X5,X6,X8)&~(X5=X6))&![X4]:(path(X5,X6,X4)=>less_or_equal(length_of(X8),length_of(X4))))),file('/tmp/SRASS.s.p', shortest_path_defn)).
% fof(12, axiom,![X7]:(edge(X7)=>(vertex(head_of(X7))&vertex(tail_of(X7)))),file('/tmp/SRASS.s.p', edge_ends_are_vertices)).
% fof(13, axiom,![X5]:![X6]:![X4]:![X7]:((path(X5,X6,X4)&on_path(X7,X4))=>((edge(X7)&in_path(head_of(X7),X4))&in_path(tail_of(X7),X4))),file('/tmp/SRASS.s.p', on_path_properties)).
% fof(14, axiom,![X5]:![X6]:![X4]:![X9]:((path(X5,X6,X4)&in_path(X9,X4))=>(vertex(X9)&?[X7]:(on_path(X7,X4)&(X9=head_of(X7)|X9=tail_of(X7))))),file('/tmp/SRASS.s.p', in_path_properties)).
% fof(18, conjecture,(complete=>![X5]:![X6]:![X1]:![X2]:![X4]:(((shortest_path(X5,X6,X4)&precedes(X1,X2,X4))&sequential(X1,X2))=>?[X3]:triangle(X1,X2,X3))),file('/tmp/SRASS.s.p', sequential_is_triangle)).
% fof(19, negated_conjecture,~((complete=>![X5]:![X6]:![X1]:![X2]:![X4]:(((shortest_path(X5,X6,X4)&precedes(X1,X2,X4))&sequential(X1,X2))=>?[X3]:triangle(X1,X2,X3)))),inference(assume_negation,[status(cth)],[18])).
% fof(20, plain,![X4]:![X5]:![X6]:(path(X5,X6,X4)=>![X1]:![X2]:(((on_path(X1,X4)&on_path(X2,X4))&(sequential(X1,X2)|?[X3]:(sequential(X1,X3)&precedes(X3,X2,X4))))=>precedes(X1,X2,X4))),inference(fof_simplification,[status(thm)],[2,theory(equality)])).
% fof(21, plain,![X4]:![X5]:![X6]:(path(X5,X6,X4)=>![X1]:![X2]:(precedes(X1,X2,X4)=>((on_path(X1,X4)&on_path(X2,X4))&~((sequential(X1,X2)<=>?[X3]:(sequential(X1,X3)&precedes(X3,X2,X4))))))),inference(fof_simplification,[status(thm)],[3,theory(equality)])).
% fof(22, plain,![X5]:![X6]:![X1]:![X2]:![X4]:((shortest_path(X5,X6,X4)&precedes(X1,X2,X4))=>(~(?[X3]:(tail_of(X3)=tail_of(X1)&head_of(X3)=head_of(X2)))&~(precedes(X2,X1,X4)))),inference(fof_simplification,[status(thm)],[4,theory(equality)])).
% fof(23, plain,(complete=>![X5]:![X6]:(((vertex(X5)&vertex(X6))&~(X5=X6))=>?[X7]:(edge(X7)&~(((X5=head_of(X7)&X6=tail_of(X7))<=>(X6=head_of(X7)&X5=tail_of(X7))))))),inference(fof_simplification,[status(thm)],[7,theory(equality)])).
% fof(26, plain,![X1]:![X2]:![X3]:((~(triangle(X1,X2,X3))|(((((edge(X1)&edge(X2))&edge(X3))&sequential(X1,X2))&sequential(X2,X3))&sequential(X3,X1)))&((((((~(edge(X1))|~(edge(X2)))|~(edge(X3)))|~(sequential(X1,X2)))|~(sequential(X2,X3)))|~(sequential(X3,X1)))|triangle(X1,X2,X3))),inference(fof_nnf,[status(thm)],[1])).
% fof(27, plain,![X4]:![X5]:![X6]:((~(triangle(X4,X5,X6))|(((((edge(X4)&edge(X5))&edge(X6))&sequential(X4,X5))&sequential(X5,X6))&sequential(X6,X4)))&((((((~(edge(X4))|~(edge(X5)))|~(edge(X6)))|~(sequential(X4,X5)))|~(sequential(X5,X6)))|~(sequential(X6,X4)))|triangle(X4,X5,X6))),inference(variable_rename,[status(thm)],[26])).
% fof(28, plain,![X4]:![X5]:![X6]:(((((((edge(X4)|~(triangle(X4,X5,X6)))&(edge(X5)|~(triangle(X4,X5,X6))))&(edge(X6)|~(triangle(X4,X5,X6))))&(sequential(X4,X5)|~(triangle(X4,X5,X6))))&(sequential(X5,X6)|~(triangle(X4,X5,X6))))&(sequential(X6,X4)|~(triangle(X4,X5,X6))))&((((((~(edge(X4))|~(edge(X5)))|~(edge(X6)))|~(sequential(X4,X5)))|~(sequential(X5,X6)))|~(sequential(X6,X4)))|triangle(X4,X5,X6))),inference(distribute,[status(thm)],[27])).
% cnf(29,plain,(triangle(X1,X2,X3)|~sequential(X3,X1)|~sequential(X2,X3)|~sequential(X1,X2)|~edge(X3)|~edge(X2)|~edge(X1)),inference(split_conjunct,[status(thm)],[28])).
% fof(36, plain,![X4]:![X5]:![X6]:(~(path(X5,X6,X4))|![X1]:![X2]:(((~(on_path(X1,X4))|~(on_path(X2,X4)))|(~(sequential(X1,X2))&![X3]:(~(sequential(X1,X3))|~(precedes(X3,X2,X4)))))|precedes(X1,X2,X4))),inference(fof_nnf,[status(thm)],[20])).
% fof(37, plain,![X7]:![X8]:![X9]:(~(path(X8,X9,X7))|![X10]:![X11]:(((~(on_path(X10,X7))|~(on_path(X11,X7)))|(~(sequential(X10,X11))&![X12]:(~(sequential(X10,X12))|~(precedes(X12,X11,X7)))))|precedes(X10,X11,X7))),inference(variable_rename,[status(thm)],[36])).
% fof(38, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:(((((~(sequential(X10,X12))|~(precedes(X12,X11,X7)))&~(sequential(X10,X11)))|(~(on_path(X10,X7))|~(on_path(X11,X7))))|precedes(X10,X11,X7))|~(path(X8,X9,X7))),inference(shift_quantors,[status(thm)],[37])).
% fof(39, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:(((((~(sequential(X10,X12))|~(precedes(X12,X11,X7)))|(~(on_path(X10,X7))|~(on_path(X11,X7))))|precedes(X10,X11,X7))|~(path(X8,X9,X7)))&(((~(sequential(X10,X11))|(~(on_path(X10,X7))|~(on_path(X11,X7))))|precedes(X10,X11,X7))|~(path(X8,X9,X7)))),inference(distribute,[status(thm)],[38])).
% cnf(40,plain,(precedes(X4,X5,X3)|~path(X1,X2,X3)|~on_path(X5,X3)|~on_path(X4,X3)|~sequential(X4,X5)),inference(split_conjunct,[status(thm)],[39])).
% fof(42, plain,![X4]:![X5]:![X6]:(~(path(X5,X6,X4))|![X1]:![X2]:(~(precedes(X1,X2,X4))|((on_path(X1,X4)&on_path(X2,X4))&((~(sequential(X1,X2))|![X3]:(~(sequential(X1,X3))|~(precedes(X3,X2,X4))))&(sequential(X1,X2)|?[X3]:(sequential(X1,X3)&precedes(X3,X2,X4))))))),inference(fof_nnf,[status(thm)],[21])).
% fof(43, 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)],[42])).
% fof(44, 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,esk1_5(X7,X8,X9,X10,X11))&precedes(esk1_5(X7,X8,X9,X10,X11),X11,X7))))))),inference(skolemize,[status(esa)],[43])).
% fof(45, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:((((((~(sequential(X10,X12))|~(precedes(X12,X11,X7)))|~(sequential(X10,X11)))&(sequential(X10,X11)|(sequential(X10,esk1_5(X7,X8,X9,X10,X11))&precedes(esk1_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)],[44])).
% fof(46, 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,esk1_5(X7,X8,X9,X10,X11))|sequential(X10,X11))|~(precedes(X10,X11,X7)))|~(path(X8,X9,X7)))&(((precedes(esk1_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)],[45])).
% cnf(47,plain,(on_path(X5,X3)|~path(X1,X2,X3)|~precedes(X4,X5,X3)),inference(split_conjunct,[status(thm)],[46])).
% cnf(48,plain,(on_path(X4,X3)|~path(X1,X2,X3)|~precedes(X4,X5,X3)),inference(split_conjunct,[status(thm)],[46])).
% fof(52, plain,![X5]:![X6]:![X1]:![X2]:![X4]:((~(shortest_path(X5,X6,X4))|~(precedes(X1,X2,X4)))|(![X3]:(~(tail_of(X3)=tail_of(X1))|~(head_of(X3)=head_of(X2)))&~(precedes(X2,X1,X4)))),inference(fof_nnf,[status(thm)],[22])).
% fof(53, 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)],[52])).
% fof(54, 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)],[53])).
% fof(55, 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)],[54])).
% cnf(56,plain,(~precedes(X1,X2,X3)|~shortest_path(X4,X5,X3)|~precedes(X2,X1,X3)),inference(split_conjunct,[status(thm)],[55])).
% cnf(57,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)],[55])).
% fof(58, plain,![X7]:(~(edge(X7))|~(head_of(X7)=tail_of(X7))),inference(fof_nnf,[status(thm)],[5])).
% fof(59, plain,![X8]:(~(edge(X8))|~(head_of(X8)=tail_of(X8))),inference(variable_rename,[status(thm)],[58])).
% cnf(60,plain,(head_of(X1)!=tail_of(X1)|~edge(X1)),inference(split_conjunct,[status(thm)],[59])).
% fof(70, plain,(~(complete)|![X5]:![X6]:(((~(vertex(X5))|~(vertex(X6)))|X5=X6)|?[X7]:(edge(X7)&(((~(X5=head_of(X7))|~(X6=tail_of(X7)))|(~(X6=head_of(X7))|~(X5=tail_of(X7))))&((X5=head_of(X7)&X6=tail_of(X7))|(X6=head_of(X7)&X5=tail_of(X7))))))),inference(fof_nnf,[status(thm)],[23])).
% fof(71, plain,(~(complete)|![X8]:![X9]:(((~(vertex(X8))|~(vertex(X9)))|X8=X9)|?[X10]:(edge(X10)&(((~(X8=head_of(X10))|~(X9=tail_of(X10)))|(~(X9=head_of(X10))|~(X8=tail_of(X10))))&((X8=head_of(X10)&X9=tail_of(X10))|(X9=head_of(X10)&X8=tail_of(X10))))))),inference(variable_rename,[status(thm)],[70])).
% fof(72, plain,(~(complete)|![X8]:![X9]:(((~(vertex(X8))|~(vertex(X9)))|X8=X9)|(edge(esk4_2(X8,X9))&(((~(X8=head_of(esk4_2(X8,X9)))|~(X9=tail_of(esk4_2(X8,X9))))|(~(X9=head_of(esk4_2(X8,X9)))|~(X8=tail_of(esk4_2(X8,X9)))))&((X8=head_of(esk4_2(X8,X9))&X9=tail_of(esk4_2(X8,X9)))|(X9=head_of(esk4_2(X8,X9))&X8=tail_of(esk4_2(X8,X9)))))))),inference(skolemize,[status(esa)],[71])).
% fof(73, plain,![X8]:![X9]:((((~(vertex(X8))|~(vertex(X9)))|X8=X9)|(edge(esk4_2(X8,X9))&(((~(X8=head_of(esk4_2(X8,X9)))|~(X9=tail_of(esk4_2(X8,X9))))|(~(X9=head_of(esk4_2(X8,X9)))|~(X8=tail_of(esk4_2(X8,X9)))))&((X8=head_of(esk4_2(X8,X9))&X9=tail_of(esk4_2(X8,X9)))|(X9=head_of(esk4_2(X8,X9))&X8=tail_of(esk4_2(X8,X9)))))))|~(complete)),inference(shift_quantors,[status(thm)],[72])).
% fof(74, plain,![X8]:![X9]:(((edge(esk4_2(X8,X9))|((~(vertex(X8))|~(vertex(X9)))|X8=X9))|~(complete))&(((((~(X8=head_of(esk4_2(X8,X9)))|~(X9=tail_of(esk4_2(X8,X9))))|(~(X9=head_of(esk4_2(X8,X9)))|~(X8=tail_of(esk4_2(X8,X9)))))|((~(vertex(X8))|~(vertex(X9)))|X8=X9))|~(complete))&(((((X9=head_of(esk4_2(X8,X9))|X8=head_of(esk4_2(X8,X9)))|((~(vertex(X8))|~(vertex(X9)))|X8=X9))|~(complete))&(((X8=tail_of(esk4_2(X8,X9))|X8=head_of(esk4_2(X8,X9)))|((~(vertex(X8))|~(vertex(X9)))|X8=X9))|~(complete)))&((((X9=head_of(esk4_2(X8,X9))|X9=tail_of(esk4_2(X8,X9)))|((~(vertex(X8))|~(vertex(X9)))|X8=X9))|~(complete))&(((X8=tail_of(esk4_2(X8,X9))|X9=tail_of(esk4_2(X8,X9)))|((~(vertex(X8))|~(vertex(X9)))|X8=X9))|~(complete)))))),inference(distribute,[status(thm)],[73])).
% cnf(75,plain,(X1=X2|X2=tail_of(esk4_2(X1,X2))|X1=tail_of(esk4_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[74])).
% cnf(76,plain,(X1=X2|X2=tail_of(esk4_2(X1,X2))|X2=head_of(esk4_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[74])).
% cnf(77,plain,(X1=X2|X1=head_of(esk4_2(X1,X2))|X1=tail_of(esk4_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[74])).
% cnf(78,plain,(X1=X2|X1=head_of(esk4_2(X1,X2))|X2=head_of(esk4_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[74])).
% cnf(80,plain,(X1=X2|edge(esk4_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[74])).
% fof(81, plain,![X1]:![X2]:((~(sequential(X1,X2))|(((edge(X1)&edge(X2))&~(X1=X2))&head_of(X1)=tail_of(X2)))&((((~(edge(X1))|~(edge(X2)))|X1=X2)|~(head_of(X1)=tail_of(X2)))|sequential(X1,X2))),inference(fof_nnf,[status(thm)],[8])).
% fof(82, plain,![X3]:![X4]:((~(sequential(X3,X4))|(((edge(X3)&edge(X4))&~(X3=X4))&head_of(X3)=tail_of(X4)))&((((~(edge(X3))|~(edge(X4)))|X3=X4)|~(head_of(X3)=tail_of(X4)))|sequential(X3,X4))),inference(variable_rename,[status(thm)],[81])).
% fof(83, plain,![X3]:![X4]:(((((edge(X3)|~(sequential(X3,X4)))&(edge(X4)|~(sequential(X3,X4))))&(~(X3=X4)|~(sequential(X3,X4))))&(head_of(X3)=tail_of(X4)|~(sequential(X3,X4))))&((((~(edge(X3))|~(edge(X4)))|X3=X4)|~(head_of(X3)=tail_of(X4)))|sequential(X3,X4))),inference(distribute,[status(thm)],[82])).
% cnf(84,plain,(sequential(X1,X2)|X1=X2|head_of(X1)!=tail_of(X2)|~edge(X2)|~edge(X1)),inference(split_conjunct,[status(thm)],[83])).
% cnf(85,plain,(head_of(X1)=tail_of(X2)|~sequential(X1,X2)),inference(split_conjunct,[status(thm)],[83])).
% cnf(87,plain,(edge(X2)|~sequential(X1,X2)),inference(split_conjunct,[status(thm)],[83])).
% cnf(88,plain,(edge(X1)|~sequential(X1,X2)),inference(split_conjunct,[status(thm)],[83])).
% fof(89, plain,![X5]:![X6]:![X8]:((~(shortest_path(X5,X6,X8))|((path(X5,X6,X8)&~(X5=X6))&![X4]:(~(path(X5,X6,X4))|less_or_equal(length_of(X8),length_of(X4)))))&(((~(path(X5,X6,X8))|X5=X6)|?[X4]:(path(X5,X6,X4)&~(less_or_equal(length_of(X8),length_of(X4)))))|shortest_path(X5,X6,X8))),inference(fof_nnf,[status(thm)],[9])).
% fof(90, 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)],[89])).
% fof(91, 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,esk5_3(X9,X10,X11))&~(less_or_equal(length_of(X11),length_of(esk5_3(X9,X10,X11))))))|shortest_path(X9,X10,X11))),inference(skolemize,[status(esa)],[90])).
% fof(92, 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,esk5_3(X9,X10,X11))&~(less_or_equal(length_of(X11),length_of(esk5_3(X9,X10,X11))))))|shortest_path(X9,X10,X11))),inference(shift_quantors,[status(thm)],[91])).
% fof(93, 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,esk5_3(X9,X10,X11))|(~(path(X9,X10,X11))|X9=X10))|shortest_path(X9,X10,X11))&((~(less_or_equal(length_of(X11),length_of(esk5_3(X9,X10,X11))))|(~(path(X9,X10,X11))|X9=X10))|shortest_path(X9,X10,X11)))),inference(distribute,[status(thm)],[92])).
% cnf(97,plain,(path(X1,X2,X3)|~shortest_path(X1,X2,X3)),inference(split_conjunct,[status(thm)],[93])).
% fof(105, plain,![X7]:(~(edge(X7))|(vertex(head_of(X7))&vertex(tail_of(X7)))),inference(fof_nnf,[status(thm)],[12])).
% fof(106, plain,![X8]:(~(edge(X8))|(vertex(head_of(X8))&vertex(tail_of(X8)))),inference(variable_rename,[status(thm)],[105])).
% fof(107, plain,![X8]:((vertex(head_of(X8))|~(edge(X8)))&(vertex(tail_of(X8))|~(edge(X8)))),inference(distribute,[status(thm)],[106])).
% cnf(108,plain,(vertex(tail_of(X1))|~edge(X1)),inference(split_conjunct,[status(thm)],[107])).
% fof(110, plain,![X5]:![X6]:![X4]:![X7]:((~(path(X5,X6,X4))|~(on_path(X7,X4)))|((edge(X7)&in_path(head_of(X7),X4))&in_path(tail_of(X7),X4))),inference(fof_nnf,[status(thm)],[13])).
% fof(111, 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)],[110])).
% fof(112, 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)],[111])).
% cnf(113,plain,(in_path(tail_of(X1),X2)|~on_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[112])).
% cnf(114,plain,(in_path(head_of(X1),X2)|~on_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[112])).
% fof(116, plain,![X5]:![X6]:![X4]:![X9]:((~(path(X5,X6,X4))|~(in_path(X9,X4)))|(vertex(X9)&?[X7]:(on_path(X7,X4)&(X9=head_of(X7)|X9=tail_of(X7))))),inference(fof_nnf,[status(thm)],[14])).
% fof(117, plain,![X10]:![X11]:![X12]:![X13]:((~(path(X10,X11,X12))|~(in_path(X13,X12)))|(vertex(X13)&?[X14]:(on_path(X14,X12)&(X13=head_of(X14)|X13=tail_of(X14))))),inference(variable_rename,[status(thm)],[116])).
% fof(118, plain,![X10]:![X11]:![X12]:![X13]:((~(path(X10,X11,X12))|~(in_path(X13,X12)))|(vertex(X13)&(on_path(esk6_4(X10,X11,X12,X13),X12)&(X13=head_of(esk6_4(X10,X11,X12,X13))|X13=tail_of(esk6_4(X10,X11,X12,X13)))))),inference(skolemize,[status(esa)],[117])).
% fof(119, plain,![X10]:![X11]:![X12]:![X13]:((vertex(X13)|(~(path(X10,X11,X12))|~(in_path(X13,X12))))&((on_path(esk6_4(X10,X11,X12,X13),X12)|(~(path(X10,X11,X12))|~(in_path(X13,X12))))&((X13=head_of(esk6_4(X10,X11,X12,X13))|X13=tail_of(esk6_4(X10,X11,X12,X13)))|(~(path(X10,X11,X12))|~(in_path(X13,X12)))))),inference(distribute,[status(thm)],[118])).
% cnf(122,plain,(vertex(X1)|~in_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[119])).
% fof(145, negated_conjecture,(complete&?[X5]:?[X6]:?[X1]:?[X2]:?[X4]:(((shortest_path(X5,X6,X4)&precedes(X1,X2,X4))&sequential(X1,X2))&![X3]:~(triangle(X1,X2,X3)))),inference(fof_nnf,[status(thm)],[19])).
% fof(146, negated_conjecture,(complete&?[X7]:?[X8]:?[X9]:?[X10]:?[X11]:(((shortest_path(X7,X8,X11)&precedes(X9,X10,X11))&sequential(X9,X10))&![X12]:~(triangle(X9,X10,X12)))),inference(variable_rename,[status(thm)],[145])).
% fof(147, negated_conjecture,(complete&(((shortest_path(esk9_0,esk10_0,esk13_0)&precedes(esk11_0,esk12_0,esk13_0))&sequential(esk11_0,esk12_0))&![X12]:~(triangle(esk11_0,esk12_0,X12)))),inference(skolemize,[status(esa)],[146])).
% fof(148, negated_conjecture,![X12]:((~(triangle(esk11_0,esk12_0,X12))&((shortest_path(esk9_0,esk10_0,esk13_0)&precedes(esk11_0,esk12_0,esk13_0))&sequential(esk11_0,esk12_0)))&complete),inference(shift_quantors,[status(thm)],[147])).
% cnf(149,negated_conjecture,(complete),inference(split_conjunct,[status(thm)],[148])).
% cnf(150,negated_conjecture,(sequential(esk11_0,esk12_0)),inference(split_conjunct,[status(thm)],[148])).
% cnf(151,negated_conjecture,(precedes(esk11_0,esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[148])).
% cnf(152,negated_conjecture,(shortest_path(esk9_0,esk10_0,esk13_0)),inference(split_conjunct,[status(thm)],[148])).
% cnf(153,negated_conjecture,(~triangle(esk11_0,esk12_0,X1)),inference(split_conjunct,[status(thm)],[148])).
% cnf(156,plain,(X1=X2|edge(esk4_2(X1,X2))|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[80,149,theory(equality)])).
% cnf(157,plain,(X1=X2|edge(esk4_2(X1,X2))|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[156,theory(equality)])).
% cnf(158,plain,(X1=X2|tail_of(esk4_2(X1,X2))=X2|tail_of(esk4_2(X1,X2))=X1|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[75,149,theory(equality)])).
% cnf(159,plain,(X1=X2|tail_of(esk4_2(X1,X2))=X2|tail_of(esk4_2(X1,X2))=X1|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[158,theory(equality)])).
% cnf(160,plain,(X1=X2|tail_of(esk4_2(X1,X2))=X2|head_of(esk4_2(X1,X2))=X2|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[76,149,theory(equality)])).
% cnf(161,plain,(X1=X2|tail_of(esk4_2(X1,X2))=X2|head_of(esk4_2(X1,X2))=X2|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[160,theory(equality)])).
% cnf(162,plain,(X1=X2|tail_of(esk4_2(X1,X2))=X1|head_of(esk4_2(X1,X2))=X1|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[77,149,theory(equality)])).
% cnf(163,plain,(X1=X2|tail_of(esk4_2(X1,X2))=X1|head_of(esk4_2(X1,X2))=X1|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[162,theory(equality)])).
% cnf(164,plain,(triangle(X1,X2,X3)|~sequential(X3,X1)|~sequential(X2,X3)|~sequential(X1,X2)|~edge(X3)|~edge(X2)),inference(csr,[status(thm)],[29,88])).
% cnf(165,plain,(triangle(X1,X2,X3)|~sequential(X3,X1)|~sequential(X2,X3)|~sequential(X1,X2)|~edge(X3)),inference(csr,[status(thm)],[164,88])).
% cnf(166,plain,(triangle(X1,X2,X3)|~sequential(X3,X1)|~sequential(X2,X3)|~sequential(X1,X2)),inference(csr,[status(thm)],[165,88])).
% cnf(168,plain,(X1=X2|head_of(esk4_2(X1,X2))=X2|head_of(esk4_2(X1,X2))=X1|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[78,149,theory(equality)])).
% cnf(169,plain,(X1=X2|head_of(esk4_2(X1,X2))=X2|head_of(esk4_2(X1,X2))=X1|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[168,theory(equality)])).
% cnf(171,negated_conjecture,(edge(esk12_0)),inference(spm,[status(thm)],[87,150,theory(equality)])).
% cnf(172,negated_conjecture,(edge(esk11_0)),inference(spm,[status(thm)],[88,150,theory(equality)])).
% cnf(173,negated_conjecture,(path(esk9_0,esk10_0,esk13_0)),inference(spm,[status(thm)],[97,152,theory(equality)])).
% cnf(174,negated_conjecture,(~sequential(X1,esk11_0)|~sequential(esk12_0,X1)|~sequential(esk11_0,esk12_0)),inference(spm,[status(thm)],[153,166,theory(equality)])).
% cnf(181,negated_conjecture,(~sequential(X1,esk11_0)|~sequential(esk12_0,X1)|$false),inference(rw,[status(thm)],[174,150,theory(equality)])).
% cnf(182,negated_conjecture,(~sequential(X1,esk11_0)|~sequential(esk12_0,X1)),inference(cn,[status(thm)],[181,theory(equality)])).
% cnf(183,negated_conjecture,(head_of(esk11_0)=tail_of(esk12_0)),inference(spm,[status(thm)],[85,150,theory(equality)])).
% cnf(184,negated_conjecture,(~precedes(X1,X2,esk13_0)|~precedes(X2,X1,esk13_0)),inference(spm,[status(thm)],[56,152,theory(equality)])).
% cnf(185,negated_conjecture,(on_path(esk12_0,esk13_0)|~path(X1,X2,esk13_0)),inference(spm,[status(thm)],[47,151,theory(equality)])).
% cnf(186,negated_conjecture,(on_path(esk11_0,esk13_0)|~path(X1,X2,esk13_0)),inference(spm,[status(thm)],[48,151,theory(equality)])).
% cnf(190,plain,(esk4_2(X1,X2)=X3|sequential(esk4_2(X1,X2),X3)|X1=X2|head_of(esk4_2(X1,X2))!=tail_of(X3)|~edge(X3)|~vertex(X2)|~vertex(X1)),inference(spm,[status(thm)],[84,157,theory(equality)])).
% cnf(216,negated_conjecture,(tail_of(X1)!=tail_of(X2)|head_of(X3)!=head_of(X2)|~precedes(X1,X3,esk13_0)),inference(spm,[status(thm)],[57,152,theory(equality)])).
% cnf(218,plain,(head_of(esk4_2(X1,tail_of(X2)))=tail_of(X2)|head_of(esk4_2(X1,tail_of(X2)))=X1|X1=tail_of(X2)|~vertex(X1)|~edge(X2)),inference(spm,[status(thm)],[169,108,theory(equality)])).
% cnf(252,negated_conjecture,(~precedes(esk12_0,esk11_0,esk13_0)),inference(spm,[status(thm)],[184,151,theory(equality)])).
% cnf(254,negated_conjecture,(esk12_0=X1|sequential(esk12_0,X1)|head_of(esk12_0)!=tail_of(X1)|~edge(X1)),inference(spm,[status(thm)],[84,171,theory(equality)])).
% cnf(260,negated_conjecture,(vertex(X1)|~in_path(X1,esk13_0)),inference(spm,[status(thm)],[122,173,theory(equality)])).
% cnf(261,negated_conjecture,(in_path(tail_of(X1),esk13_0)|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[113,173,theory(equality)])).
% cnf(262,negated_conjecture,(in_path(head_of(X1),esk13_0)|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[114,173,theory(equality)])).
% cnf(265,negated_conjecture,(precedes(X1,X2,esk13_0)|~on_path(X2,esk13_0)|~on_path(X1,esk13_0)|~sequential(X1,X2)),inference(spm,[status(thm)],[40,173,theory(equality)])).
% cnf(282,negated_conjecture,(head_of(esk11_0)!=head_of(esk12_0)|~edge(esk12_0)),inference(spm,[status(thm)],[60,183,theory(equality)])).
% cnf(285,negated_conjecture,(head_of(esk11_0)!=head_of(esk12_0)|$false),inference(rw,[status(thm)],[282,171,theory(equality)])).
% cnf(286,negated_conjecture,(head_of(esk11_0)!=head_of(esk12_0)),inference(cn,[status(thm)],[285,theory(equality)])).
% cnf(294,negated_conjecture,(tail_of(esk11_0)!=tail_of(X1)|head_of(esk12_0)!=head_of(X1)),inference(spm,[status(thm)],[216,151,theory(equality)])).
% cnf(306,negated_conjecture,(tail_of(esk11_0)!=head_of(esk11_0)),inference(spm,[status(thm)],[294,183,theory(equality)])).
% cnf(311,negated_conjecture,(on_path(esk12_0,esk13_0)),inference(spm,[status(thm)],[185,173,theory(equality)])).
% cnf(315,negated_conjecture,(on_path(esk11_0,esk13_0)),inference(spm,[status(thm)],[186,173,theory(equality)])).
% cnf(321,negated_conjecture,(vertex(tail_of(X1))|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[260,261,theory(equality)])).
% cnf(332,negated_conjecture,(vertex(tail_of(esk11_0))),inference(spm,[status(thm)],[321,315,theory(equality)])).
% cnf(348,negated_conjecture,(tail_of(esk4_2(X1,tail_of(esk11_0)))=tail_of(esk11_0)|tail_of(esk4_2(X1,tail_of(esk11_0)))=X1|X1=tail_of(esk11_0)|~vertex(X1)),inference(spm,[status(thm)],[159,332,theory(equality)])).
% cnf(350,negated_conjecture,(vertex(head_of(X1))|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[260,262,theory(equality)])).
% cnf(351,negated_conjecture,(vertex(head_of(esk12_0))),inference(spm,[status(thm)],[350,311,theory(equality)])).
% cnf(359,negated_conjecture,(esk4_2(X1,X2)=esk11_0|X1=X2|~sequential(esk12_0,esk4_2(X1,X2))|head_of(esk4_2(X1,X2))!=tail_of(esk11_0)|~vertex(X2)|~vertex(X1)|~edge(esk11_0)),inference(spm,[status(thm)],[182,190,theory(equality)])).
% cnf(363,negated_conjecture,(esk4_2(X1,X2)=esk11_0|X1=X2|~sequential(esk12_0,esk4_2(X1,X2))|head_of(esk4_2(X1,X2))!=tail_of(esk11_0)|~vertex(X2)|~vertex(X1)|$false),inference(rw,[status(thm)],[359,172,theory(equality)])).
% cnf(364,negated_conjecture,(esk4_2(X1,X2)=esk11_0|X1=X2|~sequential(esk12_0,esk4_2(X1,X2))|head_of(esk4_2(X1,X2))!=tail_of(esk11_0)|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[363,theory(equality)])).
% cnf(369,negated_conjecture,(~on_path(esk11_0,esk13_0)|~on_path(esk12_0,esk13_0)|~sequential(esk12_0,esk11_0)),inference(spm,[status(thm)],[252,265,theory(equality)])).
% cnf(377,negated_conjecture,($false|~on_path(esk12_0,esk13_0)|~sequential(esk12_0,esk11_0)),inference(rw,[status(thm)],[369,315,theory(equality)])).
% cnf(378,negated_conjecture,($false|$false|~sequential(esk12_0,esk11_0)),inference(rw,[status(thm)],[377,311,theory(equality)])).
% cnf(379,negated_conjecture,(~sequential(esk12_0,esk11_0)),inference(cn,[status(thm)],[378,theory(equality)])).
% cnf(975,negated_conjecture,(head_of(esk4_2(head_of(esk12_0),tail_of(X1)))=tail_of(X1)|head_of(esk4_2(head_of(esk12_0),tail_of(X1)))=head_of(esk12_0)|head_of(esk12_0)=tail_of(X1)|~edge(X1)),inference(spm,[status(thm)],[218,351,theory(equality)])).
% cnf(2718,negated_conjecture,(tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=tail_of(esk11_0)|tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|head_of(esk12_0)=tail_of(esk11_0)),inference(spm,[status(thm)],[348,351,theory(equality)])).
% cnf(5708,negated_conjecture,(tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|tail_of(esk11_0)=head_of(esk12_0)|head_of(esk12_0)!=head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))),inference(spm,[status(thm)],[294,2718,theory(equality)])).
% cnf(5721,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|~vertex(tail_of(esk11_0))|~vertex(head_of(esk12_0))),inference(spm,[status(thm)],[163,2718,theory(equality)])).
% cnf(5723,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|$false|~vertex(head_of(esk12_0))),inference(rw,[status(thm)],[5721,332,theory(equality)])).
% cnf(5724,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|$false|$false),inference(rw,[status(thm)],[5723,351,theory(equality)])).
% cnf(5725,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)),inference(cn,[status(thm)],[5724,theory(equality)])).
% cnf(9648,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk12_0)!=head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))|~edge(esk4_2(head_of(esk12_0),tail_of(esk11_0)))),inference(spm,[status(thm)],[60,5708,theory(equality)])).
% cnf(9673,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=head_of(esk12_0)|~vertex(tail_of(esk11_0))|~vertex(head_of(esk12_0))),inference(spm,[status(thm)],[9648,157,theory(equality)])).
% cnf(9674,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=head_of(esk12_0)|$false|~vertex(head_of(esk12_0))),inference(rw,[status(thm)],[9673,332,theory(equality)])).
% cnf(9675,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=head_of(esk12_0)|$false|$false),inference(rw,[status(thm)],[9674,351,theory(equality)])).
% cnf(9676,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=head_of(esk12_0)),inference(cn,[status(thm)],[9675,theory(equality)])).
% cnf(9678,negated_conjecture,(tail_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=head_of(esk12_0)|tail_of(esk11_0)=head_of(esk12_0)),inference(csr,[status(thm)],[5725,9676])).
% cnf(9682,negated_conjecture,(esk12_0=esk4_2(head_of(esk12_0),tail_of(esk11_0))|sequential(esk12_0,esk4_2(head_of(esk12_0),tail_of(esk11_0)))|tail_of(esk11_0)=head_of(esk12_0)|~edge(esk4_2(head_of(esk12_0),tail_of(esk11_0)))),inference(spm,[status(thm)],[254,9678,theory(equality)])).
% cnf(9699,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=tail_of(esk11_0)|~vertex(tail_of(esk11_0))|~vertex(head_of(esk12_0))),inference(spm,[status(thm)],[161,9678,theory(equality)])).
% cnf(9702,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=tail_of(esk11_0)|$false|~vertex(head_of(esk12_0))),inference(rw,[status(thm)],[9699,332,theory(equality)])).
% cnf(9703,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=tail_of(esk11_0)|$false|$false),inference(rw,[status(thm)],[9702,351,theory(equality)])).
% cnf(9704,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))=tail_of(esk11_0)),inference(cn,[status(thm)],[9703,theory(equality)])).
% cnf(27428,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|tail_of(esk11_0)=head_of(esk12_0)|sequential(esk12_0,esk4_2(head_of(esk12_0),tail_of(esk11_0)))|~vertex(tail_of(esk11_0))|~vertex(head_of(esk12_0))),inference(spm,[status(thm)],[9682,157,theory(equality)])).
% cnf(27429,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|tail_of(esk11_0)=head_of(esk12_0)|sequential(esk12_0,esk4_2(head_of(esk12_0),tail_of(esk11_0)))|$false|~vertex(head_of(esk12_0))),inference(rw,[status(thm)],[27428,332,theory(equality)])).
% cnf(27430,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|tail_of(esk11_0)=head_of(esk12_0)|sequential(esk12_0,esk4_2(head_of(esk12_0),tail_of(esk11_0)))|$false|$false),inference(rw,[status(thm)],[27429,351,theory(equality)])).
% cnf(27431,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|tail_of(esk11_0)=head_of(esk12_0)|sequential(esk12_0,esk4_2(head_of(esk12_0),tail_of(esk11_0)))),inference(cn,[status(thm)],[27430,theory(equality)])).
% cnf(27435,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=tail_of(esk11_0)|~vertex(tail_of(esk11_0))|~vertex(head_of(esk12_0))),inference(spm,[status(thm)],[364,27431,theory(equality)])).
% cnf(27437,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=tail_of(esk11_0)|$false|~vertex(head_of(esk12_0))),inference(rw,[status(thm)],[27435,332,theory(equality)])).
% cnf(27438,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=tail_of(esk11_0)|$false|$false),inference(rw,[status(thm)],[27437,351,theory(equality)])).
% cnf(27439,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|head_of(esk4_2(head_of(esk12_0),tail_of(esk11_0)))!=tail_of(esk11_0)),inference(cn,[status(thm)],[27438,theory(equality)])).
% cnf(36796,negated_conjecture,(esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk12_0|tail_of(esk11_0)=head_of(esk12_0)),inference(csr,[status(thm)],[27439,9704])).
% cnf(36799,negated_conjecture,(tail_of(esk12_0)=tail_of(esk11_0)|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|~vertex(tail_of(esk11_0))|~vertex(head_of(esk12_0))),inference(spm,[status(thm)],[161,36796,theory(equality)])).
% cnf(36822,negated_conjecture,(head_of(esk11_0)=tail_of(esk11_0)|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|~vertex(tail_of(esk11_0))|~vertex(head_of(esk12_0))),inference(rw,[status(thm)],[36799,183,theory(equality)])).
% cnf(36823,negated_conjecture,(head_of(esk11_0)=tail_of(esk11_0)|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|$false|~vertex(head_of(esk12_0))),inference(rw,[status(thm)],[36822,332,theory(equality)])).
% cnf(36824,negated_conjecture,(head_of(esk11_0)=tail_of(esk11_0)|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0|$false|$false),inference(rw,[status(thm)],[36823,351,theory(equality)])).
% cnf(36825,negated_conjecture,(head_of(esk11_0)=tail_of(esk11_0)|head_of(esk12_0)=tail_of(esk11_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0),inference(cn,[status(thm)],[36824,theory(equality)])).
% cnf(36826,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|esk4_2(head_of(esk12_0),tail_of(esk11_0))=esk11_0),inference(sr,[status(thm)],[36825,306,theory(equality)])).
% cnf(36887,negated_conjecture,(head_of(esk11_0)=head_of(esk12_0)|head_of(esk11_0)=tail_of(esk11_0)|tail_of(esk11_0)=head_of(esk12_0)|~edge(esk11_0)),inference(spm,[status(thm)],[975,36826,theory(equality)])).
% cnf(36958,negated_conjecture,(head_of(esk11_0)=head_of(esk12_0)|head_of(esk11_0)=tail_of(esk11_0)|tail_of(esk11_0)=head_of(esk12_0)|$false),inference(rw,[status(thm)],[36887,172,theory(equality)])).
% cnf(36959,negated_conjecture,(head_of(esk11_0)=head_of(esk12_0)|head_of(esk11_0)=tail_of(esk11_0)|tail_of(esk11_0)=head_of(esk12_0)),inference(cn,[status(thm)],[36958,theory(equality)])).
% cnf(36960,negated_conjecture,(tail_of(esk11_0)=head_of(esk11_0)|tail_of(esk11_0)=head_of(esk12_0)),inference(sr,[status(thm)],[36959,286,theory(equality)])).
% cnf(36961,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)),inference(sr,[status(thm)],[36960,306,theory(equality)])).
% cnf(36971,negated_conjecture,(esk12_0=esk11_0|sequential(esk12_0,esk11_0)|~edge(esk11_0)),inference(spm,[status(thm)],[254,36961,theory(equality)])).
% cnf(37735,negated_conjecture,(esk12_0=esk11_0|sequential(esk12_0,esk11_0)|$false),inference(rw,[status(thm)],[36971,172,theory(equality)])).
% cnf(37736,negated_conjecture,(esk12_0=esk11_0|sequential(esk12_0,esk11_0)),inference(cn,[status(thm)],[37735,theory(equality)])).
% cnf(37737,negated_conjecture,(esk12_0=esk11_0),inference(sr,[status(thm)],[37736,379,theory(equality)])).
% cnf(38695,negated_conjecture,($false),inference(rw,[status(thm)],[286,37737,theory(equality)])).
% cnf(38696,negated_conjecture,($false),inference(cn,[status(thm)],[38695,theory(equality)])).
% cnf(38697,negated_conjecture,($false),38696,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 4378
% # ...of these trivial : 307
% # ...subsumed : 2389
% # ...remaining for further processing: 1682
% # Other redundant clauses eliminated : 37
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 243
% # Backward-rewritten : 708
% # Generated clauses : 25772
% # ...of the previous two non-trivial : 22427
% # Contextual simplify-reflections : 4677
% # Paramodulations : 25522
% # Factorizations : 109
% # Equation resolutions : 100
% # Current number of processed clauses: 652
% # Positive orientable unit clauses: 28
% # Positive unorientable unit clauses: 0
% # Negative unit clauses : 15
% # Non-unit-clauses : 609
% # Current number of unprocessed clauses: 5338
% # ...number of literals in the above : 40239
% # Clause-clause subsumption calls (NU) : 141190
% # Rec. Clause-clause subsumption calls : 18544
% # Unit Clause-clause subsumption calls : 4282
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 18
% # Indexed BW rewrite successes : 18
% # Backwards rewriting index: 429 leaves, 1.98+/-3.248 terms/leaf
% # Paramod-from index: 139 leaves, 1.34+/-1.103 terms/leaf
% # Paramod-into index: 321 leaves, 1.59+/-1.685 terms/leaf
% # -------------------------------------------------
% # User time : 1.949 s
% # System time : 0.058 s
% # Total time : 2.007 s
% # Maximum resident set size: 0 pages
% PrfWatch: 2.87 CPU 2.98 WC
% FINAL PrfWatch: 2.87 CPU 2.98 WC
% SZS output end Solution for /tmp/SystemOnTPTP18749/GRA008+1.tptp
%
%------------------------------------------------------------------------------