TSTP Solution File: GRA007+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : GRA007+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 : art07.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 05:40:51 EST 2010
% Result : Theorem 1.15s
% Output : Solution 1.15s
% 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/SystemOnTPTP31714/GRA007+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP31714/GRA007+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP31714/GRA007+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 31810
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Preprocessing time : 0.018 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(2, axiom,![X2]:![X3]:![X4]:![X5]:![X6]:((shortest_path(X2,X3,X6)&precedes(X4,X5,X6))=>(~(?[X7]:(tail_of(X7)=tail_of(X4)&head_of(X7)=head_of(X5)))&~(precedes(X5,X4,X6)))),file('/tmp/SRASS.s.p', shortest_path_properties)).
% fof(3, axiom,(complete=>![X2]:![X3]:(((vertex(X2)&vertex(X3))&~(X2=X3))=>?[X1]:(edge(X1)&((X2=head_of(X1)&X3=tail_of(X1))<~>(X3=head_of(X1)&X2=tail_of(X1)))))),file('/tmp/SRASS.s.p', complete_properties)).
% fof(4, axiom,![X4]:![X5]:(sequential(X4,X5)<=>(((edge(X4)&edge(X5))&~(X4=X5))&head_of(X4)=tail_of(X5))),file('/tmp/SRASS.s.p', sequential_defn)).
% fof(6, axiom,![X2]:![X3]:![X6]:![X1]:((path(X2,X3,X6)&on_path(X1,X6))=>((edge(X1)&in_path(head_of(X1),X6))&in_path(tail_of(X1),X6))),file('/tmp/SRASS.s.p', on_path_properties)).
% fof(9, axiom,![X2]:![X3]:![X9]:(shortest_path(X2,X3,X9)<=>((path(X2,X3,X9)&~(X2=X3))&![X6]:(path(X2,X3,X6)=>less_or_equal(length_of(X9),length_of(X6))))),file('/tmp/SRASS.s.p', shortest_path_defn)).
% fof(10, axiom,![X6]:![X2]:![X3]:(path(X2,X3,X6)=>![X4]:![X5]:(precedes(X4,X5,X6)<=((on_path(X4,X6)&on_path(X5,X6))&(sequential(X4,X5)|?[X7]:(sequential(X4,X7)&precedes(X7,X5,X6)))))),file('/tmp/SRASS.s.p', precedes_defn)).
% fof(11, axiom,![X6]:![X2]:![X3]:(path(X2,X3,X6)=>![X4]:![X5]:(precedes(X4,X5,X6)=>((on_path(X4,X6)&on_path(X5,X6))&(sequential(X4,X5)<~>?[X7]:(sequential(X4,X7)&precedes(X7,X5,X6)))))),file('/tmp/SRASS.s.p', precedes_properties)).
% fof(13, axiom,![X2]:![X3]:![X6]:![X10]:((path(X2,X3,X6)&in_path(X10,X6))=>(vertex(X10)&?[X1]:(on_path(X1,X6)&(X10=head_of(X1)|X10=tail_of(X1))))),file('/tmp/SRASS.s.p', in_path_properties)).
% fof(18, conjecture,(complete=>![X2]:![X3]:![X4]:![X5]:![X6]:((shortest_path(X2,X3,X6)&precedes(X4,X5,X6))=>?[X7]:((edge(X7)&tail_of(X7)=head_of(X5))&head_of(X7)=tail_of(X4)))),file('/tmp/SRASS.s.p', back_edge)).
% fof(19, negated_conjecture,~((complete=>![X2]:![X3]:![X4]:![X5]:![X6]:((shortest_path(X2,X3,X6)&precedes(X4,X5,X6))=>?[X7]:((edge(X7)&tail_of(X7)=head_of(X5))&head_of(X7)=tail_of(X4))))),inference(assume_negation,[status(cth)],[18])).
% fof(20, plain,![X2]:![X3]:![X4]:![X5]:![X6]:((shortest_path(X2,X3,X6)&precedes(X4,X5,X6))=>(~(?[X7]:(tail_of(X7)=tail_of(X4)&head_of(X7)=head_of(X5)))&~(precedes(X5,X4,X6)))),inference(fof_simplification,[status(thm)],[2,theory(equality)])).
% fof(21, plain,(complete=>![X2]:![X3]:(((vertex(X2)&vertex(X3))&~(X2=X3))=>?[X1]:(edge(X1)&~(((X2=head_of(X1)&X3=tail_of(X1))<=>(X3=head_of(X1)&X2=tail_of(X1))))))),inference(fof_simplification,[status(thm)],[3,theory(equality)])).
% fof(24, plain,![X6]:![X2]:![X3]:(path(X2,X3,X6)=>![X4]:![X5]:(((on_path(X4,X6)&on_path(X5,X6))&(sequential(X4,X5)|?[X7]:(sequential(X4,X7)&precedes(X7,X5,X6))))=>precedes(X4,X5,X6))),inference(fof_simplification,[status(thm)],[10,theory(equality)])).
% fof(25, plain,![X6]:![X2]:![X3]:(path(X2,X3,X6)=>![X4]:![X5]:(precedes(X4,X5,X6)=>((on_path(X4,X6)&on_path(X5,X6))&~((sequential(X4,X5)<=>?[X7]:(sequential(X4,X7)&precedes(X7,X5,X6))))))),inference(fof_simplification,[status(thm)],[11,theory(equality)])).
% fof(29, plain,![X2]:![X3]:![X4]:![X5]:![X6]:((~(shortest_path(X2,X3,X6))|~(precedes(X4,X5,X6)))|(![X7]:(~(tail_of(X7)=tail_of(X4))|~(head_of(X7)=head_of(X5)))&~(precedes(X5,X4,X6)))),inference(fof_nnf,[status(thm)],[20])).
% fof(30, plain,![X8]:![X9]:![X10]:![X11]:![X12]:((~(shortest_path(X8,X9,X12))|~(precedes(X10,X11,X12)))|(![X13]:(~(tail_of(X13)=tail_of(X10))|~(head_of(X13)=head_of(X11)))&~(precedes(X11,X10,X12)))),inference(variable_rename,[status(thm)],[29])).
% fof(31, plain,![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:(((~(tail_of(X13)=tail_of(X10))|~(head_of(X13)=head_of(X11)))&~(precedes(X11,X10,X12)))|(~(shortest_path(X8,X9,X12))|~(precedes(X10,X11,X12)))),inference(shift_quantors,[status(thm)],[30])).
% fof(32, plain,![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:(((~(tail_of(X13)=tail_of(X10))|~(head_of(X13)=head_of(X11)))|(~(shortest_path(X8,X9,X12))|~(precedes(X10,X11,X12))))&(~(precedes(X11,X10,X12))|(~(shortest_path(X8,X9,X12))|~(precedes(X10,X11,X12))))),inference(distribute,[status(thm)],[31])).
% cnf(33,plain,(~precedes(X1,X2,X3)|~shortest_path(X4,X5,X3)|~precedes(X2,X1,X3)),inference(split_conjunct,[status(thm)],[32])).
% cnf(34,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)],[32])).
% fof(35, plain,(~(complete)|![X2]:![X3]:(((~(vertex(X2))|~(vertex(X3)))|X2=X3)|?[X1]:(edge(X1)&(((~(X2=head_of(X1))|~(X3=tail_of(X1)))|(~(X3=head_of(X1))|~(X2=tail_of(X1))))&((X2=head_of(X1)&X3=tail_of(X1))|(X3=head_of(X1)&X2=tail_of(X1))))))),inference(fof_nnf,[status(thm)],[21])).
% fof(36, plain,(~(complete)|![X4]:![X5]:(((~(vertex(X4))|~(vertex(X5)))|X4=X5)|?[X6]:(edge(X6)&(((~(X4=head_of(X6))|~(X5=tail_of(X6)))|(~(X5=head_of(X6))|~(X4=tail_of(X6))))&((X4=head_of(X6)&X5=tail_of(X6))|(X5=head_of(X6)&X4=tail_of(X6))))))),inference(variable_rename,[status(thm)],[35])).
% fof(37, plain,(~(complete)|![X4]:![X5]:(((~(vertex(X4))|~(vertex(X5)))|X4=X5)|(edge(esk1_2(X4,X5))&(((~(X4=head_of(esk1_2(X4,X5)))|~(X5=tail_of(esk1_2(X4,X5))))|(~(X5=head_of(esk1_2(X4,X5)))|~(X4=tail_of(esk1_2(X4,X5)))))&((X4=head_of(esk1_2(X4,X5))&X5=tail_of(esk1_2(X4,X5)))|(X5=head_of(esk1_2(X4,X5))&X4=tail_of(esk1_2(X4,X5)))))))),inference(skolemize,[status(esa)],[36])).
% fof(38, plain,![X4]:![X5]:((((~(vertex(X4))|~(vertex(X5)))|X4=X5)|(edge(esk1_2(X4,X5))&(((~(X4=head_of(esk1_2(X4,X5)))|~(X5=tail_of(esk1_2(X4,X5))))|(~(X5=head_of(esk1_2(X4,X5)))|~(X4=tail_of(esk1_2(X4,X5)))))&((X4=head_of(esk1_2(X4,X5))&X5=tail_of(esk1_2(X4,X5)))|(X5=head_of(esk1_2(X4,X5))&X4=tail_of(esk1_2(X4,X5)))))))|~(complete)),inference(shift_quantors,[status(thm)],[37])).
% fof(39, plain,![X4]:![X5]:(((edge(esk1_2(X4,X5))|((~(vertex(X4))|~(vertex(X5)))|X4=X5))|~(complete))&(((((~(X4=head_of(esk1_2(X4,X5)))|~(X5=tail_of(esk1_2(X4,X5))))|(~(X5=head_of(esk1_2(X4,X5)))|~(X4=tail_of(esk1_2(X4,X5)))))|((~(vertex(X4))|~(vertex(X5)))|X4=X5))|~(complete))&(((((X5=head_of(esk1_2(X4,X5))|X4=head_of(esk1_2(X4,X5)))|((~(vertex(X4))|~(vertex(X5)))|X4=X5))|~(complete))&(((X4=tail_of(esk1_2(X4,X5))|X4=head_of(esk1_2(X4,X5)))|((~(vertex(X4))|~(vertex(X5)))|X4=X5))|~(complete)))&((((X5=head_of(esk1_2(X4,X5))|X5=tail_of(esk1_2(X4,X5)))|((~(vertex(X4))|~(vertex(X5)))|X4=X5))|~(complete))&(((X4=tail_of(esk1_2(X4,X5))|X5=tail_of(esk1_2(X4,X5)))|((~(vertex(X4))|~(vertex(X5)))|X4=X5))|~(complete)))))),inference(distribute,[status(thm)],[38])).
% cnf(41,plain,(X1=X2|X2=tail_of(esk1_2(X1,X2))|X2=head_of(esk1_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[39])).
% cnf(42,plain,(X1=X2|X1=head_of(esk1_2(X1,X2))|X1=tail_of(esk1_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[39])).
% cnf(43,plain,(X1=X2|X1=head_of(esk1_2(X1,X2))|X2=head_of(esk1_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[39])).
% cnf(45,plain,(X1=X2|edge(esk1_2(X1,X2))|~complete|~vertex(X2)|~vertex(X1)),inference(split_conjunct,[status(thm)],[39])).
% fof(46, plain,![X4]:![X5]:((~(sequential(X4,X5))|(((edge(X4)&edge(X5))&~(X4=X5))&head_of(X4)=tail_of(X5)))&((((~(edge(X4))|~(edge(X5)))|X4=X5)|~(head_of(X4)=tail_of(X5)))|sequential(X4,X5))),inference(fof_nnf,[status(thm)],[4])).
% fof(47, plain,![X6]:![X7]:((~(sequential(X6,X7))|(((edge(X6)&edge(X7))&~(X6=X7))&head_of(X6)=tail_of(X7)))&((((~(edge(X6))|~(edge(X7)))|X6=X7)|~(head_of(X6)=tail_of(X7)))|sequential(X6,X7))),inference(variable_rename,[status(thm)],[46])).
% fof(48, plain,![X6]:![X7]:(((((edge(X6)|~(sequential(X6,X7)))&(edge(X7)|~(sequential(X6,X7))))&(~(X6=X7)|~(sequential(X6,X7))))&(head_of(X6)=tail_of(X7)|~(sequential(X6,X7))))&((((~(edge(X6))|~(edge(X7)))|X6=X7)|~(head_of(X6)=tail_of(X7)))|sequential(X6,X7))),inference(distribute,[status(thm)],[47])).
% cnf(49,plain,(sequential(X1,X2)|X1=X2|head_of(X1)!=tail_of(X2)|~edge(X2)|~edge(X1)),inference(split_conjunct,[status(thm)],[48])).
% fof(59, plain,![X2]:![X3]:![X6]:![X1]:((~(path(X2,X3,X6))|~(on_path(X1,X6)))|((edge(X1)&in_path(head_of(X1),X6))&in_path(tail_of(X1),X6))),inference(fof_nnf,[status(thm)],[6])).
% fof(60, plain,![X7]:![X8]:![X9]:![X10]:((~(path(X7,X8,X9))|~(on_path(X10,X9)))|((edge(X10)&in_path(head_of(X10),X9))&in_path(tail_of(X10),X9))),inference(variable_rename,[status(thm)],[59])).
% fof(61, plain,![X7]:![X8]:![X9]:![X10]:(((edge(X10)|(~(path(X7,X8,X9))|~(on_path(X10,X9))))&(in_path(head_of(X10),X9)|(~(path(X7,X8,X9))|~(on_path(X10,X9)))))&(in_path(tail_of(X10),X9)|(~(path(X7,X8,X9))|~(on_path(X10,X9))))),inference(distribute,[status(thm)],[60])).
% cnf(62,plain,(in_path(tail_of(X1),X2)|~on_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[61])).
% cnf(63,plain,(in_path(head_of(X1),X2)|~on_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[61])).
% cnf(64,plain,(edge(X1)|~on_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[61])).
% fof(85, plain,![X2]:![X3]:![X9]:((~(shortest_path(X2,X3,X9))|((path(X2,X3,X9)&~(X2=X3))&![X6]:(~(path(X2,X3,X6))|less_or_equal(length_of(X9),length_of(X6)))))&(((~(path(X2,X3,X9))|X2=X3)|?[X6]:(path(X2,X3,X6)&~(less_or_equal(length_of(X9),length_of(X6)))))|shortest_path(X2,X3,X9))),inference(fof_nnf,[status(thm)],[9])).
% fof(86, plain,![X10]:![X11]:![X12]:((~(shortest_path(X10,X11,X12))|((path(X10,X11,X12)&~(X10=X11))&![X13]:(~(path(X10,X11,X13))|less_or_equal(length_of(X12),length_of(X13)))))&(((~(path(X10,X11,X12))|X10=X11)|?[X14]:(path(X10,X11,X14)&~(less_or_equal(length_of(X12),length_of(X14)))))|shortest_path(X10,X11,X12))),inference(variable_rename,[status(thm)],[85])).
% fof(87, plain,![X10]:![X11]:![X12]:((~(shortest_path(X10,X11,X12))|((path(X10,X11,X12)&~(X10=X11))&![X13]:(~(path(X10,X11,X13))|less_or_equal(length_of(X12),length_of(X13)))))&(((~(path(X10,X11,X12))|X10=X11)|(path(X10,X11,esk4_3(X10,X11,X12))&~(less_or_equal(length_of(X12),length_of(esk4_3(X10,X11,X12))))))|shortest_path(X10,X11,X12))),inference(skolemize,[status(esa)],[86])).
% fof(88, plain,![X10]:![X11]:![X12]:![X13]:((((~(path(X10,X11,X13))|less_or_equal(length_of(X12),length_of(X13)))&(path(X10,X11,X12)&~(X10=X11)))|~(shortest_path(X10,X11,X12)))&(((~(path(X10,X11,X12))|X10=X11)|(path(X10,X11,esk4_3(X10,X11,X12))&~(less_or_equal(length_of(X12),length_of(esk4_3(X10,X11,X12))))))|shortest_path(X10,X11,X12))),inference(shift_quantors,[status(thm)],[87])).
% fof(89, plain,![X10]:![X11]:![X12]:![X13]:((((~(path(X10,X11,X13))|less_or_equal(length_of(X12),length_of(X13)))|~(shortest_path(X10,X11,X12)))&((path(X10,X11,X12)|~(shortest_path(X10,X11,X12)))&(~(X10=X11)|~(shortest_path(X10,X11,X12)))))&(((path(X10,X11,esk4_3(X10,X11,X12))|(~(path(X10,X11,X12))|X10=X11))|shortest_path(X10,X11,X12))&((~(less_or_equal(length_of(X12),length_of(esk4_3(X10,X11,X12))))|(~(path(X10,X11,X12))|X10=X11))|shortest_path(X10,X11,X12)))),inference(distribute,[status(thm)],[88])).
% cnf(93,plain,(path(X1,X2,X3)|~shortest_path(X1,X2,X3)),inference(split_conjunct,[status(thm)],[89])).
% fof(95, plain,![X6]:![X2]:![X3]:(~(path(X2,X3,X6))|![X4]:![X5]:(((~(on_path(X4,X6))|~(on_path(X5,X6)))|(~(sequential(X4,X5))&![X7]:(~(sequential(X4,X7))|~(precedes(X7,X5,X6)))))|precedes(X4,X5,X6))),inference(fof_nnf,[status(thm)],[24])).
% fof(96, plain,![X8]:![X9]:![X10]:(~(path(X9,X10,X8))|![X11]:![X12]:(((~(on_path(X11,X8))|~(on_path(X12,X8)))|(~(sequential(X11,X12))&![X13]:(~(sequential(X11,X13))|~(precedes(X13,X12,X8)))))|precedes(X11,X12,X8))),inference(variable_rename,[status(thm)],[95])).
% fof(97, plain,![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:(((((~(sequential(X11,X13))|~(precedes(X13,X12,X8)))&~(sequential(X11,X12)))|(~(on_path(X11,X8))|~(on_path(X12,X8))))|precedes(X11,X12,X8))|~(path(X9,X10,X8))),inference(shift_quantors,[status(thm)],[96])).
% fof(98, plain,![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:(((((~(sequential(X11,X13))|~(precedes(X13,X12,X8)))|(~(on_path(X11,X8))|~(on_path(X12,X8))))|precedes(X11,X12,X8))|~(path(X9,X10,X8)))&(((~(sequential(X11,X12))|(~(on_path(X11,X8))|~(on_path(X12,X8))))|precedes(X11,X12,X8))|~(path(X9,X10,X8)))),inference(distribute,[status(thm)],[97])).
% cnf(99,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)],[98])).
% fof(101, plain,![X6]:![X2]:![X3]:(~(path(X2,X3,X6))|![X4]:![X5]:(~(precedes(X4,X5,X6))|((on_path(X4,X6)&on_path(X5,X6))&((~(sequential(X4,X5))|![X7]:(~(sequential(X4,X7))|~(precedes(X7,X5,X6))))&(sequential(X4,X5)|?[X7]:(sequential(X4,X7)&precedes(X7,X5,X6))))))),inference(fof_nnf,[status(thm)],[25])).
% fof(102, plain,![X8]:![X9]:![X10]:(~(path(X9,X10,X8))|![X11]:![X12]:(~(precedes(X11,X12,X8))|((on_path(X11,X8)&on_path(X12,X8))&((~(sequential(X11,X12))|![X13]:(~(sequential(X11,X13))|~(precedes(X13,X12,X8))))&(sequential(X11,X12)|?[X14]:(sequential(X11,X14)&precedes(X14,X12,X8))))))),inference(variable_rename,[status(thm)],[101])).
% fof(103, plain,![X8]:![X9]:![X10]:(~(path(X9,X10,X8))|![X11]:![X12]:(~(precedes(X11,X12,X8))|((on_path(X11,X8)&on_path(X12,X8))&((~(sequential(X11,X12))|![X13]:(~(sequential(X11,X13))|~(precedes(X13,X12,X8))))&(sequential(X11,X12)|(sequential(X11,esk5_5(X8,X9,X10,X11,X12))&precedes(esk5_5(X8,X9,X10,X11,X12),X12,X8))))))),inference(skolemize,[status(esa)],[102])).
% fof(104, plain,![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:((((((~(sequential(X11,X13))|~(precedes(X13,X12,X8)))|~(sequential(X11,X12)))&(sequential(X11,X12)|(sequential(X11,esk5_5(X8,X9,X10,X11,X12))&precedes(esk5_5(X8,X9,X10,X11,X12),X12,X8))))&(on_path(X11,X8)&on_path(X12,X8)))|~(precedes(X11,X12,X8)))|~(path(X9,X10,X8))),inference(shift_quantors,[status(thm)],[103])).
% fof(105, plain,![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:((((((~(sequential(X11,X13))|~(precedes(X13,X12,X8)))|~(sequential(X11,X12)))|~(precedes(X11,X12,X8)))|~(path(X9,X10,X8)))&((((sequential(X11,esk5_5(X8,X9,X10,X11,X12))|sequential(X11,X12))|~(precedes(X11,X12,X8)))|~(path(X9,X10,X8)))&(((precedes(esk5_5(X8,X9,X10,X11,X12),X12,X8)|sequential(X11,X12))|~(precedes(X11,X12,X8)))|~(path(X9,X10,X8)))))&(((on_path(X11,X8)|~(precedes(X11,X12,X8)))|~(path(X9,X10,X8)))&((on_path(X12,X8)|~(precedes(X11,X12,X8)))|~(path(X9,X10,X8))))),inference(distribute,[status(thm)],[104])).
% cnf(106,plain,(on_path(X5,X3)|~path(X1,X2,X3)|~precedes(X4,X5,X3)),inference(split_conjunct,[status(thm)],[105])).
% cnf(107,plain,(on_path(X4,X3)|~path(X1,X2,X3)|~precedes(X4,X5,X3)),inference(split_conjunct,[status(thm)],[105])).
% fof(121, plain,![X2]:![X3]:![X6]:![X10]:((~(path(X2,X3,X6))|~(in_path(X10,X6)))|(vertex(X10)&?[X1]:(on_path(X1,X6)&(X10=head_of(X1)|X10=tail_of(X1))))),inference(fof_nnf,[status(thm)],[13])).
% fof(122, plain,![X11]:![X12]:![X13]:![X14]:((~(path(X11,X12,X13))|~(in_path(X14,X13)))|(vertex(X14)&?[X15]:(on_path(X15,X13)&(X14=head_of(X15)|X14=tail_of(X15))))),inference(variable_rename,[status(thm)],[121])).
% fof(123, plain,![X11]:![X12]:![X13]:![X14]:((~(path(X11,X12,X13))|~(in_path(X14,X13)))|(vertex(X14)&(on_path(esk6_4(X11,X12,X13,X14),X13)&(X14=head_of(esk6_4(X11,X12,X13,X14))|X14=tail_of(esk6_4(X11,X12,X13,X14)))))),inference(skolemize,[status(esa)],[122])).
% fof(124, plain,![X11]:![X12]:![X13]:![X14]:((vertex(X14)|(~(path(X11,X12,X13))|~(in_path(X14,X13))))&((on_path(esk6_4(X11,X12,X13,X14),X13)|(~(path(X11,X12,X13))|~(in_path(X14,X13))))&((X14=head_of(esk6_4(X11,X12,X13,X14))|X14=tail_of(esk6_4(X11,X12,X13,X14)))|(~(path(X11,X12,X13))|~(in_path(X14,X13)))))),inference(distribute,[status(thm)],[123])).
% cnf(127,plain,(vertex(X1)|~in_path(X1,X2)|~path(X3,X4,X2)),inference(split_conjunct,[status(thm)],[124])).
% fof(145, negated_conjecture,(complete&?[X2]:?[X3]:?[X4]:?[X5]:?[X6]:((shortest_path(X2,X3,X6)&precedes(X4,X5,X6))&![X7]:((~(edge(X7))|~(tail_of(X7)=head_of(X5)))|~(head_of(X7)=tail_of(X4))))),inference(fof_nnf,[status(thm)],[19])).
% fof(146, negated_conjecture,(complete&?[X8]:?[X9]:?[X10]:?[X11]:?[X12]:((shortest_path(X8,X9,X12)&precedes(X10,X11,X12))&![X13]:((~(edge(X13))|~(tail_of(X13)=head_of(X11)))|~(head_of(X13)=tail_of(X10))))),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))&![X13]:((~(edge(X13))|~(tail_of(X13)=head_of(esk12_0)))|~(head_of(X13)=tail_of(esk11_0))))),inference(skolemize,[status(esa)],[146])).
% fof(148, negated_conjecture,![X13]:((((~(edge(X13))|~(tail_of(X13)=head_of(esk12_0)))|~(head_of(X13)=tail_of(esk11_0)))&(shortest_path(esk9_0,esk10_0,esk13_0)&precedes(esk11_0,esk12_0,esk13_0)))&complete),inference(shift_quantors,[status(thm)],[147])).
% cnf(149,negated_conjecture,(complete),inference(split_conjunct,[status(thm)],[148])).
% cnf(150,negated_conjecture,(precedes(esk11_0,esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[148])).
% cnf(151,negated_conjecture,(shortest_path(esk9_0,esk10_0,esk13_0)),inference(split_conjunct,[status(thm)],[148])).
% cnf(152,negated_conjecture,(head_of(X1)!=tail_of(esk11_0)|tail_of(X1)!=head_of(esk12_0)|~edge(X1)),inference(split_conjunct,[status(thm)],[148])).
% cnf(155,plain,(X1=X2|edge(esk1_2(X1,X2))|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[45,149,theory(equality)])).
% cnf(156,plain,(X1=X2|edge(esk1_2(X1,X2))|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[155,theory(equality)])).
% cnf(157,plain,(X1=X2|head_of(esk1_2(X1,X2))=X2|head_of(esk1_2(X1,X2))=X1|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[43,149,theory(equality)])).
% cnf(158,plain,(X1=X2|head_of(esk1_2(X1,X2))=X2|head_of(esk1_2(X1,X2))=X1|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[157,theory(equality)])).
% cnf(159,plain,(X1=X2|head_of(esk1_2(X1,X2))=X2|tail_of(esk1_2(X1,X2))=X2|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[41,149,theory(equality)])).
% cnf(160,plain,(X1=X2|head_of(esk1_2(X1,X2))=X2|tail_of(esk1_2(X1,X2))=X2|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[159,theory(equality)])).
% cnf(161,plain,(X1=X2|head_of(esk1_2(X1,X2))=X1|tail_of(esk1_2(X1,X2))=X1|$false|~vertex(X2)|~vertex(X1)),inference(rw,[status(thm)],[42,149,theory(equality)])).
% cnf(162,plain,(X1=X2|head_of(esk1_2(X1,X2))=X1|tail_of(esk1_2(X1,X2))=X1|~vertex(X2)|~vertex(X1)),inference(cn,[status(thm)],[161,theory(equality)])).
% cnf(170,negated_conjecture,(path(esk9_0,esk10_0,esk13_0)),inference(spm,[status(thm)],[93,151,theory(equality)])).
% cnf(175,negated_conjecture,(~precedes(esk12_0,esk11_0,esk13_0)|~shortest_path(X1,X2,esk13_0)),inference(spm,[status(thm)],[33,150,theory(equality)])).
% cnf(176,negated_conjecture,(head_of(esk12_0)!=head_of(X1)|tail_of(esk11_0)!=tail_of(X1)|~shortest_path(X2,X3,esk13_0)),inference(spm,[status(thm)],[34,150,theory(equality)])).
% cnf(196,negated_conjecture,(head_of(esk1_2(X1,X2))=X2|X1=X2|X2!=head_of(esk12_0)|tail_of(esk11_0)!=head_of(esk1_2(X1,X2))|~edge(esk1_2(X1,X2))|~vertex(X2)|~vertex(X1)),inference(spm,[status(thm)],[152,160,theory(equality)])).
% cnf(258,negated_conjecture,(~precedes(esk12_0,esk11_0,esk13_0)),inference(spm,[status(thm)],[175,151,theory(equality)])).
% fof(259, plain,(~(epred1_0)<=>![X1]:(~(tail_of(esk11_0)=tail_of(X1))|~(head_of(esk12_0)=head_of(X1)))),introduced(definition),['split']).
% cnf(260,plain,(epred1_0|tail_of(esk11_0)!=tail_of(X1)|head_of(esk12_0)!=head_of(X1)),inference(split_equiv,[status(thm)],[259])).
% fof(261, plain,(~(epred2_0)<=>![X3]:![X2]:~(shortest_path(X2,X3,esk13_0))),introduced(definition),['split']).
% cnf(262,plain,(epred2_0|~shortest_path(X2,X3,esk13_0)),inference(split_equiv,[status(thm)],[261])).
% cnf(263,negated_conjecture,(~epred2_0|~epred1_0),inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[176,259,theory(equality)]),261,theory(equality)]),['split']).
% cnf(268,negated_conjecture,(edge(X1)|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[64,170,theory(equality)])).
% cnf(269,negated_conjecture,(vertex(X1)|~in_path(X1,esk13_0)),inference(spm,[status(thm)],[127,170,theory(equality)])).
% cnf(270,negated_conjecture,(in_path(head_of(X1),esk13_0)|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[63,170,theory(equality)])).
% cnf(271,negated_conjecture,(in_path(tail_of(X1),esk13_0)|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[62,170,theory(equality)])).
% cnf(272,negated_conjecture,(on_path(X1,esk13_0)|~precedes(X2,X1,esk13_0)),inference(spm,[status(thm)],[106,170,theory(equality)])).
% cnf(273,negated_conjecture,(on_path(X1,esk13_0)|~precedes(X1,X2,esk13_0)),inference(spm,[status(thm)],[107,170,theory(equality)])).
% cnf(276,negated_conjecture,(precedes(X1,X2,esk13_0)|~on_path(X2,esk13_0)|~on_path(X1,esk13_0)|~sequential(X1,X2)),inference(spm,[status(thm)],[99,170,theory(equality)])).
% cnf(282,negated_conjecture,(epred2_0),inference(spm,[status(thm)],[262,151,theory(equality)])).
% cnf(284,negated_conjecture,($false|~epred1_0),inference(rw,[status(thm)],[263,282,theory(equality)])).
% cnf(285,negated_conjecture,(~epred1_0),inference(cn,[status(thm)],[284,theory(equality)])).
% cnf(287,negated_conjecture,(tail_of(esk11_0)!=tail_of(X1)|head_of(esk12_0)!=head_of(X1)),inference(sr,[status(thm)],[260,285,theory(equality)])).
% cnf(288,negated_conjecture,(head_of(esk12_0)!=head_of(esk11_0)),inference(er,[status(thm)],[287,theory(equality)])).
% cnf(292,negated_conjecture,(head_of(esk1_2(X1,X2))=X1|X1=X2|tail_of(esk11_0)!=X1|head_of(esk12_0)!=head_of(esk1_2(X1,X2))|~vertex(X2)|~vertex(X1)),inference(spm,[status(thm)],[287,162,theory(equality)])).
% cnf(297,negated_conjecture,(on_path(esk12_0,esk13_0)),inference(spm,[status(thm)],[272,150,theory(equality)])).
% cnf(299,negated_conjecture,(edge(esk12_0)),inference(spm,[status(thm)],[268,297,theory(equality)])).
% cnf(305,negated_conjecture,(on_path(esk11_0,esk13_0)),inference(spm,[status(thm)],[273,150,theory(equality)])).
% cnf(307,negated_conjecture,(edge(esk11_0)),inference(spm,[status(thm)],[268,305,theory(equality)])).
% cnf(309,negated_conjecture,(head_of(esk1_2(X1,X2))=X2|X1=X2|head_of(esk1_2(X1,X2))!=tail_of(esk11_0)|X2!=head_of(esk12_0)|~vertex(X2)|~vertex(X1)),inference(csr,[status(thm)],[196,156])).
% cnf(312,negated_conjecture,(vertex(head_of(X1))|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[269,270,theory(equality)])).
% cnf(313,negated_conjecture,(vertex(head_of(esk12_0))),inference(spm,[status(thm)],[312,297,theory(equality)])).
% cnf(323,negated_conjecture,(head_of(esk1_2(X1,head_of(esk12_0)))=head_of(esk12_0)|head_of(esk1_2(X1,head_of(esk12_0)))=X1|X1=head_of(esk12_0)|~vertex(X1)),inference(spm,[status(thm)],[158,313,theory(equality)])).
% cnf(327,negated_conjecture,(vertex(tail_of(X1))|~on_path(X1,esk13_0)),inference(spm,[status(thm)],[269,271,theory(equality)])).
% cnf(333,negated_conjecture,(vertex(tail_of(esk11_0))),inference(spm,[status(thm)],[327,305,theory(equality)])).
% cnf(361,negated_conjecture,(~on_path(esk11_0,esk13_0)|~on_path(esk12_0,esk13_0)|~sequential(esk12_0,esk11_0)),inference(spm,[status(thm)],[258,276,theory(equality)])).
% cnf(369,negated_conjecture,($false|~on_path(esk12_0,esk13_0)|~sequential(esk12_0,esk11_0)),inference(rw,[status(thm)],[361,305,theory(equality)])).
% cnf(370,negated_conjecture,($false|$false|~sequential(esk12_0,esk11_0)),inference(rw,[status(thm)],[369,297,theory(equality)])).
% cnf(371,negated_conjecture,(~sequential(esk12_0,esk11_0)),inference(cn,[status(thm)],[370,theory(equality)])).
% cnf(2871,negated_conjecture,(head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0)))=head_of(esk12_0)|head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0)))=tail_of(esk11_0)|tail_of(esk11_0)=head_of(esk12_0)),inference(spm,[status(thm)],[323,333,theory(equality)])).
% cnf(3653,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0)))=head_of(esk12_0)|~vertex(head_of(esk12_0))|~vertex(tail_of(esk11_0))),inference(spm,[status(thm)],[309,2871,theory(equality)])).
% cnf(3658,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0)))=head_of(esk12_0)|$false|~vertex(tail_of(esk11_0))),inference(rw,[status(thm)],[3653,313,theory(equality)])).
% cnf(3659,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0)))=head_of(esk12_0)|$false|$false),inference(rw,[status(thm)],[3658,333,theory(equality)])).
% cnf(3660,negated_conjecture,(tail_of(esk11_0)=head_of(esk12_0)|head_of(esk1_2(tail_of(esk11_0),head_of(esk12_0)))=head_of(esk12_0)),inference(cn,[status(thm)],[3659,theory(equality)])).
% cnf(3678,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)|~vertex(head_of(esk12_0))|~vertex(tail_of(esk11_0))),inference(spm,[status(thm)],[292,3660,theory(equality)])).
% cnf(3685,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)|$false|~vertex(tail_of(esk11_0))),inference(rw,[status(thm)],[3678,313,theory(equality)])).
% cnf(3686,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)|$false|$false),inference(rw,[status(thm)],[3685,333,theory(equality)])).
% cnf(3687,negated_conjecture,(head_of(esk12_0)=tail_of(esk11_0)),inference(cn,[status(thm)],[3686,theory(equality)])).
% cnf(3697,negated_conjecture,(X1=esk11_0|sequential(X1,esk11_0)|head_of(esk12_0)!=head_of(X1)|~edge(esk11_0)|~edge(X1)),inference(spm,[status(thm)],[49,3687,theory(equality)])).
% cnf(3834,negated_conjecture,(X1=esk11_0|sequential(X1,esk11_0)|head_of(esk12_0)!=head_of(X1)|$false|~edge(X1)),inference(rw,[status(thm)],[3697,307,theory(equality)])).
% cnf(3835,negated_conjecture,(X1=esk11_0|sequential(X1,esk11_0)|head_of(esk12_0)!=head_of(X1)|~edge(X1)),inference(cn,[status(thm)],[3834,theory(equality)])).
% cnf(3907,negated_conjecture,(esk12_0=esk11_0|~edge(esk12_0)),inference(spm,[status(thm)],[371,3835,theory(equality)])).
% cnf(3911,negated_conjecture,(esk12_0=esk11_0|$false),inference(rw,[status(thm)],[3907,299,theory(equality)])).
% cnf(3912,negated_conjecture,(esk12_0=esk11_0),inference(cn,[status(thm)],[3911,theory(equality)])).
% cnf(4110,negated_conjecture,($false),inference(rw,[status(thm)],[288,3912,theory(equality)])).
% cnf(4111,negated_conjecture,($false),inference(cn,[status(thm)],[4110,theory(equality)])).
% cnf(4112,negated_conjecture,($false),4111,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 820
% # ...of these trivial : 82
% # ...subsumed : 252
% # ...remaining for further processing: 486
% # Other redundant clauses eliminated : 7
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 26
% # Backward-rewritten : 167
% # Generated clauses : 2609
% # ...of the previous two non-trivial : 2412
% # Contextual simplify-reflections : 310
% # Paramodulations : 2525
% # Factorizations : 49
% # Equation resolutions : 20
% # Current number of processed clauses: 224
% # Positive orientable unit clauses: 18
% # Positive unorientable unit clauses: 0
% # Negative unit clauses : 7
% # Non-unit-clauses : 199
% # Current number of unprocessed clauses: 670
% # ...number of literals in the above : 3872
% # Clause-clause subsumption calls (NU) : 10062
% # Rec. Clause-clause subsumption calls : 3547
% # Unit Clause-clause subsumption calls : 388
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 7
% # Indexed BW rewrite successes : 7
% # Backwards rewriting index: 204 leaves, 1.71+/-2.906 terms/leaf
% # Paramod-from index: 82 leaves, 1.07+/-0.304 terms/leaf
% # Paramod-into index: 158 leaves, 1.39+/-1.479 terms/leaf
% # -------------------------------------------------
% # User time : 0.180 s
% # System time : 0.012 s
% # Total time : 0.192 s
% # Maximum resident set size: 0 pages
% PrfWatch: 0.34 CPU 0.44 WC
% FINAL PrfWatch: 0.34 CPU 0.44 WC
% SZS output end Solution for /tmp/SystemOnTPTP31714/GRA007+1.tptp
%
%------------------------------------------------------------------------------