TSTP Solution File: SEU214+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : SEU214+1 : TPTP v5.0.0. Released v3.3.0.
% 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 : Thu Dec 30 01:54:13 EST 2010
% Result : Theorem 11.79s
% Output : Solution 11.79s
% 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/SystemOnTPTP12747/SEU214+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP12747/SEU214+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP12747/SEU214+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 12843
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.92 CPU 2.01 WC
% PrfWatch: 3.91 CPU 4.01 WC
% PrfWatch: 5.91 CPU 6.02 WC
% PrfWatch: 7.90 CPU 8.03 WC
% # Preprocessing time : 0.016 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 9.88 CPU 10.03 WC
% # SZS output start CNFRefutation.
% fof(2, axiom,![X1]:![X2]:((relation(X1)&relation(X2))=>relation(relation_composition(X1,X2))),file('/tmp/SRASS.s.p', dt_k5_relat_1)).
% fof(3, axiom,![X1]:![X2]:((((relation(X1)&function(X1))&relation(X2))&function(X2))=>(relation(relation_composition(X1,X2))&function(relation_composition(X1,X2)))),file('/tmp/SRASS.s.p', fc1_funct_1)).
% fof(5, axiom,![X1]:(relation(X1)=>![X2]:(X2=relation_dom(X1)<=>![X3]:(in(X3,X2)<=>?[X4]:in(ordered_pair(X3,X4),X1)))),file('/tmp/SRASS.s.p', d4_relat_1)).
% fof(6, axiom,![X1]:(relation(X1)=>![X2]:(relation(X2)=>![X3]:(relation(X3)=>(X3=relation_composition(X1,X2)<=>![X4]:![X5]:(in(ordered_pair(X4,X5),X3)<=>?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2))))))),file('/tmp/SRASS.s.p', d8_relat_1)).
% fof(11, axiom,![X1]:((relation(X1)&function(X1))=>![X2]:![X3]:((in(X2,relation_dom(X1))=>(X3=apply(X1,X2)<=>in(ordered_pair(X2,X3),X1)))&(~(in(X2,relation_dom(X1)))=>(X3=apply(X1,X2)<=>X3=empty_set)))),file('/tmp/SRASS.s.p', d4_funct_1)).
% fof(21, axiom,![X1]:![X2]:unordered_pair(X1,X2)=unordered_pair(X2,X1),file('/tmp/SRASS.s.p', commutativity_k2_tarski)).
% fof(30, axiom,![X1]:![X2]:ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1)),file('/tmp/SRASS.s.p', d5_tarski)).
% fof(40, conjecture,![X1]:![X2]:((relation(X2)&function(X2))=>![X3]:((relation(X3)&function(X3))=>(in(X1,relation_dom(relation_composition(X3,X2)))=>apply(relation_composition(X3,X2),X1)=apply(X2,apply(X3,X1))))),file('/tmp/SRASS.s.p', t22_funct_1)).
% fof(41, negated_conjecture,~(![X1]:![X2]:((relation(X2)&function(X2))=>![X3]:((relation(X3)&function(X3))=>(in(X1,relation_dom(relation_composition(X3,X2)))=>apply(relation_composition(X3,X2),X1)=apply(X2,apply(X3,X1)))))),inference(assume_negation,[status(cth)],[40])).
% fof(44, plain,![X1]:((relation(X1)&function(X1))=>![X2]:![X3]:((in(X2,relation_dom(X1))=>(X3=apply(X1,X2)<=>in(ordered_pair(X2,X3),X1)))&(~(in(X2,relation_dom(X1)))=>(X3=apply(X1,X2)<=>X3=empty_set)))),inference(fof_simplification,[status(thm)],[11,theory(equality)])).
% fof(53, plain,![X1]:![X2]:((~(relation(X1))|~(relation(X2)))|relation(relation_composition(X1,X2))),inference(fof_nnf,[status(thm)],[2])).
% fof(54, plain,![X3]:![X4]:((~(relation(X3))|~(relation(X4)))|relation(relation_composition(X3,X4))),inference(variable_rename,[status(thm)],[53])).
% cnf(55,plain,(relation(relation_composition(X1,X2))|~relation(X2)|~relation(X1)),inference(split_conjunct,[status(thm)],[54])).
% fof(56, plain,![X1]:![X2]:((((~(relation(X1))|~(function(X1)))|~(relation(X2)))|~(function(X2)))|(relation(relation_composition(X1,X2))&function(relation_composition(X1,X2)))),inference(fof_nnf,[status(thm)],[3])).
% fof(57, plain,![X3]:![X4]:((((~(relation(X3))|~(function(X3)))|~(relation(X4)))|~(function(X4)))|(relation(relation_composition(X3,X4))&function(relation_composition(X3,X4)))),inference(variable_rename,[status(thm)],[56])).
% fof(58, plain,![X3]:![X4]:((relation(relation_composition(X3,X4))|(((~(relation(X3))|~(function(X3)))|~(relation(X4)))|~(function(X4))))&(function(relation_composition(X3,X4))|(((~(relation(X3))|~(function(X3)))|~(relation(X4)))|~(function(X4))))),inference(distribute,[status(thm)],[57])).
% cnf(59,plain,(function(relation_composition(X2,X1))|~function(X1)|~relation(X1)|~function(X2)|~relation(X2)),inference(split_conjunct,[status(thm)],[58])).
% fof(65, plain,![X1]:(~(relation(X1))|![X2]:((~(X2=relation_dom(X1))|![X3]:((~(in(X3,X2))|?[X4]:in(ordered_pair(X3,X4),X1))&(![X4]:~(in(ordered_pair(X3,X4),X1))|in(X3,X2))))&(?[X3]:((~(in(X3,X2))|![X4]:~(in(ordered_pair(X3,X4),X1)))&(in(X3,X2)|?[X4]:in(ordered_pair(X3,X4),X1)))|X2=relation_dom(X1)))),inference(fof_nnf,[status(thm)],[5])).
% fof(66, plain,![X5]:(~(relation(X5))|![X6]:((~(X6=relation_dom(X5))|![X7]:((~(in(X7,X6))|?[X8]:in(ordered_pair(X7,X8),X5))&(![X9]:~(in(ordered_pair(X7,X9),X5))|in(X7,X6))))&(?[X10]:((~(in(X10,X6))|![X11]:~(in(ordered_pair(X10,X11),X5)))&(in(X10,X6)|?[X12]:in(ordered_pair(X10,X12),X5)))|X6=relation_dom(X5)))),inference(variable_rename,[status(thm)],[65])).
% fof(67, plain,![X5]:(~(relation(X5))|![X6]:((~(X6=relation_dom(X5))|![X7]:((~(in(X7,X6))|in(ordered_pair(X7,esk2_3(X5,X6,X7)),X5))&(![X9]:~(in(ordered_pair(X7,X9),X5))|in(X7,X6))))&(((~(in(esk3_2(X5,X6),X6))|![X11]:~(in(ordered_pair(esk3_2(X5,X6),X11),X5)))&(in(esk3_2(X5,X6),X6)|in(ordered_pair(esk3_2(X5,X6),esk4_2(X5,X6)),X5)))|X6=relation_dom(X5)))),inference(skolemize,[status(esa)],[66])).
% fof(68, plain,![X5]:![X6]:![X7]:![X9]:![X11]:(((((~(in(ordered_pair(esk3_2(X5,X6),X11),X5))|~(in(esk3_2(X5,X6),X6)))&(in(esk3_2(X5,X6),X6)|in(ordered_pair(esk3_2(X5,X6),esk4_2(X5,X6)),X5)))|X6=relation_dom(X5))&(((~(in(ordered_pair(X7,X9),X5))|in(X7,X6))&(~(in(X7,X6))|in(ordered_pair(X7,esk2_3(X5,X6,X7)),X5)))|~(X6=relation_dom(X5))))|~(relation(X5))),inference(shift_quantors,[status(thm)],[67])).
% fof(69, plain,![X5]:![X6]:![X7]:![X9]:![X11]:(((((~(in(ordered_pair(esk3_2(X5,X6),X11),X5))|~(in(esk3_2(X5,X6),X6)))|X6=relation_dom(X5))|~(relation(X5)))&(((in(esk3_2(X5,X6),X6)|in(ordered_pair(esk3_2(X5,X6),esk4_2(X5,X6)),X5))|X6=relation_dom(X5))|~(relation(X5))))&((((~(in(ordered_pair(X7,X9),X5))|in(X7,X6))|~(X6=relation_dom(X5)))|~(relation(X5)))&(((~(in(X7,X6))|in(ordered_pair(X7,esk2_3(X5,X6,X7)),X5))|~(X6=relation_dom(X5)))|~(relation(X5))))),inference(distribute,[status(thm)],[68])).
% cnf(71,plain,(in(X3,X2)|~relation(X1)|X2!=relation_dom(X1)|~in(ordered_pair(X3,X4),X1)),inference(split_conjunct,[status(thm)],[69])).
% fof(74, plain,![X1]:(~(relation(X1))|![X2]:(~(relation(X2))|![X3]:(~(relation(X3))|((~(X3=relation_composition(X1,X2))|![X4]:![X5]:((~(in(ordered_pair(X4,X5),X3))|?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2)))&(![X6]:(~(in(ordered_pair(X4,X6),X1))|~(in(ordered_pair(X6,X5),X2)))|in(ordered_pair(X4,X5),X3))))&(?[X4]:?[X5]:((~(in(ordered_pair(X4,X5),X3))|![X6]:(~(in(ordered_pair(X4,X6),X1))|~(in(ordered_pair(X6,X5),X2))))&(in(ordered_pair(X4,X5),X3)|?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2))))|X3=relation_composition(X1,X2)))))),inference(fof_nnf,[status(thm)],[6])).
% fof(75, plain,![X7]:(~(relation(X7))|![X8]:(~(relation(X8))|![X9]:(~(relation(X9))|((~(X9=relation_composition(X7,X8))|![X10]:![X11]:((~(in(ordered_pair(X10,X11),X9))|?[X12]:(in(ordered_pair(X10,X12),X7)&in(ordered_pair(X12,X11),X8)))&(![X13]:(~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))))&(?[X14]:?[X15]:((~(in(ordered_pair(X14,X15),X9))|![X16]:(~(in(ordered_pair(X14,X16),X7))|~(in(ordered_pair(X16,X15),X8))))&(in(ordered_pair(X14,X15),X9)|?[X17]:(in(ordered_pair(X14,X17),X7)&in(ordered_pair(X17,X15),X8))))|X9=relation_composition(X7,X8)))))),inference(variable_rename,[status(thm)],[74])).
% fof(76, plain,![X7]:(~(relation(X7))|![X8]:(~(relation(X8))|![X9]:(~(relation(X9))|((~(X9=relation_composition(X7,X8))|![X10]:![X11]:((~(in(ordered_pair(X10,X11),X9))|(in(ordered_pair(X10,esk5_5(X7,X8,X9,X10,X11)),X7)&in(ordered_pair(esk5_5(X7,X8,X9,X10,X11),X11),X8)))&(![X13]:(~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))))&(((~(in(ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)),X9))|![X16]:(~(in(ordered_pair(esk6_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk7_3(X7,X8,X9)),X8))))&(in(ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)),X9)|(in(ordered_pair(esk6_3(X7,X8,X9),esk8_3(X7,X8,X9)),X7)&in(ordered_pair(esk8_3(X7,X8,X9),esk7_3(X7,X8,X9)),X8))))|X9=relation_composition(X7,X8)))))),inference(skolemize,[status(esa)],[75])).
% fof(77, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X13]:![X16]:((((((((~(in(ordered_pair(esk6_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk7_3(X7,X8,X9)),X8)))|~(in(ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)),X9)))&(in(ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)),X9)|(in(ordered_pair(esk6_3(X7,X8,X9),esk8_3(X7,X8,X9)),X7)&in(ordered_pair(esk8_3(X7,X8,X9),esk7_3(X7,X8,X9)),X8))))|X9=relation_composition(X7,X8))&((((~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))&(~(in(ordered_pair(X10,X11),X9))|(in(ordered_pair(X10,esk5_5(X7,X8,X9,X10,X11)),X7)&in(ordered_pair(esk5_5(X7,X8,X9,X10,X11),X11),X8))))|~(X9=relation_composition(X7,X8))))|~(relation(X9)))|~(relation(X8)))|~(relation(X7))),inference(shift_quantors,[status(thm)],[76])).
% fof(78, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X13]:![X16]:((((((((~(in(ordered_pair(esk6_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk7_3(X7,X8,X9)),X8)))|~(in(ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)),X9)))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&((((((in(ordered_pair(esk6_3(X7,X8,X9),esk8_3(X7,X8,X9)),X7)|in(ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)),X9))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&(((((in(ordered_pair(esk8_3(X7,X8,X9),esk7_3(X7,X8,X9)),X8)|in(ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)),X9))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))))&(((((((~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&((((((in(ordered_pair(X10,esk5_5(X7,X8,X9,X10,X11)),X7)|~(in(ordered_pair(X10,X11),X9)))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&(((((in(ordered_pair(esk5_5(X7,X8,X9,X10,X11),X11),X8)|~(in(ordered_pair(X10,X11),X9)))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))))),inference(distribute,[status(thm)],[77])).
% cnf(79,plain,(in(ordered_pair(esk5_5(X1,X2,X3,X4,X5),X5),X2)|~relation(X1)|~relation(X2)|~relation(X3)|X3!=relation_composition(X1,X2)|~in(ordered_pair(X4,X5),X3)),inference(split_conjunct,[status(thm)],[78])).
% cnf(80,plain,(in(ordered_pair(X4,esk5_5(X1,X2,X3,X4,X5)),X1)|~relation(X1)|~relation(X2)|~relation(X3)|X3!=relation_composition(X1,X2)|~in(ordered_pair(X4,X5),X3)),inference(split_conjunct,[status(thm)],[78])).
% fof(103, plain,![X1]:((~(relation(X1))|~(function(X1)))|![X2]:![X3]:((~(in(X2,relation_dom(X1)))|((~(X3=apply(X1,X2))|in(ordered_pair(X2,X3),X1))&(~(in(ordered_pair(X2,X3),X1))|X3=apply(X1,X2))))&(in(X2,relation_dom(X1))|((~(X3=apply(X1,X2))|X3=empty_set)&(~(X3=empty_set)|X3=apply(X1,X2)))))),inference(fof_nnf,[status(thm)],[44])).
% fof(104, plain,![X4]:((~(relation(X4))|~(function(X4)))|![X5]:![X6]:((~(in(X5,relation_dom(X4)))|((~(X6=apply(X4,X5))|in(ordered_pair(X5,X6),X4))&(~(in(ordered_pair(X5,X6),X4))|X6=apply(X4,X5))))&(in(X5,relation_dom(X4))|((~(X6=apply(X4,X5))|X6=empty_set)&(~(X6=empty_set)|X6=apply(X4,X5)))))),inference(variable_rename,[status(thm)],[103])).
% fof(105, plain,![X4]:![X5]:![X6]:(((~(in(X5,relation_dom(X4)))|((~(X6=apply(X4,X5))|in(ordered_pair(X5,X6),X4))&(~(in(ordered_pair(X5,X6),X4))|X6=apply(X4,X5))))&(in(X5,relation_dom(X4))|((~(X6=apply(X4,X5))|X6=empty_set)&(~(X6=empty_set)|X6=apply(X4,X5)))))|(~(relation(X4))|~(function(X4)))),inference(shift_quantors,[status(thm)],[104])).
% fof(106, plain,![X4]:![X5]:![X6]:(((((~(X6=apply(X4,X5))|in(ordered_pair(X5,X6),X4))|~(in(X5,relation_dom(X4))))|(~(relation(X4))|~(function(X4))))&(((~(in(ordered_pair(X5,X6),X4))|X6=apply(X4,X5))|~(in(X5,relation_dom(X4))))|(~(relation(X4))|~(function(X4)))))&((((~(X6=apply(X4,X5))|X6=empty_set)|in(X5,relation_dom(X4)))|(~(relation(X4))|~(function(X4))))&(((~(X6=empty_set)|X6=apply(X4,X5))|in(X5,relation_dom(X4)))|(~(relation(X4))|~(function(X4)))))),inference(distribute,[status(thm)],[105])).
% cnf(109,plain,(X3=apply(X1,X2)|~function(X1)|~relation(X1)|~in(X2,relation_dom(X1))|~in(ordered_pair(X2,X3),X1)),inference(split_conjunct,[status(thm)],[106])).
% cnf(110,plain,(in(ordered_pair(X2,X3),X1)|~function(X1)|~relation(X1)|~in(X2,relation_dom(X1))|X3!=apply(X1,X2)),inference(split_conjunct,[status(thm)],[106])).
% fof(140, plain,![X3]:![X4]:unordered_pair(X3,X4)=unordered_pair(X4,X3),inference(variable_rename,[status(thm)],[21])).
% cnf(141,plain,(unordered_pair(X1,X2)=unordered_pair(X2,X1)),inference(split_conjunct,[status(thm)],[140])).
% fof(162, plain,![X3]:![X4]:ordered_pair(X3,X4)=unordered_pair(unordered_pair(X3,X4),singleton(X3)),inference(variable_rename,[status(thm)],[30])).
% cnf(163,plain,(ordered_pair(X1,X2)=unordered_pair(unordered_pair(X1,X2),singleton(X1))),inference(split_conjunct,[status(thm)],[162])).
% fof(176, negated_conjecture,?[X1]:?[X2]:((relation(X2)&function(X2))&?[X3]:((relation(X3)&function(X3))&(in(X1,relation_dom(relation_composition(X3,X2)))&~(apply(relation_composition(X3,X2),X1)=apply(X2,apply(X3,X1)))))),inference(fof_nnf,[status(thm)],[41])).
% fof(177, negated_conjecture,?[X4]:?[X5]:((relation(X5)&function(X5))&?[X6]:((relation(X6)&function(X6))&(in(X4,relation_dom(relation_composition(X6,X5)))&~(apply(relation_composition(X6,X5),X4)=apply(X5,apply(X6,X4)))))),inference(variable_rename,[status(thm)],[176])).
% fof(178, negated_conjecture,((relation(esk16_0)&function(esk16_0))&((relation(esk17_0)&function(esk17_0))&(in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0)))&~(apply(relation_composition(esk17_0,esk16_0),esk15_0)=apply(esk16_0,apply(esk17_0,esk15_0)))))),inference(skolemize,[status(esa)],[177])).
% cnf(179,negated_conjecture,(apply(relation_composition(esk17_0,esk16_0),esk15_0)!=apply(esk16_0,apply(esk17_0,esk15_0))),inference(split_conjunct,[status(thm)],[178])).
% cnf(180,negated_conjecture,(in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0)))),inference(split_conjunct,[status(thm)],[178])).
% cnf(181,negated_conjecture,(function(esk17_0)),inference(split_conjunct,[status(thm)],[178])).
% cnf(182,negated_conjecture,(relation(esk17_0)),inference(split_conjunct,[status(thm)],[178])).
% cnf(183,negated_conjecture,(function(esk16_0)),inference(split_conjunct,[status(thm)],[178])).
% cnf(184,negated_conjecture,(relation(esk16_0)),inference(split_conjunct,[status(thm)],[178])).
% cnf(186,plain,(in(X3,X2)|relation_dom(X1)!=X2|~relation(X1)|~in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1)),inference(rw,[status(thm)],[71,163,theory(equality)]),['unfolding']).
% cnf(191,plain,(apply(X1,X2)=X3|~relation(X1)|~function(X1)|~in(X2,relation_dom(X1))|~in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1)),inference(rw,[status(thm)],[109,163,theory(equality)]),['unfolding']).
% cnf(192,plain,(in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1)|apply(X1,X2)!=X3|~relation(X1)|~function(X1)|~in(X2,relation_dom(X1))),inference(rw,[status(thm)],[110,163,theory(equality)]),['unfolding']).
% cnf(193,plain,(in(unordered_pair(unordered_pair(X4,esk5_5(X1,X2,X3,X4,X5)),singleton(X4)),X1)|relation_composition(X1,X2)!=X3|~relation(X3)|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[80,163,theory(equality)]),163,theory(equality)]),['unfolding']).
% cnf(194,plain,(in(unordered_pair(unordered_pair(esk5_5(X1,X2,X3,X4,X5),X5),singleton(esk5_5(X1,X2,X3,X4,X5))),X2)|relation_composition(X1,X2)!=X3|~relation(X3)|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[79,163,theory(equality)]),163,theory(equality)]),['unfolding']).
% cnf(273,plain,(in(X1,relation_dom(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2)),inference(er,[status(thm)],[186,theory(equality)])).
% cnf(281,plain,(in(unordered_pair(unordered_pair(X1,apply(X2,X1)),singleton(X1)),X2)|~function(X2)|~relation(X2)|~in(X1,relation_dom(X2))),inference(er,[status(thm)],[192,theory(equality)])).
% cnf(350,plain,(in(unordered_pair(singleton(X4),unordered_pair(X4,esk5_5(X1,X2,X3,X4,X5))),X1)|relation_composition(X1,X2)!=X3|~relation(X3)|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)),inference(rw,[status(thm)],[193,141,theory(equality)])).
% cnf(351,plain,(in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_5(X2,X3,relation_composition(X2,X3),X1,X4))),X2)|~relation(relation_composition(X2,X3))|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),relation_composition(X2,X3))),inference(er,[status(thm)],[350,theory(equality)])).
% cnf(356,plain,(in(unordered_pair(unordered_pair(X5,esk5_5(X1,X2,X3,X4,X5)),singleton(esk5_5(X1,X2,X3,X4,X5))),X2)|relation_composition(X1,X2)!=X3|~relation(X3)|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)),inference(rw,[status(thm)],[194,141,theory(equality)])).
% cnf(357,plain,(in(unordered_pair(unordered_pair(X1,esk5_5(X2,X3,relation_composition(X2,X3),X4,X1)),singleton(esk5_5(X2,X3,relation_composition(X2,X3),X4,X1))),X3)|~relation(relation_composition(X2,X3))|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X4,X1),singleton(X4)),relation_composition(X2,X3))),inference(er,[status(thm)],[356,theory(equality)])).
% cnf(1985,plain,(in(X1,relation_dom(X2))|~relation(X2)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)),inference(spm,[status(thm)],[273,141,theory(equality)])).
% cnf(2162,plain,(in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X1))),X2)|~function(X2)|~relation(X2)|~in(X1,relation_dom(X2))),inference(rw,[status(thm)],[281,141,theory(equality)])).
% cnf(2172,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~function(relation_composition(esk17_0,esk16_0))|~relation(relation_composition(esk17_0,esk16_0))),inference(spm,[status(thm)],[2162,180,theory(equality)])).
% cnf(2357,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~relation(relation_composition(esk17_0,esk16_0))|~function(esk17_0)|~function(esk16_0)|~relation(esk17_0)|~relation(esk16_0)),inference(spm,[status(thm)],[2172,59,theory(equality)])).
% cnf(2368,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~relation(relation_composition(esk17_0,esk16_0))|$false|~function(esk16_0)|~relation(esk17_0)|~relation(esk16_0)),inference(rw,[status(thm)],[2357,181,theory(equality)])).
% cnf(2369,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~relation(relation_composition(esk17_0,esk16_0))|$false|$false|~relation(esk17_0)|~relation(esk16_0)),inference(rw,[status(thm)],[2368,183,theory(equality)])).
% cnf(2370,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~relation(relation_composition(esk17_0,esk16_0))|$false|$false|$false|~relation(esk16_0)),inference(rw,[status(thm)],[2369,182,theory(equality)])).
% cnf(2371,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~relation(relation_composition(esk17_0,esk16_0))|$false|$false|$false|$false),inference(rw,[status(thm)],[2370,184,theory(equality)])).
% cnf(2372,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~relation(relation_composition(esk17_0,esk16_0))),inference(cn,[status(thm)],[2371,theory(equality)])).
% cnf(2382,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|~relation(esk16_0)|~relation(esk17_0)),inference(spm,[status(thm)],[2372,55,theory(equality)])).
% cnf(2396,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|$false|~relation(esk17_0)),inference(rw,[status(thm)],[2382,184,theory(equality)])).
% cnf(2397,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))|$false|$false),inference(rw,[status(thm)],[2396,182,theory(equality)])).
% cnf(2398,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))),inference(cn,[status(thm)],[2397,theory(equality)])).
% cnf(5047,plain,(in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_5(X2,X3,relation_composition(X2,X3),X1,X4))),X2)|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),relation_composition(X2,X3))),inference(csr,[status(thm)],[351,55])).
% cnf(5076,plain,(in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_5(X2,X3,relation_composition(X2,X3),X1,X4))),X2)|~relation(X3)|~relation(X2)|~in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),relation_composition(X2,X3))),inference(spm,[status(thm)],[5047,141,theory(equality)])).
% cnf(5129,plain,(in(unordered_pair(unordered_pair(X1,esk5_5(X2,X3,relation_composition(X2,X3),X4,X1)),singleton(esk5_5(X2,X3,relation_composition(X2,X3),X4,X1))),X3)|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X4,X1),singleton(X4)),relation_composition(X2,X3))),inference(csr,[status(thm)],[357,55])).
% cnf(5158,plain,(in(unordered_pair(unordered_pair(X1,esk5_5(X2,X3,relation_composition(X2,X3),X4,X1)),singleton(esk5_5(X2,X3,relation_composition(X2,X3),X4,X1))),X3)|~relation(X3)|~relation(X2)|~in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),relation_composition(X2,X3))),inference(spm,[status(thm)],[5129,141,theory(equality)])).
% cnf(226651,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk5_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0)))),esk17_0)|~relation(esk16_0)|~relation(esk17_0)),inference(spm,[status(thm)],[5076,2398,theory(equality)])).
% cnf(226687,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk5_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0)))),esk17_0)|$false|~relation(esk17_0)),inference(rw,[status(thm)],[226651,184,theory(equality)])).
% cnf(226688,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk5_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0)))),esk17_0)|$false|$false),inference(rw,[status(thm)],[226687,182,theory(equality)])).
% cnf(226689,negated_conjecture,(in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk5_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0)))),esk17_0)),inference(cn,[status(thm)],[226688,theory(equality)])).
% cnf(226695,negated_conjecture,(in(esk15_0,relation_dom(esk17_0))|~relation(esk17_0)),inference(spm,[status(thm)],[1985,226689,theory(equality)])).
% cnf(226770,negated_conjecture,(in(esk15_0,relation_dom(esk17_0))|$false),inference(rw,[status(thm)],[226695,182,theory(equality)])).
% cnf(226771,negated_conjecture,(in(esk15_0,relation_dom(esk17_0))),inference(cn,[status(thm)],[226770,theory(equality)])).
% cnf(226818,negated_conjecture,(apply(esk17_0,esk15_0)=X1|~function(esk17_0)|~relation(esk17_0)|~in(unordered_pair(unordered_pair(esk15_0,X1),singleton(esk15_0)),esk17_0)),inference(spm,[status(thm)],[191,226771,theory(equality)])).
% cnf(227031,negated_conjecture,(apply(esk17_0,esk15_0)=X1|$false|~relation(esk17_0)|~in(unordered_pair(unordered_pair(esk15_0,X1),singleton(esk15_0)),esk17_0)),inference(rw,[status(thm)],[226818,181,theory(equality)])).
% cnf(227032,negated_conjecture,(apply(esk17_0,esk15_0)=X1|$false|$false|~in(unordered_pair(unordered_pair(esk15_0,X1),singleton(esk15_0)),esk17_0)),inference(rw,[status(thm)],[227031,182,theory(equality)])).
% cnf(227033,negated_conjecture,(apply(esk17_0,esk15_0)=X1|~in(unordered_pair(unordered_pair(esk15_0,X1),singleton(esk15_0)),esk17_0)),inference(cn,[status(thm)],[227032,theory(equality)])).
% cnf(227464,negated_conjecture,(apply(esk17_0,esk15_0)=X1|~in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,X1)),esk17_0)),inference(spm,[status(thm)],[227033,141,theory(equality)])).
% cnf(227571,negated_conjecture,(apply(esk17_0,esk15_0)=esk5_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),inference(spm,[status(thm)],[227464,226689,theory(equality)])).
% cnf(233108,negated_conjecture,(in(unordered_pair(unordered_pair(apply(relation_composition(esk17_0,esk16_0),esk15_0),esk5_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),singleton(esk5_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0)))),esk16_0)|~relation(esk16_0)|~relation(esk17_0)),inference(spm,[status(thm)],[5158,2398,theory(equality)])).
% cnf(233144,negated_conjecture,(in(unordered_pair(unordered_pair(apply(relation_composition(esk17_0,esk16_0),esk15_0),apply(esk17_0,esk15_0)),singleton(apply(esk17_0,esk15_0))),esk16_0)|~relation(esk16_0)|~relation(esk17_0)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[233108,227571,theory(equality)]),227571,theory(equality)])).
% cnf(233145,negated_conjecture,(in(unordered_pair(unordered_pair(apply(relation_composition(esk17_0,esk16_0),esk15_0),apply(esk17_0,esk15_0)),singleton(apply(esk17_0,esk15_0))),esk16_0)|$false|~relation(esk17_0)),inference(rw,[status(thm)],[233144,184,theory(equality)])).
% cnf(233146,negated_conjecture,(in(unordered_pair(unordered_pair(apply(relation_composition(esk17_0,esk16_0),esk15_0),apply(esk17_0,esk15_0)),singleton(apply(esk17_0,esk15_0))),esk16_0)|$false|$false),inference(rw,[status(thm)],[233145,182,theory(equality)])).
% cnf(233147,negated_conjecture,(in(unordered_pair(unordered_pair(apply(relation_composition(esk17_0,esk16_0),esk15_0),apply(esk17_0,esk15_0)),singleton(apply(esk17_0,esk15_0))),esk16_0)),inference(cn,[status(thm)],[233146,theory(equality)])).
% cnf(233148,negated_conjecture,(in(unordered_pair(singleton(apply(esk17_0,esk15_0)),unordered_pair(apply(esk17_0,esk15_0),apply(relation_composition(esk17_0,esk16_0),esk15_0))),esk16_0)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[233147,141,theory(equality)]),141,theory(equality)])).
% cnf(233152,negated_conjecture,(in(apply(esk17_0,esk15_0),relation_dom(esk16_0))|~relation(esk16_0)),inference(spm,[status(thm)],[1985,233148,theory(equality)])).
% cnf(233224,negated_conjecture,(in(apply(esk17_0,esk15_0),relation_dom(esk16_0))|$false),inference(rw,[status(thm)],[233152,184,theory(equality)])).
% cnf(233225,negated_conjecture,(in(apply(esk17_0,esk15_0),relation_dom(esk16_0))),inference(cn,[status(thm)],[233224,theory(equality)])).
% cnf(233260,negated_conjecture,(apply(esk16_0,apply(esk17_0,esk15_0))=X1|~function(esk16_0)|~relation(esk16_0)|~in(unordered_pair(unordered_pair(apply(esk17_0,esk15_0),X1),singleton(apply(esk17_0,esk15_0))),esk16_0)),inference(spm,[status(thm)],[191,233225,theory(equality)])).
% cnf(233310,negated_conjecture,(apply(esk16_0,apply(esk17_0,esk15_0))=X1|$false|~relation(esk16_0)|~in(unordered_pair(unordered_pair(apply(esk17_0,esk15_0),X1),singleton(apply(esk17_0,esk15_0))),esk16_0)),inference(rw,[status(thm)],[233260,183,theory(equality)])).
% cnf(233311,negated_conjecture,(apply(esk16_0,apply(esk17_0,esk15_0))=X1|$false|$false|~in(unordered_pair(unordered_pair(apply(esk17_0,esk15_0),X1),singleton(apply(esk17_0,esk15_0))),esk16_0)),inference(rw,[status(thm)],[233310,184,theory(equality)])).
% cnf(233312,negated_conjecture,(apply(esk16_0,apply(esk17_0,esk15_0))=X1|~in(unordered_pair(unordered_pair(apply(esk17_0,esk15_0),X1),singleton(apply(esk17_0,esk15_0))),esk16_0)),inference(cn,[status(thm)],[233311,theory(equality)])).
% cnf(234215,negated_conjecture,(apply(esk16_0,apply(esk17_0,esk15_0))=X1|~in(unordered_pair(singleton(apply(esk17_0,esk15_0)),unordered_pair(apply(esk17_0,esk15_0),X1)),esk16_0)),inference(spm,[status(thm)],[233312,141,theory(equality)])).
% cnf(234428,negated_conjecture,(apply(esk16_0,apply(esk17_0,esk15_0))=apply(relation_composition(esk17_0,esk16_0),esk15_0)),inference(spm,[status(thm)],[234215,233148,theory(equality)])).
% cnf(234438,negated_conjecture,($false),inference(sr,[status(thm)],[234428,179,theory(equality)])).
% cnf(234439,negated_conjecture,($false),234438,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 20382
% # ...of these trivial : 4
% # ...subsumed : 18902
% # ...remaining for further processing: 1476
% # Other redundant clauses eliminated : 224
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 124
% # Backward-rewritten : 329
% # Generated clauses : 163926
% # ...of the previous two non-trivial : 147752
% # Contextual simplify-reflections : 17180
% # Paramodulations : 163452
% # Factorizations : 0
% # Equation resolutions : 278
% # Current number of processed clauses: 938
% # Positive orientable unit clauses: 87
% # Positive unorientable unit clauses: 1
% # Negative unit clauses : 68
% # Non-unit-clauses : 782
% # Current number of unprocessed clauses: 100000
% # ...number of literals in the above : 486291
% # Clause-clause subsumption calls (NU) : 2201156
% # Rec. Clause-clause subsumption calls : 997818
% # Unit Clause-clause subsumption calls : 58232
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 106
% # Indexed BW rewrite successes : 64
% # Backwards rewriting index: 447 leaves, 2.29+/-5.202 terms/leaf
% # Paramod-from index: 134 leaves, 2.10+/-5.131 terms/leaf
% # Paramod-into index: 356 leaves, 1.81+/-4.095 terms/leaf
% # -------------------------------------------------
% # User time : 7.768 s
% # System time : 0.160 s
% # Total time : 7.928 s
% # Maximum resident set size: 0 pages
% PrfWatch: 10.92 CPU 11.08 WC
% FINAL PrfWatch: 10.92 CPU 11.08 WC
% SZS output end Solution for /tmp/SystemOnTPTP12747/SEU214+1.tptp
%
%------------------------------------------------------------------------------