TSTP Solution File: SWC122+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC122+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %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 : Sun Dec 26 10:20:37 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 72 ( 18 unt; 0 def)
% Number of atoms : 346 ( 70 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 447 ( 173 ~; 176 |; 77 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 62 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpbq0UGK/sel_SWC122+1.p_1',ax84) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpbq0UGK/sel_SWC122+1.p_1',ax26) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/tmp/tmpbq0UGK/sel_SWC122+1.p_1',ax6) ).
fof(16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpbq0UGK/sel_SWC122+1.p_1',ax7) ).
fof(23,axiom,
ssList(nil),
file('/tmp/tmpbq0UGK/sel_SWC122+1.p_1',ax17) ).
fof(33,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ( nil != X3
& nil = X4 )
| ( neq(X1,nil)
& segmentP(X2,X1) )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
file('/tmp/tmpbq0UGK/sel_SWC122+1.p_1',co1) ).
fof(34,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ( nil != X3
& nil = X4 )
| ( neq(X1,nil)
& segmentP(X2,X1) )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[33]) ).
fof(35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ( nil != X3
& nil = X4 )
| ( neq(X1,nil)
& segmentP(X2,X1) )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[34,theory(equality)]) ).
fof(36,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(37,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[36]) ).
cnf(38,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(72,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(73,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[72]) ).
fof(74,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[73]) ).
cnf(75,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(98,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ rearsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X3,X2) != X1 )
| rearsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(99,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X6,X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X7,X5) != X4 )
| rearsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5) )
& ( ~ rearsegP(X4,X5)
| ( ssList(esk5_2(X4,X5))
& app(esk5_2(X4,X5),X5) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X7,X5) != X4
| rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk5_2(X4,X5))
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(esk5_2(X4,X5),X5) = X4
| ~ rearsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(103,plain,
( app(esk5_2(X1,X2),X2) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(104,plain,
( ssList(esk5_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(106,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(app(X3,X2),X4) != X1 ) )
| segmentP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(107,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,X6),X8) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk6_2(X5,X6))
& ssList(esk7_2(X5,X6))
& app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[107]) ).
fof(109,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk6_2(X5,X6))
& ssList(esk7_2(X5,X6))
& app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[108]) ).
fof(110,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk6_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk7_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk6_2(X5,X6),X6),esk7_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[109]) ).
cnf(114,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(141,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[23]) ).
fof(179,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& ( nil = X3
| nil != X4 )
& ( ~ neq(X1,nil)
| ~ segmentP(X2,X1) )
& ( ~ neq(X4,nil)
| ( neq(X3,nil)
& rearsegP(X4,X3) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(180,negated_conjecture,
? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& X6 = X8
& X5 = X7
& neq(X6,nil)
& ( nil = X7
| nil != X8 )
& ( ~ neq(X5,nil)
| ~ segmentP(X6,X5) )
& ( ~ neq(X8,nil)
| ( neq(X7,nil)
& rearsegP(X8,X7) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[179]) ).
fof(181,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& neq(esk9_0,nil)
& ( nil = esk10_0
| nil != esk11_0 )
& ( ~ neq(esk8_0,nil)
| ~ segmentP(esk9_0,esk8_0) )
& ( ~ neq(esk11_0,nil)
| ( neq(esk10_0,nil)
& rearsegP(esk11_0,esk10_0) ) ) ),
inference(skolemize,[status(esa)],[180]) ).
fof(182,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& neq(esk9_0,nil)
& ( nil = esk10_0
| nil != esk11_0 )
& ( ~ neq(esk8_0,nil)
| ~ segmentP(esk9_0,esk8_0) )
& ( neq(esk10_0,nil)
| ~ neq(esk11_0,nil) )
& ( rearsegP(esk11_0,esk10_0)
| ~ neq(esk11_0,nil) ) ),
inference(distribute,[status(thm)],[181]) ).
cnf(183,negated_conjecture,
( rearsegP(esk11_0,esk10_0)
| ~ neq(esk11_0,nil) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(184,negated_conjecture,
( neq(esk10_0,nil)
| ~ neq(esk11_0,nil) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(185,negated_conjecture,
( ~ segmentP(esk9_0,esk8_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(187,negated_conjecture,
neq(esk9_0,nil),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(188,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[182]) ).
cnf(189,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[182]) ).
cnf(192,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(193,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(194,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[193,188,theory(equality)]) ).
cnf(195,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[192,189,theory(equality)]) ).
cnf(196,negated_conjecture,
neq(esk11_0,nil),
inference(rw,[status(thm)],[187,189,theory(equality)]) ).
cnf(197,negated_conjecture,
( rearsegP(esk11_0,esk10_0)
| $false ),
inference(rw,[status(thm)],[183,196,theory(equality)]) ).
cnf(198,negated_conjecture,
rearsegP(esk11_0,esk10_0),
inference(cn,[status(thm)],[197,theory(equality)]) ).
cnf(199,negated_conjecture,
( neq(esk10_0,nil)
| $false ),
inference(rw,[status(thm)],[184,196,theory(equality)]) ).
cnf(200,negated_conjecture,
neq(esk10_0,nil),
inference(cn,[status(thm)],[199,theory(equality)]) ).
cnf(201,negated_conjecture,
( $false
| ~ segmentP(esk9_0,esk8_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[185,188,theory(equality)]),200,theory(equality)]) ).
cnf(202,negated_conjecture,
( $false
| ~ segmentP(esk11_0,esk10_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[201,189,theory(equality)]),188,theory(equality)]) ).
cnf(203,negated_conjecture,
~ segmentP(esk11_0,esk10_0),
inference(cn,[status(thm)],[202,theory(equality)]) ).
cnf(230,negated_conjecture,
( ssList(esk5_2(esk11_0,esk10_0))
| ~ ssList(esk10_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[104,198,theory(equality)]) ).
cnf(273,negated_conjecture,
( app(esk5_2(esk11_0,esk10_0),esk10_0) = esk11_0
| ~ ssList(esk10_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[103,198,theory(equality)]) ).
cnf(306,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(spm,[status(thm)],[114,38,theory(equality)]) ).
cnf(310,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| $false
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(rw,[status(thm)],[306,141,theory(equality)]) ).
cnf(311,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X3,X2)) ),
inference(cn,[status(thm)],[310,theory(equality)]) ).
cnf(433,negated_conjecture,
( ssList(esk5_2(esk11_0,esk10_0))
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[230,194,theory(equality)]) ).
cnf(434,negated_conjecture,
( ssList(esk5_2(esk11_0,esk10_0))
| $false
| $false ),
inference(rw,[status(thm)],[433,195,theory(equality)]) ).
cnf(435,negated_conjecture,
ssList(esk5_2(esk11_0,esk10_0)),
inference(cn,[status(thm)],[434,theory(equality)]) ).
cnf(807,negated_conjecture,
( app(esk5_2(esk11_0,esk10_0),esk10_0) = esk11_0
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[273,194,theory(equality)]) ).
cnf(808,negated_conjecture,
( app(esk5_2(esk11_0,esk10_0),esk10_0) = esk11_0
| $false
| $false ),
inference(rw,[status(thm)],[807,195,theory(equality)]) ).
cnf(809,negated_conjecture,
app(esk5_2(esk11_0,esk10_0),esk10_0) = esk11_0,
inference(cn,[status(thm)],[808,theory(equality)]) ).
cnf(2214,plain,
( segmentP(X1,X2)
| app(X3,X2) != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[311,75]) ).
cnf(2217,negated_conjecture,
( segmentP(X1,esk10_0)
| esk11_0 != X1
| ~ ssList(esk5_2(esk11_0,esk10_0))
| ~ ssList(esk10_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[2214,809,theory(equality)]) ).
cnf(2229,negated_conjecture,
( segmentP(X1,esk10_0)
| esk11_0 != X1
| ~ ssList(esk5_2(esk11_0,esk10_0))
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2217,194,theory(equality)]) ).
cnf(2230,negated_conjecture,
( segmentP(X1,esk10_0)
| esk11_0 != X1
| ~ ssList(esk5_2(esk11_0,esk10_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2229,theory(equality)]) ).
cnf(2367,negated_conjecture,
( segmentP(X1,esk10_0)
| esk11_0 != X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[2230,435,theory(equality)]) ).
cnf(2368,negated_conjecture,
( segmentP(esk11_0,esk10_0)
| ~ ssList(esk11_0) ),
inference(er,[status(thm)],[2367,theory(equality)]) ).
cnf(2369,negated_conjecture,
( segmentP(esk11_0,esk10_0)
| $false ),
inference(rw,[status(thm)],[2368,195,theory(equality)]) ).
cnf(2370,negated_conjecture,
segmentP(esk11_0,esk10_0),
inference(cn,[status(thm)],[2369,theory(equality)]) ).
cnf(2371,negated_conjecture,
$false,
inference(sr,[status(thm)],[2370,203,theory(equality)]) ).
cnf(2372,negated_conjecture,
$false,
2371,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC122+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpbq0UGK/sel_SWC122+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC122+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC122+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC122+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
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