TSTP Solution File: CSR021+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : CSR021+1 : TPTP v5.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 : Sat Dec 25 06:00:22 EST 2010
% Result : Theorem 0.58s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 14 unt; 0 def)
% Number of atoms : 496 ( 264 equ)
% Maximal formula atoms : 149 ( 9 avg)
% Number of connectives : 641 ( 195 ~; 294 |; 141 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 88 ( 1 sgn 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( ( happens(X1,X2)
& terminates(X1,X3,X2) )
=> ~ holdsAt(X3,plus(X2,n1)) ),
file('/tmp/tmpeMJIzY/sel_CSR021+1.p_1',happens_terminates_not_holds) ).
fof(5,axiom,
! [X1,X3,X2] :
( terminates(X1,X3,X2)
<=> ( ( X1 = push
& X3 = backwards
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = forwards
& ~ happens(push,X2) )
| ( X1 = pull
& X3 = forwards
& happens(push,X2) )
| ( X1 = pull
& X3 = backwards
& happens(push,X2) )
| ( X1 = push
& X3 = spinning
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = spinning
& ~ happens(push,X2) ) ) ),
file('/tmp/tmpeMJIzY/sel_CSR021+1.p_1',terminates_all_defn) ).
fof(10,axiom,
! [X1,X2] :
( happens(X1,X2)
<=> ( ( X1 = push
& X2 = n0 )
| ( X1 = pull
& X2 = n1 )
| ( X1 = pull
& X2 = n2 )
| ( X1 = push
& X2 = n2 ) ) ),
file('/tmp/tmpeMJIzY/sel_CSR021+1.p_1',happens_all_defn) ).
fof(15,axiom,
plus(n1,n2) = n3,
file('/tmp/tmpeMJIzY/sel_CSR021+1.p_1',plus1_2) ).
fof(17,conjecture,
~ holdsAt(backwards,n3),
file('/tmp/tmpeMJIzY/sel_CSR021+1.p_1',not_backwards_3) ).
fof(29,axiom,
! [X4,X5] : plus(X4,X5) = plus(X5,X4),
file('/tmp/tmpeMJIzY/sel_CSR021+1.p_1',symmetry_of_plus) ).
fof(42,negated_conjecture,
~ ~ holdsAt(backwards,n3),
inference(assume_negation,[status(cth)],[17]) ).
fof(43,plain,
! [X1,X2,X3] :
( ( happens(X1,X2)
& terminates(X1,X3,X2) )
=> ~ holdsAt(X3,plus(X2,n1)) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(45,plain,
! [X1,X3,X2] :
( terminates(X1,X3,X2)
<=> ( ( X1 = push
& X3 = backwards
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = forwards
& ~ happens(push,X2) )
| ( X1 = pull
& X3 = forwards
& happens(push,X2) )
| ( X1 = pull
& X3 = backwards
& happens(push,X2) )
| ( X1 = push
& X3 = spinning
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = spinning
& ~ happens(push,X2) ) ) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(49,negated_conjecture,
holdsAt(backwards,n3),
inference(fof_simplification,[status(thm)],[42,theory(equality)]) ).
fof(56,plain,
! [X1,X3,X2] :
( epred2_3(X2,X3,X1)
<=> ( ( X1 = push
& X3 = backwards
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = forwards
& ~ happens(push,X2) )
| ( X1 = pull
& X3 = forwards
& happens(push,X2) ) ) ),
introduced(definition) ).
fof(57,plain,
! [X1,X3,X2] :
( epred3_3(X2,X3,X1)
<=> ( ( X1 = push
& X3 = backwards
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = forwards
& ~ happens(push,X2) )
| ( X1 = pull
& X3 = forwards
& happens(push,X2) )
| ( X1 = pull
& X3 = backwards
& happens(push,X2) )
| ( X1 = push
& X3 = spinning
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = spinning
& ~ happens(push,X2) ) ) ),
introduced(definition) ).
fof(59,plain,
! [X1,X3,X2] :
( terminates(X1,X3,X2)
<=> epred3_3(X2,X3,X1) ),
inference(apply_def,[status(esa)],[45,57,theory(equality)]) ).
fof(60,plain,
! [X1,X3,X2] :
( epred3_3(X2,X3,X1)
<=> ( epred2_3(X2,X3,X1)
| ( X1 = pull
& X3 = backwards
& happens(push,X2) )
| ( X1 = push
& X3 = spinning
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = spinning
& ~ happens(push,X2) ) ) ),
inference(apply_def,[status(esa)],[57,56,theory(equality)]) ).
fof(61,plain,
! [X1,X2,X3] :
( ~ happens(X1,X2)
| ~ terminates(X1,X3,X2)
| ~ holdsAt(X3,plus(X2,n1)) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(62,plain,
! [X4,X5,X6] :
( ~ happens(X4,X5)
| ~ terminates(X4,X6,X5)
| ~ holdsAt(X6,plus(X5,n1)) ),
inference(variable_rename,[status(thm)],[61]) ).
cnf(63,plain,
( ~ holdsAt(X1,plus(X2,n1))
| ~ terminates(X3,X1,X2)
| ~ happens(X3,X2) ),
inference(split_conjunct,[status(thm)],[62]) ).
fof(70,plain,
! [X1,X3,X2] :
( ( ~ terminates(X1,X3,X2)
| epred3_3(X2,X3,X1) )
& ( ~ epred3_3(X2,X3,X1)
| terminates(X1,X3,X2) ) ),
inference(fof_nnf,[status(thm)],[59]) ).
fof(71,plain,
! [X4,X5,X6] :
( ( ~ terminates(X4,X5,X6)
| epred3_3(X6,X5,X4) )
& ( ~ epred3_3(X6,X5,X4)
| terminates(X4,X5,X6) ) ),
inference(variable_rename,[status(thm)],[70]) ).
cnf(72,plain,
( terminates(X1,X2,X3)
| ~ epred3_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(92,plain,
! [X1,X2] :
( ( ~ happens(X1,X2)
| ( X1 = push
& X2 = n0 )
| ( X1 = pull
& X2 = n1 )
| ( X1 = pull
& X2 = n2 )
| ( X1 = push
& X2 = n2 ) )
& ( ( ( X1 != push
| X2 != n0 )
& ( X1 != pull
| X2 != n1 )
& ( X1 != pull
| X2 != n2 )
& ( X1 != push
| X2 != n2 ) )
| happens(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(93,plain,
! [X3,X4] :
( ( ~ happens(X3,X4)
| ( X3 = push
& X4 = n0 )
| ( X3 = pull
& X4 = n1 )
| ( X3 = pull
& X4 = n2 )
| ( X3 = push
& X4 = n2 ) )
& ( ( ( X3 != push
| X4 != n0 )
& ( X3 != pull
| X4 != n1 )
& ( X3 != pull
| X4 != n2 )
& ( X3 != push
| X4 != n2 ) )
| happens(X3,X4) ) ),
inference(variable_rename,[status(thm)],[92]) ).
fof(94,plain,
! [X3,X4] :
( ( X3 = push
| X3 = pull
| X3 = pull
| X3 = push
| ~ happens(X3,X4) )
& ( X4 = n2
| X3 = pull
| X3 = pull
| X3 = push
| ~ happens(X3,X4) )
& ( X3 = push
| X4 = n2
| X3 = pull
| X3 = push
| ~ happens(X3,X4) )
& ( X4 = n2
| X4 = n2
| X3 = pull
| X3 = push
| ~ happens(X3,X4) )
& ( X3 = push
| X3 = pull
| X4 = n1
| X3 = push
| ~ happens(X3,X4) )
& ( X4 = n2
| X3 = pull
| X4 = n1
| X3 = push
| ~ happens(X3,X4) )
& ( X3 = push
| X4 = n2
| X4 = n1
| X3 = push
| ~ happens(X3,X4) )
& ( X4 = n2
| X4 = n2
| X4 = n1
| X3 = push
| ~ happens(X3,X4) )
& ( X3 = push
| X3 = pull
| X3 = pull
| X4 = n0
| ~ happens(X3,X4) )
& ( X4 = n2
| X3 = pull
| X3 = pull
| X4 = n0
| ~ happens(X3,X4) )
& ( X3 = push
| X4 = n2
| X3 = pull
| X4 = n0
| ~ happens(X3,X4) )
& ( X4 = n2
| X4 = n2
| X3 = pull
| X4 = n0
| ~ happens(X3,X4) )
& ( X3 = push
| X3 = pull
| X4 = n1
| X4 = n0
| ~ happens(X3,X4) )
& ( X4 = n2
| X3 = pull
| X4 = n1
| X4 = n0
| ~ happens(X3,X4) )
& ( X3 = push
| X4 = n2
| X4 = n1
| X4 = n0
| ~ happens(X3,X4) )
& ( X4 = n2
| X4 = n2
| X4 = n1
| X4 = n0
| ~ happens(X3,X4) )
& ( X3 != push
| X4 != n0
| happens(X3,X4) )
& ( X3 != pull
| X4 != n1
| happens(X3,X4) )
& ( X3 != pull
| X4 != n2
| happens(X3,X4) )
& ( X3 != push
| X4 != n2
| happens(X3,X4) ) ),
inference(distribute,[status(thm)],[93]) ).
cnf(95,plain,
( happens(X1,X2)
| X2 != n2
| X1 != push ),
inference(split_conjunct,[status(thm)],[94]) ).
cnf(96,plain,
( happens(X1,X2)
| X2 != n2
| X1 != pull ),
inference(split_conjunct,[status(thm)],[94]) ).
cnf(126,plain,
plus(n1,n2) = n3,
inference(split_conjunct,[status(thm)],[15]) ).
cnf(128,negated_conjecture,
holdsAt(backwards,n3),
inference(split_conjunct,[status(thm)],[49]) ).
fof(146,plain,
! [X6,X7] : plus(X6,X7) = plus(X7,X6),
inference(variable_rename,[status(thm)],[29]) ).
cnf(147,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[146]) ).
fof(260,plain,
! [X1,X3,X2] :
( ( ~ epred3_3(X2,X3,X1)
| epred2_3(X2,X3,X1)
| ( X1 = pull
& X3 = backwards
& happens(push,X2) )
| ( X1 = push
& X3 = spinning
& ~ happens(pull,X2) )
| ( X1 = pull
& X3 = spinning
& ~ happens(push,X2) ) )
& ( ( ~ epred2_3(X2,X3,X1)
& ( X1 != pull
| X3 != backwards
| ~ happens(push,X2) )
& ( X1 != push
| X3 != spinning
| happens(pull,X2) )
& ( X1 != pull
| X3 != spinning
| happens(push,X2) ) )
| epred3_3(X2,X3,X1) ) ),
inference(fof_nnf,[status(thm)],[60]) ).
fof(261,plain,
! [X4,X5,X6] :
( ( ~ epred3_3(X6,X5,X4)
| epred2_3(X6,X5,X4)
| ( X4 = pull
& X5 = backwards
& happens(push,X6) )
| ( X4 = push
& X5 = spinning
& ~ happens(pull,X6) )
| ( X4 = pull
& X5 = spinning
& ~ happens(push,X6) ) )
& ( ( ~ epred2_3(X6,X5,X4)
& ( X4 != pull
| X5 != backwards
| ~ happens(push,X6) )
& ( X4 != push
| X5 != spinning
| happens(pull,X6) )
& ( X4 != pull
| X5 != spinning
| happens(push,X6) ) )
| epred3_3(X6,X5,X4) ) ),
inference(variable_rename,[status(thm)],[260]) ).
fof(262,plain,
! [X4,X5,X6] :
( ( X4 = pull
| X4 = push
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| X4 = push
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| X4 = push
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| X5 = spinning
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| X5 = spinning
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| X5 = spinning
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| ~ happens(pull,X6)
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| ~ happens(pull,X6)
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| ~ happens(pull,X6)
| X4 = pull
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| X4 = push
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| X4 = push
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| X4 = push
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| X5 = spinning
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| X5 = spinning
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| X5 = spinning
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| ~ happens(pull,X6)
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| ~ happens(pull,X6)
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| ~ happens(pull,X6)
| X5 = backwards
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| X4 = push
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| X4 = push
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| X4 = push
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| X5 = spinning
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| X5 = spinning
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| X5 = spinning
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X4 = pull
| ~ happens(pull,X6)
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( X5 = spinning
| ~ happens(pull,X6)
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ happens(push,X6)
| ~ happens(pull,X6)
| happens(push,X6)
| epred2_3(X6,X5,X4)
| ~ epred3_3(X6,X5,X4) )
& ( ~ epred2_3(X6,X5,X4)
| epred3_3(X6,X5,X4) )
& ( X4 != pull
| X5 != backwards
| ~ happens(push,X6)
| epred3_3(X6,X5,X4) )
& ( X4 != push
| X5 != spinning
| happens(pull,X6)
| epred3_3(X6,X5,X4) )
& ( X4 != pull
| X5 != spinning
| happens(push,X6)
| epred3_3(X6,X5,X4) ) ),
inference(distribute,[status(thm)],[261]) ).
cnf(265,plain,
( epred3_3(X1,X2,X3)
| ~ happens(push,X1)
| X2 != backwards
| X3 != pull ),
inference(split_conjunct,[status(thm)],[262]) ).
cnf(403,plain,
( ~ holdsAt(X1,plus(n1,X2))
| ~ terminates(X3,X1,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[63,147,theory(equality)]) ).
cnf(907,plain,
( ~ holdsAt(X1,n3)
| ~ terminates(X2,X1,n2)
| ~ happens(X2,n2) ),
inference(spm,[status(thm)],[403,126,theory(equality)]) ).
cnf(1607,plain,
( ~ holdsAt(X1,n3)
| ~ happens(X2,n2)
| ~ epred3_3(n2,X1,X2) ),
inference(spm,[status(thm)],[907,72,theory(equality)]) ).
cnf(1836,plain,
( ~ holdsAt(X1,n3)
| ~ happens(X2,n2)
| pull != X2
| backwards != X1
| ~ happens(push,n2) ),
inference(spm,[status(thm)],[1607,265,theory(equality)]) ).
fof(5715,plain,
( ~ epred16_0
<=> ! [X2] :
( ~ happens(X2,n2)
| ~ happens(push,n2)
| pull != X2 ) ),
introduced(definition),
[split] ).
cnf(5716,plain,
( epred16_0
| ~ happens(X2,n2)
| ~ happens(push,n2)
| pull != X2 ),
inference(split_equiv,[status(thm)],[5715]) ).
fof(5717,plain,
( ~ epred17_0
<=> ! [X1] :
( ~ holdsAt(X1,n3)
| backwards != X1 ) ),
introduced(definition),
[split] ).
cnf(5718,plain,
( epred17_0
| ~ holdsAt(X1,n3)
| backwards != X1 ),
inference(split_equiv,[status(thm)],[5717]) ).
cnf(5719,plain,
( ~ epred17_0
| ~ epred16_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[1836,5715,theory(equality)]),5717,theory(equality)]),
[split] ).
cnf(5720,negated_conjecture,
epred17_0,
inference(spm,[status(thm)],[5718,128,theory(equality)]) ).
cnf(5728,plain,
( $false
| ~ epred16_0 ),
inference(rw,[status(thm)],[5719,5720,theory(equality)]) ).
cnf(5729,plain,
~ epred16_0,
inference(cn,[status(thm)],[5728,theory(equality)]) ).
cnf(5739,plain,
( ~ happens(X2,n2)
| ~ happens(push,n2)
| pull != X2 ),
inference(sr,[status(thm)],[5716,5729,theory(equality)]) ).
cnf(5742,plain,
( pull != X1
| ~ happens(X1,n2) ),
inference(spm,[status(thm)],[5739,95,theory(equality)]) ).
cnf(5760,plain,
pull != X1,
inference(spm,[status(thm)],[5742,96,theory(equality)]) ).
cnf(5811,plain,
$false,
inference(er,[status(thm)],[5760,theory(equality)]) ).
cnf(5817,plain,
$false,
5811,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/CSR/CSR021+1.p
% --creating new selector for [CSR001+0.ax, CSR001+2.ax]
% -running prover on /tmp/tmpeMJIzY/sel_CSR021+1.p_1 with time limit 29
% -prover status Theorem
% Problem CSR021+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/CSR/CSR021+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/CSR/CSR021+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
%
%------------------------------------------------------------------------------