TSTP Solution File: SWW186+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW186+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 Mar 6 14:50:40 EST 2011
% Result : Theorem 5.14s
% Output : CNFRefutation 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 15 unt; 0 def)
% Number of atoms : 129 ( 80 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 122 ( 52 ~; 52 |; 9 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 70 ( 10 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(272,axiom,
! [X52] :
( class_Rings_Ocomm__semiring__0(X52)
=> class_Groups_Ocomm__monoid__add(X52) ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
fof(281,axiom,
! [X3,X2,X14,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X14,X2),c_Polynomial_OpCons(X4,X3,X2)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
=> X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ) ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_offset__poly__eq__0__lemma) ).
fof(450,axiom,
! [X52] :
( class_Rings_Ocomm__semiring__0(X52)
=> class_Groups_Ozero(X52) ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(585,axiom,
! [X3,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> c_Polynomial_Osmult(X4,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_smult__0__right) ).
fof(603,axiom,
! [X28,X18,X19] :
( class_Groups_Ozero(X19)
=> ( c_Polynomial_OpCons(X19,X18,X28) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))
<=> ( X18 = c_Groups_Ozero__class_Ozero(X19)
& X28 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) ) ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_pCons__eq__0__iff) ).
fof(719,axiom,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',conj_1) ).
fof(722,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',conj_0) ).
fof(788,axiom,
! [X1,X4] :
( class_Groups_Ocomm__monoid__add(X4)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X1) = X1 ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_add__poly__code_I1_J) ).
fof(1105,conjecture,
( v_a = c_Groups_Ozero__class_Ozero(t_a)
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',conj_2) ).
fof(1148,axiom,
class_Rings_Ocomm__semiring__0(t_a),
file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',tfree_0) ).
fof(1183,negated_conjecture,
~ ( v_a = c_Groups_Ozero__class_Ozero(t_a)
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(assume_negation,[status(cth)],[1105]) ).
fof(2149,plain,
! [X52] :
( ~ class_Rings_Ocomm__semiring__0(X52)
| class_Groups_Ocomm__monoid__add(X52) ),
inference(fof_nnf,[status(thm)],[272]) ).
fof(2150,plain,
! [X53] :
( ~ class_Rings_Ocomm__semiring__0(X53)
| class_Groups_Ocomm__monoid__add(X53) ),
inference(variable_rename,[status(thm)],[2149]) ).
cnf(2151,plain,
( class_Groups_Ocomm__monoid__add(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[2150]) ).
fof(2181,plain,
! [X3,X2,X14,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X14,X2),c_Polynomial_OpCons(X4,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
| X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_nnf,[status(thm)],[281]) ).
fof(2182,plain,
! [X15,X16,X17,X18] :
( ~ class_Rings_Ocomm__semiring__0(X18)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X18),c_Polynomial_Osmult(X18,X17,X16),c_Polynomial_OpCons(X18,X15,X16)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
| X16 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X18)) ),
inference(variable_rename,[status(thm)],[2181]) ).
cnf(2183,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X2,X4,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[2182]) ).
fof(2697,plain,
! [X52] :
( ~ class_Rings_Ocomm__semiring__0(X52)
| class_Groups_Ozero(X52) ),
inference(fof_nnf,[status(thm)],[450]) ).
fof(2698,plain,
! [X53] :
( ~ class_Rings_Ocomm__semiring__0(X53)
| class_Groups_Ozero(X53) ),
inference(variable_rename,[status(thm)],[2697]) ).
cnf(2699,plain,
( class_Groups_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[2698]) ).
fof(3121,plain,
! [X3,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| c_Polynomial_Osmult(X4,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
inference(fof_nnf,[status(thm)],[585]) ).
fof(3122,plain,
! [X5,X6] :
( ~ class_Rings_Ocomm__semiring__0(X6)
| c_Polynomial_Osmult(X6,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
inference(variable_rename,[status(thm)],[3121]) ).
cnf(3123,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[3122]) ).
fof(3181,plain,
! [X28,X18,X19] :
( ~ class_Groups_Ozero(X19)
| ( ( c_Polynomial_OpCons(X19,X18,X28) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))
| ( X18 = c_Groups_Ozero__class_Ozero(X19)
& X28 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) )
& ( X18 != c_Groups_Ozero__class_Ozero(X19)
| X28 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))
| c_Polynomial_OpCons(X19,X18,X28) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) ) ),
inference(fof_nnf,[status(thm)],[603]) ).
fof(3182,plain,
! [X29,X30,X31] :
( ~ class_Groups_Ozero(X31)
| ( ( c_Polynomial_OpCons(X31,X30,X29) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
| ( X30 = c_Groups_Ozero__class_Ozero(X31)
& X29 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31)) ) )
& ( X30 != c_Groups_Ozero__class_Ozero(X31)
| X29 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
| c_Polynomial_OpCons(X31,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31)) ) ) ),
inference(variable_rename,[status(thm)],[3181]) ).
fof(3183,plain,
! [X29,X30,X31] :
( ( X30 = c_Groups_Ozero__class_Ozero(X31)
| c_Polynomial_OpCons(X31,X30,X29) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
| ~ class_Groups_Ozero(X31) )
& ( X29 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
| c_Polynomial_OpCons(X31,X30,X29) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
| ~ class_Groups_Ozero(X31) )
& ( X30 != c_Groups_Ozero__class_Ozero(X31)
| X29 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
| c_Polynomial_OpCons(X31,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
| ~ class_Groups_Ozero(X31) ) ),
inference(distribute,[status(thm)],[3182]) ).
cnf(3186,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[3183]) ).
cnf(3549,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(split_conjunct,[status(thm)],[719]) ).
fof(3556,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(fof_nnf,[status(thm)],[722]) ).
cnf(3557,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(split_conjunct,[status(thm)],[3556]) ).
fof(3786,plain,
! [X1,X4] :
( ~ class_Groups_Ocomm__monoid__add(X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X1) = X1 ),
inference(fof_nnf,[status(thm)],[788]) ).
fof(3787,plain,
! [X5,X6] :
( ~ class_Groups_Ocomm__monoid__add(X6)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X5) = X5 ),
inference(variable_rename,[status(thm)],[3786]) ).
cnf(3788,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[3787]) ).
fof(4851,negated_conjecture,
( v_a != c_Groups_Ozero__class_Ozero(t_a)
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(fof_nnf,[status(thm)],[1183]) ).
cnf(4852,negated_conjecture,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_a != c_Groups_Ozero__class_Ozero(t_a) ),
inference(split_conjunct,[status(thm)],[4851]) ).
cnf(4985,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(split_conjunct,[status(thm)],[1148]) ).
cnf(5376,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[3788,2151,theory(equality)]) ).
cnf(5415,plain,
( c_Groups_Ozero__class_Ozero(X1) = X2
| c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[3186,2699,theory(equality)]) ).
cnf(7217,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[2183,3549,theory(equality)]) ).
cnf(7220,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
| $false ),
inference(rw,[status(thm)],[7217,4985,theory(equality)]) ).
cnf(7221,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h),
inference(cn,[status(thm)],[7220,theory(equality)]) ).
cnf(55320,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3549,7221,theory(equality)]),7221,theory(equality)]) ).
cnf(55321,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p
| $false ),
inference(rw,[status(thm)],[3557,7221,theory(equality)]) ).
cnf(55322,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
inference(cn,[status(thm)],[55321,theory(equality)]) ).
cnf(55333,plain,
( c_Polynomial_Osmult(t_a,X1,v_p) = v_p
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[3123,55322,theory(equality)]) ).
cnf(55418,negated_conjecture,
( $false
| c_Groups_Ozero__class_Ozero(t_a) != v_a ),
inference(rw,[status(thm)],[4852,55322,theory(equality)]) ).
cnf(55419,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) != v_a,
inference(cn,[status(thm)],[55418,theory(equality)]) ).
cnf(55420,plain,
( c_Polynomial_Osmult(t_a,X1,v_p) = v_p
| $false ),
inference(rw,[status(thm)],[55333,4985,theory(equality)]) ).
cnf(55421,plain,
c_Polynomial_Osmult(t_a,X1,v_p) = v_p,
inference(cn,[status(thm)],[55420,theory(equality)]) ).
cnf(58883,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[5376,55322,theory(equality)]) ).
cnf(58916,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1
| $false ),
inference(rw,[status(thm)],[58883,4985,theory(equality)]) ).
cnf(58917,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1,
inference(cn,[status(thm)],[58916,theory(equality)]) ).
cnf(60778,plain,
( c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Polynomial_OpCons(t_a,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(spm,[status(thm)],[5415,4985,theory(equality)]) ).
cnf(60782,plain,
( c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Polynomial_OpCons(t_a,X1,X2) != v_p ),
inference(rw,[status(thm)],[60778,55322,theory(equality)]) ).
cnf(64791,plain,
c_Polynomial_OpCons(t_a,v_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[55320,55322,theory(equality)]),55421,theory(equality)]),55322,theory(equality)]),58917,theory(equality)]) ).
cnf(64792,plain,
c_Polynomial_OpCons(t_a,v_a,v_p) = v_p,
inference(rw,[status(thm)],[64791,55322,theory(equality)]) ).
cnf(64811,plain,
c_Groups_Ozero__class_Ozero(t_a) = v_a,
inference(spm,[status(thm)],[60782,64792,theory(equality)]) ).
cnf(64842,plain,
$false,
inference(sr,[status(thm)],[64811,55419,theory(equality)]) ).
cnf(64843,plain,
$false,
64842,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW186+1.p
% --creating new selector for []
% -running prover on /tmp/tmp_ggpwJ/sel_SWW186+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW186+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW186+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW186+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
%
%------------------------------------------------------------------------------