TSTP Solution File: SWW182+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWW182+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:01:41 EDT 2022
% Result : Theorem 8.93s 2.82s
% Output : CNFRefutation 8.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 15 unt; 0 nHn; 33 RR)
% Number of literals : 129 ( 75 equ; 65 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_1438,plain,
( X1 = c_Polynomial_Osynthetic__div(X2,X3,X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X1)) != c_Polynomial_OpCons(X2,X5,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1438) ).
cnf(i_0_256,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) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_256) ).
cnf(i_0_174,plain,
( class_Groups_Ocomm__monoid__add(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_174) ).
cnf(i_0_1575,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1575) ).
cnf(i_0_1351,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1351) ).
cnf(i_0_255,plain,
( c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X4,X5)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X4),c_Polynomial_OpCons(X1,X3,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_255) ).
cnf(i_0_1171,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1171) ).
cnf(i_0_176,plain,
( class_Groups_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_176) ).
cnf(i_0_1433,plain,
( c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),c_Polynomial_Osynthetic__div(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1433) ).
cnf(i_0_1432,plain,
( c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1432) ).
cnf(i_0_1354,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X4,X3)) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1354) ).
cnf(i_0_257,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_257) ).
cnf(i_0_1352,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) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1352) ).
cnf(i_0_1355,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1355) ).
cnf(i_0_186,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_186) ).
cnf(i_0_1101,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2)),c_Polynomial_OpCons(X1,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X4,X3),X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1101) ).
cnf(i_0_1100,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_1100) ).
cnf(i_0_181,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) != c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-h46wkbwl/lgb.p',i_0_181) ).
cnf(c_0_1594,plain,
( X1 = c_Polynomial_Osynthetic__div(X2,X3,X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X1)) != c_Polynomial_OpCons(X2,X5,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
i_0_1438 ).
cnf(c_0_1595,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) ),
i_0_256 ).
cnf(c_0_1596,plain,
( class_Groups_Ocomm__monoid__add(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_174 ).
cnf(c_0_1597,plain,
( X1 = c_Polynomial_Osynthetic__div(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),X3)
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_1594,c_0_1595]),c_0_1596]) ).
cnf(c_0_1598,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
i_0_1575 ).
cnf(c_0_1599,hypothesis,
( X1 = c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X2)
| c_Polynomial_Osmult(t_a,X2,X1) != c_Polynomial_OpCons(t_a,X3,X1) ),
inference(spm,[status(thm)],[c_0_1597,c_0_1598]) ).
cnf(c_0_1600,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_1351 ).
cnf(c_0_1601,plain,
( c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X4,X5)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X4),c_Polynomial_OpCons(X1,X3,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
i_0_255 ).
cnf(c_0_1602,plain,
( c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
i_0_1171 ).
cnf(c_0_1603,plain,
( X1 = c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a))
| c_Polynomial_OpCons(t_a,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1599,c_0_1600]),c_0_1598])]) ).
cnf(c_0_1604,plain,
( c_Polynomial_OpCons(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_OpCons(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1)
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(spm,[status(thm)],[c_0_1601,c_0_1602]) ).
cnf(c_0_1605,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_OpCons(t_a,X2,X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a)
| ~ class_Groups_Ocomm__monoid__add(t_a) ),
inference(spm,[status(thm)],[c_0_1603,c_0_1604]) ).
cnf(c_0_1606,plain,
( class_Groups_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_176 ).
cnf(c_0_1607,plain,
( c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,X2),X3),c_Polynomial_Osynthetic__div(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X3,c_Polynomial_Osynthetic__div(X1,X2,X3)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_1433 ).
cnf(c_0_1608,plain,
( c_Polynomial_Osynthetic__div(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_1432 ).
cnf(c_0_1609,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_OpCons(t_a,X2,X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ocomm__monoid__add(t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1605,c_0_1606]),c_0_1598])]) ).
cnf(c_0_1610,plain,
( c_Polynomial_OpCons(X1,hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_1607,c_0_1608]) ).
cnf(c_0_1611,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X4,X3)) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_1354 ).
cnf(c_0_1612,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_OpCons(t_a,X2,X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1609,c_0_1596]),c_0_1598])]) ).
cnf(c_0_1613,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
i_0_257 ).
cnf(c_0_1614,plain,
( c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Polynomial_Osmult(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1603,c_0_1610]),c_0_1598])]) ).
cnf(c_0_1615,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2),X3)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_1611,c_0_1600]) ).
cnf(c_0_1616,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a))
| c_Polynomial_OpCons(t_a,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ocomm__monoid__add(t_a) ),
inference(spm,[status(thm)],[c_0_1612,c_0_1613]) ).
cnf(c_0_1617,plain,
( c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Osmult(t_a,c_Groups_Oplus__class_Oplus(t_a,c_Groups_Ozero__class_Ozero(t_a),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1614,c_0_1615]),c_0_1598])]) ).
cnf(c_0_1618,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) ),
i_0_1352 ).
cnf(c_0_1619,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a))
| c_Polynomial_OpCons(t_a,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1616,c_0_1596]),c_0_1598])]) ).
cnf(c_0_1620,plain,
c_Polynomial_Osynthetic__div(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1617,c_0_1618]),c_0_1598])]) ).
cnf(c_0_1621,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_OpCons(t_a,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(rw,[status(thm)],[c_0_1619,c_0_1620]) ).
cnf(c_0_1622,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Polynomial_Osmult(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1621,c_0_1610]),c_0_1598])]) ).
cnf(c_0_1623,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_Osmult(X1,X2,X4)) = c_Polynomial_Osmult(X1,X2,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_1355 ).
cnf(c_0_1624,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Osmult(t_a,c_Groups_Oplus__class_Oplus(t_a,c_Groups_Ozero__class_Ozero(t_a),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1622,c_0_1615]),c_0_1598])]) ).
cnf(c_0_1625,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_1623,c_0_1600]) ).
cnf(c_0_1626,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1624,c_0_1618]),c_0_1598])]) ).
cnf(c_0_1627,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)),X3)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_1611,c_0_1600]) ).
cnf(c_0_1628,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1625,c_0_1626]),c_0_1598])]) ).
cnf(c_0_1629,plain,
c_Polynomial_Osmult(t_a,c_Groups_Oplus__class_Oplus(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1627,c_0_1628]),c_0_1598])]) ).
cnf(c_0_1630,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_1611,c_0_1618]) ).
cnf(c_0_1631,plain,
c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1618,c_0_1629]),c_0_1598])]) ).
cnf(c_0_1632,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
i_0_186 ).
cnf(c_0_1633,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2)),c_Polynomial_OpCons(X1,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X4,X3),X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_1101 ).
cnf(c_0_1634,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
i_0_1100 ).
cnf(c_0_1635,plain,
c_Polynomial_Osmult(t_a,c_Groups_Oplus__class_Oplus(t_a,c_Groups_Ozero__class_Ozero(t_a),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1630,c_0_1631]),c_0_1626]),c_0_1598])]) ).
cnf(c_0_1636,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_1632,c_0_1596]) ).
cnf(c_0_1637,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),c_Polynomial_OpCons(X1,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_1633,c_0_1634]) ).
cnf(c_0_1638,plain,
c_Polynomial_Osmult(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1635,c_0_1636]),c_0_1598])]) ).
cnf(c_0_1639,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) != c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
i_0_181 ).
cnf(c_0_1640,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Polynomial_OpCons(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1637,c_0_1638]),c_0_1598])]) ).
cnf(c_0_1641,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),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_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(rw,[status(thm)],[c_0_1639,c_0_1640]) ).
cnf(c_0_1642,plain,
~ class_Groups_Ocomm__monoid__add(t_a),
inference(spm,[status(thm)],[c_0_1641,c_0_1595]) ).
cnf(c_0_1643,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1642,c_0_1596]),c_0_1598])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW182+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 5 18:38:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.45 # ENIGMATIC: Selected SinE mode:
% 0.20/0.51 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.51 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.20/0.51 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.20/0.51 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 8.93/2.82 # ENIGMATIC: Solved by autoschedule-lgb:
% 8.93/2.82 # No SInE strategy applied
% 8.93/2.82 # Trying AutoSched0 for 150 seconds
% 8.93/2.82 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 8.93/2.82 # and selection function SelectComplexExceptUniqMaxHorn.
% 8.93/2.82 #
% 8.93/2.82 # Preprocessing time : 0.025 s
% 8.93/2.82 # Presaturation interreduction done
% 8.93/2.82
% 8.93/2.82 # Proof found!
% 8.93/2.82 # SZS status Theorem
% 8.93/2.82 # SZS output start CNFRefutation
% See solution above
% 8.93/2.82 # Training examples: 0 positive, 0 negative
% 8.93/2.82
% 8.93/2.82 # -------------------------------------------------
% 8.93/2.82 # User time : 0.124 s
% 8.93/2.82 # System time : 0.004 s
% 8.93/2.82 # Total time : 0.128 s
% 8.93/2.82 # Maximum resident set size: 7368 pages
% 8.93/2.82
%------------------------------------------------------------------------------