TSTP Solution File: ALG347-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG347-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n006.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 : 300s
% DateTime : Wed Aug 30 16:07:25 EDT 2023
% Result : Unsatisfiable 1.30s 1.39s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 109
% Syntax : Number of formulae : 120 ( 10 unt; 102 typ; 0 def)
% Number of atoms : 31 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 156 ( 97 >; 59 *; 0 +; 0 <<)
% Number of predicates : 71 ( 69 usr; 1 prp; 0-5 aty)
% Number of functors : 33 ( 33 usr; 5 con; 0-4 aty)
% Number of variables : 19 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Power_Opower: $i > $o ).
tff(decl_23,type,
tc_nat: $i ).
tff(decl_24,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_25,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_27,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_28,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_30,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_31,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_33,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_36,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_37,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_40,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_41,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_42,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_43,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_44,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_45,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_46,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_47,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_48,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_49,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_50,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_51,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_52,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_53,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_54,type,
c_Suc: $i > $i ).
tff(decl_55,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
c_Parity_Oeven__odd__class_Oeven: ( $i * $i ) > $o ).
tff(decl_57,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_58,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_59,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_60,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_61,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_62,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_63,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_64,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_65,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_66,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_67,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_72,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_73,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_74,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_75,type,
c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_79,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_80,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_82,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_84,type,
c_Polynomial_Ocoeff: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_88,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_89,type,
c_Polynomial_Opdivmod: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(decl_91,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_92,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_93,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
class_HOL_Ozero: $i > $o ).
tff(decl_95,type,
class_HOL_Oeq: $i > $o ).
tff(decl_96,type,
c_HOL_Oeq__class_Oeq: ( $i * $i * $i ) > $o ).
tff(decl_97,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_98,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_99,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_102,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_103,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_105,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_106,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_107,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_108,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_109,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_110,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_111,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_112,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_113,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_114,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_115,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_116,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_117,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_118,type,
t_a: $i ).
tff(decl_119,type,
v_pa: $i ).
tff(decl_120,type,
v_h: $i ).
tff(decl_121,type,
v_a: $i ).
tff(decl_122,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_123,type,
tc_prod: ( $i * $i ) > $i ).
cnf(cls_degree__pCons__eq_0,axiom,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X2,X3,X1),X1) = c_Suc(c_Polynomial_Odegree(X3,X1))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
cnf(clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero,axiom,
( class_HOL_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_offset__poly__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
cnf(cls_conjecture_1,negated_conjecture,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_7,axiom,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X2,X3,X1),X1) = c_Suc(c_Polynomial_Odegree(X3,X1))
| X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ),
cls_degree__pCons__eq_0 ).
cnf(c_0_8,axiom,
( class_HOL_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsrel_Ring__and__Field_Ocomm__semiring__0_HOL_Ozero ).
cnf(c_0_9,plain,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,X3),X3) = c_Suc(c_Polynomial_Odegree(X2,X3))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,negated_conjecture,
class_Ring__and__Field_Ocomm__semiring__0(t_a),
tfree_tcs ).
cnf(c_0_11,negated_conjecture,
c_Polynomial_Odegree(c_Polynomial_OpCons(v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a),t_a) != c_Suc(c_Polynomial_Odegree(v_pa,t_a)),
cls_conjecture_2 ).
cnf(c_0_12,negated_conjecture,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,t_a),t_a) = c_Suc(c_Polynomial_Odegree(X2,t_a))
| X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a),t_a) = c_Polynomial_Odegree(v_pa,t_a),
cls_conjecture_0 ).
cnf(c_0_14,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
cls_offset__poly__eq__0__iff_0 ).
cnf(c_0_15,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_pa,v_h,t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,negated_conjecture,
v_pa != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
cls_conjecture_1 ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_10])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG347-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 05:09:06 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 1.30/1.39 % Version : CSE_E---1.5
% 1.30/1.39 % Problem : theBenchmark.p
% 1.30/1.39 % Proof found
% 1.30/1.39 % SZS status Theorem for theBenchmark.p
% 1.30/1.39 % SZS output start Proof
% See solution above
% 1.30/1.40 % Total time : 0.772000 s
% 1.30/1.40 % SZS output end Proof
% 1.30/1.40 % Total time : 0.802000 s
%------------------------------------------------------------------------------