TSTP Solution File: ALG347-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------