TSTP Solution File: ALG419-1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG419-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n013.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 : Sat May  4 07:16:37 EDT 2024

% Result   : Unsatisfiable 22.91s 3.53s
% Output   : CNFRefutation 22.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   22
% Syntax   : Number of clauses     :   76 (  35 unt;  10 nHn;  48 RR)
%            Number of literals    :  134 (  71 equ;  55 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   5 con; 0-3 aty)
%            Number of variables   :   97 (  10 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clsarity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
    ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ofield(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).

cnf(cls_mod__mult__self2__is__0_0,axiom,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_mod__mult__self2__is__0_0) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

cnf(cls_conjecture_2,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_conjecture_2) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).

cnf(cls_mod__div__equality2_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1),c_Divides_Odiv__class_Omod(X3,X2,X1),X1) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_mod__div__equality2_0) ).

cnf(cls_s_0,axiom,
    v_pa____ = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_s_0) ).

cnf(cls_div__mult__self2__is__id_0,axiom,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_div__mult__self2__is__id_0) ).

cnf(cls_sne_0,axiom,
    v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_sne_0) ).

cnf(cls_mod__div__decomp_0,axiom,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_mod__div__decomp_0) ).

cnf(cls_natgb_Oadd__r0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_natgb_Oadd__r0__iff_0) ).

cnf(cls_degree__mult__eq_0,axiom,
    ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X3,X1),tc_nat)
    | X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_degree__mult__eq_0) ).

cnf(cls_degree__linear__power_0,axiom,
    ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X2,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X3,tc_Polynomial_Opoly(X1)),X1) = X3
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_degree__linear__power_0) ).

cnf(cls_mod__poly__less_0,axiom,
    ( c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)) = X2
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X3,X1),tc_nat) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_mod__poly__less_0) ).

cnf(cls_nat__neq__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_nat__neq__iff_0) ).

cnf(cls_pne_0,axiom,
    v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_pne_0) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

cnf(cls_oa_0,axiom,
    c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_oa_0) ).

cnf(cls_mult__poly__0__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',cls_mult__poly__0__left_0) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

cnf(c_0_22,plain,
    ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ofield(X1) ),
    inference(fof_simplification,[status(thm)],[clsarity_Polynomial__Opoly__Divides_Osemiring__div]) ).

cnf(c_0_23,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(fof_simplification,[status(thm)],[cls_mod__mult__self2__is__0_0]) ).

cnf(c_0_24,plain,
    ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ofield(X1) ),
    c_0_22 ).

cnf(c_0_25,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).

cnf(c_0_26,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat),
    inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).

cnf(c_0_27,plain,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I6_J_0]) ).

cnf(c_0_28,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1]) ).

cnf(c_0_29,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1),c_Divides_Odiv__class_Omod(X3,X2,X1),X1) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(fof_simplification,[status(thm)],[cls_mod__div__equality2_0]) ).

cnf(c_0_30,plain,
    ( c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_23 ).

cnf(c_0_31,axiom,
    v_pa____ = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    cls_s_0 ).

cnf(c_0_32,plain,
    class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_33,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(fof_simplification,[status(thm)],[cls_div__mult__self2__is__id_0]) ).

cnf(c_0_34,plain,
    v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(fof_simplification,[status(thm)],[cls_sne_0]) ).

cnf(c_0_35,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_nat),
    c_0_26 ).

cnf(c_0_36,plain,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(fof_simplification,[status(thm)],[cls_mod__div__decomp_0]) ).

cnf(c_0_37,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    inference(fof_simplification,[status(thm)],[cls_natgb_Oadd__r0__iff_0]) ).

cnf(c_0_38,plain,
    ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X3,X1),tc_nat)
    | X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    inference(fof_simplification,[status(thm)],[cls_degree__mult__eq_0]) ).

cnf(c_0_39,plain,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_27 ).

cnf(c_0_40,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_28 ).

cnf(c_0_41,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X3,X2,X1),X1),c_Divides_Odiv__class_Omod(X3,X2,X1),X1) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_29 ).

cnf(c_0_42,plain,
    c_Divides_Odiv__class_Omod(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).

cnf(c_0_43,plain,
    ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X2,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X3,tc_Polynomial_Opoly(X1)),X1) = X3
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[cls_degree__linear__power_0]) ).

cnf(c_0_44,plain,
    ( c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = X2
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_33 ).

cnf(c_0_45,plain,
    v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    c_0_34 ).

cnf(c_0_46,plain,
    ( c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)) = X2
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X3,X1),tc_nat) ),
    inference(fof_simplification,[status(thm)],[cls_mod__poly__less_0]) ).

cnf(c_0_47,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),tc_nat),
    inference(spm,[status(thm)],[c_0_35,c_0_31]) ).

cnf(c_0_48,axiom,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
    | c_HOL_Oord__class_Oless(X2,X1,tc_nat)
    | X2 = X1 ),
    cls_nat__neq__iff_0 ).

cnf(c_0_49,plain,
    v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(fof_simplification,[status(thm)],[cls_pne_0]) ).

cnf(c_0_50,plain,
    ( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X3,X1),X3,X1),c_Divides_Odiv__class_Omod(X2,X3,X1),X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_36 ).

cnf(c_0_51,plain,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 != c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
    c_0_37 ).

cnf(c_0_52,plain,
    ( c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X3,X1),tc_nat)
    | X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | X2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Oidom(X1) ),
    c_0_38 ).

cnf(c_0_53,plain,
    ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_54,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_s____,c_Divides_Odiv__class_Odiv(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_32])]) ).

cnf(c_0_55,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).

cnf(c_0_56,plain,
    ( c_Polynomial_Odegree(c_Power_Opower__class_Opower(c_Polynomial_OpCons(X2,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1),X3,tc_Polynomial_Opoly(X1)),X1) = X3
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_43 ).

cnf(c_0_57,plain,
    c_Power_Opower__class_Opower(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(v_a____,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Odiv(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_31]),c_0_45]),c_0_32])]) ).

cnf(c_0_58,plain,
    ( c_Divides_Odiv__class_Omod(X2,X3,tc_Polynomial_Opoly(X1)) = X2
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(X2,X1),c_Polynomial_Odegree(X3,X1),tc_nat) ),
    c_0_46 ).

cnf(c_0_59,negated_conjecture,
    ( c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex)
    | c_HOL_Oord__class_Oless(c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_nat) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_60,plain,
    v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    c_0_49 ).

cnf(c_0_61,plain,
    c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
    inference(fof_simplification,[status(thm)],[cls_oa_0]) ).

cnf(c_0_62,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    inference(fof_simplification,[status(thm)],[cls_mult__poly__0__left_0]) ).

cnf(c_0_63,plain,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_32])]) ).

cnf(c_0_64,plain,
    ( c_Polynomial_Odegree(X1,X2) = c_HOL_Ozero__class_Ozero(tc_nat)
    | X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | X3 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(X3,X1,tc_Polynomial_Opoly(X2)),X2) != c_Polynomial_Odegree(X3,X2)
    | ~ class_Ring__and__Field_Oidom(X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_65,plain,
    c_HOL_Otimes__class_Otimes(v_s____,c_Divides_Odiv__class_Odiv(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).

cnf(c_0_66,plain,
    c_Polynomial_Odegree(c_Divides_Odiv__class_Odiv(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_55])]) ).

cnf(c_0_67,negated_conjecture,
    c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex) = c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_42]),c_0_25])]),c_0_60]) ).

cnf(c_0_68,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).

cnf(c_0_69,plain,
    c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
    c_0_61 ).

cnf(c_0_70,plain,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
    c_0_62 ).

cnf(c_0_71,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).

cnf(c_0_72,plain,
    c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_63]),c_0_55])]) ).

cnf(c_0_73,plain,
    c_Divides_Odiv__class_Odiv(v_pa____,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]),c_0_68])]),c_0_69]),c_0_45]) ).

cnf(c_0_74,plain,
    c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_75,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_60]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.21  % Problem    : ALG419-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.22  % Command    : run_E %s %d THM
% 0.23/0.43  % Computer : n013.cluster.edu
% 0.23/0.43  % Model    : x86_64 x86_64
% 0.23/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.43  % Memory   : 8042.1875MB
% 0.23/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.23/0.43  % CPULimit   : 300
% 0.23/0.43  % WCLimit    : 300
% 0.23/0.43  % DateTime   : Fri May  3 13:49:04 EDT 2024
% 0.23/0.43  % CPUTime    : 
% 0.48/0.65  Running first-order theorem proving
% 0.48/0.65  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.OYARhJb8LB/E---3.1_10245.p
% 22.91/3.53  # Version: 3.1.0
% 22.91/3.53  # Preprocessing class: FSLMSMSMSSSNFFN.
% 22.91/3.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.91/3.53  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 22.91/3.53  # Starting new_bool_3 with 600s (2) cores
% 22.91/3.53  # Starting new_bool_1 with 300s (1) cores
% 22.91/3.53  # Starting sh5l with 300s (1) cores
% 22.91/3.53  # new_bool_3 with pid 10330 completed with status 0
% 22.91/3.53  # Result found by new_bool_3
% 22.91/3.53  # Preprocessing class: FSLMSMSMSSSNFFN.
% 22.91/3.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.91/3.53  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 22.91/3.53  # Starting new_bool_3 with 600s (2) cores
% 22.91/3.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 22.91/3.53  # Search class: FGHSM-FSLM32-DFFFFFNN
% 22.91/3.53  # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 22.91/3.53  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 45s (1) cores
% 22.91/3.53  # Starting new_bool_3 with 61s (1) cores
% 22.91/3.53  # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 10334 completed with status 0
% 22.91/3.53  # Result found by G-E--_301_C18_F1_URBAN_S5PRR_S0Y
% 22.91/3.53  # Preprocessing class: FSLMSMSMSSSNFFN.
% 22.91/3.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 22.91/3.53  # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 22.91/3.53  # Starting new_bool_3 with 600s (2) cores
% 22.91/3.53  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 22.91/3.53  # Search class: FGHSM-FSLM32-DFFFFFNN
% 22.91/3.53  # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 22.91/3.53  # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 45s (1) cores
% 22.91/3.53  # Preprocessing time       : 0.016 s
% 22.91/3.53  
% 22.91/3.53  # Proof found!
% 22.91/3.53  # SZS status Unsatisfiable
% 22.91/3.53  # SZS output start CNFRefutation
% See solution above
% 22.91/3.53  # Parsed axioms                        : 998
% 22.91/3.53  # Removed by relevancy pruning/SinE    : 624
% 22.91/3.53  # Initial clauses                      : 374
% 22.91/3.53  # Removed in clause preprocessing      : 0
% 22.91/3.53  # Initial clauses in saturation        : 374
% 22.91/3.53  # Processed clauses                    : 7647
% 22.91/3.53  # ...of these trivial                  : 274
% 22.91/3.53  # ...subsumed                          : 4873
% 22.91/3.53  # ...remaining for further processing  : 2500
% 22.91/3.53  # Other redundant clauses eliminated   : 57
% 22.91/3.53  # Clauses deleted for lack of memory   : 0
% 22.91/3.53  # Backward-subsumed                    : 198
% 22.91/3.53  # Backward-rewritten                   : 201
% 22.91/3.53  # Generated clauses                    : 155001
% 22.91/3.53  # ...of the previous two non-redundant : 138713
% 22.91/3.53  # ...aggressively subsumed             : 0
% 22.91/3.53  # Contextual simplify-reflections      : 47
% 22.91/3.53  # Paramodulations                      : 154846
% 22.91/3.53  # Factorizations                       : 36
% 22.91/3.53  # NegExts                              : 0
% 22.91/3.53  # Equation resolutions                 : 116
% 22.91/3.53  # Disequality decompositions           : 0
% 22.91/3.53  # Total rewrite steps                  : 92537
% 22.91/3.53  # ...of those cached                   : 88737
% 22.91/3.53  # Propositional unsat checks           : 0
% 22.91/3.53  #    Propositional check models        : 0
% 22.91/3.53  #    Propositional check unsatisfiable : 0
% 22.91/3.53  #    Propositional clauses             : 0
% 22.91/3.53  #    Propositional clauses after purity: 0
% 22.91/3.53  #    Propositional unsat core size     : 0
% 22.91/3.53  #    Propositional preprocessing time  : 0.000
% 22.91/3.53  #    Propositional encoding time       : 0.000
% 22.91/3.53  #    Propositional solver time         : 0.000
% 22.91/3.53  #    Success case prop preproc time    : 0.000
% 22.91/3.53  #    Success case prop encoding time   : 0.000
% 22.91/3.53  #    Success case prop solver time     : 0.000
% 22.91/3.53  # Current number of processed clauses  : 2098
% 22.91/3.53  #    Positive orientable unit clauses  : 241
% 22.91/3.53  #    Positive unorientable unit clauses: 22
% 22.91/3.53  #    Negative unit clauses             : 112
% 22.91/3.53  #    Non-unit-clauses                  : 1723
% 22.91/3.53  # Current number of unprocessed clauses: 130668
% 22.91/3.53  # ...number of literals in the above   : 450739
% 22.91/3.53  # Current number of archived formulas  : 0
% 22.91/3.53  # Current number of archived clauses   : 402
% 22.91/3.53  # Clause-clause subsumption calls (NU) : 442086
% 22.91/3.53  # Rec. Clause-clause subsumption calls : 215033
% 22.91/3.53  # Non-unit clause-clause subsumptions  : 3448
% 22.91/3.53  # Unit Clause-clause subsumption calls : 14470
% 22.91/3.53  # Rewrite failures with RHS unbound    : 0
% 22.91/3.53  # BW rewrite match attempts            : 2268
% 22.91/3.53  # BW rewrite match successes           : 234
% 22.91/3.53  # Condensation attempts                : 0
% 22.91/3.53  # Condensation successes               : 0
% 22.91/3.53  # Termbank termtop insertions          : 2905083
% 22.91/3.53  # Search garbage collected termcells   : 2518
% 22.91/3.53  
% 22.91/3.53  # -------------------------------------------------
% 22.91/3.53  # User time                : 2.723 s
% 22.91/3.53  # System time              : 0.089 s
% 22.91/3.53  # Total time               : 2.811 s
% 22.91/3.53  # Maximum resident set size: 2876 pages
% 22.91/3.53  
% 22.91/3.53  # -------------------------------------------------
% 22.91/3.53  # User time                : 5.547 s
% 22.91/3.53  # System time              : 0.091 s
% 22.91/3.53  # Total time               : 5.637 s
% 22.91/3.53  # Maximum resident set size: 2368 pages
% 22.91/3.53  % E---3.1 exiting
% 22.91/3.53  % E exiting
%------------------------------------------------------------------------------