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