%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:51:11 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 17
% Syntax : Number of formulae : 200 ( 200 unt; 0 def)
% Number of atoms : 200 ( 199 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 408 ( 16 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq2(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(ifeq_axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c_2,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_001]) ).
fof(cls_Ring__and__Field_Oabs__mult_0,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(class_Ring__and__Field_Oordered__idom(VAR_0),true,c_times(c_HOL_Oabs(VAR_1,VAR_0),c_HOL_Oabs(VAR_2,VAR_0),VAR_0),c_HOL_Oabs(c_times(VAR_1,VAR_2,VAR_0),VAR_0)) = c_HOL_Oabs(c_times(VAR_1,VAR_2,VAR_0),VAR_0),
file('theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(c_3,plain,
ifeq2(class_Ring__and__Field_Oordered__idom(A),true,c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),c_HOL_Oabs(c_times(B,C,A),A)) = c_HOL_Oabs(c_times(B,C,A),A),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]) ).
fof(cls_Ring__and__Field_Omult__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : ifeq(c_lessequals(c_0,VAR_0,VAR_1),true,ifeq(c_lessequals(c_0,VAR_2,VAR_1),true,ifeq(c_lessequals(VAR_3,VAR_0,VAR_1),true,ifeq(c_lessequals(VAR_2,VAR_4,VAR_1),true,ifeq(class_Ring__and__Field_Opordered__semiring(VAR_1),true,c_lessequals(c_times(VAR_3,VAR_2,VAR_1),c_times(VAR_0,VAR_4,VAR_1),VAR_1),true),true),true),true),true) = true,
file('theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
cnf(c_4,plain,
ifeq(c_lessequals(c_0,A,B),true,ifeq(c_lessequals(c_0,C,B),true,ifeq(c_lessequals(D,A,B),true,ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(clausify,[status(thm)],[cls_Ring__and__Field_Omult__mono_0]) ).
fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(class_Ring__and__Field_Opordered__cancel__semiring(VAR_0),true,ifeq(c_lessequals(c_0,VAR_1,VAR_0),true,ifeq(c_lessequals(c_0,VAR_2,VAR_0),true,c_lessequals(c_0,c_times(VAR_1,VAR_2,VAR_0),VAR_0),true),true),true) = true,
file('theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(c_5,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),true,ifeq(c_lessequals(c_0,B,A),true,ifeq(c_lessequals(c_0,C,A),true,c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(clausify,[status(thm)],[cls_Ring__and__Field_Omult__nonneg__nonneg_0]) ).
fof(cls_Orderings_Oorder__less__imp__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(c_less(VAR_0,VAR_1,VAR_2),true,ifeq(class_Orderings_Oorder(VAR_2),true,c_lessequals(VAR_0,VAR_1,VAR_2),true),true) = true,
file('theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(c_6,plain,
ifeq(c_less(A,B,C),true,ifeq(class_Orderings_Oorder(C),true,c_lessequals(A,B,C),true),true) = true,
inference(clausify,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]) ).
fof(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
! [VAR_0,VAR_1] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(VAR_0),true,c_lessequals(c_0,c_HOL_Oabs(VAR_1,VAR_0),VAR_0),true) = true,
file('theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(c_7,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),true,c_lessequals(c_0,c_HOL_Oabs(B,A),A),true) = true,
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
fof(cls_conjecture_0,axiom,
c_less(c_0,v_c,t_b) = true,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_8,plain,
c_less(c_0,v_c,t_b) = true,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_9,plain,
true = c_less(c_0,v_c,t_b),
inference(copy,[status(thm)],[c_8]) ).
fof(cls_conjecture_2,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_10,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_94,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_11,plain,
c_less(c_0,v_c,t_b) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(copy,[status(thm)],[c_94]) ).
fof(cls_conjecture_3,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_12,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_95,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_12]) ).
cnf(c_13,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_95]) ).
fof(cls_conjecture_4,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_14,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_15,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(copy,[status(thm)],[c_14]) ).
fof(cls_conjecture_5,axiom,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_16,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_96,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_16]) ).
cnf(c_17,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_96]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('theBenchmark.p',tfree_tcs) ).
cnf(c_18,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_97,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_18]) ).
cnf(c_98,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_97]) ).
cnf(c_19,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_98]) ).
fof(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
! [VAR_0] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(VAR_0),true,class_Orderings_Oorder(VAR_0),true) = true,
file('theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
cnf(c_20,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),true,class_Orderings_Oorder(A),true) = true,
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_17]) ).
cnf(c_99,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),c_less(c_0,v_c,t_b),class_Orderings_Oorder(A),true) = true,
inference(paramod,[status(thm)],[c_9,c_20]) ).
cnf(c_100,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Orderings_Oorder(A),true) = true,
inference(paramod,[status(thm)],[c_11,c_99]) ).
cnf(c_101,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),true) = true,
inference(paramod,[status(thm)],[c_19,c_100]) ).
cnf(c_102,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_101]) ).
cnf(c_103,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_102]) ).
cnf(c_104,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_103]) ).
cnf(c_105,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_104]) ).
cnf(c_106,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_105]) ).
cnf(c_21,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_106]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
! [VAR_0] : ifeq(class_Ring__and__Field_Oordered__idom(VAR_0),true,class_Ring__and__Field_Opordered__cancel__semiring(VAR_0),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(c_22,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_Ring__and__Field_Opordered__cancel__semiring(A),true) = true,
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_40]) ).
cnf(c_107,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_less(c_0,v_c,t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),true) = true,
inference(paramod,[status(thm)],[c_9,c_22]) ).
cnf(c_108,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),true) = true,
inference(paramod,[status(thm)],[c_11,c_107]) ).
cnf(c_109,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),true) = true,
inference(paramod,[status(thm)],[c_19,c_108]) ).
cnf(c_110,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_109]) ).
cnf(c_111,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_110]) ).
cnf(c_112,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_111]) ).
cnf(c_113,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_112]) ).
cnf(c_114,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_113]) ).
cnf(c_23,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_114]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
! [VAR_0] : ifeq(class_Ring__and__Field_Oordered__idom(VAR_0),true,class_Ring__and__Field_Opordered__semiring(VAR_0),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(c_24,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_Ring__and__Field_Opordered__semiring(A),true) = true,
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(c_115,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_less(c_0,v_c,t_b),class_Ring__and__Field_Opordered__semiring(A),true) = true,
inference(paramod,[status(thm)],[c_9,c_24]) ).
cnf(c_116,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(A),true) = true,
inference(paramod,[status(thm)],[c_11,c_115]) ).
cnf(c_117,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(A),true) = true,
inference(paramod,[status(thm)],[c_19,c_116]) ).
cnf(c_118,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(A),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_117]) ).
cnf(c_119,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_118]) ).
cnf(c_120,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_119]) ).
cnf(c_121,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_120]) ).
cnf(c_122,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_121]) ).
cnf(c_25,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_122]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
! [VAR_0] : ifeq(class_Ring__and__Field_Oordered__idom(VAR_0),true,class_OrderedGroup_Olordered__ab__group__abs(VAR_0),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(c_26,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_OrderedGroup_Olordered__ab__group__abs(A),true) = true,
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(c_123,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_less(c_0,v_c,t_b),class_OrderedGroup_Olordered__ab__group__abs(A),true) = true,
inference(paramod,[status(thm)],[c_9,c_26]) ).
cnf(c_124,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_OrderedGroup_Olordered__ab__group__abs(A),true) = true,
inference(paramod,[status(thm)],[c_11,c_123]) ).
cnf(c_125,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(A),true) = true,
inference(paramod,[status(thm)],[c_19,c_124]) ).
cnf(c_126,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(A),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_125]) ).
cnf(c_127,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_126]) ).
cnf(c_128,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_127]) ).
cnf(c_129,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_128]) ).
cnf(c_130,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_129]) ).
cnf(c_27,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_130]) ).
cnf(c_131,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),c_less(c_0,v_c,t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),true) = true,
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_132,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),true) = true,
inference(paramod,[status(thm)],[c_11,c_131]) ).
cnf(c_133,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),true) = true,
inference(paramod,[status(thm)],[c_19,c_132]) ).
cnf(c_134,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_133]) ).
cnf(c_135,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_134]) ).
cnf(c_136,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_135]) ).
cnf(c_137,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_136]) ).
cnf(c_138,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_137]) ).
cnf(c_28,plain,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(B,A),A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_138]) ).
cnf(c_139,plain,
ifeq(c_less(A,B,C),c_less(c_0,v_c,t_b),ifeq(class_Orderings_Oorder(C),true,c_lessequals(A,B,C),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_140,plain,
ifeq(c_less(A,B,C),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),ifeq(class_Orderings_Oorder(C),true,c_lessequals(A,B,C),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_139]) ).
cnf(c_141,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),true,c_lessequals(A,B,C),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_140]) ).
cnf(c_142,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),c_less(c_0,v_c,t_b),c_lessequals(A,B,C),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_141]) ).
cnf(c_143,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),c_lessequals(A,B,C),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_142]) ).
cnf(c_144,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_143]) ).
cnf(c_145,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),c_less(c_0,v_c,t_b)),true) = true,
inference(paramod,[status(thm)],[c_9,c_144]) ).
cnf(c_146,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)),true) = true,
inference(paramod,[status(thm)],[c_11,c_145]) ).
cnf(c_147,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),class_Ring__and__Field_Oordered__idom(t_b)),true) = true,
inference(paramod,[status(thm)],[c_19,c_146]) ).
cnf(c_148,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),class_Ring__and__Field_Oordered__idom(t_b)),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_147]) ).
cnf(c_149,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_148]) ).
cnf(c_150,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_149]) ).
cnf(c_151,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_150]) ).
cnf(c_152,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_151]) ).
cnf(c_29,plain,
ifeq(c_less(A,B,C),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(C),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,B,C),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_152]) ).
cnf(c_153,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),c_less(c_0,v_c,t_b),ifeq(c_lessequals(c_0,B,A),true,ifeq(c_lessequals(c_0,C,A),true,c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_5]) ).
cnf(c_154,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),ifeq(c_lessequals(c_0,B,A),true,ifeq(c_lessequals(c_0,C,A),true,c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_153]) ).
cnf(c_155,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),true,ifeq(c_lessequals(c_0,C,A),true,c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_154]) ).
cnf(c_156,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),c_less(c_0,v_c,t_b),ifeq(c_lessequals(c_0,C,A),true,c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_155]) ).
cnf(c_157,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),ifeq(c_lessequals(c_0,C,A),true,c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_156]) ).
cnf(c_158,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),true,c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_157]) ).
cnf(c_159,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),c_less(c_0,v_c,t_b),c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_158]) ).
cnf(c_160,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_159]) ).
cnf(c_161,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_160]) ).
cnf(c_162,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),c_less(c_0,v_c,t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_161]) ).
cnf(c_163,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_162]) ).
cnf(c_164,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_163]) ).
cnf(c_165,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),c_less(c_0,v_c,t_b)),true) = true,
inference(paramod,[status(thm)],[c_9,c_164]) ).
cnf(c_166,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)),true) = true,
inference(paramod,[status(thm)],[c_11,c_165]) ).
cnf(c_167,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),true) = true,
inference(paramod,[status(thm)],[c_19,c_166]) ).
cnf(c_168,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_167]) ).
cnf(c_169,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_168]) ).
cnf(c_170,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_169]) ).
cnf(c_171,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_170]) ).
cnf(c_172,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_171]) ).
cnf(c_30,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,B,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(B,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_172]) ).
cnf(c_173,plain,
ifeq(c_lessequals(c_0,A,B),c_less(c_0,v_c,t_b),ifeq(c_lessequals(c_0,C,B),true,ifeq(c_lessequals(D,A,B),true,ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_174,plain,
ifeq(c_lessequals(c_0,A,B),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),ifeq(c_lessequals(c_0,C,B),true,ifeq(c_lessequals(D,A,B),true,ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_173]) ).
cnf(c_175,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),true,ifeq(c_lessequals(D,A,B),true,ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_174]) ).
cnf(c_176,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),c_less(c_0,v_c,t_b),ifeq(c_lessequals(D,A,B),true,ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_175]) ).
cnf(c_177,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),ifeq(c_lessequals(D,A,B),true,ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_176]) ).
cnf(c_178,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),true,ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_177]) ).
cnf(c_179,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),c_less(c_0,v_c,t_b),ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_178]) ).
cnf(c_180,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_179]) ).
cnf(c_181,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),true,ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_180]) ).
cnf(c_182,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),c_less(c_0,v_c,t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_181]) ).
cnf(c_183,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_182]) ).
cnf(c_184,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),true,c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_183]) ).
cnf(c_185,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),c_less(c_0,v_c,t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_184]) ).
cnf(c_186,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_185]) ).
cnf(c_187,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),true),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_186]) ).
cnf(c_188,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),c_less(c_0,v_c,t_b)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_187]) ).
cnf(c_189,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_188]) ).
cnf(c_190,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_189]) ).
cnf(c_191,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),c_less(c_0,v_c,t_b)),true),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_190]) ).
cnf(c_192,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)),true),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_191]) ).
cnf(c_193,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),true),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_192]) ).
cnf(c_194,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_less(c_0,v_c,t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_9,c_193]) ).
cnf(c_195,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_11,c_194]) ).
cnf(c_196,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_195]) ).
cnf(c_197,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_less(c_0,v_c,t_b)),true) = true,
inference(paramod,[status(thm)],[c_9,c_196]) ).
cnf(c_198,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)),true) = true,
inference(paramod,[status(thm)],[c_11,c_197]) ).
cnf(c_199,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),true) = true,
inference(paramod,[status(thm)],[c_19,c_198]) ).
cnf(c_200,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_less(c_0,v_c,t_b)) = true,
inference(paramod,[status(thm)],[c_9,c_199]) ).
cnf(c_201,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_11,c_200]) ).
cnf(c_202,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_19,c_201]) ).
cnf(c_203,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_less(c_0,v_c,t_b),
inference(paramod,[status(thm)],[c_9,c_202]) ).
cnf(c_204,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11,c_203]) ).
cnf(c_31,plain,
ifeq(c_lessequals(c_0,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,C,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(D,A,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,E,B),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(B),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(D,C,B),c_times(A,E,B),B),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_204]) ).
cnf(c_205,plain,
ifeq2(class_Ring__and__Field_Oordered__idom(A),c_less(c_0,v_c,t_b),c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),c_HOL_Oabs(c_times(B,C,A),A)) = c_HOL_Oabs(c_times(B,C,A),A),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_206,plain,
ifeq2(class_Ring__and__Field_Oordered__idom(A),c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),c_HOL_Oabs(c_times(B,C,A),A)) = c_HOL_Oabs(c_times(B,C,A),A),
inference(paramod,[status(thm)],[c_11,c_205]) ).
cnf(c_32,plain,
ifeq2(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),c_HOL_Oabs(c_times(B,C,A),A)) = c_HOL_Oabs(c_times(B,C,A),A),
inference(paramod,[status(thm)],[c_19,c_206]) ).
cnf(c_34,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_35,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_13]) ).
cnf(c_36,plain,
c_less(c_0,v_c,t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_11]) ).
cnf(c_207,plain,
class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_37,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_207]) ).
cnf(c_208,plain,
class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__semiring(t_b),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_38,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_209,plain,
class_Ring__and__Field_Oordered__idom(t_b) = class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_39,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_209]) ).
cnf(c_210,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,B,t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),A,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),B,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_19,c_31]) ).
cnf(c_211,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,B,t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),A,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),B,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_38,c_210]) ).
cnf(c_212,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,B,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),A,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),B,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_211]) ).
cnf(c_42,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,B,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),A,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),B,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_212]) ).
cnf(c_213,plain,
c_HOL_Oabs(c_times(A,B,t_b),t_b) = c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b),
inference(paramod,[status(thm)],[c_32,c_1]) ).
cnf(c_44,plain,
c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b) = c_HOL_Oabs(c_times(A,B,t_b),t_b),
inference(copy,[status(thm)],[c_213]) ).
cnf(c_214,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,v_c,t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_36,c_29]) ).
cnf(c_48,plain,
ifeq(class_Orderings_Oorder(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,v_c,t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_214]) ).
cnf(c_215,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_39,c_21]) ).
cnf(c_51,plain,
class_Orderings_Oorder(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_215]) ).
cnf(c_216,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_39,c_28]) ).
cnf(c_52,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_216]) ).
cnf(c_217,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,v_c,t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_51,c_48]) ).
cnf(c_53,plain,
c_lessequals(c_0,v_c,t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_217]) ).
cnf(c_218,plain,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(v_c,A,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_53,c_30]) ).
cnf(c_219,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(v_c,A,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_37,c_218]) ).
cnf(c_220,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(v_c,A,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_219]) ).
cnf(c_59,plain,
ifeq(c_lessequals(c_0,A,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(v_c,A,t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_220]) ).
cnf(c_221,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_35,c_42]) ).
cnf(c_222,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_52,c_221]) ).
cnf(c_223,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_44,c_222]) ).
cnf(c_224,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_15,c_223]) ).
cnf(c_225,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_224]) ).
cnf(c_75,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_225]) ).
cnf(c_226,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(A,t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_52,c_59]) ).
cnf(c_87,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(A,t_b),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_226]) ).
cnf(c_227,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_87,c_75]) ).
cnf(c_92,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_227]) ).
cnf(c_93,plain,
$false,
inference(resolve,[status(thm)],[c_92,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 22:14:14 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2789607 was started by sandbox on n001,
% 0.18/0.44 % Sat Sep 26 22:14:14 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.50
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50
% 0.18/0.50 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.18/0.50 % Length of proof is 49.
% 0.18/0.50 % Level of proof is 11.
% 0.18/0.50 % Maximum clause weight is 100.000.
% 0.18/0.50 % Given clauses 30.
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------