%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 06:51:08 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 155 ( 155 unt; 0 def)
% Number of atoms : 155 ( 154 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 306 ( 2 sgn 24 !; 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_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
! [VAR_0,VAR_1] : ifeq2(class_OrderedGroup_Ocomm__monoid__add(VAR_0),true,c_plus(c_0,VAR_1,VAR_0),VAR_1) = VAR_1,
file('theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(c_3,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(A),true,c_plus(c_0,B,A),B) = B,
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(class_OrderedGroup_Opordered__ab__group__add(VAR_0),true,ifeq(c_lessequals(VAR_1,c_minus(VAR_2,VAR_3,VAR_0),VAR_0),true,c_lessequals(c_plus(VAR_1,VAR_3,VAR_0),VAR_2,VAR_0),true),true) = true,
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
cnf(c_4,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),true,ifeq(c_lessequals(B,c_minus(C,D,A),A),true,c_lessequals(c_plus(B,D,A),C,A),true),true) = true,
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(class_OrderedGroup_Opordered__ab__group__add(VAR_0),true,ifeq(c_lessequals(c_plus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0),true,c_lessequals(VAR_1,c_minus(VAR_3,VAR_2,VAR_0),VAR_0),true),true) = true,
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(c_5,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),true,ifeq(c_lessequals(c_plus(B,C,A),D,A),true,c_lessequals(B,c_minus(D,C,A),A),true),true) = true,
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_1]) ).
fof(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(class_Orderings_Oorder(VAR_0),true,ifeq(c_lessequals(VAR_1,VAR_2,VAR_0),true,ifeq(c_lessequals(VAR_2,VAR_3,VAR_0),true,c_lessequals(VAR_1,VAR_3,VAR_0),true),true),true) = true,
file('theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(c_6,plain,
ifeq(class_Orderings_Oorder(A),true,ifeq(c_lessequals(B,C,A),true,ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true,
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
fof(cls_conjecture_1,axiom,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_7,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_8,plain,
true = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(copy,[status(thm)],[c_7]) ).
fof(cls_conjecture_2,axiom,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_9,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_78,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_10,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(copy,[status(thm)],[c_78]) ).
fof(cls_conjecture_3,axiom,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_11,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_79,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_11]) ).
cnf(c_12,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_79]) ).
fof(clsrel_Orderings_Olinorder_4,axiom,
! [VAR_0] : ifeq(class_Orderings_Olinorder(VAR_0),true,class_Orderings_Oorder(VAR_0),true) = true,
file('theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
cnf(c_13,plain,
ifeq(class_Orderings_Olinorder(A),true,class_Orderings_Oorder(A),true) = true,
inference(clausify,[status(thm)],[clsrel_Orderings_Olinorder_4]) ).
cnf(c_80,plain,
ifeq(class_Orderings_Olinorder(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),class_Orderings_Oorder(A),true) = true,
inference(paramod,[status(thm)],[c_8,c_13]) ).
cnf(c_81,plain,
ifeq(class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(A),true) = true,
inference(paramod,[status(thm)],[c_10,c_80]) ).
cnf(c_82,plain,
ifeq(class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_8,c_81]) ).
cnf(c_83,plain,
ifeq(class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = true,
inference(paramod,[status(thm)],[c_10,c_82]) ).
cnf(c_84,plain,
ifeq(class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_83]) ).
cnf(c_14,plain,
ifeq(class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_84]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
! [VAR_0] : ifeq(class_Ring__and__Field_Oordered__idom(VAR_0),true,class_OrderedGroup_Ocomm__monoid__add(VAR_0),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(c_15,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_OrderedGroup_Ocomm__monoid__add(A),true) = true,
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_23]) ).
cnf(c_85,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),class_OrderedGroup_Ocomm__monoid__add(A),true) = true,
inference(paramod,[status(thm)],[c_8,c_15]) ).
cnf(c_86,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(A),true) = true,
inference(paramod,[status(thm)],[c_10,c_85]) ).
cnf(c_87,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_8,c_86]) ).
cnf(c_88,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = true,
inference(paramod,[status(thm)],[c_10,c_87]) ).
cnf(c_89,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_88]) ).
cnf(c_16,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_89]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
! [VAR_0] : ifeq(class_Ring__and__Field_Oordered__idom(VAR_0),true,class_Orderings_Olinorder(VAR_0),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(c_17,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_Orderings_Olinorder(A),true) = true,
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
cnf(c_90,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),class_Orderings_Olinorder(A),true) = true,
inference(paramod,[status(thm)],[c_8,c_17]) ).
cnf(c_91,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(A),true) = true,
inference(paramod,[status(thm)],[c_10,c_90]) ).
cnf(c_92,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_8,c_91]) ).
cnf(c_93,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = true,
inference(paramod,[status(thm)],[c_10,c_92]) ).
cnf(c_94,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_93]) ).
cnf(c_18,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_94]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
! [VAR_0] : ifeq(class_Ring__and__Field_Oordered__idom(VAR_0),true,class_OrderedGroup_Opordered__ab__group__add(VAR_0),true) = true,
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(c_19,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),true,class_OrderedGroup_Opordered__ab__group__add(A),true) = true,
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_54]) ).
cnf(c_95,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),class_OrderedGroup_Opordered__ab__group__add(A),true) = true,
inference(paramod,[status(thm)],[c_8,c_19]) ).
cnf(c_96,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(A),true) = true,
inference(paramod,[status(thm)],[c_10,c_95]) ).
cnf(c_97,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_8,c_96]) ).
cnf(c_98,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = true,
inference(paramod,[status(thm)],[c_10,c_97]) ).
cnf(c_99,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_98]) ).
cnf(c_20,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_99]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('theBenchmark.p',tfree_tcs) ).
cnf(c_21,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_100,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_21]) ).
cnf(c_101,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_100]) ).
cnf(c_22,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_102,plain,
ifeq(class_Orderings_Oorder(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(B,C,A),true,ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_103,plain,
ifeq(class_Orderings_Oorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(B,C,A),true,ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_102]) ).
cnf(c_104,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),true,ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_103]) ).
cnf(c_105,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_104]) ).
cnf(c_106,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_105]) ).
cnf(c_107,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),true,c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_106]) ).
cnf(c_108,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_107]) ).
cnf(c_109,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_108]) ).
cnf(c_110,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),true),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_109]) ).
cnf(c_111,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_110]) ).
cnf(c_112,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),c_lessequals(v_k(v_x),v_f(v_x),t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_111]) ).
cnf(c_113,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),class_Ring__and__Field_Oordered__idom(t_b)),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_112]) ).
cnf(c_114,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),true) = true,
inference(paramod,[status(thm)],[c_8,c_113]) ).
cnf(c_115,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),true) = true,
inference(paramod,[status(thm)],[c_10,c_114]) ).
cnf(c_116,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),true) = true,
inference(paramod,[status(thm)],[c_22,c_115]) ).
cnf(c_117,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_8,c_116]) ).
cnf(c_118,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = true,
inference(paramod,[status(thm)],[c_10,c_117]) ).
cnf(c_119,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,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_22,c_118]) ).
cnf(c_120,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,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_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_119]) ).
cnf(c_121,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,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(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_120]) ).
cnf(c_23,plain,
ifeq(class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,C,A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(C,D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,D,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_22,c_121]) ).
cnf(c_122,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),true,c_lessequals(B,c_minus(D,C,A),A),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_123,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),true,c_lessequals(B,c_minus(D,C,A),A),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_122]) ).
cnf(c_124,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),true,c_lessequals(B,c_minus(D,C,A),A),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_123]) ).
cnf(c_125,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(B,c_minus(D,C,A),A),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_124]) ).
cnf(c_126,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(B,c_minus(D,C,A),A),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_125]) ).
cnf(c_127,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_126]) ).
cnf(c_128,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),true) = true,
inference(paramod,[status(thm)],[c_8,c_127]) ).
cnf(c_129,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),c_lessequals(v_k(v_x),v_f(v_x),t_b)),true) = true,
inference(paramod,[status(thm)],[c_10,c_128]) ).
cnf(c_130,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),true) = true,
inference(paramod,[status(thm)],[c_22,c_129]) ).
cnf(c_131,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_8,c_130]) ).
cnf(c_132,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = true,
inference(paramod,[status(thm)],[c_10,c_131]) ).
cnf(c_133,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_22,c_132]) ).
cnf(c_134,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_133]) ).
cnf(c_135,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,C,A),A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_134]) ).
cnf(c_24,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(B,C,A),D,A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(B,c_minus(D,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),
inference(paramod,[status(thm)],[c_22,c_135]) ).
cnf(c_136,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),true,c_lessequals(c_plus(B,D,A),C,A),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_137,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),true,c_lessequals(c_plus(B,D,A),C,A),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_136]) ).
cnf(c_138,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),true,c_lessequals(c_plus(B,D,A),C,A),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_137]) ).
cnf(c_139,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(B,D,A),C,A),true),true) = true,
inference(paramod,[status(thm)],[c_8,c_138]) ).
cnf(c_140,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(B,D,A),C,A),true),true) = true,
inference(paramod,[status(thm)],[c_10,c_139]) ).
cnf(c_141,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),true),true) = true,
inference(paramod,[status(thm)],[c_22,c_140]) ).
cnf(c_142,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),true) = true,
inference(paramod,[status(thm)],[c_8,c_141]) ).
cnf(c_143,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),c_lessequals(v_k(v_x),v_f(v_x),t_b)),true) = true,
inference(paramod,[status(thm)],[c_10,c_142]) ).
cnf(c_144,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),class_Ring__and__Field_Oordered__idom(t_b)),true) = true,
inference(paramod,[status(thm)],[c_22,c_143]) ).
cnf(c_145,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = true,
inference(paramod,[status(thm)],[c_8,c_144]) ).
cnf(c_146,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = true,
inference(paramod,[status(thm)],[c_10,c_145]) ).
cnf(c_147,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = true,
inference(paramod,[status(thm)],[c_22,c_146]) ).
cnf(c_148,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_8,c_147]) ).
cnf(c_149,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,A),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_10,c_148]) ).
cnf(c_25,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(B,c_minus(C,D,A),A),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(B,D,A),C,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),
inference(paramod,[status(thm)],[c_22,c_149]) ).
cnf(c_150,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(A),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_plus(c_0,B,A),B) = B,
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_151,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_plus(c_0,B,A),B) = B,
inference(paramod,[status(thm)],[c_10,c_150]) ).
cnf(c_26,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(A),class_Ring__and__Field_Oordered__idom(t_b),c_plus(c_0,B,A),B) = B,
inference(paramod,[status(thm)],[c_22,c_151]) ).
cnf(c_152,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_153,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_152]) ).
cnf(c_28,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_22,c_153]) ).
cnf(c_154,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_18]) ).
cnf(c_155,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_154]) ).
cnf(c_29,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_22,c_155]) ).
cnf(c_156,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_16]) ).
cnf(c_157,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_156]) ).
cnf(c_30,plain,
ifeq(class_Ring__and__Field_Oordered__idom(A),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(A),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_22,c_157]) ).
cnf(c_158,plain,
ifeq(class_Orderings_Olinorder(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_14]) ).
cnf(c_159,plain,
ifeq(class_Orderings_Olinorder(A),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(A),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_22,c_158]) ).
cnf(c_31,plain,
ifeq(class_Orderings_Olinorder(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_22,c_159]) ).
cnf(c_32,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_22,c_12]) ).
cnf(c_33,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_22,c_10]) ).
cnf(c_160,plain,
ifeq(class_Orderings_Oorder(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,v_k(v_x),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(A,v_f(v_x),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_22,c_23]) ).
cnf(c_35,plain,
ifeq(class_Orderings_Oorder(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,v_k(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,v_f(v_x),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_160]) ).
cnf(c_161,plain,
class_Ring__and__Field_Oordered__idom(t_b) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_37,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_162,plain,
class_Ring__and__Field_Oordered__idom(t_b) = class_Orderings_Olinorder(t_b),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_38,plain,
class_Orderings_Olinorder(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_163,plain,
class_Ring__and__Field_Oordered__idom(t_b) = class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_39,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_164,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(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_plus(c_0,v_g(v_x),t_b),v_k(v_x),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_33,c_25]) ).
cnf(c_165,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),c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),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_164]) ).
cnf(c_166,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),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_165]) ).
cnf(c_44,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_166]) ).
cnf(c_167,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_38,c_31]) ).
cnf(c_48,plain,
class_Orderings_Oorder(t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_167]) ).
cnf(c_168,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(A,v_k(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,v_f(v_x),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_48,c_35]) ).
cnf(c_54,plain,
ifeq(c_lessequals(A,v_k(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(A,v_f(v_x),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_168]) ).
cnf(c_169,plain,
ifeq2(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_plus(c_0,A,t_b),A) = A,
inference(paramod,[status(thm)],[c_39,c_26]) ).
cnf(c_56,plain,
c_plus(c_0,A,t_b) = A,
inference(paramod,[status(thm)],[c_1,c_169]) ).
cnf(c_57,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_56,c_44]) ).
cnf(c_170,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(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_0,c_minus(B,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_56,c_24]) ).
cnf(c_171,plain,
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_0,c_minus(B,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_37,c_170]) ).
cnf(c_59,plain,
ifeq(c_lessequals(A,B,t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_minus(B,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_171]) ).
cnf(c_172,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_g(v_x),v_f(v_x),t_b),class_Ring__and__Field_Oordered__idom(t_b)) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_57,c_54]) ).
cnf(c_65,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_172]) ).
cnf(c_173,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),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_65,c_59]) ).
cnf(c_76,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(paramod,[status(thm)],[c_2,c_173]) ).
cnf(c_77,plain,
$false,
inference(resolve,[status(thm)],[c_76,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 22:06:01 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 6017 was started by sandbox2 on n014,
% 0.12/0.39 % Sat Sep 26 22:06:01 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 0.12/0.42
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.42
% 0.12/0.42 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.42 % Length of proof is 45.
% 0.12/0.42 % Level of proof is 10.
% 0.12/0.42 % Maximum clause weight is 32.000.
% 0.12/0.42 % Given clauses 39.
% 0.12/0.42
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------