%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Tue Sep 29 09:30:37 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.25s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 14
% Syntax : Number of clauses : 313 ( 313 unt; 0 nHn; 96 RR)
% Number of literals : 313 ( 312 equ; 1 neg)
% Maximal clause size : 1 ( 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 : 618 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c3,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),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)) = c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = ifeq(c_lessequals(c_0,c_minus(v_k(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),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(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c10,axiom,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c11,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c13,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c14,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = class_Ring__and__Field_Oordered__idom(t_b),
inference(transitivity,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c11,c15]) ).
cnf(c17,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(transitivity,[status(thm)],[c9,c16]) ).
cnf(c18,plain,
ifeq(class_Orderings_Olinorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c19,plain,
ifeq(class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c20,plain,
ifeq(class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Olinorder(X),true,class_Orderings_Oorder(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c21,plain,
ifeq(class_Orderings_Olinorder(X),true,class_Orderings_Oorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Olinorder(X),true,class_Orderings_Oorder(X),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c22,axiom,
ifeq(class_Orderings_Olinorder(T),true,class_Orderings_Oorder(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
cnf(c23,plain,
ifeq(class_Orderings_Olinorder(X),true,class_Orderings_Oorder(X),true) = true,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c25,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c26,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
ifeq(class_Orderings_Olinorder(X),true,class_Orderings_Oorder(X),true) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c23,c26]) ).
cnf(c28,plain,
ifeq(class_Orderings_Olinorder(X),true,class_Orderings_Oorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c21,c27]) ).
cnf(c29,plain,
ifeq(class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c20,c28]) ).
cnf(c30,plain,
ifeq(class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(X),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(transitivity,[status(thm)],[c19,c29]) ).
cnf(c31,plain,
ifeq(class_Orderings_Olinorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(X),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(transitivity,[status(thm)],[c18,c30]) ).
cnf(c32,plain,
ifeq(class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(t_b),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(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = ifeq(class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c35,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c36,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c37,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_Orderings_Olinorder(X),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c38,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T2),true,class_Orderings_Olinorder(T2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(c39,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_Orderings_Olinorder(X),true) = true,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c41,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c42,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_Orderings_Olinorder(X),true) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c37,c43]) ).
cnf(c45,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c36,c44]) ).
cnf(c46,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Olinorder(X),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(transitivity,[status(thm)],[c35,c45]) ).
cnf(c47,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(X),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(transitivity,[status(thm)],[c34,c46]) ).
cnf(c48,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(t_b),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(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c51,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_Orderings_Olinorder(t_b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_Orderings_Olinorder(t_b),
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = class_Orderings_Olinorder(t_b),
inference(transitivity,[status(thm)],[c49,c53]) ).
cnf(c55,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = class_Orderings_Olinorder(t_b),
inference(transitivity,[status(thm)],[c17,c54]) ).
cnf(c56,plain,
class_Orderings_Olinorder(t_b) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq(class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(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),class_Orderings_Oorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,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(symmetry,[status(thm)],[c17]) ).
cnf(c59,plain,
ifeq(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),class_Orderings_Oorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(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),class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,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(symmetry,[status(thm)],[c17]) ).
cnf(c61,plain,
ifeq(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),class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_0,c_minus(v_k(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),class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = class_Orderings_Oorder(t_b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
ifeq(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),class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
ifeq(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),class_Orderings_Oorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[c59,c63]) ).
cnf(c65,plain,
ifeq(class_Orderings_Olinorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_Orderings_Oorder(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[c57,c64]) ).
cnf(c66,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[c33,c65]) ).
cnf(c67,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = class_Orderings_Oorder(t_b),
inference(transitivity,[status(thm)],[c17,c66]) ).
cnf(c68,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c70,plain,
ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(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(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c72,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c73,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Opordered__ab__group__add(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c74,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Opordered__ab__group__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Opordered__ab__group__add(X),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c75,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T2),true,class_OrderedGroup_Opordered__ab__group__add(T2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(c76,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Opordered__ab__group__add(X),true) = true,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c78,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c79,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Opordered__ab__group__add(X),true) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c76,c79]) ).
cnf(c81,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Opordered__ab__group__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c74,c80]) ).
cnf(c82,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c73,c81]) ).
cnf(c83,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Opordered__ab__group__add(X),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(transitivity,[status(thm)],[c72,c82]) ).
cnf(c84,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(X),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(transitivity,[status(thm)],[c71,c83]) ).
cnf(c85,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(t_b),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(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c88,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c90,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(transitivity,[status(thm)],[c88,c89]) ).
cnf(c91,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(transitivity,[status(thm)],[c86,c90]) ).
cnf(c92,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(transitivity,[status(thm)],[c17,c91]) ).
cnf(c93,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c92]) ).
cnf(c94,axiom,
ifeq2(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c95,plain,
ifeq2(c_lessequals(c_0,c_minus(v_k(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),c_plus(c_0,X,t_b),X) = c_plus(c_0,X,t_b),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
c_plus(c_0,X,t_b) = ifeq2(c_lessequals(c_0,c_minus(v_k(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),c_plus(c_0,X,t_b),X),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c98,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(X),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c99,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Ocomm__monoid__add(X),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c100,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Ocomm__monoid__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Ocomm__monoid__add(X),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c101,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T2),true,class_OrderedGroup_Ocomm__monoid__add(T2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(c102,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Ocomm__monoid__add(X),true) = true,
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c104,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c105,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Ocomm__monoid__add(X),true) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c102,c105]) ).
cnf(c107,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),true,class_OrderedGroup_Ocomm__monoid__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c100,c106]) ).
cnf(c108,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(X),class_Ring__and__Field_Oordered__idom(t_b)) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c99,c107]) ).
cnf(c109,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Ocomm__monoid__add(X),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(transitivity,[status(thm)],[c98,c108]) ).
cnf(c110,plain,
ifeq(class_Ring__and__Field_Oordered__idom(X),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(X),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(transitivity,[status(thm)],[c97,c109]) ).
cnf(c111,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(t_b),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(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c114,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
ifeq(c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c116,plain,
ifeq(class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b),class_OrderedGroup_Ocomm__monoid__add(t_b),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(transitivity,[status(thm)],[c112,c116]) ).
cnf(c118,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(transitivity,[status(thm)],[c17,c117]) ).
cnf(c119,plain,
ifeq2(c_lessequals(c_0,c_minus(v_k(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),c_plus(c_0,X,t_b),X) = ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_plus(c_0,X,t_b),X),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_plus(c_0,X,X2),X) = ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_plus(c_0,X,X2),X),
inference(congruence,[status(thm)],[c17]) ).
cnf(c121,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_plus(c_0,X,X2),X) = ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),class_Ring__and__Field_Oordered__idom(t_b),c_plus(c_0,X,X2),X),
inference(congruence,[status(thm)],[c14]) ).
cnf(c122,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),class_Ring__and__Field_Oordered__idom(t_b),c_plus(c_0,X,X2),X) = ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),true,c_plus(c_0,X,X2),X),
inference(congruence,[status(thm)],[c10]) ).
cnf(c123,axiom,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(T_a),true,c_plus(c_0,V_y,T_a),V_y) = V_y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(c124,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),true,c_plus(c_0,X,X2),X) = X,
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),class_Ring__and__Field_Oordered__idom(t_b),c_plus(c_0,X,X2),X) = X,
inference(transitivity,[status(thm)],[c122,c124]) ).
cnf(c126,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_plus(c_0,X,X2),X) = X,
inference(transitivity,[status(thm)],[c121,c125]) ).
cnf(c127,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(X2),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_plus(c_0,X,X2),X) = X,
inference(transitivity,[status(thm)],[c120,c126]) ).
cnf(c128,plain,
ifeq2(class_OrderedGroup_Ocomm__monoid__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_plus(c_0,X,t_b),X) = X,
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
ifeq2(c_lessequals(c_0,c_minus(v_k(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),c_plus(c_0,X,t_b),X) = X,
inference(transitivity,[status(thm)],[c119,c128]) ).
cnf(c130,plain,
c_plus(c_0,X,t_b) = X,
inference(transitivity,[status(thm)],[c96,c129]) ).
cnf(c131,plain,
X = c_plus(c_0,X,t_b),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
c_lessequals(X,X2,t_b) = c_lessequals(c_plus(c_0,X,t_b),X2,t_b),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(c_0,X,t_b),X2,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(c_0,X,t_b),X2,t_b),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X2),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X,c_minus(X4,X3,X2),X2),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(X,X3,X2),X4,X2),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X2),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X,c_minus(X4,X3,X2),X2),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(X,X3,X2),X4,X2),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c17]) ).
cnf(c136,plain,
ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c137,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c139,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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(congruence,[status(thm)],[c17]) ).
cnf(c141,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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(congruence,[status(thm)],[c14]) ).
cnf(c142,plain,
ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c143,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c145,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c147,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c148,plain,
ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c149,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c151,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),true),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),true),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),true),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c153,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a2),true,ifeq(c_lessequals(V_a,c_minus(V_c,V_b,T_a2),T_a2),true,c_lessequals(c_plus(V_a,V_b,T_a2),V_c,T_a2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
cnf(c154,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),true),true) = true,
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c156,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c157,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(symmetry,[status(thm)],[c17]) ).
cnf(c158,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(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
true = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c155,c158]) ).
cnf(c160,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),true),true) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c154,c159]) ).
cnf(c161,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),true),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(transitivity,[status(thm)],[c152,c160]) ).
cnf(c162,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),true,c_lessequals(c_plus(X3,X,X4),X2,X4),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(transitivity,[status(thm)],[c151,c161]) ).
cnf(c163,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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(transitivity,[status(thm)],[c149,c162]) ).
cnf(c164,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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(transitivity,[status(thm)],[c147,c163]) ).
cnf(c165,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),class_Ring__and__Field_Oordered__idom(t_b)),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(transitivity,[status(thm)],[c146,c164]) ).
cnf(c166,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c145,c165]) ).
cnf(c167,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c143,c166]) ).
cnf(c168,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c141,c167]) ).
cnf(c169,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c140,c168]) ).
cnf(c170,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c139,c169]) ).
cnf(c171,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c137,c170]) ).
cnf(c172,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X3,c_minus(X2,X,X4),X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(X3,X,X4),X2,X4),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c135,c171]) ).
cnf(c173,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_plus(c_0,X,t_b),X2,t_b),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c134,c173]) ).
cnf(c175,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c93,c174]) ).
cnf(c176,plain,
ifeq(c_lessequals(c_0,c_minus(X2,X,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X,X2,t_b),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c70,c175]) ).
cnf(c177,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),c_lessequals(v_g(v_x),v_k(v_x),t_b),c_lessequals(c_0,c_minus(v_k(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(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = ifeq(c_lessequals(c_0,c_minus(v_k(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),c_lessequals(v_g(v_x),v_k(v_x),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),c_lessequals(v_g(v_x),v_k(v_x),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c180,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(transitivity,[status(thm)],[c178,c179]) ).
cnf(c181,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
ifeq(class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c184,plain,
ifeq(c_lessequals(X3,X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c17]) ).
cnf(c185,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c187,plain,
ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c190,plain,
ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),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)) = ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c17]) ).
cnf(c193,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),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)),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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)) = ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(congruence,[status(thm)],[c17]) ).
cnf(c195,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(congruence,[status(thm)],[c14]) ).
cnf(c196,plain,
ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c14]) ).
cnf(c197,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c199,plain,
ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c202,plain,
ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),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(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c205,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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)) = ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c14]) ).
cnf(c207,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c10]) ).
cnf(c208,plain,
ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c209,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c211,plain,
ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),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(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c214,plain,
ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c217,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),true),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),true),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),true),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c219,axiom,
ifeq(class_Orderings_Oorder(T_a2),true,ifeq(c_lessequals(V_x,V_y2,T_a2),true,ifeq(c_lessequals(V_y2,V_z,T_a2),true,c_lessequals(V_x,V_z,T_a2),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(c220,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),true),true) = true,
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c222,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c223,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(symmetry,[status(thm)],[c17]) ).
cnf(c224,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(transitivity,[status(thm)],[c222,c223]) ).
cnf(c225,plain,
true = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c221,c224]) ).
cnf(c226,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),true),true) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c220,c225]) ).
cnf(c227,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),true),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(transitivity,[status(thm)],[c218,c226]) ).
cnf(c228,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),true),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(transitivity,[status(thm)],[c217,c227]) ).
cnf(c229,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),true,c_lessequals(X3,X,X4),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(transitivity,[status(thm)],[c215,c228]) ).
cnf(c230,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),true,ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(transitivity,[status(thm)],[c212,c229]) ).
cnf(c231,plain,
ifeq(class_Orderings_Oorder(X4),true,ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(transitivity,[status(thm)],[c209,c230]) ).
cnf(c232,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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(transitivity,[status(thm)],[c207,c231]) ).
cnf(c233,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c206,c232]) ).
cnf(c234,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c205,c233]) ).
cnf(c235,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c203,c234]) ).
cnf(c236,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c200,c235]) ).
cnf(c237,plain,
ifeq(class_Orderings_Oorder(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c197,c236]) ).
cnf(c238,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c195,c237]) ).
cnf(c239,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c194,c238]) ).
cnf(c240,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),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)),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c193,c239]) ).
cnf(c241,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c191,c240]) ).
cnf(c242,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c188,c241]) ).
cnf(c243,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c185,c242]) ).
cnf(c244,plain,
ifeq(class_Orderings_Oorder(X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X3,X2,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,X,X4),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c183,c243]) ).
cnf(c245,plain,
ifeq(class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(v_g(v_x),v_k(v_x),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(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(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
ifeq(class_Orderings_Oorder(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c182,c245]) ).
cnf(c247,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c68,c246]) ).
cnf(c248,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c8,c247]) ).
cnf(c249,plain,
ifeq(c_lessequals(v_k(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(v_g(v_x),X,t_b),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c6,c248]) ).
cnf(c250,plain,
ifeq(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),c_lessequals(v_g(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(substitution,[status(thm)],[c249]) ).
cnf(c251,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = ifeq(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),c_lessequals(v_g(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(symmetry,[status(thm)],[c250]) ).
cnf(c252,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(symmetry,[status(thm)],[c17]) ).
cnf(c253,plain,
ifeq(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),c_lessequals(v_g(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)) = ifeq(c_lessequals(c_0,c_minus(v_k(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),c_lessequals(v_g(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(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),c_lessequals(v_g(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)) = c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c255,plain,
ifeq(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),c_lessequals(v_g(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)) = c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c253,c254]) ).
cnf(c256,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(transitivity,[status(thm)],[c251,c255]) ).
cnf(c257,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),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)) = ifeq(c_lessequals(v_g(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),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(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c259,plain,
ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c92]) ).
cnf(c261,plain,
X = c_plus(c_0,X,t_b),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c262,plain,
c_lessequals(X2,X,t_b) = c_lessequals(c_plus(c_0,X2,t_b),X,t_b),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_plus(c_0,X2,t_b),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_plus(c_0,X2,t_b),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c17]) ).
cnf(c266,plain,
ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c267,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)) = ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c269,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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(congruence,[status(thm)],[c17]) ).
cnf(c271,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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(congruence,[status(thm)],[c14]) ).
cnf(c272,plain,
ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c273,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c275,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),c_lessequals(v_k(v_x),v_f(v_x),t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c277,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c278,plain,
ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c279,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c281,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),true),class_Ring__and__Field_Oordered__idom(t_b)),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),true),class_Ring__and__Field_Oordered__idom(t_b)) = ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),true),true),
inference(congruence,[status(thm)],[c10]) ).
cnf(c283,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(T_a2),true,ifeq(c_lessequals(c_plus(V_a2,V_b2,T_a2),V_c2,T_a2),true,c_lessequals(V_a2,c_minus(V_c2,V_b2,T_a2),T_a2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(c284,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),true),true) = true,
inference(substitution,[status(thm)],[c283]) ).
cnf(c285,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c286,plain,
class_Ring__and__Field_Oordered__idom(t_b) = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c287,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(symmetry,[status(thm)],[c17]) ).
cnf(c288,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(transitivity,[status(thm)],[c286,c287]) ).
cnf(c289,plain,
true = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c285,c288]) ).
cnf(c290,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),true),true) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c284,c289]) ).
cnf(c291,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),true),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(transitivity,[status(thm)],[c282,c290]) ).
cnf(c292,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),true,c_lessequals(X3,c_minus(X,X2,X4),X4),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(transitivity,[status(thm)],[c281,c291]) ).
cnf(c293,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),true,ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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(transitivity,[status(thm)],[c279,c292]) ).
cnf(c294,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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(transitivity,[status(thm)],[c277,c293]) ).
cnf(c295,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),class_Ring__and__Field_Oordered__idom(t_b)),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(transitivity,[status(thm)],[c276,c294]) ).
cnf(c296,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c275,c295]) ).
cnf(c297,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c273,c296]) ).
cnf(c298,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(v_k(v_x),v_f(v_x),t_b)),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(transitivity,[status(thm)],[c271,c297]) ).
cnf(c299,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c270,c298]) ).
cnf(c300,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c269,c299]) ).
cnf(c301,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(v_k(v_x),v_f(v_x),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c267,c300]) ).
cnf(c302,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_plus(X3,X2,X4),X,X4),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(X3,c_minus(X,X2,X4),X4),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c265,c301]) ).
cnf(c303,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(c_plus(c_0,X2,t_b),X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(substitution,[status(thm)],[c302]) ).
cnf(c304,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c264,c303]) ).
cnf(c305,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c260,c304]) ).
cnf(c306,plain,
ifeq(c_lessequals(X2,X,t_b),c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),c_lessequals(c_0,c_minus(X,X2,t_b),t_b),c_lessequals(c_0,c_minus(v_k(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(transitivity,[status(thm)],[c259,c305]) ).
cnf(c307,plain,
ifeq(c_lessequals(v_g(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),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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(substitution,[status(thm)],[c306]) ).
cnf(c308,plain,
ifeq(c_lessequals(c_0,c_minus(v_k(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),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)) = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(transitivity,[status(thm)],[c257,c307]) ).
cnf(c309,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(transitivity,[status(thm)],[c4,c308]) ).
cnf(c310,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
inference(transitivity,[status(thm)],[c14,c10]) ).
cnf(c311,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
inference(transitivity,[status(thm)],[c17,c310]) ).
cnf(c312,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
inference(transitivity,[status(thm)],[c309,c311]) ).
cnf(c313,plain,
$false,
inference(resolution,[status(thm)],[c1,c312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n008.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 20:30:24 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.25 Command-line arguments: --flatten --complete-subsets
% 0.09/0.25
% 0.09/0.25 % SZS status Unsatisfiable
% 0.09/0.25
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.53/0.41
% 0.53/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------