TSTP Solution File: ANA022-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ANA022-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 17:13:56 EDT 2023

% Result   : Unsatisfiable 6.73s 6.81s
% Output   : CNFRefutation 6.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  152 (  15 unt;  22 typ;   0 def)
%            Number of atoms       :  376 (  39 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  476 ( 230   ~; 246   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  19   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :  222 (   6 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    v_k: $i > $i ).

tff(decl_23,type,
    v_f: $i > $i ).

tff(decl_24,type,
    t_b: $i ).

tff(decl_25,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    v_x: $i ).

tff(decl_27,type,
    v_g: $i > $i ).

tff(decl_28,type,
    c_minus: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    c_0: $i ).

tff(decl_30,type,
    c_Orderings_Omax: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    c_HOL_Oabs: ( $i * $i ) > $i ).

tff(decl_32,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(decl_33,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).

tff(decl_34,type,
    c_uminus: ( $i * $i ) > $i ).

tff(decl_35,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_36,type,
    c_plus: ( $i * $i * $i ) > $i ).

tff(decl_37,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(decl_38,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(decl_39,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(decl_40,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_41,type,
    c_less: ( $i * $i * $i ) > $o ).

tff(decl_42,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_43,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_less(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).

cnf(cls_Orderings_Olinorder__not__le_0,axiom,
    ( c_less(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).

cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

cnf(tfree_tcs,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
    ( c_lessequals(X4,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X4,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).

cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
    ( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

cnf(cls_conjecture_2,negated_conjecture,
    ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
    ( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).

cnf(cls_OrderedGroup_Odiff__self_0,axiom,
    ( c_minus(X2,X2,X1) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
    ( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).

cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
    ( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).

cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
    ( c_plus(c_0,X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

cnf(cls_OrderedGroup_Ocompare__rls__3_0,axiom,
    ( c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).

cnf(cls_OrderedGroup_Oadd__le__cancel__right_0,axiom,
    ( c_lessequals(X2,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).

cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_6,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

cnf(cls_OrderedGroup_Odiff__le__0__iff__le_1,axiom,
    ( c_lessequals(c_minus(X2,X3,X1),c_0,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).

cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

cnf(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
    ( c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).

cnf(cls_OrderedGroup_Oabs__of__nonpos_0,axiom,
    ( c_HOL_Oabs(X2,X1) = c_uminus(X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ c_lessequals(X2,c_0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).

cnf(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
    ( c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).

cnf(cls_OrderedGroup_Ocompare__rls__8_1,axiom,
    ( c_lessequals(c_minus(X2,X4,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,c_plus(X3,X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_lessequals(v_k(X1),v_f(X1),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(c_0_27,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_less(X2,X3,X1) ),
    cls_Orderings_Oorder__less__imp__le_0 ).

cnf(c_0_28,axiom,
    ( c_less(X2,X3,X1)
    | c_lessequals(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    cls_Orderings_Olinorder__not__le_0 ).

cnf(c_0_29,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    clsrel_LOrder_Ojoin__semilorder_1 ).

cnf(c_0_30,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_35 ).

cnf(c_0_31,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Orderings_Oorder(X3)
    | ~ class_Orderings_Olinorder(X3) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,axiom,
    ( class_Orderings_Olinorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_33 ).

cnf(c_0_34,plain,
    ( c_lessequals(X1,X2,X3)
    | c_lessequals(X2,X1,X3)
    | ~ class_Ring__and__Field_Oordered__idom(X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

cnf(c_0_35,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b),
    tfree_tcs ).

cnf(c_0_36,axiom,
    ( c_lessequals(X4,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X4,X2,X1) ),
    cls_Orderings_Oorder__class_Oorder__trans_0 ).

cnf(c_0_37,axiom,
    ( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    cls_OrderedGroup_Oabs__ge__zero_0 ).

cnf(c_0_38,negated_conjecture,
    ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    cls_conjecture_2 ).

cnf(c_0_39,negated_conjecture,
    ( c_lessequals(X1,X2,t_b)
    | c_lessequals(X2,X1,t_b) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
    ( c_lessequals(c_0,X1,X2)
    | ~ class_Orderings_Oorder(X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | ~ c_lessequals(c_HOL_Oabs(X3,X2),X1,X2) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),t_b),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_42,negated_conjecture,
    ( c_lessequals(c_0,c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_43,negated_conjecture,
    ( c_lessequals(c_0,X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),X1,t_b) ),
    inference(spm,[status(thm)],[c_0_36,c_0_42]) ).

cnf(c_0_44,negated_conjecture,
    ( c_lessequals(X1,c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),t_b)
    | c_lessequals(c_0,X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_43,c_0_39]) ).

cnf(c_0_45,negated_conjecture,
    ( c_lessequals(c_0,X1,t_b)
    | c_lessequals(X1,X2,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),X2,t_b) ),
    inference(spm,[status(thm)],[c_0_36,c_0_44]) ).

cnf(c_0_46,axiom,
    ( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(X4,X3,X1) ),
    cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2 ).

cnf(c_0_47,negated_conjecture,
    ( c_lessequals(c_0,X1,t_b)
    | c_lessequals(X1,X2,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X2,t_b)
    | ~ c_lessequals(c_0,X2,t_b) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_48,negated_conjecture,
    ( c_lessequals(X1,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(c_0,X2,t_b)
    | c_lessequals(X2,X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,X1,t_b) ),
    inference(spm,[status(thm)],[c_0_47,c_0_39]) ).

cnf(c_0_49,axiom,
    ( c_minus(X2,X2,X1) = c_0
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_OrderedGroup_Odiff__self_0 ).

cnf(c_0_50,axiom,
    ( class_OrderedGroup_Oab__group__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_4 ).

cnf(c_0_51,negated_conjecture,
    ( c_lessequals(X1,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(c_0,X2,t_b)
    | c_lessequals(X2,X1,t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,X1,t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_32]),c_0_35])]) ).

cnf(c_0_52,plain,
    ( c_minus(X1,X1,X2) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_53,negated_conjecture,
    ( c_lessequals(X1,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(c_0,X2,t_b)
    | c_lessequals(X2,X1,t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,X1,t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_33]),c_0_35])]) ).

cnf(c_0_54,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_50 ).

cnf(c_0_55,axiom,
    ( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_OrderedGroup_Ominus__diff__eq_0 ).

cnf(c_0_56,negated_conjecture,
    c_minus(X1,X1,t_b) = c_0,
    inference(spm,[status(thm)],[c_0_52,c_0_35]) ).

cnf(c_0_57,negated_conjecture,
    ( c_lessequals(X1,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(c_0,X2,t_b)
    | c_lessequals(X2,X1,t_b)
    | ~ c_lessequals(c_0,X1,t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_35])]) ).

cnf(c_0_58,axiom,
    ( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_OrderedGroup_Odiff__minus__eq__add_0 ).

cnf(c_0_59,negated_conjecture,
    ( c_uminus(c_0,t_b) = c_0
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).

cnf(c_0_60,negated_conjecture,
    ( c_lessequals(c_HOL_Oabs(X1,t_b),c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(X2,c_HOL_Oabs(X1,t_b),t_b)
    | c_lessequals(c_0,X2,t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_57,c_0_37]) ).

cnf(c_0_61,negated_conjecture,
    ( c_plus(X1,c_0,t_b) = c_minus(X1,c_0,t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_62,axiom,
    ( c_plus(c_0,X2,X1) = X2
    | ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
    cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 ).

cnf(c_0_63,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_23 ).

cnf(c_0_64,negated_conjecture,
    ( c_lessequals(c_HOL_Oabs(X1,t_b),c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(X2,c_HOL_Oabs(X1,t_b),t_b)
    | c_lessequals(c_0,X2,t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_54]),c_0_35])]) ).

cnf(c_0_65,negated_conjecture,
    ( c_plus(c_uminus(X1,t_b),X1,t_b) = c_0
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(spm,[status(thm)],[c_0_56,c_0_58]) ).

cnf(c_0_66,negated_conjecture,
    c_plus(X1,c_0,t_b) = c_minus(X1,c_0,t_b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_50]),c_0_35])]) ).

cnf(c_0_67,plain,
    ( c_plus(c_0,X1,X2) = X1
    | ~ class_Ring__and__Field_Oordered__idom(X2) ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_68,negated_conjecture,
    ( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b)
    | c_lessequals(c_0,X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_40,c_0_64]) ).

cnf(c_0_69,negated_conjecture,
    ( c_plus(c_minus(X1,X2,t_b),c_minus(X2,X1,t_b),t_b) = c_0
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(spm,[status(thm)],[c_0_65,c_0_55]) ).

cnf(c_0_70,negated_conjecture,
    ( c_minus(c_uminus(c_0,t_b),c_0,t_b) = c_0
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(spm,[status(thm)],[c_0_66,c_0_65]) ).

cnf(c_0_71,negated_conjecture,
    c_plus(c_0,X1,t_b) = X1,
    inference(spm,[status(thm)],[c_0_67,c_0_35]) ).

cnf(c_0_72,negated_conjecture,
    ( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b)
    | c_lessequals(c_0,X1,t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_32]),c_0_35])]) ).

cnf(c_0_73,axiom,
    ( c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_OrderedGroup_Ocompare__rls__3_0 ).

cnf(c_0_74,negated_conjecture,
    ( c_minus(c_0,c_uminus(c_0,t_b),t_b) = c_0
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).

cnf(c_0_75,negated_conjecture,
    ( ~ class_Orderings_Olinorder(t_b)
    | ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
    inference(spm,[status(thm)],[c_0_38,c_0_46]) ).

cnf(c_0_76,negated_conjecture,
    ( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | c_lessequals(X1,c_HOL_Oabs(X2,t_b),t_b)
    | c_lessequals(c_0,X1,t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_54]),c_0_35])]) ).

cnf(c_0_77,negated_conjecture,
    ( c_minus(X1,c_uminus(c_0,t_b),t_b) = X1
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_71]),c_0_71]) ).

cnf(c_0_78,negated_conjecture,
    ( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_79,negated_conjecture,
    ( c_minus(X1,c_0,t_b) = X1
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_77]),c_0_66]) ).

cnf(c_0_80,negated_conjecture,
    ( c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_78,c_0_37]) ).

cnf(c_0_81,axiom,
    ( c_lessequals(X2,X4,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X4,X3,X1),X1) ),
    cls_OrderedGroup_Oadd__le__cancel__right_0 ).

cnf(c_0_82,negated_conjecture,
    ( c_minus(c_plus(X1,X2,t_b),X1,t_b) = X2
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_56]),c_0_71]) ).

cnf(c_0_83,negated_conjecture,
    c_minus(X1,c_0,t_b) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_50]),c_0_35])]) ).

cnf(c_0_84,negated_conjecture,
    ( c_lessequals(c_0,X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X1,t_b) ),
    inference(spm,[status(thm)],[c_0_36,c_0_80]) ).

cnf(c_0_85,negated_conjecture,
    ( c_lessequals(X1,c_uminus(X2,t_b),t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
    | ~ c_lessequals(c_plus(X1,X2,t_b),c_0,t_b) ),
    inference(spm,[status(thm)],[c_0_81,c_0_65]) ).

cnf(c_0_86,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    clsrel_OrderedGroup_Olordered__ab__group__abs_6 ).

cnf(c_0_87,axiom,
    ( c_lessequals(c_minus(X2,X3,X1),c_0,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,X3,X1) ),
    cls_OrderedGroup_Odiff__le__0__iff__le_1 ).

cnf(c_0_88,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    clsrel_OrderedGroup_Olordered__ab__group__abs_1 ).

cnf(c_0_89,negated_conjecture,
    ( c_minus(c_0,c_uminus(X1,t_b),t_b) = X1
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(spm,[status(thm)],[c_0_82,c_0_65]) ).

cnf(c_0_90,negated_conjecture,
    ( c_uminus(X1,t_b) = c_minus(c_0,X1,t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(spm,[status(thm)],[c_0_55,c_0_83]) ).

cnf(c_0_91,negated_conjecture,
    ( c_lessequals(c_0,c_uminus(X1,t_b),t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_plus(c_minus(v_k(v_x),v_g(v_x),t_b),X1,t_b),c_0,t_b) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]) ).

cnf(c_0_92,negated_conjecture,
    c_lessequals(X1,X1,t_b),
    inference(ef,[status(thm)],[c_0_39]) ).

cnf(c_0_93,plain,
    ( c_lessequals(c_minus(X1,X2,X3),c_0,X3)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
    | ~ c_lessequals(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_94,negated_conjecture,
    ( c_minus(c_0,c_minus(c_0,X1,t_b),t_b) = X1
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_95,negated_conjecture,
    ( c_lessequals(c_0,c_uminus(c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_69]),c_0_92])]) ).

cnf(c_0_96,axiom,
    ( c_HOL_Oabs(c_uminus(X2,X1),X1) = c_HOL_Oabs(X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    cls_OrderedGroup_Oabs__minus__cancel_0 ).

cnf(c_0_97,axiom,
    ( c_HOL_Oabs(X2,X1) = c_uminus(X2,X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ c_lessequals(X2,c_0,X1) ),
    cls_OrderedGroup_Oabs__of__nonpos_0 ).

cnf(c_0_98,negated_conjecture,
    ( c_lessequals(X1,c_0,t_b)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
    | ~ c_lessequals(c_plus(X1,X2,t_b),X2,t_b) ),
    inference(spm,[status(thm)],[c_0_81,c_0_71]) ).

cnf(c_0_99,axiom,
    ( c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1)
    | ~ class_OrderedGroup_Oab__group__add(X1) ),
    cls_OrderedGroup_Ocompare__rls__2_0 ).

cnf(c_0_100,negated_conjecture,
    ( c_lessequals(X1,c_0,t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,c_minus(c_0,X1,t_b),t_b) ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_101,negated_conjecture,
    ( c_lessequals(c_0,c_minus(c_0,c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_95,c_0_90]) ).

cnf(c_0_102,plain,
    ( c_HOL_Oabs(c_HOL_Oabs(X1,X2),X2) = c_HOL_Oabs(X1,X2)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
    | ~ c_lessequals(X1,c_0,X2) ),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_103,plain,
    ( c_HOL_Oabs(c_minus(X1,X2,X3),X3) = c_minus(X2,X1,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
    | ~ c_lessequals(c_minus(X1,X2,X3),c_0,X3) ),
    inference(spm,[status(thm)],[c_0_97,c_0_55]) ).

cnf(c_0_104,negated_conjecture,
    ( c_lessequals(X1,c_0,t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_plus(X1,X2,t_b),X2,t_b) ),
    inference(spm,[status(thm)],[c_0_98,c_0_86]) ).

cnf(c_0_105,axiom,
    ( c_lessequals(c_minus(X2,X4,X1),X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
    | ~ c_lessequals(X2,c_plus(X3,X4,X1),X1) ),
    cls_OrderedGroup_Ocompare__rls__8_1 ).

cnf(c_0_106,plain,
    ( c_lessequals(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
    | ~ c_lessequals(c_minus(c_plus(X1,X4,X3),X5,X3),c_plus(X2,c_minus(X4,X5,X3),X3),X3) ),
    inference(spm,[status(thm)],[c_0_81,c_0_99]) ).

cnf(c_0_107,negated_conjecture,
    c_plus(X1,c_0,t_b) = X1,
    inference(rw,[status(thm)],[c_0_66,c_0_83]) ).

cnf(c_0_108,negated_conjecture,
    ( c_lessequals(c_minus(v_g(v_x),v_k(v_x),t_b),c_0,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_109,plain,
    ( c_HOL_Oabs(c_minus(X1,X2,X3),X3) = c_minus(X1,X2,X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
    | ~ c_lessequals(c_minus(X2,X1,X3),c_0,X3) ),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_110,negated_conjecture,
    ( c_lessequals(c_minus(X1,X2,t_b),c_0,t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,c_minus(X2,X1,t_b),t_b) ),
    inference(spm,[status(thm)],[c_0_104,c_0_69]) ).

cnf(c_0_111,plain,
    ( c_lessequals(c_minus(X1,X2,X3),c_minus(X4,X5,X3),X3)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ c_lessequals(X1,c_minus(c_plus(X4,X2,X3),X5,X3),X3) ),
    inference(spm,[status(thm)],[c_0_105,c_0_73]) ).

cnf(c_0_112,negated_conjecture,
    ( c_minus(c_plus(X1,X2,t_b),X2,t_b) = X1
    | ~ class_OrderedGroup_Oab__group__add(t_b) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_56]),c_0_66]),c_0_83]) ).

cnf(c_0_113,negated_conjecture,
    ( c_lessequals(X1,X2,t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
    | ~ c_lessequals(c_minus(X1,X3,t_b),c_plus(X2,c_minus(c_0,X3,t_b),t_b),t_b) ),
    inference(spm,[status(thm)],[c_0_106,c_0_107]) ).

cnf(c_0_114,negated_conjecture,
    ( c_lessequals(c_minus(v_g(v_x),v_k(v_x),t_b),X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,X1,t_b) ),
    inference(spm,[status(thm)],[c_0_36,c_0_108]) ).

cnf(c_0_115,negated_conjecture,
    ( ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_109]),c_0_110]) ).

cnf(c_0_116,negated_conjecture,
    ( c_lessequals(c_minus(X1,X2,t_b),c_minus(X3,X2,t_b),t_b)
    | ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ c_lessequals(X1,X3,t_b) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_117,negated_conjecture,
    c_lessequals(v_k(X1),v_f(X1),t_b),
    cls_conjecture_1 ).

cnf(c_0_118,plain,
    ( c_lessequals(c_0,c_minus(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
    | ~ c_lessequals(c_minus(X2,X1,X3),c_0,X3) ),
    inference(spm,[status(thm)],[c_0_37,c_0_103]) ).

cnf(c_0_119,negated_conjecture,
    ( c_lessequals(v_g(v_x),X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,c_plus(X1,c_minus(c_0,v_k(v_x),t_b),t_b),t_b) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_86]) ).

cnf(c_0_120,negated_conjecture,
    ( ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117])]),c_0_88]) ).

cnf(c_0_121,plain,
    ( c_lessequals(c_0,c_minus(X1,X2,X3),X3)
    | ~ class_OrderedGroup_Oab__group__add(X3)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
    | ~ c_lessequals(X2,X1,X3) ),
    inference(spm,[status(thm)],[c_0_118,c_0_93]) ).

cnf(c_0_122,negated_conjecture,
    ( c_lessequals(v_g(v_x),v_k(v_x),t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_69]),c_0_83]),c_0_92])]) ).

cnf(c_0_123,negated_conjecture,
    ( ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
    inference(spm,[status(thm)],[c_0_120,c_0_121]) ).

cnf(c_0_124,negated_conjecture,
    ( c_lessequals(v_g(v_x),X1,t_b)
    | ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
    | ~ c_lessequals(v_k(v_x),X1,t_b) ),
    inference(spm,[status(thm)],[c_0_36,c_0_122]) ).

cnf(c_0_125,negated_conjecture,
    ( ~ class_Orderings_Oorder(t_b)
    | ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_117])]) ).

cnf(c_0_126,negated_conjecture,
    ( ~ class_Orderings_Olinorder(t_b)
    | ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_32]),c_0_35])]) ).

cnf(c_0_127,negated_conjecture,
    ( ~ class_OrderedGroup_Oab__group__add(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_33]),c_0_35])]) ).

cnf(c_0_128,negated_conjecture,
    ~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_50]),c_0_35])]) ).

cnf(c_0_129,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_54]),c_0_35])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ANA022-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Aug 25 18:58:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 6.73/6.81  % Version  : CSE_E---1.5
% 6.73/6.81  % Problem  : theBenchmark.p
% 6.73/6.81  % Proof found
% 6.73/6.81  % SZS status Theorem for theBenchmark.p
% 6.73/6.81  % SZS output start Proof
% See solution above
% 6.73/6.83  % Total time : 6.244000 s
% 6.73/6.83  % SZS output end Proof
% 6.73/6.83  % Total time : 6.248000 s
%------------------------------------------------------------------------------