TSTP Solution File: ANA045-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ANA045-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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  : 600s
% DateTime : Thu Jul 14 19:29:04 EDT 2022

% Result   : Unsatisfiable 3.31s 3.51s
% Output   : Refutation 3.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   65
% Syntax   : Number of clauses     :  131 (  67 unt;   0 nHn; 131 RR)
%            Number of literals    :  196 (   0 equ;  68 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   62 (  61 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ c_lessequals(c_0,c_times(u,c_HOL_Oabs(v_g(v_x(u)),t_b),t_b),t_b),
    file('ANA045-1.p',unknown),
    [] ).

cnf(4,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('ANA045-1.p',unknown),
    [] ).

cnf(272,axiom,
    equal(c_IntDef_Oint(c_0),c_0),
    file('ANA045-1.p',unknown),
    [] ).

cnf(275,axiom,
    c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
    file('ANA045-1.p',unknown),
    [] ).

cnf(303,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | equal(c_IntDef_Oof__int(c_0,u),c_0) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(307,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | ~ c_lessequals(v,c_0,tc_IntDef_Oint)
    | c_lessequals(c_IntDef_Oof__int(v,u),c_0,u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(1389,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(u)
    | equal(c_times(c_0,v,u),c_0) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2421,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Ocomm__ring__1(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2422,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Ocomm__ring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2423,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Osemiring__1(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2424,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oaxclass__0__neq__1(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2425,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Omonoid__mult(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2426,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_HOL_Oone(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2427,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Ocomm__semiring__0__cancel(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2428,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Ocomm__semiring__0(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2429,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Ocomm__semiring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2430,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Oab__semigroup__mult(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2431,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Osemiring__0__cancel(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2432,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Osemiring__0(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2433,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oring__1(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2434,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Osemiring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2435,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Osemigroup__mult(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2436,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_HOL_Otimes(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2437,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Ocomm__monoid__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2438,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_HOL_Ozero(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2439,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Ocancel__ab__semigroup__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2440,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Oab__semigroup__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2441,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Ocancel__semigroup__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2442,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Osemigroup__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2443,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_HOL_Oplus(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2444,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2445,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oordered__comm__semiring__strict(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2446,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oordered__semiring__strict(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2447,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2448,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Orderings_Olinorder(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2449,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_LOrder_Olorder(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2450,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_LOrder_Ojoin__semilorder(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2451,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_LOrder_Omeet__semilorder(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2452,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2453,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2454,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Opordered__cancel__comm__semiring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2455,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Oab__group__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2456,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Opordered__cancel__semiring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2457,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Opordered__comm__semiring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2458,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Opordered__semiring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2459,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Opordered__ab__semigroup__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2460,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Orderings_Oorder(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2461,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Orderings_Oord(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2462,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oaxclass__abs__if(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2463,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oordered__ring__strict(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2464,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Olordered__ring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2465,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Opordered__ring(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2466,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_HOL_Ominus(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2467,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Olordered__ab__group__abs(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2468,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Olordered__ab__group__meet(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2469,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Olordered__ab__group__join(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2470,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Olordered__ab__group(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2471,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Opordered__ab__group__add(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2472,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oordered__semidom(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2473,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oaxclass__no__zero__divisors(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2474,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Oidom(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2475,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Ocomm__semiring__1__cancel(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2476,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Ocomm__semiring__1(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2477,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_OrderedGroup_Ocomm__monoid__mult(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2478,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | class_Ring__and__Field_Osemiring__1__cancel(u) ),
    file('ANA045-1.p',unknown),
    [] ).

cnf(2786,plain,
    c_lessequals(c_0,c_0,tc_IntDef_Oint),
    inference(rew,[status(thm),theory(equality)],[272,275]),
    [iquote('0:Rew:272.0,275.0')] ).

cnf(3032,plain,
    ( ~ c_lessequals(u,c_0,tc_IntDef_Oint)
    | c_lessequals(c_IntDef_Oof__int(u,t_b),c_0,t_b) ),
    inference(res,[status(thm),theory(equality)],[4,307]),
    [iquote('0:Res:4.0,307.0')] ).

cnf(3043,plain,
    equal(c_IntDef_Oof__int(c_0,t_b),c_0),
    inference(res,[status(thm),theory(equality)],[4,303]),
    [iquote('0:Res:4.0,303.0')] ).

cnf(3047,plain,
    class_Ring__and__Field_Ocomm__ring__1(t_b),
    inference(res,[status(thm),theory(equality)],[4,2421]),
    [iquote('0:Res:4.0,2421.0')] ).

cnf(3048,plain,
    class_Ring__and__Field_Ocomm__ring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2422]),
    [iquote('0:Res:4.0,2422.0')] ).

cnf(3049,plain,
    class_Ring__and__Field_Osemiring__1(t_b),
    inference(res,[status(thm),theory(equality)],[4,2423]),
    [iquote('0:Res:4.0,2423.0')] ).

cnf(3050,plain,
    class_Ring__and__Field_Oaxclass__0__neq__1(t_b),
    inference(res,[status(thm),theory(equality)],[4,2424]),
    [iquote('0:Res:4.0,2424.0')] ).

cnf(3051,plain,
    class_OrderedGroup_Omonoid__mult(t_b),
    inference(res,[status(thm),theory(equality)],[4,2425]),
    [iquote('0:Res:4.0,2425.0')] ).

cnf(3052,plain,
    class_HOL_Oone(t_b),
    inference(res,[status(thm),theory(equality)],[4,2426]),
    [iquote('0:Res:4.0,2426.0')] ).

cnf(3053,plain,
    class_Ring__and__Field_Ocomm__semiring__0__cancel(t_b),
    inference(res,[status(thm),theory(equality)],[4,2427]),
    [iquote('0:Res:4.0,2427.0')] ).

cnf(3054,plain,
    class_Ring__and__Field_Ocomm__semiring__0(t_b),
    inference(res,[status(thm),theory(equality)],[4,2428]),
    [iquote('0:Res:4.0,2428.0')] ).

cnf(3055,plain,
    class_Ring__and__Field_Ocomm__semiring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2429]),
    [iquote('0:Res:4.0,2429.0')] ).

cnf(3056,plain,
    class_OrderedGroup_Oab__semigroup__mult(t_b),
    inference(res,[status(thm),theory(equality)],[4,2430]),
    [iquote('0:Res:4.0,2430.0')] ).

cnf(3057,plain,
    class_Ring__and__Field_Osemiring__0__cancel(t_b),
    inference(res,[status(thm),theory(equality)],[4,2431]),
    [iquote('0:Res:4.0,2431.0')] ).

cnf(3058,plain,
    class_Ring__and__Field_Osemiring__0(t_b),
    inference(res,[status(thm),theory(equality)],[4,2432]),
    [iquote('0:Res:4.0,2432.0')] ).

cnf(3059,plain,
    class_Ring__and__Field_Oring__1(t_b),
    inference(res,[status(thm),theory(equality)],[4,2433]),
    [iquote('0:Res:4.0,2433.0')] ).

cnf(3060,plain,
    class_Ring__and__Field_Osemiring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2434]),
    [iquote('0:Res:4.0,2434.0')] ).

cnf(3061,plain,
    class_OrderedGroup_Osemigroup__mult(t_b),
    inference(res,[status(thm),theory(equality)],[4,2435]),
    [iquote('0:Res:4.0,2435.0')] ).

cnf(3062,plain,
    class_HOL_Otimes(t_b),
    inference(res,[status(thm),theory(equality)],[4,2436]),
    [iquote('0:Res:4.0,2436.0')] ).

cnf(3063,plain,
    class_OrderedGroup_Ocomm__monoid__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2437]),
    [iquote('0:Res:4.0,2437.0')] ).

cnf(3064,plain,
    class_HOL_Ozero(t_b),
    inference(res,[status(thm),theory(equality)],[4,2438]),
    [iquote('0:Res:4.0,2438.0')] ).

cnf(3065,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2439]),
    [iquote('0:Res:4.0,2439.0')] ).

cnf(3066,plain,
    class_OrderedGroup_Oab__semigroup__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2440]),
    [iquote('0:Res:4.0,2440.0')] ).

cnf(3067,plain,
    class_OrderedGroup_Ocancel__semigroup__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2441]),
    [iquote('0:Res:4.0,2441.0')] ).

cnf(3068,plain,
    class_OrderedGroup_Osemigroup__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2442]),
    [iquote('0:Res:4.0,2442.0')] ).

cnf(3069,plain,
    class_HOL_Oplus(t_b),
    inference(res,[status(thm),theory(equality)],[4,2443]),
    [iquote('0:Res:4.0,2443.0')] ).

cnf(3070,plain,
    class_Ring__and__Field_Oring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2444]),
    [iquote('0:Res:4.0,2444.0')] ).

cnf(3071,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict(t_b),
    inference(res,[status(thm),theory(equality)],[4,2445]),
    [iquote('0:Res:4.0,2445.0')] ).

cnf(3072,plain,
    class_Ring__and__Field_Oordered__semiring__strict(t_b),
    inference(res,[status(thm),theory(equality)],[4,2446]),
    [iquote('0:Res:4.0,2446.0')] ).

cnf(3073,plain,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2447]),
    [iquote('0:Res:4.0,2447.0')] ).

cnf(3074,plain,
    class_Orderings_Olinorder(t_b),
    inference(res,[status(thm),theory(equality)],[4,2448]),
    [iquote('0:Res:4.0,2448.0')] ).

cnf(3075,plain,
    class_LOrder_Olorder(t_b),
    inference(res,[status(thm),theory(equality)],[4,2449]),
    [iquote('0:Res:4.0,2449.0')] ).

cnf(3076,plain,
    class_LOrder_Ojoin__semilorder(t_b),
    inference(res,[status(thm),theory(equality)],[4,2450]),
    [iquote('0:Res:4.0,2450.0')] ).

cnf(3077,plain,
    class_LOrder_Omeet__semilorder(t_b),
    inference(res,[status(thm),theory(equality)],[4,2451]),
    [iquote('0:Res:4.0,2451.0')] ).

cnf(3078,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
    inference(res,[status(thm),theory(equality)],[4,2452]),
    [iquote('0:Res:4.0,2452.0')] ).

cnf(3079,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2453]),
    [iquote('0:Res:4.0,2453.0')] ).

cnf(3080,plain,
    class_Ring__and__Field_Opordered__cancel__comm__semiring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2454]),
    [iquote('0:Res:4.0,2454.0')] ).

cnf(3081,plain,
    class_OrderedGroup_Oab__group__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2455]),
    [iquote('0:Res:4.0,2455.0')] ).

cnf(3082,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2456]),
    [iquote('0:Res:4.0,2456.0')] ).

cnf(3083,plain,
    class_Ring__and__Field_Opordered__comm__semiring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2457]),
    [iquote('0:Res:4.0,2457.0')] ).

cnf(3084,plain,
    class_Ring__and__Field_Opordered__semiring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2458]),
    [iquote('0:Res:4.0,2458.0')] ).

cnf(3085,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2459]),
    [iquote('0:Res:4.0,2459.0')] ).

cnf(3086,plain,
    class_Orderings_Oorder(t_b),
    inference(res,[status(thm),theory(equality)],[4,2460]),
    [iquote('0:Res:4.0,2460.0')] ).

cnf(3087,plain,
    class_Orderings_Oord(t_b),
    inference(res,[status(thm),theory(equality)],[4,2461]),
    [iquote('0:Res:4.0,2461.0')] ).

cnf(3088,plain,
    class_Ring__and__Field_Oaxclass__abs__if(t_b),
    inference(res,[status(thm),theory(equality)],[4,2462]),
    [iquote('0:Res:4.0,2462.0')] ).

cnf(3089,plain,
    class_Ring__and__Field_Oordered__ring__strict(t_b),
    inference(res,[status(thm),theory(equality)],[4,2463]),
    [iquote('0:Res:4.0,2463.0')] ).

cnf(3090,plain,
    class_Ring__and__Field_Olordered__ring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2464]),
    [iquote('0:Res:4.0,2464.0')] ).

cnf(3091,plain,
    class_Ring__and__Field_Opordered__ring(t_b),
    inference(res,[status(thm),theory(equality)],[4,2465]),
    [iquote('0:Res:4.0,2465.0')] ).

cnf(3092,plain,
    class_HOL_Ominus(t_b),
    inference(res,[status(thm),theory(equality)],[4,2466]),
    [iquote('0:Res:4.0,2466.0')] ).

cnf(3093,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(res,[status(thm),theory(equality)],[4,2467]),
    [iquote('0:Res:4.0,2467.0')] ).

cnf(3094,plain,
    class_OrderedGroup_Olordered__ab__group__meet(t_b),
    inference(res,[status(thm),theory(equality)],[4,2468]),
    [iquote('0:Res:4.0,2468.0')] ).

cnf(3095,plain,
    class_OrderedGroup_Olordered__ab__group__join(t_b),
    inference(res,[status(thm),theory(equality)],[4,2469]),
    [iquote('0:Res:4.0,2469.0')] ).

cnf(3096,plain,
    class_OrderedGroup_Olordered__ab__group(t_b),
    inference(res,[status(thm),theory(equality)],[4,2470]),
    [iquote('0:Res:4.0,2470.0')] ).

cnf(3097,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b),
    inference(res,[status(thm),theory(equality)],[4,2471]),
    [iquote('0:Res:4.0,2471.0')] ).

cnf(3098,plain,
    class_Ring__and__Field_Oordered__semidom(t_b),
    inference(res,[status(thm),theory(equality)],[4,2472]),
    [iquote('0:Res:4.0,2472.0')] ).

cnf(3099,plain,
    class_Ring__and__Field_Oaxclass__no__zero__divisors(t_b),
    inference(res,[status(thm),theory(equality)],[4,2473]),
    [iquote('0:Res:4.0,2473.0')] ).

cnf(3100,plain,
    class_Ring__and__Field_Oidom(t_b),
    inference(res,[status(thm),theory(equality)],[4,2474]),
    [iquote('0:Res:4.0,2474.0')] ).

cnf(3101,plain,
    class_Ring__and__Field_Ocomm__semiring__1__cancel(t_b),
    inference(res,[status(thm),theory(equality)],[4,2475]),
    [iquote('0:Res:4.0,2475.0')] ).

cnf(3102,plain,
    class_Ring__and__Field_Ocomm__semiring__1(t_b),
    inference(res,[status(thm),theory(equality)],[4,2476]),
    [iquote('0:Res:4.0,2476.0')] ).

cnf(3103,plain,
    class_OrderedGroup_Ocomm__monoid__mult(t_b),
    inference(res,[status(thm),theory(equality)],[4,2477]),
    [iquote('0:Res:4.0,2477.0')] ).

cnf(3104,plain,
    class_Ring__and__Field_Osemiring__1__cancel(t_b),
    inference(res,[status(thm),theory(equality)],[4,2478]),
    [iquote('0:Res:4.0,2478.0')] ).

cnf(6328,plain,
    ( ~ c_lessequals(c_0,c_0,tc_IntDef_Oint)
    | c_lessequals(c_0,c_0,t_b) ),
    inference(spr,[status(thm),theory(equality)],[3043,3032]),
    [iquote('0:SpR:3043.0,3032.1')] ).

cnf(6331,plain,
    c_lessequals(c_0,c_0,t_b),
    inference(mrr,[status(thm)],[6328,2786]),
    [iquote('0:MRR:6328.0,2786.0')] ).

cnf(10079,plain,
    ( ~ class_Ring__and__Field_Osemiring__0__cancel(t_b)
    | ~ c_lessequals(c_0,c_0,t_b) ),
    inference(spl,[status(thm),theory(equality)],[1389,3]),
    [iquote('0:SpL:1389.1,3.0')] ).

cnf(10085,plain,
    ~ c_lessequals(c_0,c_0,t_b),
    inference(ssi,[status(thm)],[10079,4,3088,3099,3050,3077,3076,3075,3073,3051,3095,3094,3083,3092,3079,3056,3084,3103,3082,3080,3055,3049,3091,3085,3059,3048,3104,3102,3053,3054,3072,3052,3078,3070,3100,3090,3071,3093,3057,3065,3058,3067,3060,3061,3086,3101,3096,3081,3064,3062,3066,3063,3087,3068,3069,3097,3089,3098,3047,3074]),
    [iquote('0:SSi:10079.0,4.0,3088.0,3099.0,3050.0,3077.0,3076.0,3075.0,3073.0,3051.0,3095.0,3094.0,3083.0,3092.0,3079.0,3056.0,3084.0,3103.0,3082.0,3080.0,3055.0,3049.0,3091.0,3085.0,3059.0,3048.0,3104.0,3102.0,3053.0,3054.0,3072.0,3052.0,3078.0,3070.0,3100.0,3090.0,3071.0,3093.0,3057.0,3065.0,3058.0,3067.0,3060.0,3061.0,3086.0,3101.0,3096.0,3081.0,3064.0,3062.0,3066.0,3063.0,3087.0,3068.0,3069.0,3097.0,3089.0,3098.0,3047.0,3074.0')] ).

cnf(10086,plain,
    $false,
    inference(mrr,[status(thm)],[10085,6331]),
    [iquote('0:MRR:10085.0,6331.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : ANA045-1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Fri Jul  8 02:43:16 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 3.31/3.51  
% 3.31/3.51  SPASS V 3.9 
% 3.31/3.51  SPASS beiseite: Proof found.
% 3.31/3.51  % SZS status Theorem
% 3.31/3.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 3.31/3.51  SPASS derived 6106 clauses, backtracked 0 clauses, performed 1 splits and kept 3920 clauses.
% 3.31/3.51  SPASS allocated 84279 KBytes.
% 3.31/3.51  SPASS spent	0:00:03.14 on the problem.
% 3.31/3.51  		0:00:00.21 for the input.
% 3.31/3.51  		0:00:00.00 for the FLOTTER CNF translation.
% 3.31/3.51  		0:00:00.19 for inferences.
% 3.31/3.51  		0:00:00.00 for the backtracking.
% 3.31/3.51  		0:00:02.08 for the reduction.
% 3.31/3.51  
% 3.31/3.51  
% 3.31/3.51  Here is a proof with depth 2, length 131 :
% 3.31/3.51  % SZS output start Refutation
% See solution above
% 3.38/3.60  Formulae used in the proof : cls_conjecture_0 tfree_tcs cls_IntDef_Oint__eq__0__conv_1 cls_IntDef_Oint__le__0__conv_1 cls_IntDef_Oof__int__eq__0__iff_1 cls_IntDef_Oof__int__le__0__iff_1 cls_Ring__and__Field_Omult__zero__left_0 clsrel_Ring__and__Field_Oordered__idom_0 clsrel_Ring__and__Field_Oordered__idom_1 clsrel_Ring__and__Field_Oordered__idom_10 clsrel_Ring__and__Field_Oordered__idom_11 clsrel_Ring__and__Field_Oordered__idom_12 clsrel_Ring__and__Field_Oordered__idom_13 clsrel_Ring__and__Field_Oordered__idom_14 clsrel_Ring__and__Field_Oordered__idom_15 clsrel_Ring__and__Field_Oordered__idom_16 clsrel_Ring__and__Field_Oordered__idom_17 clsrel_Ring__and__Field_Oordered__idom_18 clsrel_Ring__and__Field_Oordered__idom_19 clsrel_Ring__and__Field_Oordered__idom_2 clsrel_Ring__and__Field_Oordered__idom_20 clsrel_Ring__and__Field_Oordered__idom_21 clsrel_Ring__and__Field_Oordered__idom_22 clsrel_Ring__and__Field_Oordered__idom_23 clsrel_Ring__and__Field_Oordered__idom_24 clsrel_Ring__and__Field_Oordered__idom_25 clsrel_Ring__and__Field_Oordered__idom_26 clsrel_Ring__and__Field_Oordered__idom_27 clsrel_Ring__and__Field_Oordered__idom_28 clsrel_Ring__and__Field_Oordered__idom_29 clsrel_Ring__and__Field_Oordered__idom_3 clsrel_Ring__and__Field_Oordered__idom_30 clsrel_Ring__and__Field_Oordered__idom_31 clsrel_Ring__and__Field_Oordered__idom_32 clsrel_Ring__and__Field_Oordered__idom_33 clsrel_Ring__and__Field_Oordered__idom_34 clsrel_Ring__and__Field_Oordered__idom_35 clsrel_Ring__and__Field_Oordered__idom_36 clsrel_Ring__and__Field_Oordered__idom_37 clsrel_Ring__and__Field_Oordered__idom_38 clsrel_Ring__and__Field_Oordered__idom_39 clsrel_Ring__and__Field_Oordered__idom_4 clsrel_Ring__and__Field_Oordered__idom_40 clsrel_Ring__and__Field_Oordered__idom_41 clsrel_Ring__and__Field_Oordered__idom_42 clsrel_Ring__and__Field_Oordered__idom_43 clsrel_Ring__and__Field_Oordered__idom_44 clsrel_Ring__and__Field_Oordered__idom_45 clsrel_Ring__and__Field_Oordered__idom_46 clsrel_Ring__and__Field_Oordered__idom_47 clsrel_Ring__and__Field_Oordered__idom_48 clsrel_Ring__and__Field_Oordered__idom_49 clsrel_Ring__and__Field_Oordered__idom_5 clsrel_Ring__and__Field_Oordered__idom_50 clsrel_Ring__and__Field_Oordered__idom_51 clsrel_Ring__and__Field_Oordered__idom_52 clsrel_Ring__and__Field_Oordered__idom_53 clsrel_Ring__and__Field_Oordered__idom_54 clsrel_Ring__and__Field_Oordered__idom_55 clsrel_Ring__and__Field_Oordered__idom_56 clsrel_Ring__and__Field_Oordered__idom_57 clsrel_Ring__and__Field_Oordered__idom_6 clsrel_Ring__and__Field_Oordered__idom_7 clsrel_Ring__and__Field_Oordered__idom_8 clsrel_Ring__and__Field_Oordered__idom_9
% 3.38/3.60  
%------------------------------------------------------------------------------