TSTP Solution File: SWV620-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWV620-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 : Wed Jul 20 21:44:35 EDT 2022

% Result   : Unsatisfiable 1.78s 2.06s
% Output   : Refutation 1.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   65
% Syntax   : Number of clauses     :   83 (  66 unt;   4 nHn;  83 RR)
%            Number of literals    :  117 (   0 equ;  39 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   55 (  54 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;  10 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(115,axiom,
    ~ equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
    file('SWV620-1.p',unknown),
    [] ).

cnf(126,axiom,
    ( ~ class_Orderings_Olinorder(u)
    | c_lessequals(v,w,u)
    | c_HOL_Oord__class_Oless(w,v,u) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(139,axiom,
    ( ~ class_Orderings_Oorder(u)
    | ~ c_lessequals(v,w,u)
    | equal(w,v)
    | c_HOL_Oord__class_Oless(v,w,u) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(315,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(u)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(u),v,u)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(u),w,u)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(u),c_HOL_Oinverse__class_Odivide(v,w,u),u) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(373,axiom,
    ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_lessequals(v,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(419,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(u)
    | ~ class_Ring__and__Field_Oordered__field(u)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(u),v,u)
    | c_HOL_Oord__class_Oless(w,c_HOL_Ozero__class_Ozero(u),u)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(u),w,u)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(x,w,u),v,u) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(457,axiom,
    ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(u,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(460,axiom,
    ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(553,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(u)
    | ~ c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)
    | c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(645,axiom,
    ( ~ class_Int_Onumber__ring(u)
    | equal(c_HOL_Otimes__class_Otimes(v,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),u),u),c_HOL_Oplus__class_Oplus(v,v,u)) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(711,axiom,
    equal(c_HOL_Otimes__class_Otimes(u,v,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v,u,tc_RealDef_Oreal)),
    file('SWV620-1.p',unknown),
    [] ).

cnf(718,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file('SWV620-1.p',unknown),
    [] ).

cnf(719,axiom,
    c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
    file('SWV620-1.p',unknown),
    [] ).

cnf(797,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(798,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(799,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(800,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(801,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(802,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(803,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(804,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(805,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(806,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(807,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(808,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(809,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(810,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(811,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(812,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(813,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(814,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(815,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(816,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(817,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(818,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(819,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(820,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(821,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(822,axiom,
    class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(823,axiom,
    class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(824,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(825,axiom,
    class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(826,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(827,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(828,axiom,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(829,axiom,
    class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(830,axiom,
    class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(831,axiom,
    class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(832,axiom,
    class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(833,axiom,
    class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(834,axiom,
    class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(835,axiom,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(836,axiom,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(837,axiom,
    class_RealVector_Oreal__field(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(838,axiom,
    class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(839,axiom,
    class_Ring__and__Field_Oring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(840,axiom,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(841,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(842,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(843,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(844,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(845,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(846,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(847,axiom,
    class_Int_Onumber(tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(877,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('SWV620-1.p',unknown),
    [] ).

cnf(919,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(rew,[status(thm),theory(equality)],[711,877]),
    [iquote('0:Rew:711.0,877.0')] ).

cnf(922,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(v_k,tc_nat),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(rew,[status(thm),theory(equality)],[711,718]),
    [iquote('0:Rew:711.0,718.2,711.0,718.0')] ).

cnf(923,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(mrr,[status(thm)],[922,719,919]),
    [iquote('0:MRR:922.1,922.2,719.0,919.0')] ).

cnf(997,plain,
    ( ~ class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[315,923]),
    [iquote('0:Res:315.3,923.0')] ).

cnf(1051,plain,
    ( ~ class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal)
    | ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_RealDef_Oreal(v_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[419,919]),
    [iquote('0:Res:419.3,919.0')] ).

cnf(1055,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(mrr,[status(thm)],[997,823]),
    [iquote('0:MRR:997.0,823.0')] ).

cnf(1061,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(mrr,[status(thm)],[1051,823,815,457,1055]),
    [iquote('0:MRR:1051.0,1051.1,1051.3,1051.4,823.0,815.0,457.0,1055.0')] ).

cnf(2872,plain,
    ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
    | c_lessequals(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[126,1061]),
    [iquote('0:Res:126.2,1061.0')] ).

cnf(2873,plain,
    c_lessequals(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(ssi,[status(thm)],[2872,837,844,829,801,799,846,833,832,827,824,821,820,819,813,812,806,835,825,814,811,805,803,800,834,831,816,810,797,842,839,828,847,818,840,843,841,826,830,822,804,798,809,802,836,817,845,808,838,807,815,823]),
    [iquote('0:SSi:2872.0,837.0,844.0,829.0,801.0,799.0,846.0,833.0,832.0,827.0,824.0,821.0,820.0,819.0,813.0,812.0,806.0,835.0,825.0,814.0,811.0,805.0,803.0,800.0,834.0,831.0,816.0,810.0,797.0,842.0,839.0,828.0,847.0,818.0,840.0,843.0,841.0,826.0,830.0,822.0,804.0,798.0,809.0,802.0,836.0,817.0,845.0,808.0,838.0,807.0,815.0,823.0')] ).

cnf(12143,plain,
    ( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
    | ~ c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi) ),
    inference(res,[status(thm),theory(equality)],[139,460]),
    [iquote('0:Res:139.3,460.0')] ).

cnf(12775,plain,
    ( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(spr,[status(thm),theory(equality)],[645,2873]),
    [iquote('0:SpR:645.1,2873.0')] ).

cnf(12863,plain,
    c_lessequals(c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(ssi,[status(thm)],[12775,837,844,829,801,799,846,833,832,827,824,821,820,819,813,812,806,835,825,814,811,805,803,800,834,831,816,810,797,842,839,828,847,818,840,843,841,826,830,822,804,798,809,802,836,817,845,808,838,807,815,823]),
    [iquote('0:SSi:12775.0,837.0,844.0,829.0,801.0,799.0,846.0,833.0,832.0,827.0,824.0,821.0,820.0,819.0,813.0,812.0,806.0,835.0,825.0,814.0,811.0,805.0,803.0,800.0,834.0,831.0,816.0,810.0,797.0,842.0,839.0,828.0,847.0,818.0,840.0,843.0,841.0,826.0,830.0,822.0,804.0,798.0,809.0,802.0,836.0,817.0,845.0,808.0,838.0,807.0,815.0,823.0')] ).

cnf(12970,plain,
    c_lessequals(c_Transcendental_Opi,c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(res,[status(thm),theory(equality)],[12863,373]),
    [iquote('0:Res:12863.0,373.0')] ).

cnf(12981,plain,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
    | c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[12970,553]),
    [iquote('0:Res:12970.0,553.1')] ).

cnf(12987,plain,
    c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(ssi,[status(thm)],[12981,837,844,829,801,799,846,833,832,827,824,821,820,819,813,812,806,835,825,814,811,805,803,800,834,831,816,810,797,842,839,828,847,818,840,843,841,826,830,822,804,798,809,802,836,817,845,808,838,807,815,823]),
    [iquote('0:SSi:12981.0,837.0,844.0,829.0,801.0,799.0,846.0,833.0,832.0,827.0,824.0,821.0,820.0,819.0,813.0,812.0,806.0,835.0,825.0,814.0,811.0,805.0,803.0,800.0,834.0,831.0,816.0,810.0,797.0,842.0,839.0,828.0,847.0,818.0,840.0,843.0,841.0,826.0,830.0,822.0,804.0,798.0,809.0,802.0,836.0,817.0,845.0,808.0,838.0,807.0,815.0,823.0')] ).

cnf(13011,plain,
    ( ~ c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi) ),
    inference(ssi,[status(thm)],[12143,837,844,829,801,799,846,833,832,827,824,821,820,819,813,812,806,835,825,814,811,805,803,800,834,831,816,810,797,842,839,828,847,818,840,843,841,826,830,822,804,798,809,802,836,817,845,808,838,807,815,823]),
    [iquote('0:SSi:12143.0,837.0,844.0,829.0,801.0,799.0,846.0,833.0,832.0,827.0,824.0,821.0,820.0,819.0,813.0,812.0,806.0,835.0,825.0,814.0,811.0,805.0,803.0,800.0,834.0,831.0,816.0,810.0,797.0,842.0,839.0,828.0,847.0,818.0,840.0,843.0,841.0,826.0,830.0,822.0,804.0,798.0,809.0,802.0,836.0,817.0,845.0,808.0,838.0,807.0,815.0,823.0')] ).

cnf(13012,plain,
    ~ c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(mrr,[status(thm)],[13011,115]),
    [iquote('0:MRR:13011.1,115.0')] ).

cnf(13013,plain,
    $false,
    inference(mrr,[status(thm)],[13012,12987]),
    [iquote('0:MRR:13012.0,12987.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWV620-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n020.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 : Tue Jun 14 19:46:04 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 1.78/2.06  
% 1.78/2.06  SPASS V 3.9 
% 1.78/2.06  SPASS beiseite: Proof found.
% 1.78/2.06  % SZS status Theorem
% 1.78/2.06  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.78/2.06  SPASS derived 9657 clauses, backtracked 128 clauses, performed 2 splits and kept 2521 clauses.
% 1.78/2.06  SPASS allocated 83813 KBytes.
% 1.78/2.06  SPASS spent	0:00:01.69 on the problem.
% 1.78/2.06  		0:00:00.07 for the input.
% 1.78/2.06  		0:00:00.00 for the FLOTTER CNF translation.
% 1.78/2.06  		0:00:00.10 for inferences.
% 1.78/2.06  		0:00:00.02 for the backtracking.
% 1.78/2.06  		0:00:01.37 for the reduction.
% 1.78/2.06  
% 1.78/2.06  
% 1.78/2.06  Here is a proof with depth 5, length 83 :
% 1.78/2.06  % SZS output start Refutation
% See solution above
% 1.78/2.06  Formulae used in the proof : cls_pi__neq__zero_0 cls_not__leE_0 cls_xt1_I11_J_0 cls_divide__pos__pos_0 cls_real__add__le__0__iff_0 cls_divide__less__eq_3 cls_not__real__of__nat__less__zero_0 cls_pi__not__less__zero_0 cls_le__minus__self__iff_0 cls_mult__2__right_0 cls_real__mult__commute_0 cls_CHAINED_0 cls_CHAINED_0_01 clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring clsarity_RealDef__Oreal__RealVector_Oreal__normed__field clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1 clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult clsarity_RealDef__Oreal__Ring__and__Field_Osemiring clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add clsarity_RealDef__Oreal__RealVector_Oreal__field clsarity_RealDef__Oreal__Ring__and__Field_Ofield clsarity_RealDef__Oreal__Ring__and__Field_Oring clsarity_RealDef__Oreal__Ring__and__Field_Oidom clsarity_RealDef__Oreal__Orderings_Opreorder clsarity_RealDef__Oreal__Orderings_Olinorder clsarity_RealDef__Oreal__Orderings_Oorder clsarity_RealDef__Oreal__Int_Oring__char__0 clsarity_RealDef__Oreal__Int_Onumber__ring clsarity_RealDef__Oreal__Power_Opower clsarity_RealDef__Oreal__Int_Onumber cls_conjecture_0
% 1.92/2.14  
%------------------------------------------------------------------------------