TSTP Solution File: ALG406-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG406-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 18:03:35 EDT 2022

% Result   : Unsatisfiable 1.58s 1.79s
% Output   : Refutation 1.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   69
% Syntax   : Number of clauses     :   85 (  71 unt;   1 nHn;  85 RR)
%            Number of literals    :  109 (   0 equ;  34 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   62 (  61 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(27,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(118,axiom,
    ( ~ class_Orderings_Oorder(u)
    | ~ c_HOL_Oord__class_Oless(v,w,u)
    | c_lessequals(v,w,u) ),
    file('ALG406-1.p',unknown),
    [] ).

cnf(379,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(u)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)
    | c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) ),
    file('ALG406-1.p',unknown),
    [] ).

cnf(430,axiom,
    ( ~ class_Ring__and__Field_Oabs__if(u)
    | equal(c_HOL_Oabs__class_Oabs(v,u),v)
    | c_HOL_Oord__class_Oless(v,c_HOL_Ozero__class_Ozero(u),u) ),
    file('ALG406-1.p',unknown),
    [] ).

cnf(452,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(u)
    | c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Oabs__class_Oabs(v,u),u) ),
    file('ALG406-1.p',unknown),
    [] ).

cnf(457,axiom,
    ( ~ class_Orderings_Olinorder(u)
    | ~ c_HOL_Oord__class_Oless(v,w,u)
    | ~ c_HOL_Oord__class_Oless(w,v,u) ),
    file('ALG406-1.p',unknown),
    [] ).

cnf(506,axiom,
    c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(508,axiom,
    c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(510,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(u)
    | ~ c_lessequals(v,c_HOL_Oone__class_Oone(u),u)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)
    | c_lessequals(c_HOL_Otimes__class_Otimes(v,w,u),w,u) ),
    file('ALG406-1.p',unknown),
    [] ).

cnf(552,axiom,
    equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),u,tc_RealDef_Oreal),u),
    file('ALG406-1.p',unknown),
    [] ).

cnf(589,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(590,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(591,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(592,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(593,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(594,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(595,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(596,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(597,axiom,
    class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(598,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(599,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(600,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(601,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(602,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(603,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(604,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(605,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(606,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(607,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(608,axiom,
    class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(609,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(610,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(611,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(612,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(613,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(614,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(615,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(616,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(617,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(618,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(619,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(620,axiom,
    class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(621,axiom,
    class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(622,axiom,
    class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(623,axiom,
    class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(624,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(625,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(626,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(627,axiom,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(628,axiom,
    class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(629,axiom,
    class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(630,axiom,
    class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(631,axiom,
    class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(632,axiom,
    class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(633,axiom,
    class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(634,axiom,
    class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(635,axiom,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(636,axiom,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(637,axiom,
    class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(638,axiom,
    class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(639,axiom,
    class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(640,axiom,
    class_Ring__and__Field_Oring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(641,axiom,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(642,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(643,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(644,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(645,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(646,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(678,axiom,
    ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('ALG406-1.p',unknown),
    [] ).

cnf(683,plain,
    ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(rew,[status(thm),theory(equality)],[552,678]),
    [iquote('0:Rew:552.0,678.0')] ).

cnf(726,plain,
    ( ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
    | ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[510,683]),
    [iquote('0:Res:510.4,683.0')] ).

cnf(728,plain,
    ( ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(mrr,[status(thm)],[726,627]),
    [iquote('0:MRR:726.0,627.0')] ).

cnf(3858,plain,
    ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[27,457]),
    [iquote('0:Res:27.0,457.1')] ).

cnf(3888,plain,
    ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(ssi,[status(thm)],[3858,622,638,637,628,609,602,593,591,646,634,632,624,619,616,610,607,600,597,640,635,626,620,618,611,608,606,599,595,592,631,639,633,605,589,630,629,645,641,617,643,644,642,625,636,598,590,623,604,594,603,613,627,596,614,615,612,621,601]),
    [iquote('0:SSi:3858.0,622.0,638.0,637.0,628.0,609.0,602.0,593.0,591.0,646.0,634.0,632.0,624.0,619.0,616.0,610.0,607.0,600.0,597.0,640.0,635.0,626.0,620.0,618.0,611.0,608.0,606.0,599.0,595.0,592.0,631.0,639.0,633.0,605.0,589.0,630.0,629.0,645.0,641.0,617.0,643.0,644.0,642.0,625.0,636.0,598.0,590.0,623.0,604.0,594.0,603.0,613.0,627.0,596.0,614.0,615.0,612.0,621.0,601.0')] ).

cnf(3902,plain,
    ( ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
    | equal(c_HOL_Oabs__class_Oabs(v_t____,tc_RealDef_Oreal),v_t____) ),
    inference(res,[status(thm),theory(equality)],[430,3888]),
    [iquote('0:Res:430.2,3888.0')] ).

cnf(3903,plain,
    equal(c_HOL_Oabs__class_Oabs(v_t____,tc_RealDef_Oreal),v_t____),
    inference(ssi,[status(thm)],[3902,622,638,637,628,609,602,593,591,646,634,632,624,619,616,610,607,600,597,640,635,626,620,618,611,608,606,599,595,592,631,639,633,605,589,630,629,645,641,617,643,644,642,625,636,598,590,623,604,594,603,613,627,596,614,615,612,621,601]),
    [iquote('0:SSi:3902.0,622.0,638.0,637.0,628.0,609.0,602.0,593.0,591.0,646.0,634.0,632.0,624.0,619.0,616.0,610.0,607.0,600.0,597.0,640.0,635.0,626.0,620.0,618.0,611.0,608.0,606.0,599.0,595.0,592.0,631.0,639.0,633.0,605.0,589.0,630.0,629.0,645.0,641.0,617.0,643.0,644.0,642.0,625.0,636.0,598.0,590.0,623.0,604.0,594.0,603.0,613.0,627.0,596.0,614.0,615.0,612.0,621.0,601.0')] ).

cnf(3905,plain,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
    inference(spr,[status(thm),theory(equality)],[3903,452]),
    [iquote('0:SpR:3903.0,452.1')] ).

cnf(3914,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
    inference(ssi,[status(thm)],[3905,622,638,637,628,609,602,593,591,646,634,632,624,619,616,610,607,600,597,640,635,626,620,618,611,608,606,599,595,592,631,639,633,605,589,630,629,645,641,617,643,644,642,625,636,598,590,623,604,594,603,613,627,596,614,615,612,621,601]),
    [iquote('0:SSi:3905.0,622.0,638.0,637.0,628.0,609.0,602.0,593.0,591.0,646.0,634.0,632.0,624.0,619.0,616.0,610.0,607.0,600.0,597.0,640.0,635.0,626.0,620.0,618.0,611.0,608.0,606.0,599.0,595.0,592.0,631.0,639.0,633.0,605.0,589.0,630.0,629.0,645.0,641.0,617.0,643.0,644.0,642.0,625.0,636.0,598.0,590.0,623.0,604.0,594.0,603.0,613.0,627.0,596.0,614.0,615.0,612.0,621.0,601.0')] ).

cnf(3915,plain,
    ( ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(mrr,[status(thm)],[728,3914]),
    [iquote('0:MRR:728.1,3914.0')] ).

cnf(9860,plain,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[506,379]),
    [iquote('0:Res:506.0,379.1')] ).

cnf(9878,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(ssi,[status(thm)],[9860,622,638,637,628,609,602,593,591,646,634,632,624,619,616,610,607,600,597,640,635,626,620,618,611,608,606,599,595,592,631,639,633,605,589,630,629,645,641,617,643,644,642,625,636,598,590,623,604,594,603,613,627,596,614,615,612,621,601]),
    [iquote('0:SSi:9860.0,622.0,638.0,637.0,628.0,609.0,602.0,593.0,591.0,646.0,634.0,632.0,624.0,619.0,616.0,610.0,607.0,600.0,597.0,640.0,635.0,626.0,620.0,618.0,611.0,608.0,606.0,599.0,595.0,592.0,631.0,639.0,633.0,605.0,589.0,630.0,629.0,645.0,641.0,617.0,643.0,644.0,642.0,625.0,636.0,598.0,590.0,623.0,604.0,594.0,603.0,613.0,627.0,596.0,614.0,615.0,612.0,621.0,601.0')] ).

cnf(9879,plain,
    ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(mrr,[status(thm)],[3915,9878]),
    [iquote('0:MRR:3915.1,9878.0')] ).

cnf(9888,plain,
    ( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(res,[status(thm),theory(equality)],[118,9879]),
    [iquote('0:Res:118.2,9879.0')] ).

cnf(9896,plain,
    ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(ssi,[status(thm)],[9888,622,638,637,628,609,602,593,591,646,634,632,624,619,616,610,607,600,597,640,635,626,620,618,611,608,606,599,595,592,631,639,633,605,589,630,629,645,641,617,643,644,642,625,636,598,590,623,604,594,603,613,627,596,614,615,612,621,601]),
    [iquote('0:SSi:9888.0,622.0,638.0,637.0,628.0,609.0,602.0,593.0,591.0,646.0,634.0,632.0,624.0,619.0,616.0,610.0,607.0,600.0,597.0,640.0,635.0,626.0,620.0,618.0,611.0,608.0,606.0,599.0,595.0,592.0,631.0,639.0,633.0,605.0,589.0,630.0,629.0,645.0,641.0,617.0,643.0,644.0,642.0,625.0,636.0,598.0,590.0,623.0,604.0,594.0,603.0,613.0,627.0,596.0,614.0,615.0,612.0,621.0,601.0')] ).

cnf(9897,plain,
    $false,
    inference(mrr,[status(thm)],[9896,508]),
    [iquote('0:MRR:9896.0,508.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG406-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jun  7 23:15:49 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 1.58/1.79  
% 1.58/1.79  SPASS V 3.9 
% 1.58/1.79  SPASS beiseite: Proof found.
% 1.58/1.79  % SZS status Theorem
% 1.58/1.79  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.58/1.79  SPASS derived 7243 clauses, backtracked 340 clauses, performed 1 splits and kept 2536 clauses.
% 1.58/1.79  SPASS allocated 82337 KBytes.
% 1.58/1.79  SPASS spent	0:00:01.44 on the problem.
% 1.58/1.79  		0:00:00.06 for the input.
% 1.58/1.79  		0:00:00.00 for the FLOTTER CNF translation.
% 1.58/1.79  		0:00:00.09 for inferences.
% 1.58/1.79  		0:00:00.01 for the backtracking.
% 1.58/1.79  		0:00:01.19 for the reduction.
% 1.58/1.79  
% 1.58/1.79  
% 1.58/1.79  Here is a proof with depth 3, length 85 :
% 1.58/1.79  % SZS output start Refutation
% See solution above
% 1.64/1.82  Formulae used in the proof : cls_t_I1_J_0 cls_order__le__less_1 cls_neg__less__eq__nonneg_0 cls_abs__if_1 cls_abs__ge__zero_0 cls_not__less__iff__gr__or__eq_1 cls_complex__mod__minus__le__complex__mod_0 cls_t_I2_J_0 cls_mult__left__le__one__le_0 cls_real__mult__1_0 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__ab__group__add__abs clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs 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__RealVector_Oreal__normed__div__algebra 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_Opordered__ring__abs clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1 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__RealVector_Oreal__normed__vector 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_Olordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring 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__RealVector_Oreal__algebra__1 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__Ring__and__Field_Oring__1 clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if 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_Onumber__ring clsarity_RealDef__Oreal__Power_Opower cls_conjecture_0
% 1.64/1.82  
%------------------------------------------------------------------------------