TSTP Solution File: ALG342-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG342-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 18:03:24 EDT 2022
% Result : Unsatisfiable 180.32s 180.58s
% Output : Refutation 194.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 69
% Syntax : Number of clauses : 101 ( 65 unt; 12 nHn; 101 RR)
% Number of literals : 150 ( 0 equ; 46 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 56 ( 55 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(75,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(v,w,u),c_HOL_Oplus__class_Oplus(v,x,u),u)
| c_lessequals(w,x,u) ),
file('ALG342-1.p',unknown),
[] ).
cnf(123,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(u),v,u),v) ),
file('ALG342-1.p',unknown),
[] ).
cnf(124,axiom,
( ~ class_Int_Onumber__ring(u)
| ~ class_Ring__and__Field_Oidom(u)
| equal(c_HOL_Oplus__class_Oplus(v,c_HOL_Ozero__class_Ozero(u),u),v) ),
file('ALG342-1.p',unknown),
[] ).
cnf(266,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v,w,u),x,u),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v,x,u),w,u)) ),
file('ALG342-1.p',unknown),
[] ).
cnf(268,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v,w,u),x,u),c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(w,x,u),u)) ),
file('ALG342-1.p',unknown),
[] ).
cnf(270,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v,w,u),x,u),c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(w,x,u),u)) ),
file('ALG342-1.p',unknown),
[] ).
cnf(319,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Oplus__class_Oplus(v,w,u),c_HOL_Oplus__class_Oplus(w,v,u)) ),
file('ALG342-1.p',unknown),
[] ).
cnf(386,axiom,
c_lessequals(u,u,tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(387,axiom,
( ~ c_lessequals(u,v,tc_RealDef_Oreal)
| ~ c_lessequals(v,w,tc_RealDef_Oreal)
| c_lessequals(u,w,tc_RealDef_Oreal) ),
file('ALG342-1.p',unknown),
[] ).
cnf(395,axiom,
~ c_HOL_Oord__class_Oless(u,u,tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(406,axiom,
( ~ c_lessequals(u,v,tc_RealDef_Oreal)
| equal(u,v)
| c_HOL_Oord__class_Oless(u,v,tc_RealDef_Oreal) ),
file('ALG342-1.p',unknown),
[] ).
cnf(428,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_HOL_Oord__class_Oless(v,w,u)
| ~ c_lessequals(w,v,u) ),
file('ALG342-1.p',unknown),
[] ).
cnf(434,axiom,
( ~ class_Orderings_Olinorder(u)
| c_lessequals(v,w,u)
| c_HOL_Oord__class_Oless(w,v,u) ),
file('ALG342-1.p',unknown),
[] ).
cnf(436,axiom,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('ALG342-1.p',unknown),
[] ).
cnf(437,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(442,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(443,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(444,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(445,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(446,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(447,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(448,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(449,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(450,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(451,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(452,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(453,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(454,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(455,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(456,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(457,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(458,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(459,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(460,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(461,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(462,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(463,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(464,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(465,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(466,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(467,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(468,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(469,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(470,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(471,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(472,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(473,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(474,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(475,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(476,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(477,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(478,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(479,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(480,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(481,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(482,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(483,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(484,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(485,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(486,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(487,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(488,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(489,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(490,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(491,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(492,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(493,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
file('ALG342-1.p',unknown),
[] ).
cnf(564,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(u),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('ALG342-1.p',unknown),
[] ).
cnf(565,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(u),tc_Complex_Ocomplex),tc_Complex_Ocomplex),u,tc_RealDef_Oreal) ),
file('ALG342-1.p',unknown),
[] ).
cnf(570,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(w,x,u),u),c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(x,w,u),u)) ),
inference(rew,[status(thm),theory(equality)],[270,266]),
[iquote('0:Rew:270.1,266.1,270.1,266.1')] ).
cnf(1148,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_lessequals(u,v,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(u,w,tc_RealDef_Oreal)
| c_lessequals(w,v,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[434,387]),
[iquote('0:Res:434.1,387.0')] ).
cnf(1151,plain,
( ~ c_lessequals(u,v,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(u,w,tc_RealDef_Oreal)
| c_lessequals(w,v,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[1148,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:1148.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(1672,plain,
( c_HOL_Oord__class_Oless(u,v,tc_RealDef_Oreal)
| c_lessequals(v,u,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[386,1151]),
[iquote('0:Res:386.0,1151.0')] ).
cnf(22180,plain,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,w,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(w,v,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[1672,75]),
[iquote('0:Res:1672.1,75.1')] ).
cnf(22220,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,w,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(w,v,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[22180,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:22180.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(44448,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(w,u,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(w,v,tc_RealDef_Oreal) ),
inference(spr,[status(thm),theory(equality)],[319,22220]),
[iquote('0:SpR:319.1,22220.0')] ).
cnf(44504,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(w,u,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(w,v,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[44448,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:44448.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(48901,plain,
( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal),v,tc_RealDef_Oreal)
| c_lessequals(v,u,tc_RealDef_Oreal) ),
inference(spr,[status(thm),theory(equality)],[124,44504]),
[iquote('0:SpR:124.2,44504.0')] ).
cnf(48973,plain,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal),v,tc_RealDef_Oreal)
| c_lessequals(v,u,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[48901,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:48901.1,48901.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(49079,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal),u,tc_RealDef_Oreal),
inference(res,[status(thm),theory(equality)],[48973,395]),
[iquote('0:Res:48973.0,395.0')] ).
cnf(49190,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spr,[status(thm),theory(equality)],[570,49079]),
[iquote('0:SpR:570.1,49079.0')] ).
cnf(49194,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(u,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[49079,428]),
[iquote('0:Res:49079.0,428.2')] ).
cnf(49240,plain,
~ c_HOL_Oord__class_Oless(u,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[49194,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:49194.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(49248,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[123,49190]),
[iquote('0:Rew:123.1,49190.1')] ).
cnf(49249,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[49248,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:49248.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(49859,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spl,[status(thm),theory(equality)],[570,49240]),
[iquote('0:SpL:570.1,49240.0')] ).
cnf(49928,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[123,49859]),
[iquote('0:Rew:123.1,49859.1')] ).
cnf(49929,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[49928,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:49928.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(49999,plain,
( equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal))
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[49249,406]),
[iquote('0:Res:49249.0,406.0')] ).
cnf(50422,plain,
equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal)),
inference(mrr,[status(thm)],[49999,49929]),
[iquote('0:MRR:49999.1,49929.0')] ).
cnf(50486,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[50422,437]),
[iquote('0:Rew:50422.0,437.0')] ).
cnf(50487,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[50422,436]),
[iquote('0:Rew:50422.0,436.1')] ).
cnf(51174,plain,
( ~ class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(u,w,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[50422,268]),
[iquote('0:SpR:50422.0,268.1')] ).
cnf(51438,plain,
( ~ class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oplus__class_Oplus(v,w,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(u,w,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[268,51174]),
[iquote('0:Rew:268.1,51174.1')] ).
cnf(51439,plain,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oplus__class_Oplus(v,w,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(u,w,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[51438,485,478,456,446,492,483,482,481,476,474,473,470,469,467,460,459,455,453,448,484,461,458,450,447,443,493,480,479,471,452,442,463,444,466,491,489,465,468,457,490,488,487,451,445,475,449,486,464,477,454,462,472]),
[iquote('0:SSi:51438.0,485.0,478.0,456.0,446.0,492.0,483.0,482.0,481.0,476.0,474.0,473.0,470.0,469.0,467.0,460.0,459.0,455.0,453.0,448.0,484.0,461.0,458.0,450.0,447.0,443.0,493.0,480.0,479.0,471.0,452.0,442.0,463.0,444.0,466.0,491.0,489.0,465.0,468.0,457.0,490.0,488.0,487.0,451.0,445.0,475.0,449.0,486.0,464.0,477.0,454.0,462.0,472.0')] ).
cnf(51440,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[51439,50486]),
[iquote('0:Rew:51439.0,50486.0')] ).
cnf(51441,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[51439,50487]),
[iquote('0:Rew:51439.0,50487.1')] ).
cnf(51463,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[50422,51440]),
[iquote('0:Rew:50422.0,51440.0')] ).
cnf(51464,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rew,[status(thm),theory(equality)],[50422,51441]),
[iquote('0:Rew:50422.0,51441.1')] ).
cnf(163654,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_r,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[51464,565]),
[iquote('0:Res:51464.1,565.1')] ).
cnf(163659,plain,
$false,
inference(mrr,[status(thm)],[163654,564,51463]),
[iquote('0:MRR:163654.0,163654.1,564.1,51463.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ALG342-1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Wed Jun 8 12:37:06 EDT 2022
% 0.09/0.28 % CPUTime :
% 180.32/180.58
% 180.32/180.58 SPASS V 3.9
% 180.32/180.58 SPASS beiseite: Proof found.
% 180.32/180.58 % SZS status Theorem
% 180.32/180.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 180.32/180.58 SPASS derived 134142 clauses, backtracked 9950 clauses, performed 14 splits and kept 39415 clauses.
% 180.32/180.58 SPASS allocated 187548 KBytes.
% 180.32/180.58 SPASS spent 0:03:00.03 on the problem.
% 180.32/180.58 0:00:00.05 for the input.
% 180.32/180.58 0:00:00.00 for the FLOTTER CNF translation.
% 180.32/180.58 0:00:01.41 for inferences.
% 180.32/180.58 0:00:07.91 for the backtracking.
% 180.32/180.58 0:2:49.59 for the reduction.
% 180.32/180.58
% 180.32/180.58
% 180.32/180.58 Here is a proof with depth 9, length 101 :
% 180.32/180.58 % SZS output start Refutation
% See solution above
% 194.37/194.62 Formulae used in the proof : cls_add__le__cancel__left_0 cls_class__semiring_Oadd__0_0 cls_class__ringb_Oadd__r0__iff_1 cls_class__semiring_Osemiring__rules_I23_J_0 cls_ab__semigroup__add__class_Oadd__ac_I1_J_0 cls_class__semiring_Oadd__a_0 cls_class__semiring_Oadd__c_0 cls_real__le__refl_0 cls_real__le__trans_0 cls_real__less__def_1 cls_real__less__def_2 cls_less__le__not__le_1 cls_linorder__not__le_0 cls_CHAINED_0 cls_CHAINED_0_01 clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1 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__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_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__Ring__and__Field_Ocomm__semiring__0 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_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__Ring__and__Field_Osgn__if clsarity_RealDef__Oreal__Ring__and__Field_Ofield 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 clsarity_RealDef__Oreal__HOL_Ozero cls_conjecture_0 cls_conjecture_1
% 194.37/194.62
%------------------------------------------------------------------------------