TSTP Solution File: ALG379-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG379-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 18:03:31 EDT 2022
% Result : Unsatisfiable 9.94s 10.10s
% Output : Refutation 9.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 78
% Syntax : Number of clauses : 102 ( 81 unt; 1 nHn; 102 RR)
% Number of literals : 127 ( 0 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 69 ( 68 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(18,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),v,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('ALG379-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ c_lessequals(u,v,tc_RealDef_Oreal)
| equal(u,v)
| c_HOL_Oord__class_Oless(u,v,tc_RealDef_Oreal) ),
file('ALG379-1.p',unknown),
[] ).
cnf(199,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(v,c_HOL_Ouminus__class_Ouminus(w,u),u),c_HOL_Ominus__class_Ominus(v,w,u)) ),
file('ALG379-1.p',unknown),
[] ).
cnf(596,axiom,
~ c_HOL_Oord__class_Oless(u,u,tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(623,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),v,u),c_HOL_Ozero__class_Ozero(u)) ),
file('ALG379-1.p',unknown),
[] ).
cnf(626,axiom,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('ALG379-1.p',unknown),
[] ).
cnf(695,axiom,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),v,tc_RealDef_Oreal) ),
file('ALG379-1.p',unknown),
[] ).
cnf(713,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v,w,u),w,u),v) ),
file('ALG379-1.p',unknown),
[] ).
cnf(759,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(u)
| ~ equal(c_HOL_Oabs__class_Oabs(v,u),c_HOL_Ozero__class_Ozero(u))
| equal(v,c_HOL_Ozero__class_Ozero(u)) ),
file('ALG379-1.p',unknown),
[] ).
cnf(774,axiom,
c_lessequals(u,u,tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(832,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Oplus__class_Oplus(w,v,u),u),w) ),
file('ALG379-1.p',unknown),
[] ).
cnf(910,axiom,
equal(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('ALG379-1.p',unknown),
[] ).
cnf(913,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(947,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(948,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(949,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(950,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(951,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(952,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(953,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(954,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(955,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(956,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(957,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(958,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(959,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(960,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(961,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(962,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(963,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(964,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(965,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(966,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(967,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(968,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(969,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(970,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(971,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(972,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(973,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(974,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(975,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(976,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(977,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(978,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(979,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(980,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(981,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(982,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(983,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(984,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(985,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(986,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(987,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(988,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(989,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(990,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(991,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(992,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(993,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(994,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(995,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(996,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(997,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(998,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(999,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1000,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1001,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1002,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1003,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1004,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1005,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1006,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1007,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1008,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1009,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1010,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('ALG379-1.p',unknown),
[] ).
cnf(1097,axiom,
~ equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal)),
file('ALG379-1.p',unknown),
[] ).
cnf(1175,plain,
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[20,1097]),
[iquote('0:Res:20.2,1097.0')] ).
cnf(21113,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ouminus__class_Ouminus(v,u)) ),
inference(spr,[status(thm),theory(equality)],[623,832]),
[iquote('0:SpR:623.1,832.1')] ).
cnf(21191,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ouminus__class_Ouminus(v,u)) ),
inference(obv,[status(thm),theory(equality)],[21113]),
[iquote('0:Obv:21113.0')] ).
cnf(24662,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),u) ),
inference(spr,[status(thm),theory(equality)],[626,832]),
[iquote('0:SpR:626.0,832.1')] ).
cnf(24684,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),u) ),
inference(rew,[status(thm),theory(equality)],[21191,24662]),
[iquote('0:Rew:21191.1,24662.1')] ).
cnf(24685,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),u),
inference(ssi,[status(thm)],[24684,980,959,1001,996,988,954,949,1002,1000,995,992,985,982,977,976,974,968,967,966,964,957,997,994,991,965,963,956,952,950,1006,913,1004,993,962,947,989,987,983,972,970,1010,1007,973,998,978,955,1008,948,1009,984,990,981,961,951,999,1005,960,975,953,1003,971,958,986,969,979]),
[iquote('0:SSi:24684.0,980.0,959.0,1001.0,996.0,988.0,954.0,949.0,1002.0,1000.0,995.0,992.0,985.0,982.0,977.0,976.0,974.0,968.0,967.0,966.0,964.0,957.0,997.0,994.0,991.0,965.0,963.0,956.0,952.0,950.0,1006.0,913.0,1004.0,993.0,962.0,947.0,989.0,987.0,983.0,972.0,970.0,1010.0,1007.0,973.0,998.0,978.0,955.0,1008.0,948.0,1009.0,984.0,990.0,981.0,961.0,951.0,999.0,1005.0,960.0,975.0,953.0,1003.0,971.0,958.0,986.0,969.0,979.0')] ).
cnf(24792,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oplus__class_Oplus(v,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),v) ),
inference(spr,[status(thm),theory(equality)],[24685,832]),
[iquote('0:SpR:24685.0,832.1')] ).
cnf(24797,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[24685,199]),
[iquote('0:SpR:24685.0,199.1')] ).
cnf(24843,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ominus__class_Ominus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal),v) ),
inference(rew,[status(thm),theory(equality)],[199,24792]),
[iquote('0:Rew:199.1,24792.1')] ).
cnf(24844,plain,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ominus__class_Ominus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal),v),
inference(ssi,[status(thm)],[24843,980,959,1001,996,988,954,949,1002,1000,995,992,985,982,977,976,974,968,967,966,964,957,997,994,991,965,963,956,952,950,1006,913,1004,993,962,947,989,987,983,972,970,1010,1007,973,998,978,955,1008,948,1009,984,990,981,961,951,999,1005,960,975,953,1003,971,958,986,969,979]),
[iquote('0:SSi:24843.0,980.0,959.0,1001.0,996.0,988.0,954.0,949.0,1002.0,1000.0,995.0,992.0,985.0,982.0,977.0,976.0,974.0,968.0,967.0,966.0,964.0,957.0,997.0,994.0,991.0,965.0,963.0,956.0,952.0,950.0,1006.0,913.0,1004.0,993.0,962.0,947.0,989.0,987.0,983.0,972.0,970.0,1010.0,1007.0,973.0,998.0,978.0,955.0,1008.0,948.0,1009.0,984.0,990.0,981.0,961.0,951.0,999.0,1005.0,960.0,975.0,953.0,1003.0,971.0,958.0,986.0,969.0,979.0')] ).
cnf(24845,plain,
equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[24797,980,959,1001,996,988,954,949,1002,1000,995,992,985,982,977,976,974,968,967,966,964,957,997,994,991,965,963,956,952,950,1006,913,1004,993,962,947,989,987,983,972,970,1010,1007,973,998,978,955,1008,948,1009,984,990,981,961,951,999,1005,960,975,953,1003,971,958,986,969,979]),
[iquote('0:SSi:24797.0,980.0,959.0,1001.0,996.0,988.0,954.0,949.0,1002.0,1000.0,995.0,992.0,985.0,982.0,977.0,976.0,974.0,968.0,967.0,966.0,964.0,957.0,997.0,994.0,991.0,965.0,963.0,956.0,952.0,950.0,1006.0,913.0,1004.0,993.0,962.0,947.0,989.0,987.0,983.0,972.0,970.0,1010.0,1007.0,973.0,998.0,978.0,955.0,1008.0,948.0,1009.0,984.0,990.0,981.0,961.0,951.0,999.0,1005.0,960.0,975.0,953.0,1003.0,971.0,958.0,986.0,969.0,979.0')] ).
cnf(24846,plain,
equal(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rew,[status(thm),theory(equality)],[24845,910]),
[iquote('0:Rew:24845.0,910.0')] ).
cnf(25208,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[713,24844]),
[iquote('0:SpR:713.1,24844.0')] ).
cnf(25216,plain,
equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[25208,980,959,1001,996,988,954,949,1002,1000,995,992,985,982,977,976,974,968,967,966,964,957,997,994,991,965,963,956,952,950,1006,913,1004,993,962,947,989,987,983,972,970,1010,1007,973,998,978,955,1008,948,1009,984,990,981,961,951,999,1005,960,975,953,1003,971,958,986,969,979]),
[iquote('0:SSi:25208.0,980.0,959.0,1001.0,996.0,988.0,954.0,949.0,1002.0,1000.0,995.0,992.0,985.0,982.0,977.0,976.0,974.0,968.0,967.0,966.0,964.0,957.0,997.0,994.0,991.0,965.0,963.0,956.0,952.0,950.0,1006.0,913.0,1004.0,993.0,962.0,947.0,989.0,987.0,983.0,972.0,970.0,1010.0,1007.0,973.0,998.0,978.0,955.0,1008.0,948.0,1009.0,984.0,990.0,981.0,961.0,951.0,999.0,1005.0,960.0,975.0,953.0,1003.0,971.0,958.0,986.0,969.0,979.0')] ).
cnf(25265,plain,
equal(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(v_s____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rew,[status(thm),theory(equality)],[25216,24846]),
[iquote('0:Rew:25216.0,24846.0')] ).
cnf(29261,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(c_HOL_Oplus__class_Oplus(v_s____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spl,[status(thm),theory(equality)],[25265,759]),
[iquote('0:SpL:25265.0,759.1')] ).
cnf(29273,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(v_s____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(obv,[status(thm),theory(equality)],[29261]),
[iquote('0:Obv:29261.1')] ).
cnf(29274,plain,
equal(c_HOL_Oplus__class_Oplus(v_s____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[29273,980,959,1001,996,988,954,949,1002,1000,995,992,985,982,977,976,974,968,967,966,964,957,997,994,991,965,963,956,952,950,1006,913,1004,993,962,947,989,987,983,972,970,1010,1007,973,998,978,955,1008,948,1009,984,990,981,961,951,999,1005,960,975,953,1003,971,958,986,969,979]),
[iquote('0:SSi:29273.0,980.0,959.0,1001.0,996.0,988.0,954.0,949.0,1002.0,1000.0,995.0,992.0,985.0,982.0,977.0,976.0,974.0,968.0,967.0,966.0,964.0,957.0,997.0,994.0,991.0,965.0,963.0,956.0,952.0,950.0,1006.0,913.0,1004.0,993.0,962.0,947.0,989.0,987.0,983.0,972.0,970.0,1010.0,1007.0,973.0,998.0,978.0,955.0,1008.0,948.0,1009.0,984.0,990.0,981.0,961.0,951.0,999.0,1005.0,960.0,975.0,953.0,1003.0,971.0,958.0,986.0,969.0,979.0')] ).
cnf(34244,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spr,[status(thm),theory(equality)],[29274,18]),
[iquote('0:SpR:29274.0,18.1')] ).
cnf(34261,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(spl,[status(thm),theory(equality)],[29274,695]),
[iquote('0:SpL:29274.0,695.0')] ).
cnf(34281,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(mrr,[status(thm)],[34244,596]),
[iquote('0:MRR:34244.1,596.0')] ).
cnf(34282,plain,
~ c_lessequals(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(mrr,[status(thm)],[1175,34281]),
[iquote('0:MRR:1175.1,34281.0')] ).
cnf(34287,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(mrr,[status(thm)],[34261,774]),
[iquote('0:MRR:34261.0,774.0')] ).
cnf(34288,plain,
$false,
inference(mrr,[status(thm)],[34287,34282]),
[iquote('0:MRR:34287.0,34282.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG379-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n023.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 : Wed Jun 8 10:56:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 9.94/10.10
% 9.94/10.10 SPASS V 3.9
% 9.94/10.10 SPASS beiseite: Proof found.
% 9.94/10.10 % SZS status Theorem
% 9.94/10.10 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.94/10.10 SPASS derived 24774 clauses, backtracked 696 clauses, performed 4 splits and kept 8217 clauses.
% 9.94/10.10 SPASS allocated 98439 KBytes.
% 9.94/10.10 SPASS spent 0:00:09.72 on the problem.
% 9.94/10.10 0:00:00.08 for the input.
% 9.94/10.10 0:00:00.00 for the FLOTTER CNF translation.
% 9.94/10.10 0:00:00.25 for inferences.
% 9.94/10.10 0:00:00.25 for the backtracking.
% 9.94/10.10 0:00:08.93 for the reduction.
% 9.94/10.10
% 9.94/10.10
% 9.94/10.10 Here is a proof with depth 3, length 102 :
% 9.94/10.10 % SZS output start Refutation
% See solution above
% 9.94/10.10 Formulae used in the proof : cls_real__0__less__add__iff_1 cls_real__less__def_2 cls_ab__diff__minus_0 cls_real__less__def_1 cls_ab__left__minus_0 cls_real__add__eq__0__iff_1 cls_real__0__le__add__iff_0 cls_add__diff__cancel_0 cls_abs__eq__0_0 cls_real__le__refl_0 cls_add__cancel__end_1 cls_CHAINED_0 clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add 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_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__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_Olordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring 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_Ocomm__ring__1 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__Ring__and__Field_Ocomm__ring clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult clsarity_RealDef__Oreal__Ring__and__Field_Osemiring clsarity_RealDef__Oreal__RealVector_Oreal__algebra clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add clsarity_RealDef__Oreal__RealVector_Oreal__vector clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if 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__Ring__and__Field_Odvd clsarity_RealDef__Oreal__Orderings_Opreorder clsarity_RealDef__Oreal__Orderings_Olinorder clsarity_RealDef__Oreal__Orderings_Oorder clsarity_RealDef__Oreal__Int_Onumber__ring cls_conjecture_0
% 10.06/10.28
%------------------------------------------------------------------------------