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
%------------------------------------------------------------------------------