TSTP Solution File: ALG371-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG371-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 18:03:30 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 33
% Syntax : Number of clauses : 40 ( 33 unt; 0 nHn; 40 RR)
% Number of literals : 51 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(376,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_HOL_Oord__class_Oless(x,v,u)
| c_HOL_Oord__class_Oless(x,w,u) ),
file('ALG371-1.p',unknown),
[] ).
cnf(393,axiom,
( ~ class_RealVector_Oreal__normed__vector(u)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v,u),tc_RealDef_Oreal) ),
file('ALG371-1.p',unknown),
[] ).
cnf(420,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_HOL_Oord__class_Oless(v,w,u)
| ~ c_lessequals(w,v,u) ),
file('ALG371-1.p',unknown),
[] ).
cnf(471,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('ALG371-1.p',unknown),
[] ).
cnf(473,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('ALG371-1.p',unknown),
[] ).
cnf(476,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(477,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(478,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(479,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(480,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(481,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(482,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(483,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(484,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(485,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(486,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(487,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(488,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(489,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(490,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(491,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(492,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(493,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(494,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(495,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(496,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(497,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(498,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(499,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(500,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(501,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('ALG371-1.p',unknown),
[] ).
cnf(502,axiom,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('ALG371-1.p',unknown),
[] ).
cnf(503,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('ALG371-1.p',unknown),
[] ).
cnf(538,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_r,u,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[502,376]),
[iquote('0:Res:502.0,376.1')] ).
cnf(648,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_r,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[503,420]),
[iquote('0:Res:503.0,420.1')] ).
cnf(693,plain,
~ c_HOL_Oord__class_Oless(v_r,c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(mrr,[status(thm)],[648,471]),
[iquote('0:MRR:648.0,471.0')] ).
cnf(695,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),u,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_r,u,tc_RealDef_Oreal) ),
inference(mrr,[status(thm)],[538,473]),
[iquote('0:MRR:538.0,473.0')] ).
cnf(796,plain,
( ~ class_RealVector_Oreal__normed__vector(u)
| c_HOL_Oord__class_Oless(v_r,c_RealVector_Onorm__class_Onorm(v,u),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[393,695]),
[iquote('0:Res:393.1,695.0')] ).
cnf(815,plain,
~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(res,[status(thm),theory(equality)],[796,693]),
[iquote('0:Res:796.1,693.0')] ).
cnf(816,plain,
$false,
inference(ssi,[status(thm)],[815,501,496,495,492,489,488,487,485,478,476,497,493,490,481,480,479,494,477,500,499,484,491,486,498,483,482]),
[iquote('0:SSi:815.0,501.0,496.0,495.0,492.0,489.0,488.0,487.0,485.0,478.0,476.0,497.0,493.0,490.0,481.0,480.0,479.0,494.0,477.0,500.0,499.0,484.0,491.0,486.0,498.0,483.0,482.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG371-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 09:37:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 159 clauses, backtracked 13 clauses, performed 1 splits and kept 527 clauses.
% 0.19/0.53 SPASS allocated 76529 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.18 on the problem.
% 0.19/0.53 0:00:00.05 for the input.
% 0.19/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.00 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.07 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 3, length 40 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : cls_xt1_I8_J_0 cls_norm__ge__zero_0 cls_less__le__not__le_1 clsarity_RealDef__Oreal__Orderings_Opreorder clsarity_RealDef__Oreal__Orderings_Oorder clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add clsarity_Complex__Ocomplex__Ring__and__Field_Ofield clsarity_Complex__Ocomplex__Ring__and__Field_Oidom clsarity_Complex__Ocomplex__Int_Onumber__ring clsarity_Complex__Ocomplex__Power_Opower cls_conjecture_0 cls_conjecture_1
% 0.19/0.53
%------------------------------------------------------------------------------