TSTP Solution File: ALG371-1 by SPASS---3.9

View Problem - 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  
%------------------------------------------------------------------------------