TSTP Solution File: ALG211+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 18:03:00 EDT 2022

% Result   : Theorem 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   19 (   7 unt;   0 nHn;  19 RR)
%            Number of literals    :   37 (   0 equ;  23 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    a_vector_space(skc2),
    file('ALG211+1.p',unknown),
    [] ).

cnf(2,axiom,
    a_vector_subspace_of(skc3,skc2),
    file('ALG211+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ a_vector_subspace_of(u,v)
    | a_vector_space(u) ),
    file('ALG211+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ basis_of(u,v)
    | lin_ind_subset(u,v) ),
    file('ALG211+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ a_vector_space(u)
    | basis_of(skf3(u),u) ),
    file('ALG211+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ basis_of(u,v)
    | a_subset_of(u,vec_to_class(v)) ),
    file('ALG211+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ basis_of(u,skc3)
    | ~ basis_of(union(u,v),skc2) ),
    file('ALG211+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ basis_of(u,v)
    | ~ lin_ind_subset(w,v)
    | basis_of(union(w,skf2(u,v,w)),v) ),
    file('ALG211+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ a_vector_subspace_of(u,v)
    | ~ lin_ind_subset(w,u)
    | ~ a_subset_of(w,vec_to_class(u))
    | lin_ind_subset(w,v) ),
    file('ALG211+1.p',unknown),
    [] ).

cnf(12,plain,
    basis_of(skf3(skc2),skc2),
    inference(res,[status(thm),theory(equality)],[1,5]),
    [iquote('0:Res:1.0,5.0')] ).

cnf(13,plain,
    a_vector_space(skc3),
    inference(res,[status(thm),theory(equality)],[2,3]),
    [iquote('0:Res:2.0,3.0')] ).

cnf(15,plain,
    ( ~ lin_ind_subset(u,skc3)
    | ~ a_subset_of(u,vec_to_class(skc3))
    | lin_ind_subset(u,skc2) ),
    inference(res,[status(thm),theory(equality)],[2,10]),
    [iquote('0:Res:2.0,10.1')] ).

cnf(22,plain,
    ( ~ basis_of(u,skc3)
    | ~ lin_ind_subset(u,skc3)
    | lin_ind_subset(u,skc2) ),
    inference(res,[status(thm),theory(equality)],[6,15]),
    [iquote('0:Res:6.1,15.1')] ).

cnf(23,plain,
    ( ~ basis_of(u,skc3)
    | lin_ind_subset(u,skc2) ),
    inference(mrr,[status(thm)],[22,4]),
    [iquote('0:MRR:22.1,4.1')] ).

cnf(42,plain,
    ( ~ basis_of(u,skc2)
    | ~ lin_ind_subset(v,skc2)
    | ~ basis_of(v,skc3) ),
    inference(res,[status(thm),theory(equality)],[9,7]),
    [iquote('0:Res:9.2,7.1')] ).

cnf(43,plain,
    ( ~ basis_of(u,skc2)
    | ~ basis_of(v,skc3) ),
    inference(mrr,[status(thm)],[42,23]),
    [iquote('0:MRR:42.1,23.1')] ).

cnf(45,plain,
    ~ basis_of(u,skc3),
    inference(res,[status(thm),theory(equality)],[12,43]),
    [iquote('0:Res:12.0,43.0')] ).

cnf(48,plain,
    ~ a_vector_space(skc3),
    inference(res,[status(thm),theory(equality)],[5,45]),
    [iquote('0:Res:5.1,45.0')] ).

cnf(50,plain,
    $false,
    inference(ssi,[status(thm)],[48,13]),
    [iquote('0:SSi:48.0,13.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n022.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 06:41:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 29 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.18/0.42  SPASS allocated 97645 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.08 on the problem.
% 0.18/0.42  		0:00:00.03 for the input.
% 0.18/0.42  		0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.00 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 3, length 19 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : bg_2_4_3 bg_2_4_a basis_of bg_remark_63_a bg_2_2_5 bg_2_4_2
% 0.18/0.42  
%------------------------------------------------------------------------------