TSTP Solution File: SET014-2 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 : Tue Jul 19 05:22:29 EDT 2022

% Result   : Unsatisfiable 2.04s 2.19s
% Output   : Refutation 2.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   17 (   6 unt;   6 nHn;  17 RR)
%            Number of literals    :   32 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subset(as,cs),
    file('SET014-2.p',unknown),
    [] ).

cnf(2,axiom,
    subset(bs,cs),
    file('SET014-2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ subset(union(as,bs),cs),
    file('SET014-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ subset(u,v)
    | ~ member(w,u)
    | member(w,v) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( subset(u,v)
    | member(member_of_1_not_of_2(u,v),u) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ member(member_of_1_not_of_2(u,v),v)
    | subset(u,v) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ member(u,union(v,w))
    | member(u,w)
    | member(u,v) ),
    file('SET014-2.p',unknown),
    [] ).

cnf(43,plain,
    ( ~ member(u,bs)
    | member(u,cs) ),
    inference(res,[status(thm),theory(equality)],[2,5]),
    [iquote('0:Res:2.0,5.0')] ).

cnf(44,plain,
    ( ~ member(u,as)
    | member(u,cs) ),
    inference(res,[status(thm),theory(equality)],[1,5]),
    [iquote('0:Res:1.0,5.0')] ).

cnf(48,plain,
    ( ~ member(member_of_1_not_of_2(u,cs),bs)
    | subset(u,cs) ),
    inference(res,[status(thm),theory(equality)],[43,7]),
    [iquote('0:Res:43.1,7.0')] ).

cnf(85,plain,
    ( subset(union(u,v),w)
    | member(member_of_1_not_of_2(union(u,v),w),v)
    | member(member_of_1_not_of_2(union(u,v),w),u) ),
    inference(res,[status(thm),theory(equality)],[6,12]),
    [iquote('0:Res:6.1,12.0')] ).

cnf(320,plain,
    ( subset(union(u,bs),cs)
    | member(member_of_1_not_of_2(union(u,bs),cs),u)
    | subset(union(u,bs),cs) ),
    inference(res,[status(thm),theory(equality)],[85,48]),
    [iquote('0:Res:85.1,48.0')] ).

cnf(339,plain,
    ( member(member_of_1_not_of_2(union(u,bs),cs),u)
    | subset(union(u,bs),cs) ),
    inference(obv,[status(thm),theory(equality)],[320]),
    [iquote('0:Obv:320.0')] ).

cnf(6735,plain,
    ( subset(union(as,bs),cs)
    | member(member_of_1_not_of_2(union(as,bs),cs),cs) ),
    inference(res,[status(thm),theory(equality)],[339,44]),
    [iquote('0:Res:339.0,44.0')] ).

cnf(6740,plain,
    member(member_of_1_not_of_2(union(as,bs),cs),cs),
    inference(mrr,[status(thm)],[6735,3]),
    [iquote('0:MRR:6735.0,3.0')] ).

cnf(6753,plain,
    subset(union(as,bs),cs),
    inference(res,[status(thm),theory(equality)],[6740,7]),
    [iquote('0:Res:6740.0,7.0')] ).

cnf(6754,plain,
    $false,
    inference(mrr,[status(thm)],[6753,3]),
    [iquote('0:MRR:6753.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n017.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 09:38:33 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.04/2.19  
% 2.04/2.19  SPASS V 3.9 
% 2.04/2.19  SPASS beiseite: Proof found.
% 2.04/2.19  % SZS status Theorem
% 2.04/2.19  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 2.04/2.19  SPASS derived 5275 clauses, backtracked 0 clauses, performed 0 splits and kept 4193 clauses.
% 2.04/2.19  SPASS allocated 71838 KBytes.
% 2.04/2.19  SPASS spent	0:00:01.75 on the problem.
% 2.04/2.19  		0:00:00.04 for the input.
% 2.04/2.19  		0:00:00.00 for the FLOTTER CNF translation.
% 2.04/2.19  		0:00:00.08 for inferences.
% 2.04/2.19  		0:00:00.00 for the backtracking.
% 2.04/2.19  		0:00:01.56 for the reduction.
% 2.04/2.19  
% 2.04/2.19  
% 2.04/2.19  Here is a proof with depth 5, length 17 :
% 2.04/2.19  % SZS output start Refutation
% See solution above
% 2.04/2.19  Formulae used in the proof : a_subset_of_c b_subset_of_c prove_a_union_b_subset_of_c membership_in_subsets subsets_axiom1 subsets_axiom2 member_of_union_is_member_of_one_set
% 2.04/2.19  
%------------------------------------------------------------------------------