TSTP Solution File: SET014+3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 05:22:30 EDT 2022

% Result   : Theorem 1.38s 1.58s
% Output   : Refutation 1.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   18 (   7 unt;   7 nHn;  18 RR)
%            Number of literals    :   34 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 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(skc5,skc3),
    file('SET014+3.p',unknown),
    [] ).

cnf(2,axiom,
    subset(skc4,skc3),
    file('SET014+3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ subset(union(skc5,skc4),skc3),
    file('SET014+3.p',unknown),
    [] ).

cnf(5,axiom,
    equal(union(u,v),union(v,u)),
    file('SET014+3.p',unknown),
    [] ).

cnf(6,axiom,
    ( subset(u,v)
    | member(skf2(v,u),u) ),
    file('SET014+3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ member(skf2(u,v),u)
    | subset(w,u) ),
    file('SET014+3.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ member(u,v)
    | ~ subset(v,w)
    | member(u,w) ),
    file('SET014+3.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ member(u,union(v,w))
    | member(u,v)
    | member(u,w) ),
    file('SET014+3.p',unknown),
    [] ).

cnf(16,plain,
    ~ subset(union(skc4,skc5),skc3),
    inference(rew,[status(thm),theory(equality)],[5,4]),
    [iquote('0:Rew:5.0,4.0')] ).

cnf(17,plain,
    ( ~ member(u,skc4)
    | member(u,skc3) ),
    inference(res,[status(thm),theory(equality)],[2,10]),
    [iquote('0:Res:2.0,10.0')] ).

cnf(18,plain,
    ( ~ member(u,skc5)
    | member(u,skc3) ),
    inference(res,[status(thm),theory(equality)],[1,10]),
    [iquote('0:Res:1.0,10.0')] ).

cnf(62,plain,
    ( subset(union(u,v),w)
    | member(skf2(w,union(u,v)),u)
    | member(skf2(w,union(u,v)),v) ),
    inference(res,[status(thm),theory(equality)],[6,13]),
    [iquote('0:Res:6.1,13.0')] ).

cnf(867,plain,
    ( subset(union(u,skc5),v)
    | member(skf2(v,union(u,skc5)),u)
    | member(skf2(v,union(u,skc5)),skc3) ),
    inference(res,[status(thm),theory(equality)],[62,18]),
    [iquote('0:Res:62.2,18.0')] ).

cnf(2491,plain,
    ( subset(union(skc4,skc5),u)
    | member(skf2(u,union(skc4,skc5)),skc3)
    | member(skf2(u,union(skc4,skc5)),skc3) ),
    inference(res,[status(thm),theory(equality)],[867,17]),
    [iquote('0:Res:867.1,17.0')] ).

cnf(2506,plain,
    ( subset(union(skc4,skc5),u)
    | member(skf2(u,union(skc4,skc5)),skc3) ),
    inference(obv,[status(thm),theory(equality)],[2491]),
    [iquote('0:Obv:2491.1')] ).

cnf(4394,plain,
    ( subset(union(skc4,skc5),skc3)
    | subset(u,skc3) ),
    inference(res,[status(thm),theory(equality)],[2506,9]),
    [iquote('0:Res:2506.1,9.0')] ).

cnf(4405,plain,
    subset(union(skc4,skc5),skc3),
    inference(con,[status(thm)],[4394]),
    [iquote('0:Con:4394.1')] ).

cnf(4406,plain,
    $false,
    inference(mrr,[status(thm)],[4405,16]),
    [iquote('0:MRR:4405.0,16.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13  % Problem  : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jul 10 13:28:32 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 1.38/1.58  
% 1.38/1.58  SPASS V 3.9 
% 1.38/1.58  SPASS beiseite: Proof found.
% 1.38/1.58  % SZS status Theorem
% 1.38/1.58  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.38/1.58  SPASS derived 3681 clauses, backtracked 220 clauses, performed 4 splits and kept 1873 clauses.
% 1.38/1.58  SPASS allocated 88549 KBytes.
% 1.38/1.58  SPASS spent	0:00:01.20 on the problem.
% 1.38/1.58  		0:00:00.04 for the input.
% 1.38/1.58  		0:00:00.03 for the FLOTTER CNF translation.
% 1.38/1.58  		0:00:00.05 for inferences.
% 1.38/1.58  		0:00:00.00 for the backtracking.
% 1.38/1.58  		0:00:01.05 for the reduction.
% 1.38/1.58  
% 1.38/1.58  
% 1.38/1.58  Here is a proof with depth 4, length 18 :
% 1.38/1.58  % SZS output start Refutation
% See solution above
% 1.38/1.58  Formulae used in the proof : prove_union_subset commutativity_of_union subset_defn union_defn
% 1.38/1.58  
%------------------------------------------------------------------------------