%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 05:24:55 EDT 2022

% Result   : Theorem 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   5 unt;   2 nHn;  10 RR)
%            Number of literals    :   15 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   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(2,axiom,
    ~ subset(skc3,union(skc3,skc2)),
    file('SET194+3.p',unknown),
    [] ).

cnf(3,axiom,
    equal(union(u,v),union(v,u)),
    file('SET194+3.p',unknown),
    [] ).

cnf(4,axiom,
    ( subset(u,v)
    | member(skf2(v,u),u) ),
    file('SET194+3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ member(u,v)
    | member(u,union(w,v)) ),
    file('SET194+3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ member(skf2(u,v),u)
    | subset(w,u) ),
    file('SET194+3.p',unknown),
    [] ).

cnf(14,plain,
    ~ subset(skc3,union(skc2,skc3)),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(26,plain,
    ( ~ member(skf2(union(u,v),w),v)
    | subset(x,union(u,v)) ),
    inference(res,[status(thm),theory(equality)],[6,7]),
    [iquote('0:Res:6.1,7.0')] ).

cnf(43,plain,
    ( subset(u,union(v,u))
    | subset(w,union(v,u)) ),
    inference(res,[status(thm),theory(equality)],[4,26]),
    [iquote('0:Res:4.1,26.0')] ).

cnf(47,plain,
    subset(u,union(v,u)),
    inference(con,[status(thm)],[43]),
    [iquote('0:Con:43.1')] ).

cnf(48,plain,
    $false,
    inference(unc,[status(thm)],[47,14]),
    [iquote('0:UnC:47.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n009.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 13:20:07 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.45  
% 0.21/0.45  SPASS V 3.9 
% 0.21/0.45  SPASS beiseite: Proof found.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.45  SPASS derived 30 clauses, backtracked 0 clauses, performed 0 splits and kept 26 clauses.
% 0.21/0.45  SPASS allocated 85268 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.21/0.45  		0:00:00.03 for the input.
% 0.21/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45  		0:00:00.00 for inferences.
% 0.21/0.45  		0:00:00.00 for the backtracking.
% 0.21/0.45  		0:00:00.00 for the reduction.
% 0.21/0.45  
% 0.21/0.45  
% 0.21/0.45  Here is a proof with depth 2, length 10 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : prove_subset_of_union commutativity_of_union subset_defn union_defn
% 0.21/0.45  
%------------------------------------------------------------------------------