TSTP Solution File: SET603+4 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET603+4 : TPTP v8.1.0. Released v2.2.0.
% 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 : Tue Jul 19 05:27:21 EDT 2022

% Result   : Theorem 2.35s 2.56s
% Output   : Refutation 2.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   17 (   6 unt;   7 nHn;  17 RR)
%            Number of literals    :   32 (   0 equ;  11 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,
    ~ member(u,empty_set),
    file('SET603+4.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal_set(difference(skc1,empty_set),skc1),
    file('SET603+4.p',unknown),
    [] ).

cnf(7,axiom,
    ( subset(u,v)
    | member(skf3(v,u),u) ),
    file('SET603+4.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ member(skf3(u,v),u)
    | subset(w,u) ),
    file('SET603+4.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ member(u,difference(v,w))
    | member(u,v) ),
    file('SET603+4.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ subset(u,v)
    | ~ subset(v,u)
    | equal_set(v,u) ),
    file('SET603+4.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ member(u,v)
    | member(u,w)
    | member(u,difference(v,w)) ),
    file('SET603+4.p',unknown),
    [] ).

cnf(31,plain,
    ( ~ subset(skc1,difference(skc1,empty_set))
    | ~ subset(difference(skc1,empty_set),skc1) ),
    inference(res,[status(thm),theory(equality)],[24,3]),
    [iquote('0:Res:24.2,3.0')] ).

cnf(49,plain,
    ( subset(difference(u,v),w)
    | member(skf3(w,difference(u,v)),u) ),
    inference(res,[status(thm),theory(equality)],[7,17]),
    [iquote('0:Res:7.1,17.0')] ).

cnf(148,plain,
    ( ~ member(skf3(difference(u,v),w),u)
    | member(skf3(difference(u,v),w),v)
    | subset(x,difference(u,v)) ),
    inference(res,[status(thm),theory(equality)],[26,12]),
    [iquote('0:Res:26.2,12.0')] ).

cnf(520,plain,
    ( subset(difference(u,v),u)
    | subset(w,u) ),
    inference(res,[status(thm),theory(equality)],[49,12]),
    [iquote('0:Res:49.1,12.0')] ).

cnf(522,plain,
    subset(difference(u,v),u),
    inference(con,[status(thm)],[520]),
    [iquote('0:Con:520.1')] ).

cnf(523,plain,
    ~ subset(skc1,difference(skc1,empty_set)),
    inference(mrr,[status(thm)],[31,522]),
    [iquote('0:MRR:31.1,522.0')] ).

cnf(3514,plain,
    ( subset(u,difference(u,v))
    | member(skf3(difference(u,v),u),v)
    | subset(w,difference(u,v)) ),
    inference(res,[status(thm),theory(equality)],[7,148]),
    [iquote('0:Res:7.1,148.0')] ).

cnf(3523,plain,
    ( subset(u,difference(u,v))
    | member(skf3(difference(u,v),u),v) ),
    inference(con,[status(thm)],[3514]),
    [iquote('0:Con:3514.2')] ).

cnf(6929,plain,
    subset(u,difference(u,empty_set)),
    inference(res,[status(thm),theory(equality)],[3523,1]),
    [iquote('0:Res:3523.1,1.0')] ).

cnf(6967,plain,
    $false,
    inference(unc,[status(thm)],[6929,523]),
    [iquote('0:UnC:6929.0,523.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET603+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n022.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 20:31:10 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 2.35/2.56  
% 2.35/2.56  SPASS V 3.9 
% 2.35/2.56  SPASS beiseite: Proof found.
% 2.35/2.56  % SZS status Theorem
% 2.35/2.56  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.35/2.56  SPASS derived 6020 clauses, backtracked 0 clauses, performed 0 splits and kept 3729 clauses.
% 2.35/2.56  SPASS allocated 91049 KBytes.
% 2.35/2.56  SPASS spent	0:00:02.14 on the problem.
% 2.35/2.56  		0:00:00.04 for the input.
% 2.35/2.56  		0:00:00.04 for the FLOTTER CNF translation.
% 2.35/2.56  		0:00:00.07 for inferences.
% 2.35/2.56  		0:00:00.00 for the backtracking.
% 2.35/2.56  		0:00:01.93 for the reduction.
% 2.35/2.56  
% 2.35/2.56  
% 2.35/2.56  Here is a proof with depth 3, length 17 :
% 2.35/2.56  % SZS output start Refutation
% See solution above
% 2.35/2.56  Formulae used in the proof : empty_set thI30 subset difference equal_set
% 2.35/2.56  
%------------------------------------------------------------------------------