TSTP Solution File: SET009+3 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 05:22:23 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   25 (   5 unt;  12 nHn;  25 RR)
%            Number of literals    :   52 (   0 equ;  15 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subset(skc3,skc4),
    file('SET009+3.p',unknown),
    [] ).

cnf(3,axiom,
    ~ subset(difference(skc5,skc4),difference(skc5,skc3)),
    file('SET009+3.p',unknown),
    [] ).

cnf(4,axiom,
    ( subset(u,v)
    | member(skf1(v,u),u) ),
    file('SET009+3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(u,difference(v,w))
    | member(u,v) ),
    file('SET009+3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ member(skf1(u,v),u)
    | subset(w,u) ),
    file('SET009+3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ member(u,v)
    | ~ member(u,difference(w,v)) ),
    file('SET009+3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ member(u,v)
    | ~ subset(v,w)
    | member(u,w) ),
    file('SET009+3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ member(u,v)
    | member(u,w)
    | member(u,difference(v,w)) ),
    file('SET009+3.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ member(u,skc3)
    | member(u,skc4) ),
    inference(res,[status(thm),theory(equality)],[1,8]),
    [iquote('0:Res:1.0,8.0')] ).

cnf(18,plain,
    ( subset(difference(u,v),w)
    | member(skf1(w,difference(u,v)),u) ),
    inference(res,[status(thm),theory(equality)],[4,5]),
    [iquote('0:Res:4.1,5.0')] ).

cnf(19,plain,
    ( ~ member(skf1(u,difference(v,w)),w)
    | subset(difference(v,w),u) ),
    inference(res,[status(thm),theory(equality)],[4,7]),
    [iquote('0:Res:4.1,7.1')] ).

cnf(20,plain,
    ( ~ subset(u,v)
    | subset(u,w)
    | member(skf1(w,u),v) ),
    inference(res,[status(thm),theory(equality)],[4,8]),
    [iquote('0:Res:4.1,8.0')] ).

cnf(31,plain,
    ( ~ member(skf1(difference(u,v),w),u)
    | member(skf1(difference(u,v),w),v)
    | subset(x,difference(u,v)) ),
    inference(res,[status(thm),theory(equality)],[9,6]),
    [iquote('0:Res:9.2,6.0')] ).

cnf(40,plain,
    ( ~ subset(u,difference(v,w))
    | ~ member(skf1(x,u),w)
    | subset(u,x) ),
    inference(res,[status(thm),theory(equality)],[20,7]),
    [iquote('0:Res:20.2,7.1')] ).

cnf(83,plain,
    ( subset(u,difference(u,v))
    | member(skf1(difference(u,v),u),v)
    | subset(w,difference(u,v)) ),
    inference(res,[status(thm),theory(equality)],[4,31]),
    [iquote('0:Res:4.1,31.0')] ).

cnf(85,plain,
    ( subset(difference(u,v),difference(u,w))
    | member(skf1(difference(u,w),difference(u,v)),w)
    | subset(x,difference(u,w)) ),
    inference(res,[status(thm),theory(equality)],[18,31]),
    [iquote('0:Res:18.1,31.0')] ).

cnf(90,plain,
    ( subset(u,difference(u,v))
    | member(skf1(difference(u,v),u),v) ),
    inference(con,[status(thm)],[83]),
    [iquote('0:Con:83.2')] ).

cnf(95,plain,
    ( subset(difference(u,v),difference(u,w))
    | member(skf1(difference(u,w),difference(u,v)),w) ),
    inference(con,[status(thm)],[85]),
    [iquote('0:Con:85.2')] ).

cnf(103,plain,
    ( subset(u,difference(u,skc3))
    | member(skf1(difference(u,skc3),u),skc4) ),
    inference(res,[status(thm),theory(equality)],[90,10]),
    [iquote('0:Res:90.1,10.0')] ).

cnf(115,plain,
    ( subset(difference(u,skc4),difference(difference(u,skc4),skc3))
    | subset(difference(u,skc4),difference(difference(u,skc4),skc3)) ),
    inference(res,[status(thm),theory(equality)],[103,19]),
    [iquote('0:Res:103.1,19.0')] ).

cnf(117,plain,
    subset(difference(u,skc4),difference(difference(u,skc4),skc3)),
    inference(obv,[status(thm),theory(equality)],[115]),
    [iquote('0:Obv:115.0')] ).

cnf(124,plain,
    ( ~ member(skf1(u,difference(v,skc4)),skc3)
    | subset(difference(v,skc4),u) ),
    inference(res,[status(thm),theory(equality)],[117,40]),
    [iquote('0:Res:117.0,40.0')] ).

cnf(303,plain,
    ( subset(difference(u,skc4),difference(u,skc3))
    | subset(difference(u,skc4),difference(u,skc3)) ),
    inference(res,[status(thm),theory(equality)],[95,124]),
    [iquote('0:Res:95.1,124.0')] ).

cnf(305,plain,
    subset(difference(u,skc4),difference(u,skc3)),
    inference(obv,[status(thm),theory(equality)],[303]),
    [iquote('0:Obv:303.0')] ).

cnf(306,plain,
    $false,
    inference(unc,[status(thm)],[305,3]),
    [iquote('0:UnC:305.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n011.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 : Mon Jul 11 09:52:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 241 clauses, backtracked 0 clauses, performed 0 splits and kept 130 clauses.
% 0.19/0.45  SPASS allocated 85399 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.11 on the problem.
% 0.19/0.45  		0:00:00.03 for the input.
% 0.19/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.00 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.02 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 6, length 25 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : prove_subset_difference subset_defn difference_defn
% 0.19/0.45  
%------------------------------------------------------------------------------