TSTP Solution File: SET632+3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET632+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 05:27:41 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   30 (  16 unt;   4 nHn;  30 RR)
%            Number of literals    :   47 (   0 equ;  22 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 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(skc5,skc3),
    file('SET632+3.p',unknown),
    [] ).

cnf(2,axiom,
    subset(skc5,skc4),
    file('SET632+3.p',unknown),
    [] ).

cnf(3,axiom,
    disjoint(skc3,skc4),
    file('SET632+3.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(skc5,empty_set),
    file('SET632+3.p',unknown),
    [] ).

cnf(6,axiom,
    ~ member(u,empty_set),
    file('SET632+3.p',unknown),
    [] ).

cnf(8,axiom,
    ( empty(u)
    | member(skf5(u),u) ),
    file('SET632+3.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ empty(u)
    | ~ member(v,u) ),
    file('SET632+3.p',unknown),
    [] ).

cnf(13,axiom,
    ( subset(u,v)
    | member(skf3(v,u),u) ),
    file('SET632+3.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ intersect(u,v)
    | ~ disjoint(u,v) ),
    file('SET632+3.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ member(u,v)
    | ~ subset(v,w)
    | member(u,w) ),
    file('SET632+3.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | intersect(w,v) ),
    file('SET632+3.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ subset(u,v)
    | ~ subset(v,u)
    | equal(v,u) ),
    file('SET632+3.p',unknown),
    [] ).

cnf(21,plain,
    ~ intersect(skc3,skc4),
    inference(res,[status(thm),theory(equality)],[3,14]),
    [iquote('0:Res:3.0,14.0')] ).

cnf(23,plain,
    ( ~ member(u,skc5)
    | member(u,skc4) ),
    inference(res,[status(thm),theory(equality)],[2,18]),
    [iquote('0:Res:2.0,18.0')] ).

cnf(26,plain,
    ( ~ member(u,skc5)
    | member(u,skc3) ),
    inference(res,[status(thm),theory(equality)],[1,18]),
    [iquote('0:Res:1.0,18.0')] ).

cnf(28,plain,
    ( ~ subset(empty_set,skc5)
    | ~ subset(skc5,empty_set) ),
    inference(res,[status(thm),theory(equality)],[20,5]),
    [iquote('0:Res:20.2,5.0')] ).

cnf(32,plain,
    ( empty(skc5)
    | member(skf5(skc5),skc3) ),
    inference(res,[status(thm),theory(equality)],[8,26]),
    [iquote('0:Res:8.1,26.0')] ).

cnf(35,plain,
    ( empty(skc5)
    | member(skf5(skc5),skc4) ),
    inference(res,[status(thm),theory(equality)],[8,23]),
    [iquote('0:Res:8.1,23.0')] ).

cnf(36,plain,
    empty(skc5),
    inference(spt,[spt(split,[position(s1)])],[35]),
    [iquote('1:Spt:35.0')] ).

cnf(45,plain,
    subset(empty_set,u),
    inference(res,[status(thm),theory(equality)],[13,6]),
    [iquote('0:Res:13.1,6.0')] ).

cnf(48,plain,
    ( ~ empty(u)
    | subset(u,v) ),
    inference(res,[status(thm),theory(equality)],[13,12]),
    [iquote('0:Res:13.1,12.1')] ).

cnf(49,plain,
    ~ subset(skc5,empty_set),
    inference(mrr,[status(thm)],[28,45]),
    [iquote('0:MRR:28.0,45.0')] ).

cnf(51,plain,
    ~ empty(skc5),
    inference(res,[status(thm),theory(equality)],[48,49]),
    [iquote('0:Res:48.1,49.0')] ).

cnf(54,plain,
    $false,
    inference(ssi,[status(thm)],[51,36]),
    [iquote('1:SSi:51.0,36.0')] ).

cnf(55,plain,
    ~ empty(skc5),
    inference(spt,[spt(split,[position(sa)])],[54,36]),
    [iquote('1:Spt:54.0,35.0,36.0')] ).

cnf(56,plain,
    member(skf5(skc5),skc4),
    inference(spt,[spt(split,[position(s2)])],[35]),
    [iquote('1:Spt:54.0,35.1')] ).

cnf(58,plain,
    member(skf5(skc5),skc3),
    inference(mrr,[status(thm)],[32,55]),
    [iquote('1:MRR:32.0,55.0')] ).

cnf(111,plain,
    ( ~ member(skf5(skc5),u)
    | intersect(u,skc4) ),
    inference(res,[status(thm),theory(equality)],[56,19]),
    [iquote('1:Res:56.0,19.0')] ).

cnf(123,plain,
    intersect(skc3,skc4),
    inference(res,[status(thm),theory(equality)],[58,111]),
    [iquote('1:Res:58.0,111.0')] ).

cnf(124,plain,
    $false,
    inference(mrr,[status(thm)],[123,21]),
    [iquote('1:MRR:123.0,21.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET632+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 13:29:48 EDT 2022
% 0.12/0.34  % 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/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 95 clauses, backtracked 5 clauses, performed 2 splits and kept 80 clauses.
% 0.19/0.45  SPASS allocated 97788 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.45  		0:00:00.04 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  		0:00:00.00 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 5, length 30 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : prove_th114 empty_set_defn empty_defn subset_defn disjoint_defn intersect_defn equal_defn
% 0.19/0.45  
%------------------------------------------------------------------------------