TSTP Solution File: SET131-6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET131-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 05:24:23 EDT 2022

% Result   : Unsatisfiable 8.30s 8.47s
% Output   : Refutation 8.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   23 (  12 unt;   7 nHn;  23 RR)
%            Number of literals    :   35 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(union(singleton(u),v),set_builder(u,v)),
    file('SET131-6.p',unknown),
    [] ).

cnf(2,axiom,
    member(u__dfg,universal_class),
    file('SET131-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ member(u__dfg,set_builder(x__dfg,set_builder(u__dfg,set_builder(z__dfg,null_class)))),
    file('SET131-6.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ member(u,universal_class)
    | member(u,unordered_pair(u,v)) ),
    file('SET131-6.p',unknown),
    [] ).

cnf(15,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET131-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET131-6.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET131-6.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ member(u,v)
    | ~ member(u,complement(v)) ),
    file('SET131-6.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ member(u,universal_class)
    | member(u,v)
    | member(u,complement(v)) ),
    file('SET131-6.p',unknown),
    [] ).

cnf(29,axiom,
    equal(complement(intersection(complement(u),complement(v))),union(u,v)),
    file('SET131-6.p',unknown),
    [] ).

cnf(99,plain,
    ( member(u__dfg,u)
    | member(u__dfg,complement(u)) ),
    inference(res,[status(thm),theory(equality)],[2,28]),
    [iquote('0:Res:2.0,28.0')] ).

cnf(100,plain,
    member(u__dfg,unordered_pair(u__dfg,u)),
    inference(res,[status(thm),theory(equality)],[2,12]),
    [iquote('0:Res:2.0,12.0')] ).

cnf(145,plain,
    member(u__dfg,singleton(u__dfg)),
    inference(spr,[status(thm),theory(equality)],[15,100]),
    [iquote('0:SpR:15.0,100.0')] ).

cnf(247,plain,
    ( member(u__dfg,intersection(complement(u),complement(v)))
    | member(u__dfg,union(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[29,99]),
    [iquote('0:SpR:29.0,99.1')] ).

cnf(18713,plain,
    ( member(u__dfg,union(u,v))
    | member(u__dfg,complement(u)) ),
    inference(res,[status(thm),theory(equality)],[247,24]),
    [iquote('0:Res:247.0,24.0')] ).

cnf(18714,plain,
    ( member(u__dfg,union(u,v))
    | member(u__dfg,complement(v)) ),
    inference(res,[status(thm),theory(equality)],[247,25]),
    [iquote('0:Res:247.0,25.0')] ).

cnf(18729,plain,
    ( member(u__dfg,set_builder(u,v))
    | member(u__dfg,complement(singleton(u))) ),
    inference(spr,[status(thm),theory(equality)],[1,18713]),
    [iquote('0:SpR:1.0,18713.0')] ).

cnf(18866,plain,
    ( member(u__dfg,set_builder(u,v))
    | member(u__dfg,complement(v)) ),
    inference(spr,[status(thm),theory(equality)],[1,18714]),
    [iquote('0:SpR:1.0,18714.0')] ).

cnf(21909,plain,
    member(u__dfg,complement(set_builder(u__dfg,set_builder(z__dfg,null_class)))),
    inference(res,[status(thm),theory(equality)],[18866,3]),
    [iquote('0:Res:18866.0,3.0')] ).

cnf(23284,plain,
    ~ member(u__dfg,set_builder(u__dfg,set_builder(z__dfg,null_class))),
    inference(res,[status(thm),theory(equality)],[21909,27]),
    [iquote('0:Res:21909.0,27.1')] ).

cnf(23291,plain,
    member(u__dfg,complement(singleton(u__dfg))),
    inference(res,[status(thm),theory(equality)],[18729,23284]),
    [iquote('0:Res:18729.0,23284.0')] ).

cnf(23298,plain,
    ~ member(u__dfg,singleton(u__dfg)),
    inference(res,[status(thm),theory(equality)],[23291,27]),
    [iquote('0:Res:23291.0,27.1')] ).

cnf(23299,plain,
    $false,
    inference(mrr,[status(thm)],[23298,145]),
    [iquote('0:MRR:23298.0,145.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET131-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 06:18:45 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 8.30/8.47  
% 8.30/8.47  SPASS V 3.9 
% 8.30/8.47  SPASS beiseite: Proof found.
% 8.30/8.47  % SZS status Theorem
% 8.30/8.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 8.30/8.47  SPASS derived 18955 clauses, backtracked 961 clauses, performed 9 splits and kept 9224 clauses.
% 8.30/8.47  SPASS allocated 94200 KBytes.
% 8.30/8.47  SPASS spent	0:00:07.96 on the problem.
% 8.30/8.47  		0:00:00.04 for the input.
% 8.30/8.47  		0:00:00.00 for the FLOTTER CNF translation.
% 8.30/8.47  		0:00:00.22 for inferences.
% 8.30/8.47  		0:00:00.71 for the backtracking.
% 8.30/8.47  		0:00:06.80 for the reduction.
% 8.30/8.47  
% 8.30/8.47  
% 8.30/8.47  Here is a proof with depth 8, length 23 :
% 8.30/8.47  % SZS output start Refutation
% See solution above
% 8.30/8.47  Formulae used in the proof : definition_of_set_builder prove_member_of_triple2_1 prove_member_of_triple2_2 unordered_pair2 singleton_set intersection1 intersection2 complement1 complement2 union
% 8.30/8.47  
%------------------------------------------------------------------------------