TSTP Solution File: SET130-6 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET130-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 05:24:22 EDT 2022

% Result   : Unsatisfiable 8.45s 8.68s
% Output   : Refutation 8.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   18 (  10 unt;   5 nHn;  18 RR)
%            Number of literals    :   27 (   0 equ;   7 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('SET130-6.p',unknown),
    [] ).

cnf(2,axiom,
    member(u__dfg,universal_class),
    file('SET130-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ member(u__dfg,set_builder(u__dfg,set_builder(y__dfg,set_builder(z__dfg,null_class)))),
    file('SET130-6.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ member(u,universal_class)
    | member(u,unordered_pair(u,v)) ),
    file('SET130-6.p',unknown),
    [] ).

cnf(15,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET130-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET130-6.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ member(u,v)
    | ~ member(u,complement(v)) ),
    file('SET130-6.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ member(u,universal_class)
    | member(u,v)
    | member(u,complement(v)) ),
    file('SET130-6.p',unknown),
    [] ).

cnf(29,axiom,
    equal(complement(intersection(complement(u),complement(v))),union(u,v)),
    file('SET130-6.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(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(21898,plain,
    member(u__dfg,complement(singleton(u__dfg))),
    inference(res,[status(thm),theory(equality)],[18729,3]),
    [iquote('0:Res:18729.0,3.0')] ).

cnf(22187,plain,
    ~ member(u__dfg,singleton(u__dfg)),
    inference(res,[status(thm),theory(equality)],[21898,27]),
    [iquote('0:Res:21898.0,27.1')] ).

cnf(22188,plain,
    $false,
    inference(mrr,[status(thm)],[22187,145]),
    [iquote('0:MRR:22187.0,145.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET130-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 05:25:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 8.45/8.68  
% 8.45/8.68  SPASS V 3.9 
% 8.45/8.68  SPASS beiseite: Proof found.
% 8.45/8.68  % SZS status Theorem
% 8.45/8.68  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 8.45/8.68  SPASS derived 18089 clauses, backtracked 961 clauses, performed 9 splits and kept 8863 clauses.
% 8.45/8.68  SPASS allocated 94072 KBytes.
% 8.45/8.68  SPASS spent	0:00:08.18 on the problem.
% 8.45/8.68  		0:00:00.04 for the input.
% 8.45/8.68  		0:00:00.00 for the FLOTTER CNF translation.
% 8.45/8.68  		0:00:00.23 for inferences.
% 8.45/8.68  		0:00:00.73 for the backtracking.
% 8.45/8.68  		0:00:06.98 for the reduction.
% 8.45/8.68  
% 8.45/8.68  
% 8.45/8.68  Here is a proof with depth 6, length 18 :
% 8.45/8.68  % SZS output start Refutation
% See solution above
% 8.45/8.68  Formulae used in the proof : definition_of_set_builder prove_member_of_triple1_1 prove_member_of_triple1_2 unordered_pair2 singleton_set intersection1 complement1 complement2 union
% 8.45/8.68  
%------------------------------------------------------------------------------