TSTP Solution File: SET154-6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET154-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 05:24:34 EDT 2022

% Result   : Unsatisfiable 15.36s 15.58s
% Output   : Refutation 15.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   20
% Syntax   : Number of clauses     :   87 (  32 unt;  32 nHn;  87 RR)
%            Number of literals    :  163 (   0 equ;  52 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(union(complement(x__dfg),x__dfg),universal_class),
    file('SET154-6.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(5,axiom,
    subclass(u,universal_class),
    file('SET154-6.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ equal(u,v)
    | subclass(v,u) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subclass(u,v)
    | ~ subclass(v,u)
    | equal(v,u) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(12,axiom,
    member(unordered_pair(u,v),universal_class),
    file('SET154-6.p',unknown),
    [] ).

cnf(13,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET154-6.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | member(u,intersection(w,v)) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ member(u,v)
    | ~ member(u,complement(v)) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ member(u,universal_class)
    | member(u,v)
    | member(u,complement(v)) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(27,axiom,
    equal(complement(intersection(complement(u),complement(v))),union(u,v)),
    file('SET154-6.p',unknown),
    [] ).

cnf(44,axiom,
    equal(union(u,singleton(u)),successor(u)),
    file('SET154-6.p',unknown),
    [] ).

cnf(67,axiom,
    ( equal(u,null_class)
    | member(regular(u),u) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(68,axiom,
    ( equal(u,null_class)
    | equal(intersection(u,regular(u)),null_class) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ member(u,universal_class)
    | equal(u,null_class)
    | member(apply(choice,u),u) ),
    file('SET154-6.p',unknown),
    [] ).

cnf(117,plain,
    ( ~ subclass(union(complement(x__dfg),x__dfg),universal_class)
    | ~ subclass(universal_class,union(complement(x__dfg),x__dfg)) ),
    inference(res,[status(thm),theory(equality)],[8,1]),
    [iquote('0:Res:8.2,1.0')] ).

cnf(122,plain,
    ~ subclass(universal_class,union(complement(x__dfg),x__dfg)),
    inference(mrr,[status(thm)],[117,5]),
    [iquote('0:MRR:117.0,5.0')] ).

cnf(129,plain,
    member(singleton(u),universal_class),
    inference(spr,[status(thm),theory(equality)],[13,12]),
    [iquote('0:SpR:13.0,12.0')] ).

cnf(160,plain,
    ( ~ member(regular(complement(u)),u)
    | equal(complement(u),null_class) ),
    inference(res,[status(thm),theory(equality)],[67,25]),
    [iquote('0:Res:67.1,25.1')] ).

cnf(168,plain,
    ( equal(intersection(u,v),null_class)
    | member(regular(intersection(u,v)),v) ),
    inference(res,[status(thm),theory(equality)],[67,23]),
    [iquote('0:Res:67.1,23.0')] ).

cnf(169,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),v) ),
    inference(res,[status(thm),theory(equality)],[3,23]),
    [iquote('0:Res:3.1,23.0')] ).

cnf(178,plain,
    ( equal(intersection(u,v),null_class)
    | member(regular(intersection(u,v)),u) ),
    inference(res,[status(thm),theory(equality)],[67,22]),
    [iquote('0:Res:67.1,22.0')] ).

cnf(272,plain,
    ( ~ member(not_subclass_element(u,complement(v)),universal_class)
    | member(not_subclass_element(u,complement(v)),v)
    | subclass(u,complement(v)) ),
    inference(res,[status(thm),theory(equality)],[26,4]),
    [iquote('0:Res:26.2,4.0')] ).

cnf(343,plain,
    ( ~ subclass(u,v)
    | equal(u,null_class)
    | member(regular(u),v) ),
    inference(res,[status(thm),theory(equality)],[67,2]),
    [iquote('0:Res:67.1,2.0')] ).

cnf(344,plain,
    ( ~ subclass(u,v)
    | subclass(u,w)
    | member(not_subclass_element(u,w),v) ),
    inference(res,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Res:3.1,2.0')] ).

cnf(536,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v)
    | equal(u,v) ),
    inference(spl,[status(thm),theory(equality)],[13,9]),
    [iquote('0:SpL:13.0,9.0')] ).

cnf(548,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    inference(obv,[status(thm),theory(equality)],[536]),
    [iquote('0:Obv:536.1')] ).

cnf(551,plain,
    ( equal(singleton(u),null_class)
    | equal(regular(singleton(u)),u) ),
    inference(res,[status(thm),theory(equality)],[67,548]),
    [iquote('0:Res:67.1,548.0')] ).

cnf(552,plain,
    ( subclass(singleton(u),v)
    | equal(not_subclass_element(singleton(u),v),u) ),
    inference(res,[status(thm),theory(equality)],[3,548]),
    [iquote('0:Res:3.1,548.0')] ).

cnf(556,plain,
    ( ~ member(singleton(u),universal_class)
    | equal(singleton(u),null_class)
    | equal(apply(choice,singleton(u)),u) ),
    inference(res,[status(thm),theory(equality)],[71,548]),
    [iquote('0:Res:71.2,548.0')] ).

cnf(560,plain,
    ( equal(singleton(u),null_class)
    | equal(apply(choice,singleton(u)),u) ),
    inference(mrr,[status(thm)],[556,129]),
    [iquote('0:MRR:556.0,129.0')] ).

cnf(625,plain,
    ( equal(singleton(u),null_class)
    | equal(singleton(u),null_class)
    | member(u,singleton(u)) ),
    inference(spr,[status(thm),theory(equality)],[551,67]),
    [iquote('0:SpR:551.1,67.1')] ).

cnf(626,plain,
    ( equal(singleton(u),null_class)
    | equal(singleton(u),null_class)
    | equal(intersection(singleton(u),u),null_class) ),
    inference(spr,[status(thm),theory(equality)],[551,68]),
    [iquote('0:SpR:551.1,68.1')] ).

cnf(630,plain,
    ( equal(singleton(u),null_class)
    | member(u,singleton(u)) ),
    inference(obv,[status(thm),theory(equality)],[625]),
    [iquote('0:Obv:625.0')] ).

cnf(631,plain,
    ( equal(singleton(u),null_class)
    | equal(intersection(singleton(u),u),null_class) ),
    inference(obv,[status(thm),theory(equality)],[626]),
    [iquote('0:Obv:626.0')] ).

cnf(864,plain,
    ( ~ member(u,v)
    | ~ member(u,singleton(v))
    | equal(singleton(v),null_class)
    | member(u,null_class) ),
    inference(spr,[status(thm),theory(equality)],[631,24]),
    [iquote('0:SpR:631.1,24.2')] ).

cnf(1212,plain,
    ( subclass(singleton(u),v)
    | subclass(singleton(u),v)
    | member(u,singleton(u)) ),
    inference(spr,[status(thm),theory(equality)],[552,3]),
    [iquote('0:SpR:552.1,3.1')] ).

cnf(1217,plain,
    ( subclass(singleton(u),v)
    | member(u,singleton(u)) ),
    inference(obv,[status(thm),theory(equality)],[1212]),
    [iquote('0:Obv:1212.0')] ).

cnf(1218,plain,
    ( subclass(null_class,u)
    | member(v,singleton(v)) ),
    inference(rew,[status(thm),theory(equality)],[630,1217]),
    [iquote('0:Rew:630.0,1217.0')] ).

cnf(1222,plain,
    member(u,singleton(u)),
    inference(spt,[spt(split,[position(s1)])],[1218]),
    [iquote('1:Spt:1218.1')] ).

cnf(1227,plain,
    ( ~ subclass(singleton(u),v)
    | member(u,v) ),
    inference(res,[status(thm),theory(equality)],[1222,2]),
    [iquote('1:Res:1222.0,2.0')] ).

cnf(1270,plain,
    member(u,universal_class),
    inference(res,[status(thm),theory(equality)],[5,1227]),
    [iquote('1:Res:5.0,1227.0')] ).

cnf(1272,plain,
    ( ~ equal(u,singleton(v))
    | member(v,u) ),
    inference(res,[status(thm),theory(equality)],[7,1227]),
    [iquote('1:Res:7.1,1227.0')] ).

cnf(1280,plain,
    ( equal(u,null_class)
    | member(apply(choice,u),u) ),
    inference(mrr,[status(thm)],[71,1270]),
    [iquote('1:MRR:71.0,1270.0')] ).

cnf(1320,plain,
    equal(complement(universal_class),null_class),
    inference(res,[status(thm),theory(equality)],[1270,160]),
    [iquote('1:Res:1270.0,160.0')] ).

cnf(1343,plain,
    ( ~ member(u,universal_class)
    | ~ member(u,null_class) ),
    inference(spl,[status(thm),theory(equality)],[1320,25]),
    [iquote('1:SpL:1320.0,25.1')] ).

cnf(1345,plain,
    ~ member(u,null_class),
    inference(mrr,[status(thm)],[1343,1270]),
    [iquote('1:MRR:1343.0,1270.0')] ).

cnf(1348,plain,
    ( ~ member(u,v)
    | ~ member(u,singleton(v))
    | equal(singleton(v),null_class) ),
    inference(mrr,[status(thm)],[864,1345]),
    [iquote('1:MRR:864.3,1345.0')] ).

cnf(1858,plain,
    ~ equal(singleton(u),null_class),
    inference(res,[status(thm),theory(equality)],[1272,1345]),
    [iquote('1:Res:1272.1,1345.0')] ).

cnf(1883,plain,
    equal(apply(choice,singleton(u)),u),
    inference(mrr,[status(thm)],[560,1858]),
    [iquote('1:MRR:560.0,1858.0')] ).

cnf(1888,plain,
    ( ~ member(u,v)
    | ~ member(u,singleton(v)) ),
    inference(mrr,[status(thm)],[1348,1858]),
    [iquote('1:MRR:1348.2,1858.0')] ).

cnf(2904,plain,
    ( ~ member(regular(intersection(complement(u),v)),u)
    | equal(intersection(complement(u),v),null_class) ),
    inference(res,[status(thm),theory(equality)],[178,25]),
    [iquote('0:Res:178.1,25.1')] ).

cnf(3060,plain,
    ( ~ subclass(complement(u),u)
    | equal(complement(u),null_class)
    | equal(complement(u),null_class) ),
    inference(res,[status(thm),theory(equality)],[343,160]),
    [iquote('0:Res:343.2,160.0')] ).

cnf(3074,plain,
    ( ~ subclass(complement(u),u)
    | equal(complement(u),null_class) ),
    inference(obv,[status(thm),theory(equality)],[3060]),
    [iquote('0:Obv:3060.1')] ).

cnf(4346,plain,
    equal(complement(universal_class),null_class),
    inference(res,[status(thm),theory(equality)],[5,3074]),
    [iquote('0:Res:5.0,3074.0')] ).

cnf(4922,plain,
    ( ~ member(apply(choice,singleton(u)),u)
    | equal(singleton(u),null_class) ),
    inference(res,[status(thm),theory(equality)],[1280,1888]),
    [iquote('1:Res:1280.1,1888.1')] ).

cnf(4939,plain,
    ( ~ member(u,u)
    | equal(singleton(u),null_class) ),
    inference(rew,[status(thm),theory(equality)],[1883,4922]),
    [iquote('1:Rew:1883.0,4922.0')] ).

cnf(4940,plain,
    ~ member(u,u),
    inference(mrr,[status(thm)],[4939,1858]),
    [iquote('1:MRR:4939.1,1858.0')] ).

cnf(4941,plain,
    $false,
    inference(unc,[status(thm)],[4940,1270]),
    [iquote('1:UnC:4940.0,1270.0')] ).

cnf(4946,plain,
    subclass(null_class,u),
    inference(spt,[spt(split,[position(s2)])],[1218]),
    [iquote('1:Spt:4941.0,1218.0')] ).

cnf(4951,plain,
    ( ~ subclass(u,null_class)
    | equal(u,null_class) ),
    inference(res,[status(thm),theory(equality)],[4946,8]),
    [iquote('1:Res:4946.0,8.0')] ).

cnf(4964,plain,
    equal(complement(intersection(null_class,complement(u))),union(universal_class,u)),
    inference(spr,[status(thm),theory(equality)],[4346,27]),
    [iquote('0:SpR:4346.0,27.0')] ).

cnf(4973,plain,
    ( ~ member(u,universal_class)
    | ~ member(u,null_class) ),
    inference(spl,[status(thm),theory(equality)],[4346,25]),
    [iquote('0:SpL:4346.0,25.1')] ).

cnf(6596,plain,
    ( subclass(intersection(u,v),v)
    | subclass(intersection(u,v),v) ),
    inference(res,[status(thm),theory(equality)],[169,4]),
    [iquote('0:Res:169.1,4.0')] ).

cnf(6598,plain,
    subclass(intersection(u,v),v),
    inference(obv,[status(thm),theory(equality)],[6596]),
    [iquote('0:Obv:6596.0')] ).

cnf(6630,plain,
    equal(intersection(u,null_class),null_class),
    inference(res,[status(thm),theory(equality)],[6598,4951]),
    [iquote('1:Res:6598.0,4951.0')] ).

cnf(6855,plain,
    ( ~ member(u,null_class)
    | member(u,v) ),
    inference(spl,[status(thm),theory(equality)],[6630,22]),
    [iquote('1:SpL:6630.0,22.0')] ).

cnf(6874,plain,
    ~ member(u,null_class),
    inference(mrr,[status(thm)],[4973,6855]),
    [iquote('1:MRR:4973.0,6855.1')] ).

cnf(6904,plain,
    equal(intersection(null_class,u),null_class),
    inference(res,[status(thm),theory(equality)],[178,6874]),
    [iquote('1:Res:178.1,6874.0')] ).

cnf(6918,plain,
    equal(union(universal_class,u),complement(null_class)),
    inference(rew,[status(thm),theory(equality)],[6904,4964]),
    [iquote('1:Rew:6904.0,4964.0')] ).

cnf(7024,plain,
    equal(complement(null_class),successor(universal_class)),
    inference(spr,[status(thm),theory(equality)],[6918,44]),
    [iquote('1:SpR:6918.0,44.0')] ).

cnf(11933,plain,
    ( ~ subclass(u,universal_class)
    | subclass(u,complement(v))
    | member(not_subclass_element(u,complement(v)),v)
    | subclass(u,complement(v)) ),
    inference(res,[status(thm),theory(equality)],[344,272]),
    [iquote('0:Res:344.2,272.0')] ).

cnf(11939,plain,
    ( ~ subclass(u,universal_class)
    | member(not_subclass_element(u,complement(v)),v)
    | subclass(u,complement(v)) ),
    inference(obv,[status(thm),theory(equality)],[11933]),
    [iquote('0:Obv:11933.1')] ).

cnf(11940,plain,
    ( member(not_subclass_element(u,complement(v)),v)
    | subclass(u,complement(v)) ),
    inference(mrr,[status(thm)],[11939,5]),
    [iquote('0:MRR:11939.0,5.0')] ).

cnf(12485,plain,
    subclass(u,complement(null_class)),
    inference(res,[status(thm),theory(equality)],[11940,6874]),
    [iquote('1:Res:11940.0,6874.0')] ).

cnf(31944,plain,
    ( equal(intersection(complement(u),u),null_class)
    | equal(intersection(complement(u),u),null_class) ),
    inference(res,[status(thm),theory(equality)],[168,2904]),
    [iquote('0:Res:168.1,2904.0')] ).

cnf(31951,plain,
    equal(intersection(complement(u),u),null_class),
    inference(obv,[status(thm),theory(equality)],[31944]),
    [iquote('0:Obv:31944.0')] ).

cnf(32009,plain,
    equal(union(complement(u),u),complement(null_class)),
    inference(spr,[status(thm),theory(equality)],[31951,27]),
    [iquote('0:SpR:31951.0,27.0')] ).

cnf(32083,plain,
    subclass(u,successor(universal_class)),
    inference(rew,[status(thm),theory(equality)],[7024,12485]),
    [iquote('1:Rew:7024.0,12485.0')] ).

cnf(32112,plain,
    equal(union(complement(u),u),successor(universal_class)),
    inference(rew,[status(thm),theory(equality)],[7024,32009]),
    [iquote('1:Rew:7024.0,32009.0')] ).

cnf(32114,plain,
    ~ subclass(universal_class,successor(universal_class)),
    inference(rew,[status(thm),theory(equality)],[32112,122]),
    [iquote('1:Rew:32112.0,122.0')] ).

cnf(32121,plain,
    $false,
    inference(mrr,[status(thm)],[32114,32083]),
    [iquote('1:MRR:32114.0,32083.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET154-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n027.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 : Sat Jul  9 23:48:17 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 15.36/15.58  
% 15.36/15.58  SPASS V 3.9 
% 15.36/15.58  SPASS beiseite: Proof found.
% 15.36/15.58  % SZS status Theorem
% 15.36/15.58  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 15.36/15.58  SPASS derived 24861 clauses, backtracked 2393 clauses, performed 9 splits and kept 12609 clauses.
% 15.36/15.58  SPASS allocated 102499 KBytes.
% 15.36/15.58  SPASS spent	0:0:15.20 on the problem.
% 15.36/15.58  		0:00:00.04 for the input.
% 15.36/15.58  		0:00:00.00 for the FLOTTER CNF translation.
% 15.36/15.58  		0:00:00.29 for inferences.
% 15.36/15.58  		0:00:01.07 for the backtracking.
% 15.36/15.58  		0:0:13.58 for the reduction.
% 15.36/15.58  
% 15.36/15.58  
% 15.36/15.58  Here is a proof with depth 9, length 87 :
% 15.36/15.58  % SZS output start Refutation
% See solution above
% 15.36/15.58  Formulae used in the proof : prove_union_with_complement_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair_member unordered_pairs_in_universal singleton_set intersection1 intersection2 intersection3 complement1 complement2 union successor regularity1 regularity2 choice2
% 15.58/15.83  
%------------------------------------------------------------------------------