TSTP Solution File: SET067-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET067-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 05:23:29 EDT 2022
% Result : Unsatisfiable 0.55s 0.76s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 12 unt; 15 nHn; 38 RR)
% Number of literals : 75 ( 0 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ subclass(singleton(x__dfg),unordered_pair(x__dfg,y__dfg)),
file('SET067-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET067-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET067-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET067-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET067-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET067-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET067-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET067-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET067-6.p',unknown),
[] ).
cnf(55,axiom,
( ~ member(u,universal_class)
| member(sum_class(u),universal_class) ),
file('SET067-6.p',unknown),
[] ).
cnf(66,axiom,
( ~ function(u)
| ~ member(v,universal_class)
| member(image(u,v),universal_class) ),
file('SET067-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET067-6.p',unknown),
[] ).
cnf(69,axiom,
equal(sum_class(image(u,singleton(v))),apply(u,v)),
file('SET067-6.p',unknown),
[] ).
cnf(70,axiom,
function(choice),
file('SET067-6.p',unknown),
[] ).
cnf(71,axiom,
( ~ member(u,universal_class)
| equal(u,null_class)
| member(apply(choice,u),u) ),
file('SET067-6.p',unknown),
[] ).
cnf(100,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
cnf(123,plain,
( ~ member(image(u,singleton(v)),universal_class)
| member(apply(u,v),universal_class) ),
inference(spr,[status(thm),theory(equality)],[69,55]),
[iquote('0:SpR:69.0,55.1')] ).
cnf(141,plain,
( ~ member(u,null_class)
| equal(v,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[68,22]),
[iquote('0:SpL:68.1,22.0')] ).
cnf(172,plain,
( subclass(null_class,u)
| equal(v,null_class)
| member(not_subclass_element(null_class,u),v) ),
inference(res,[status(thm),theory(equality)],[3,141]),
[iquote('0:Res:3.1,141.0')] ).
cnf(265,plain,
( subclass(null_class,u)
| equal(u,null_class)
| subclass(null_class,u) ),
inference(res,[status(thm),theory(equality)],[172,4]),
[iquote('0:Res:172.2,4.0')] ).
cnf(268,plain,
( equal(u,null_class)
| subclass(null_class,u) ),
inference(obv,[status(thm),theory(equality)],[265]),
[iquote('0:Obv:265.0')] ).
cnf(269,plain,
subclass(null_class,u),
inference(mrr,[status(thm)],[268,7]),
[iquote('0:MRR:268.0,7.0')] ).
cnf(454,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(465,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[454]),
[iquote('0:Obv:454.1')] ).
cnf(469,plain,
( subclass(singleton(u),v)
| equal(not_subclass_element(singleton(u),v),u) ),
inference(res,[status(thm),theory(equality)],[3,465]),
[iquote('0:Res:3.1,465.0')] ).
cnf(473,plain,
( ~ member(singleton(u),universal_class)
| equal(singleton(u),null_class)
| equal(apply(choice,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[71,465]),
[iquote('0:Res:71.2,465.0')] ).
cnf(476,plain,
( equal(singleton(u),null_class)
| equal(apply(choice,singleton(u)),u) ),
inference(mrr,[status(thm)],[473,100]),
[iquote('0:MRR:473.0,100.0')] ).
cnf(1888,plain,
( ~ function(u)
| ~ member(singleton(v),universal_class)
| member(apply(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[66,123]),
[iquote('0:Res:66.2,123.0')] ).
cnf(1889,plain,
( ~ function(u)
| member(apply(u,v),universal_class) ),
inference(mrr,[status(thm)],[1888,100]),
[iquote('0:MRR:1888.1,100.0')] ).
cnf(1890,plain,
( ~ function(choice)
| equal(singleton(u),null_class)
| member(u,universal_class) ),
inference(spr,[status(thm),theory(equality)],[476,1889]),
[iquote('0:SpR:476.1,1889.1')] ).
cnf(1892,plain,
( equal(singleton(u),null_class)
| member(u,universal_class) ),
inference(ssi,[status(thm)],[1890,70]),
[iquote('0:SSi:1890.0,70.0')] ).
cnf(1937,plain,
( ~ member(u,v)
| subclass(singleton(u),v)
| subclass(singleton(u),v) ),
inference(spl,[status(thm),theory(equality)],[469,4]),
[iquote('0:SpL:469.1,4.0')] ).
cnf(1941,plain,
( ~ member(u,v)
| subclass(singleton(u),v) ),
inference(obv,[status(thm),theory(equality)],[1937]),
[iquote('0:Obv:1937.1')] ).
cnf(1950,plain,
~ member(x__dfg,unordered_pair(x__dfg,y__dfg)),
inference(res,[status(thm),theory(equality)],[1941,1]),
[iquote('0:Res:1941.1,1.0')] ).
cnf(1954,plain,
~ member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[10,1950]),
[iquote('0:Res:10.1,1950.0')] ).
cnf(1964,plain,
equal(singleton(x__dfg),null_class),
inference(res,[status(thm),theory(equality)],[1892,1954]),
[iquote('0:Res:1892.1,1954.0')] ).
cnf(1965,plain,
~ subclass(null_class,unordered_pair(x__dfg,y__dfg)),
inference(rew,[status(thm),theory(equality)],[1964,1]),
[iquote('0:Rew:1964.0,1.0')] ).
cnf(1967,plain,
$false,
inference(mrr,[status(thm)],[1965,269]),
[iquote('0:MRR:1965.0,269.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET067-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 : Sun Jul 10 10:59:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.55/0.76
% 0.55/0.76 SPASS V 3.9
% 0.55/0.76 SPASS beiseite: Proof found.
% 0.55/0.76 % SZS status Theorem
% 0.55/0.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.76 SPASS derived 1657 clauses, backtracked 0 clauses, performed 1 splits and kept 1163 clauses.
% 0.55/0.76 SPASS allocated 77679 KBytes.
% 0.55/0.76 SPASS spent 0:00:00.40 on the problem.
% 0.55/0.76 0:00:00.04 for the input.
% 0.55/0.76 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.76 0:00:00.03 for inferences.
% 0.55/0.76 0:00:00.00 for the backtracking.
% 0.55/0.76 0:00:00.30 for the reduction.
% 0.55/0.76
% 0.55/0.76
% 0.55/0.76 Here is a proof with depth 6, length 38 :
% 0.55/0.76 % SZS output start Refutation
% See solution above
% 0.55/0.76 Formulae used in the proof : prove_singleton_in_unordered_pair1_1 not_subclass_members1 not_subclass_members2 equal_implies_subclass2 unordered_pair_member unordered_pair2 unordered_pairs_in_universal singleton_set intersection1 sum_class2 replacement regularity2 apply choice1 choice2
% 0.55/0.76
%------------------------------------------------------------------------------