TSTP Solution File: SET016-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET016-6 : 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 05:22:35 EDT 2022
% Result : Unsatisfiable 1.82s 1.98s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 27 ( 16 unt; 3 nHn; 27 RR)
% Number of literals : 41 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ordered_pair(y__dfg,z__dfg),ordered_pair(w__dfg,x__dfg)),
file('SET016-6.p',unknown),
[] ).
cnf(2,axiom,
member(w__dfg,universal_class),
file('SET016-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(y__dfg,w__dfg),
file('SET016-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET016-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET016-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET016-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET016-6.p',unknown),
[] ).
cnf(14,axiom,
member(unordered_pair(u,v),universal_class),
file('SET016-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET016-6.p',unknown),
[] ).
cnf(16,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET016-6.p',unknown),
[] ).
cnf(100,plain,
member(w__dfg,unordered_pair(w__dfg,u)),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(117,plain,
( ~ member(w__dfg,unordered_pair(u,y__dfg))
| equal(w__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(128,plain,
~ member(w__dfg,unordered_pair(y__dfg,y__dfg)),
inference(res,[status(thm),theory(equality)],[117,3]),
[iquote('0:Res:117.1,3.0')] ).
cnf(132,plain,
~ member(w__dfg,singleton(y__dfg)),
inference(rew,[status(thm),theory(equality)],[15,128]),
[iquote('0:Rew:15.0,128.0')] ).
cnf(151,plain,
member(w__dfg,singleton(w__dfg)),
inference(spr,[status(thm),theory(equality)],[15,100]),
[iquote('0:SpR:15.0,100.0')] ).
cnf(153,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[15,14]),
[iquote('0:SpR:15.0,14.0')] ).
cnf(357,plain,
( ~ member(singleton(u),universal_class)
| member(singleton(u),ordered_pair(u,v)) ),
inference(spr,[status(thm),theory(equality)],[16,12]),
[iquote('0:SpR:16.0,12.1')] ).
cnf(360,plain,
member(singleton(u),ordered_pair(u,v)),
inference(mrr,[status(thm)],[357,153]),
[iquote('0:MRR:357.0,153.0')] ).
cnf(364,plain,
member(singleton(y__dfg),ordered_pair(w__dfg,x__dfg)),
inference(spr,[status(thm),theory(equality)],[1,360]),
[iquote('0:SpR:1.0,360.0')] ).
cnf(445,plain,
( ~ subclass(singleton(w__dfg),u)
| member(w__dfg,u) ),
inference(res,[status(thm),theory(equality)],[151,4]),
[iquote('0:Res:151.0,4.0')] ).
cnf(504,plain,
( ~ equal(u,singleton(w__dfg))
| member(w__dfg,u) ),
inference(res,[status(thm),theory(equality)],[9,445]),
[iquote('0:Res:9.1,445.0')] ).
cnf(507,plain,
~ equal(singleton(y__dfg),singleton(w__dfg)),
inference(res,[status(thm),theory(equality)],[504,132]),
[iquote('0:Res:504.1,132.0')] ).
cnf(604,plain,
( ~ member(u,ordered_pair(v,w))
| equal(u,unordered_pair(v,singleton(w)))
| equal(u,singleton(v)) ),
inference(spl,[status(thm),theory(equality)],[16,11]),
[iquote('0:SpL:16.0,11.0')] ).
cnf(6016,plain,
( equal(unordered_pair(w__dfg,singleton(x__dfg)),singleton(y__dfg))
| equal(singleton(y__dfg),singleton(w__dfg)) ),
inference(res,[status(thm),theory(equality)],[364,604]),
[iquote('0:Res:364.0,604.0')] ).
cnf(6025,plain,
equal(unordered_pair(w__dfg,singleton(x__dfg)),singleton(y__dfg)),
inference(mrr,[status(thm)],[6016,507]),
[iquote('0:MRR:6016.1,507.0')] ).
cnf(6031,plain,
( ~ member(w__dfg,universal_class)
| member(w__dfg,singleton(y__dfg)) ),
inference(spr,[status(thm),theory(equality)],[6025,12]),
[iquote('0:SpR:6025.0,12.1')] ).
cnf(6049,plain,
$false,
inference(mrr,[status(thm)],[6031,2,132]),
[iquote('0:MRR:6031.0,6031.1,2.0,132.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET016-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 18:52:07 EDT 2022
% 0.13/0.36 % CPUTime :
% 1.82/1.98
% 1.82/1.98 SPASS V 3.9
% 1.82/1.98 SPASS beiseite: Proof found.
% 1.82/1.98 % SZS status Theorem
% 1.82/1.98 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.82/1.98 SPASS derived 5172 clauses, backtracked 0 clauses, performed 7 splits and kept 3020 clauses.
% 1.82/1.98 SPASS allocated 81222 KBytes.
% 1.82/1.98 SPASS spent 0:00:01.58 on the problem.
% 1.82/1.98 0:00:00.04 for the input.
% 1.82/1.98 0:00:00.00 for the FLOTTER CNF translation.
% 1.82/1.98 0:00:00.07 for inferences.
% 1.82/1.98 0:00:00.06 for the backtracking.
% 1.82/1.98 0:00:01.34 for the reduction.
% 1.82/1.98
% 1.82/1.98
% 1.82/1.98 Here is a proof with depth 5, length 27 :
% 1.82/1.98 % SZS output start Refutation
% See solution above
% 1.82/1.98 Formulae used in the proof : prove_ordered_pair_determines_components1_1 prove_ordered_pair_determines_components1_2 prove_ordered_pair_determines_components1_3 subclass_members equal_implies_subclass2 unordered_pair_member unordered_pair2 unordered_pairs_in_universal singleton_set ordered_pair
% 1.82/1.98
%------------------------------------------------------------------------------