TSTP Solution File: SET105-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET105-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 05:24:07 EDT 2022
% Result : Unsatisfiable 0.18s 0.55s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 25 unt; 2 nHn; 27 RR)
% Number of literals : 29 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(21,axiom,
( member(u,universal_class)
| equal(unordered_pair(u,v),singleton(v)) ),
file('SET105-7.p',unknown),
[] ).
cnf(35,axiom,
( member(u,universal_class)
| equal(singleton(u),null_class) ),
file('SET105-7.p',unknown),
[] ).
cnf(53,axiom,
equal(union(singleton(u),singleton(v)),unordered_pair(u,v)),
file('SET105-7.p',unknown),
[] ).
cnf(57,axiom,
~ equal(unordered_pair(null_class,singleton(null_class)),ordered_pair(x__dfg,y__dfg)),
file('SET105-7.p',unknown),
[] ).
cnf(58,axiom,
~ member(x__dfg,universal_class),
file('SET105-7.p',unknown),
[] ).
cnf(59,axiom,
~ member(y__dfg,universal_class),
file('SET105-7.p',unknown),
[] ).
cnf(72,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET105-7.p',unknown),
[] ).
cnf(102,axiom,
equal(union(u,singleton(u)),successor(u)),
file('SET105-7.p',unknown),
[] ).
cnf(160,plain,
equal(singleton(y__dfg),null_class),
inference(res,[status(thm),theory(equality)],[35,59]),
[iquote('0:Res:35.0,59.0')] ).
cnf(171,plain,
equal(unordered_pair(x__dfg,u),singleton(u)),
inference(res,[status(thm),theory(equality)],[21,58]),
[iquote('0:Res:21.0,58.0')] ).
cnf(173,plain,
equal(singleton(x__dfg),null_class),
inference(res,[status(thm),theory(equality)],[35,58]),
[iquote('0:Res:35.0,58.0')] ).
cnf(534,plain,
equal(unordered_pair(u,singleton(u)),successor(singleton(u))),
inference(spr,[status(thm),theory(equality)],[53,102]),
[iquote('0:SpR:53.0,102.0')] ).
cnf(539,plain,
equal(union(null_class,singleton(u)),unordered_pair(x__dfg,u)),
inference(spr,[status(thm),theory(equality)],[173,53]),
[iquote('0:SpR:173.0,53.0')] ).
cnf(542,plain,
~ equal(ordered_pair(x__dfg,y__dfg),successor(singleton(null_class))),
inference(rew,[status(thm),theory(equality)],[534,57]),
[iquote('0:Rew:534.0,57.0')] ).
cnf(549,plain,
equal(union(null_class,singleton(u)),singleton(u)),
inference(rew,[status(thm),theory(equality)],[171,539]),
[iquote('0:Rew:171.0,539.0')] ).
cnf(559,plain,
equal(singleton(null_class),successor(null_class)),
inference(spr,[status(thm),theory(equality)],[549,102]),
[iquote('0:SpR:549.0,102.0')] ).
cnf(570,plain,
~ equal(ordered_pair(x__dfg,y__dfg),successor(successor(null_class))),
inference(rew,[status(thm),theory(equality)],[559,542]),
[iquote('0:Rew:559.0,542.0')] ).
cnf(763,plain,
equal(unordered_pair(null_class,successor(null_class)),successor(successor(null_class))),
inference(spr,[status(thm),theory(equality)],[559,534]),
[iquote('0:SpR:559.0,534.0')] ).
cnf(1216,plain,
equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,x__dfg)),
inference(spr,[status(thm),theory(equality)],[173,72]),
[iquote('0:SpR:173.0,72.0')] ).
cnf(1217,plain,
equal(unordered_pair(singleton(u),unordered_pair(u,null_class)),ordered_pair(u,y__dfg)),
inference(spr,[status(thm),theory(equality)],[160,72]),
[iquote('0:SpR:160.0,72.0')] ).
cnf(1224,plain,
equal(unordered_pair(singleton(x__dfg),singleton(singleton(u))),ordered_pair(x__dfg,u)),
inference(spr,[status(thm),theory(equality)],[171,72]),
[iquote('0:SpR:171.0,72.0')] ).
cnf(1235,plain,
equal(ordered_pair(u,y__dfg),ordered_pair(u,x__dfg)),
inference(rew,[status(thm),theory(equality)],[1216,1217]),
[iquote('0:Rew:1216.0,1217.0')] ).
cnf(1238,plain,
~ equal(ordered_pair(x__dfg,x__dfg),successor(successor(null_class))),
inference(rew,[status(thm),theory(equality)],[1235,570]),
[iquote('0:Rew:1235.0,570.0')] ).
cnf(1248,plain,
equal(unordered_pair(null_class,singleton(singleton(u))),ordered_pair(x__dfg,u)),
inference(rew,[status(thm),theory(equality)],[173,1224]),
[iquote('0:Rew:173.0,1224.0')] ).
cnf(1537,plain,
equal(unordered_pair(null_class,singleton(null_class)),ordered_pair(x__dfg,y__dfg)),
inference(spr,[status(thm),theory(equality)],[160,1248]),
[iquote('0:SpR:160.0,1248.0')] ).
cnf(1545,plain,
equal(ordered_pair(x__dfg,x__dfg),successor(successor(null_class))),
inference(rew,[status(thm),theory(equality)],[763,1537,559,1235]),
[iquote('0:Rew:763.0,1537.0,559.0,1537.0,1235.0,1537.0')] ).
cnf(1546,plain,
$false,
inference(mrr,[status(thm)],[1545,1238]),
[iquote('0:MRR:1545.0,1238.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET105-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 09:21:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.55
% 0.18/0.55 SPASS V 3.9
% 0.18/0.55 SPASS beiseite: Proof found.
% 0.18/0.55 % SZS status Theorem
% 0.18/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.55 SPASS derived 1142 clauses, backtracked 0 clauses, performed 2 splits and kept 554 clauses.
% 0.18/0.55 SPASS allocated 76894 KBytes.
% 0.18/0.55 SPASS spent 0:00:00.21 on the problem.
% 0.18/0.55 0:00:00.04 for the input.
% 0.18/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.55 0:00:00.02 for inferences.
% 0.18/0.55 0:00:00.00 for the backtracking.
% 0.18/0.55 0:00:00.11 for the reduction.
% 0.18/0.55
% 0.18/0.55
% 0.18/0.55 Here is a proof with depth 4, length 27 :
% 0.18/0.55 % SZS output start Refutation
% See solution above
% 0.18/0.55 Formulae used in the proof : unordered_pair_equals_singleton2 singleton_is_null_class unordered_pairs_and_singletons prove_property_3_of_ordered_pair_1 prove_property_3_of_ordered_pair_2 prove_property_3_of_ordered_pair_3 ordered_pair successor
% 0.18/0.55
%------------------------------------------------------------------------------