%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET099-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 05:24:01 EDT 2022
% Result : Unsatisfiable 1.12s 1.30s
% Output : Refutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 10 unt; 4 nHn; 21 RR)
% Number of literals : 35 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,universal_class) ),
file('SET099-7.p',unknown),
[] ).
cnf(15,axiom,
( equal(u,null_class)
| member(not_subclass_element(u,null_class),u) ),
file('SET099-7.p',unknown),
[] ).
cnf(31,axiom,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
file('SET099-7.p',unknown),
[] ).
cnf(50,axiom,
( equal(u,null_class)
| equal(singleton(not_subclass_element(u,null_class)),u)
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(u,null_class))),u),null_class),intersection(complement(singleton(not_subclass_element(u,null_class))),u)) ),
file('SET099-7.p',unknown),
[] ).
cnf(51,axiom,
equal(not_subclass_element(intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg),null_class),not_subclass_element(x__dfg,null_class)),
file('SET099-7.p',unknown),
[] ).
cnf(52,axiom,
~ equal(singleton(not_subclass_element(x__dfg,null_class)),x__dfg),
file('SET099-7.p',unknown),
[] ).
cnf(53,axiom,
~ equal(null_class,x__dfg),
file('SET099-7.p',unknown),
[] ).
cnf(69,axiom,
( ~ member(u,v)
| ~ member(w,x)
| member(ordered_pair(w,u),cross_product(x,v)) ),
file('SET099-7.p',unknown),
[] ).
cnf(74,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET099-7.p',unknown),
[] ).
cnf(77,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET099-7.p',unknown),
[] ).
cnf(167,plain,
member(not_subclass_element(x__dfg,null_class),x__dfg),
inference(res,[status(thm),theory(equality)],[15,53]),
[iquote('0:Res:15.0,53.0')] ).
cnf(182,plain,
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg),null_class),intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg))
| equal(null_class,x__dfg) ),
inference(res,[status(thm),theory(equality)],[50,52]),
[iquote('0:Res:50.1,52.0')] ).
cnf(215,plain,
( member(not_subclass_element(x__dfg,null_class),intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg))
| equal(null_class,x__dfg) ),
inference(rew,[status(thm),theory(equality)],[51,182]),
[iquote('0:Rew:51.0,182.0')] ).
cnf(216,plain,
member(not_subclass_element(x__dfg,null_class),intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg)),
inference(mrr,[status(thm)],[215,53]),
[iquote('0:MRR:215.1,53.0')] ).
cnf(1075,plain,
member(not_subclass_element(x__dfg,null_class),complement(singleton(not_subclass_element(x__dfg,null_class)))),
inference(res,[status(thm),theory(equality)],[216,74]),
[iquote('0:Res:216.0,74.0')] ).
cnf(1080,plain,
~ member(not_subclass_element(x__dfg,null_class),singleton(not_subclass_element(x__dfg,null_class))),
inference(res,[status(thm),theory(equality)],[1075,77]),
[iquote('0:Res:1075.0,77.1')] ).
cnf(1085,plain,
~ member(not_subclass_element(x__dfg,null_class),universal_class),
inference(res,[status(thm),theory(equality)],[31,1080]),
[iquote('0:Res:31.1,1080.0')] ).
cnf(4418,plain,
( ~ member(u,v)
| ~ member(w,x)
| member(w,universal_class) ),
inference(res,[status(thm),theory(equality)],[69,3]),
[iquote('0:Res:69.2,3.0')] ).
cnf(4420,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[4418]),
[iquote('0:Con:4418.0')] ).
cnf(4571,plain,
member(not_subclass_element(x__dfg,null_class),universal_class),
inference(res,[status(thm),theory(equality)],[167,4420]),
[iquote('0:Res:167.0,4420.0')] ).
cnf(4574,plain,
$false,
inference(mrr,[status(thm)],[4571,1085]),
[iquote('0:MRR:4571.0,1085.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET099-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.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 : Sat Jul 9 16:47:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.12/1.30
% 1.12/1.30 SPASS V 3.9
% 1.12/1.30 SPASS beiseite: Proof found.
% 1.12/1.30 % SZS status Theorem
% 1.12/1.30 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.12/1.30 SPASS derived 3566 clauses, backtracked 520 clauses, performed 2 splits and kept 2204 clauses.
% 1.12/1.30 SPASS allocated 79896 KBytes.
% 1.12/1.30 SPASS spent 0:00:00.92 on the problem.
% 1.12/1.30 0:00:00.04 for the input.
% 1.12/1.30 0:00:00.00 for the FLOTTER CNF translation.
% 1.12/1.30 0:00:00.04 for inferences.
% 1.12/1.30 0:00:00.03 for the backtracking.
% 1.12/1.30 0:00:00.76 for the reduction.
% 1.12/1.30
% 1.12/1.30
% 1.12/1.30 Here is a proof with depth 4, length 21 :
% 1.12/1.30 % SZS output start Refutation
% See solution above
% 1.12/1.31 Formulae used in the proof : corollary_1_to_cartesian_product null_class_is_unique set_in_its_singleton number_of_elements_in_class prove_corollary_2_to_number_of_elements_in_class_1 prove_corollary_2_to_number_of_elements_in_class_2 prove_corollary_2_to_number_of_elements_in_class_3 cartesian_product3 intersection1 complement1
% 1.12/1.31
%------------------------------------------------------------------------------