TSTP Solution File: SET645+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:27:48 EDT 2022
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 35 ( 9 unt; 5 nHn; 35 RR)
% Number of literals : 87 ( 0 equ; 53 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
ilf_type(u,set_type),
file('SET645+3.p',unknown),
[] ).
cnf(10,axiom,
ilf_type(skc9,relation_type(skc5,skc6)),
file('SET645+3.p',unknown),
[] ).
cnf(11,axiom,
member(ordered_pair(skc7,skc8),skc9),
file('SET645+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(skc8,skc6)
| ~ member(skc7,skc5) ),
file('SET645+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET645+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf12(v,u),u)
| member(u,power_set(v)) ),
file('SET645+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ ilf_type(u,subset_type(v))
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| ilf_type(u,member_type(power_set(v))) ),
file('SET645+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ ilf_type(u,member_type(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(u,v)
| empty(v) ),
file('SET645+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(u,relation_type(v,w))
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ilf_type(u,subset_type(cross_product(v,w))) ),
file('SET645+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ member(u,power_set(v))
| ~ ilf_type(w,set_type)
| ~ member(w,u)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(w,v) ),
file('SET645+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,set_type)
| member(v,x) ),
file('SET645+3.p',unknown),
[] ).
cnf(48,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,set_type)
| member(u,w) ),
file('SET645+3.p',unknown),
[] ).
cnf(56,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[28,5]),
[iquote('0:MRR:28.1,28.3,5.0,5.0')] ).
cnf(60,plain,
( member(u,power_set(v))
| member(skf12(v,u),u) ),
inference(mrr,[status(thm)],[29,5]),
[iquote('0:MRR:29.0,29.1,5.0,5.0')] ).
cnf(62,plain,
( ~ ilf_type(u,member_type(v))
| empty(v)
| member(u,v) ),
inference(mrr,[status(thm)],[34,5]),
[iquote('0:MRR:34.1,34.2,5.0,5.0')] ).
cnf(65,plain,
( ~ ilf_type(u,subset_type(v))
| ilf_type(u,member_type(power_set(v))) ),
inference(mrr,[status(thm)],[31,5]),
[iquote('0:MRR:31.1,31.2,5.0,5.0')] ).
cnf(66,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[36,5]),
[iquote('0:MRR:36.1,36.2,5.0,5.0')] ).
cnf(73,plain,
( ~ member(u,v)
| ~ member(v,power_set(w))
| member(u,w) ),
inference(mrr,[status(thm)],[44,5]),
[iquote('0:MRR:44.1,44.3,44.4,5.0,5.0,5.0')] ).
cnf(78,plain,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
inference(mrr,[status(thm)],[47,5]),
[iquote('0:MRR:47.1,47.2,47.3,47.4,5.0,5.0,5.0,5.0')] ).
cnf(79,plain,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,w) ),
inference(mrr,[status(thm)],[48,5]),
[iquote('0:MRR:48.1,48.2,48.3,48.4,5.0,5.0,5.0,5.0')] ).
cnf(83,plain,
( ~ member(skc9,power_set(u))
| member(ordered_pair(skc7,skc8),u) ),
inference(res,[status(thm),theory(equality)],[11,73]),
[iquote('0:Res:11.0,73.1')] ).
cnf(88,plain,
ilf_type(skc9,subset_type(cross_product(skc5,skc6))),
inference(res,[status(thm),theory(equality)],[10,66]),
[iquote('0:Res:10.0,66.0')] ).
cnf(99,plain,
( ~ empty(u)
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[60,56]),
[iquote('0:Res:60.1,56.1')] ).
cnf(100,plain,
( ~ empty(u)
| ~ empty(power_set(v)) ),
inference(res,[status(thm),theory(equality)],[99,56]),
[iquote('0:Res:99.1,56.1')] ).
cnf(101,plain,
~ empty(power_set(u)),
inference(con,[status(thm)],[100]),
[iquote('0:Con:100.0')] ).
cnf(128,plain,
( ~ ilf_type(u,subset_type(v))
| empty(power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[65,62]),
[iquote('0:Res:65.1,62.0')] ).
cnf(130,plain,
( ~ ilf_type(u,subset_type(v))
| member(u,power_set(v)) ),
inference(mrr,[status(thm)],[128,101]),
[iquote('0:MRR:128.1,101.0')] ).
cnf(145,plain,
( ~ member(skc9,power_set(cross_product(u,v)))
| member(skc8,v) ),
inference(res,[status(thm),theory(equality)],[83,78]),
[iquote('0:Res:83.1,78.0')] ).
cnf(147,plain,
( ~ ilf_type(skc9,subset_type(cross_product(u,v)))
| member(skc8,v) ),
inference(res,[status(thm),theory(equality)],[130,145]),
[iquote('0:Res:130.1,145.0')] ).
cnf(149,plain,
member(skc8,skc6),
inference(res,[status(thm),theory(equality)],[88,147]),
[iquote('0:Res:88.0,147.0')] ).
cnf(151,plain,
~ member(skc7,skc5),
inference(mrr,[status(thm)],[14,149]),
[iquote('0:MRR:14.0,149.0')] ).
cnf(153,plain,
( ~ member(skc9,power_set(cross_product(u,v)))
| member(skc7,u) ),
inference(res,[status(thm),theory(equality)],[83,79]),
[iquote('0:Res:83.1,79.0')] ).
cnf(199,plain,
( ~ ilf_type(skc9,subset_type(cross_product(u,v)))
| member(skc7,u) ),
inference(res,[status(thm),theory(equality)],[130,153]),
[iquote('0:Res:130.1,153.0')] ).
cnf(528,plain,
member(skc7,skc5),
inference(res,[status(thm),theory(equality)],[88,199]),
[iquote('0:Res:88.0,199.0')] ).
cnf(531,plain,
$false,
inference(mrr,[status(thm)],[528,151]),
[iquote('0:MRR:528.0,151.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 : Sat Jul 9 18:27:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.49
% 0.18/0.49 SPASS V 3.9
% 0.18/0.49 SPASS beiseite: Proof found.
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49 SPASS derived 432 clauses, backtracked 0 clauses, performed 0 splits and kept 407 clauses.
% 0.18/0.49 SPASS allocated 98182 KBytes.
% 0.18/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.49 0:00:00.03 for the input.
% 0.18/0.49 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.49 0:00:00.01 for inferences.
% 0.18/0.49 0:00:00.00 for the backtracking.
% 0.18/0.49 0:00:00.05 for the reduction.
% 0.18/0.49
% 0.18/0.49
% 0.18/0.49 Here is a proof with depth 4, length 35 :
% 0.18/0.49 % SZS output start Refutation
% See solution above
% 0.18/0.49 Formulae used in the proof : p21 prove_relset_1_7 p17 p13 p10 p15 p4 p1
% 0.18/0.49
%------------------------------------------------------------------------------