%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET644+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:27:48 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 45 ( 12 unt; 5 nHn; 45 RR)
% Number of literals : 115 ( 0 equ; 74 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
member(skc7,skc8),
file('SET644+3.p',unknown),
[] ).
cnf(6,axiom,
ilf_type(u,set_type),
file('SET644+3.p',unknown),
[] ).
cnf(13,axiom,
ilf_type(skc8,relation_type(skc5,skc6)),
file('SET644+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET644+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf18(v,u),u)
| member(u,power_set(v)) ),
file('SET644+3.p',unknown),
[] ).
cnf(39,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET644+3.p',unknown),
[] ).
cnf(40,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('SET644+3.p',unknown),
[] ).
cnf(43,axiom,
( ~ ilf_type(u,member_type(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(u,v)
| empty(v) ),
file('SET644+3.p',unknown),
[] ).
cnf(47,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('SET644+3.p',unknown),
[] ).
cnf(51,axiom,
( ~ relation_like(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type)
| equal(ordered_pair(skf20(v),skf21(v)),v) ),
file('SET644+3.p',unknown),
[] ).
cnf(52,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ equal(ordered_pair(u,v),skc7)
| ~ member(v,skc6)
| ~ member(u,skc5) ),
file('SET644+3.p',unknown),
[] ).
cnf(57,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('SET644+3.p',unknown),
[] ).
cnf(60,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('SET644+3.p',unknown),
[] ).
cnf(61,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('SET644+3.p',unknown),
[] ).
cnf(72,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[35,6]),
[iquote('0:MRR:35.1,35.3,6.0,6.0')] ).
cnf(77,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[39,6]),
[iquote('0:MRR:39.0,39.1,6.0,6.0')] ).
cnf(78,plain,
( member(u,power_set(v))
| member(skf18(v,u),u) ),
inference(mrr,[status(thm)],[38,6]),
[iquote('0:MRR:38.0,38.1,6.0,6.0')] ).
cnf(81,plain,
( ~ ilf_type(u,member_type(v))
| empty(v)
| member(u,v) ),
inference(mrr,[status(thm)],[43,6]),
[iquote('0:MRR:43.1,43.2,6.0,6.0')] ).
cnf(84,plain,
( ~ ilf_type(u,subset_type(v))
| ilf_type(u,member_type(power_set(v))) ),
inference(mrr,[status(thm)],[40,6]),
[iquote('0:MRR:40.1,40.2,6.0,6.0')] ).
cnf(87,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[47,6]),
[iquote('0:MRR:47.1,47.2,6.0,6.0')] ).
cnf(91,plain,
( ~ relation_like(u)
| ~ member(v,u)
| equal(ordered_pair(skf20(v),skf21(v)),v) ),
inference(mrr,[status(thm)],[51,6]),
[iquote('0:MRR:51.1,51.3,6.0,6.0')] ).
cnf(92,plain,
( ~ member(u,skc5)
| ~ member(v,skc6)
| ~ equal(ordered_pair(u,v),skc7) ),
inference(mrr,[status(thm)],[52,6]),
[iquote('0:MRR:52.0,52.1,6.0,6.0')] ).
cnf(96,plain,
( ~ member(u,v)
| ~ member(v,power_set(w))
| member(u,w) ),
inference(mrr,[status(thm)],[57,6]),
[iquote('0:MRR:57.1,57.3,57.4,6.0,6.0,6.0')] ).
cnf(101,plain,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
inference(mrr,[status(thm)],[60,6]),
[iquote('0:MRR:60.1,60.2,60.3,60.4,6.0,6.0,6.0,6.0')] ).
cnf(102,plain,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,w) ),
inference(mrr,[status(thm)],[61,6]),
[iquote('0:MRR:61.1,61.2,61.3,61.4,6.0,6.0,6.0,6.0')] ).
cnf(104,plain,
( ~ relation_like(skc8)
| equal(ordered_pair(skf20(skc7),skf21(skc7)),skc7) ),
inference(res,[status(thm),theory(equality)],[4,91]),
[iquote('0:Res:4.0,91.1')] ).
cnf(107,plain,
( ~ member(skc8,power_set(u))
| member(skc7,u) ),
inference(res,[status(thm),theory(equality)],[4,96]),
[iquote('0:Res:4.0,96.1')] ).
cnf(113,plain,
ilf_type(skc8,subset_type(cross_product(skc5,skc6))),
inference(res,[status(thm),theory(equality)],[13,87]),
[iquote('0:Res:13.0,87.0')] ).
cnf(132,plain,
relation_like(skc8),
inference(res,[status(thm),theory(equality)],[113,77]),
[iquote('0:Res:113.0,77.0')] ).
cnf(133,plain,
equal(ordered_pair(skf20(skc7),skf21(skc7)),skc7),
inference(mrr,[status(thm)],[104,132]),
[iquote('0:MRR:104.0,132.0')] ).
cnf(134,plain,
( ~ empty(u)
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[78,72]),
[iquote('0:Res:78.1,72.1')] ).
cnf(137,plain,
( ~ empty(u)
| ~ empty(power_set(v)) ),
inference(res,[status(thm),theory(equality)],[134,72]),
[iquote('0:Res:134.1,72.1')] ).
cnf(139,plain,
~ empty(power_set(u)),
inference(con,[status(thm)],[137]),
[iquote('0:Con:137.0')] ).
cnf(165,plain,
( ~ ilf_type(u,subset_type(v))
| empty(power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[84,81]),
[iquote('0:Res:84.1,81.0')] ).
cnf(167,plain,
( ~ ilf_type(u,subset_type(v))
| member(u,power_set(v)) ),
inference(mrr,[status(thm)],[165,139]),
[iquote('0:MRR:165.1,139.0')] ).
cnf(180,plain,
( ~ ilf_type(skc8,subset_type(u))
| member(skc7,u) ),
inference(res,[status(thm),theory(equality)],[167,107]),
[iquote('0:Res:167.1,107.0')] ).
cnf(194,plain,
member(skc7,cross_product(skc5,skc6)),
inference(res,[status(thm),theory(equality)],[113,180]),
[iquote('0:Res:113.0,180.0')] ).
cnf(215,plain,
( ~ member(skc7,cross_product(u,v))
| member(skf21(skc7),v) ),
inference(spl,[status(thm),theory(equality)],[133,101]),
[iquote('0:SpL:133.0,101.0')] ).
cnf(223,plain,
member(skf21(skc7),skc6),
inference(res,[status(thm),theory(equality)],[194,215]),
[iquote('0:Res:194.0,215.0')] ).
cnf(226,plain,
( ~ member(skc7,cross_product(u,v))
| member(skf20(skc7),u) ),
inference(spl,[status(thm),theory(equality)],[133,102]),
[iquote('0:SpL:133.0,102.0')] ).
cnf(307,plain,
( ~ member(skf20(skc7),skc5)
| ~ member(skf21(skc7),skc6)
| ~ equal(skc7,skc7) ),
inference(spl,[status(thm),theory(equality)],[133,92]),
[iquote('0:SpL:133.0,92.2')] ).
cnf(308,plain,
( ~ member(skf20(skc7),skc5)
| ~ member(skf21(skc7),skc6) ),
inference(obv,[status(thm),theory(equality)],[307]),
[iquote('0:Obv:307.2')] ).
cnf(309,plain,
~ member(skf20(skc7),skc5),
inference(mrr,[status(thm)],[308,223]),
[iquote('0:MRR:308.1,223.0')] ).
cnf(347,plain,
member(skf20(skc7),skc5),
inference(res,[status(thm),theory(equality)],[194,226]),
[iquote('0:Res:194.0,226.0')] ).
cnf(348,plain,
$false,
inference(mrr,[status(thm)],[347,309]),
[iquote('0:MRR:347.0,309.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET644+3 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.08/0.26 % Computer : n009.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 600
% 0.08/0.26 % DateTime : Sun Jul 10 20:55:51 EDT 2022
% 0.08/0.26 % CPUTime :
% 0.12/0.34
% 0.12/0.34 SPASS V 3.9
% 0.12/0.34 SPASS beiseite: Proof found.
% 0.12/0.34 % SZS status Theorem
% 0.12/0.34 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 SPASS derived 231 clauses, backtracked 0 clauses, performed 0 splits and kept 213 clauses.
% 0.12/0.34 SPASS allocated 97921 KBytes.
% 0.12/0.34 SPASS spent 0:00:00.07 on the problem.
% 0.12/0.34 0:00:00.02 for the input.
% 0.12/0.34 0:00:00.02 for the FLOTTER CNF translation.
% 0.12/0.34 0:00:00.00 for inferences.
% 0.12/0.34 0:00:00.00 for the backtracking.
% 0.12/0.34 0:00:00.01 for the reduction.
% 0.12/0.34
% 0.12/0.34
% 0.12/0.34 Here is a proof with depth 4, length 45 :
% 0.12/0.34 % SZS output start Refutation
% See solution above
% 0.12/0.34 Formulae used in the proof : prove_relset_1_6 p27 p25 p19 p24 p14 p21 p5 p23 p2
% 0.12/0.34
%------------------------------------------------------------------------------