TSTP Solution File: SET657+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET657+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:27:54 EDT 2022
% Result : Theorem 41.66s 41.91s
% Output : Refutation 41.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of clauses : 60 ( 13 unt; 11 nHn; 60 RR)
% Number of literals : 150 ( 0 equ; 88 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
ilf_type(u,set_type),
file('SET657+3.p',unknown),
[] ).
cnf(9,axiom,
ilf_type(skc6,relation_type(skc4,skc5)),
file('SET657+3.p',unknown),
[] ).
cnf(13,axiom,
~ subset(field_of(skc6),union(skc4,skc5)),
file('SET657+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET657+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ ilf_type(u,binary_relation_type)
| equal(union(domain_of(u),range_of(u)),field_of(u)) ),
file('SET657+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET657+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf11(v,u),u)
| subset(u,v) ),
file('SET657+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ member(skf11(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| subset(v,u) ),
file('SET657+3.p',unknown),
[] ).
cnf(39,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf13(v,u),u)
| member(u,power_set(v)) ),
file('SET657+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET657+3.p',unknown),
[] ).
cnf(41,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('SET657+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ ilf_type(u,member_type(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(u,v)
| empty(v) ),
file('SET657+3.p',unknown),
[] ).
cnf(46,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('SET657+3.p',unknown),
[] ).
cnf(48,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| ilf_type(range__dfg(u,v,w),subset_type(v)) ),
file('SET657+3.p',unknown),
[] ).
cnf(49,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| equal(range__dfg(u,v,w),range_of(w)) ),
file('SET657+3.p',unknown),
[] ).
cnf(50,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| ilf_type(domain__dfg(u,v,w),subset_type(u)) ),
file('SET657+3.p',unknown),
[] ).
cnf(51,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,relation_type(u,v))
| equal(domain__dfg(u,v,w),domain_of(w)) ),
file('SET657+3.p',unknown),
[] ).
cnf(61,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('SET657+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,set_type)
| ~ subset(w,x)
| ~ subset(u,v)
| subset(union(u,w),union(v,x)) ),
file('SET657+3.p',unknown),
[] ).
cnf(72,plain,
( ~ relation_like(u)
| ilf_type(u,binary_relation_type) ),
inference(mrr,[status(thm)],[25,4]),
[iquote('0:MRR:25.1,4.0')] ).
cnf(75,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[36,4]),
[iquote('0:MRR:36.1,36.3,4.0,4.0')] ).
cnf(78,plain,
( subset(u,v)
| member(skf11(v,u),u) ),
inference(mrr,[status(thm)],[37,4]),
[iquote('0:MRR:37.0,37.1,4.0,4.0')] ).
cnf(79,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[40,4]),
[iquote('0:MRR:40.0,40.1,4.0,4.0')] ).
cnf(80,plain,
( member(u,power_set(v))
| member(skf13(v,u),u) ),
inference(mrr,[status(thm)],[39,4]),
[iquote('0:MRR:39.0,39.1,4.0,4.0')] ).
cnf(81,plain,
( ~ member(skf11(u,v),u)
| subset(v,u) ),
inference(mrr,[status(thm)],[38,4]),
[iquote('0:MRR:38.1,38.2,4.0,4.0')] ).
cnf(83,plain,
( ~ ilf_type(u,member_type(v))
| empty(v)
| member(u,v) ),
inference(mrr,[status(thm)],[44,4]),
[iquote('0:MRR:44.1,44.2,4.0,4.0')] ).
cnf(86,plain,
( ~ ilf_type(u,subset_type(v))
| ilf_type(u,member_type(power_set(v))) ),
inference(mrr,[status(thm)],[41,4]),
[iquote('0:MRR:41.1,41.2,4.0,4.0')] ).
cnf(87,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[46,4]),
[iquote('0:MRR:46.1,46.2,4.0,4.0')] ).
cnf(89,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(range__dfg(v,w,u),subset_type(w)) ),
inference(mrr,[status(thm)],[48,4]),
[iquote('0:MRR:48.0,48.1,4.0,4.0')] ).
cnf(90,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(range__dfg(v,w,u),range_of(u)) ),
inference(mrr,[status(thm)],[49,4]),
[iquote('0:MRR:49.0,49.1,4.0,4.0')] ).
cnf(91,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(range_of(u),subset_type(w)) ),
inference(rew,[status(thm),theory(equality)],[90,89]),
[iquote('0:Rew:90.1,89.1')] ).
cnf(92,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(domain__dfg(v,w,u),subset_type(v)) ),
inference(mrr,[status(thm)],[50,4]),
[iquote('0:MRR:50.0,50.1,4.0,4.0')] ).
cnf(93,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(domain__dfg(v,w,u),domain_of(u)) ),
inference(mrr,[status(thm)],[51,4]),
[iquote('0:MRR:51.0,51.1,4.0,4.0')] ).
cnf(94,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(domain_of(u),subset_type(v)) ),
inference(rew,[status(thm),theory(equality)],[93,92]),
[iquote('0:Rew:93.1,92.1')] ).
cnf(103,plain,
( ~ member(u,v)
| ~ member(v,power_set(w))
| member(u,w) ),
inference(mrr,[status(thm)],[61,4]),
[iquote('0:MRR:61.1,61.3,61.4,4.0,4.0,4.0')] ).
cnf(108,plain,
( ~ subset(u,v)
| ~ subset(w,x)
| subset(union(u,w),union(v,x)) ),
inference(mrr,[status(thm)],[65,4]),
[iquote('0:MRR:65.0,65.1,65.2,65.3,4.0,4.0,4.0,4.0')] ).
cnf(111,plain,
ilf_type(domain_of(skc6),subset_type(skc4)),
inference(res,[status(thm),theory(equality)],[9,94]),
[iquote('0:Res:9.0,94.0')] ).
cnf(113,plain,
ilf_type(range_of(skc6),subset_type(skc5)),
inference(res,[status(thm),theory(equality)],[9,91]),
[iquote('0:Res:9.0,91.0')] ).
cnf(115,plain,
ilf_type(skc6,subset_type(cross_product(skc4,skc5))),
inference(res,[status(thm),theory(equality)],[9,87]),
[iquote('0:Res:9.0,87.0')] ).
cnf(140,plain,
relation_like(skc6),
inference(res,[status(thm),theory(equality)],[115,79]),
[iquote('0:Res:115.0,79.0')] ).
cnf(141,plain,
( ~ empty(u)
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[80,75]),
[iquote('0:Res:80.1,75.1')] ).
cnf(142,plain,
( ~ empty(u)
| ~ empty(power_set(v)) ),
inference(res,[status(thm),theory(equality)],[141,75]),
[iquote('0:Res:141.1,75.1')] ).
cnf(143,plain,
~ empty(power_set(u)),
inference(con,[status(thm)],[142]),
[iquote('0:Con:142.0')] ).
cnf(175,plain,
( ~ ilf_type(u,subset_type(v))
| empty(power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[86,83]),
[iquote('0:Res:86.1,83.0')] ).
cnf(178,plain,
( ~ ilf_type(u,subset_type(v))
| member(u,power_set(v)) ),
inference(mrr,[status(thm)],[175,143]),
[iquote('0:MRR:175.1,143.0')] ).
cnf(264,plain,
( ~ ilf_type(u,subset_type(v))
| ~ member(w,u)
| member(w,v) ),
inference(res,[status(thm),theory(equality)],[178,103]),
[iquote('0:Res:178.1,103.1')] ).
cnf(399,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ subset(domain_of(u),v)
| ~ subset(range_of(u),w)
| subset(field_of(u),union(v,w)) ),
inference(spr,[status(thm),theory(equality)],[30,108]),
[iquote('0:SpR:30.1,108.2')] ).
cnf(1496,plain,
( ~ ilf_type(skc6,binary_relation_type)
| ~ subset(domain_of(skc6),skc4)
| ~ subset(range_of(skc6),skc5) ),
inference(res,[status(thm),theory(equality)],[399,13]),
[iquote('0:Res:399.3,13.0')] ).
cnf(4308,plain,
( ~ member(u,range_of(skc6))
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[113,264]),
[iquote('0:Res:113.0,264.0')] ).
cnf(4314,plain,
( ~ member(u,domain_of(skc6))
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[111,264]),
[iquote('0:Res:111.0,264.0')] ).
cnf(4399,plain,
( subset(range_of(skc6),u)
| member(skf11(u,range_of(skc6)),skc5) ),
inference(res,[status(thm),theory(equality)],[78,4308]),
[iquote('0:Res:78.1,4308.0')] ).
cnf(5916,plain,
( subset(domain_of(skc6),u)
| member(skf11(u,domain_of(skc6)),skc4) ),
inference(res,[status(thm),theory(equality)],[78,4314]),
[iquote('0:Res:78.1,4314.0')] ).
cnf(25577,plain,
( subset(domain_of(skc6),skc4)
| subset(domain_of(skc6),skc4) ),
inference(res,[status(thm),theory(equality)],[5916,81]),
[iquote('0:Res:5916.1,81.0')] ).
cnf(25583,plain,
subset(domain_of(skc6),skc4),
inference(obv,[status(thm),theory(equality)],[25577]),
[iquote('0:Obv:25577.0')] ).
cnf(25611,plain,
( ~ ilf_type(skc6,binary_relation_type)
| ~ subset(range_of(skc6),skc5) ),
inference(mrr,[status(thm)],[1496,25583]),
[iquote('0:MRR:1496.1,25583.0')] ).
cnf(48275,plain,
( subset(range_of(skc6),skc5)
| subset(range_of(skc6),skc5) ),
inference(res,[status(thm),theory(equality)],[4399,81]),
[iquote('0:Res:4399.1,81.0')] ).
cnf(48285,plain,
subset(range_of(skc6),skc5),
inference(obv,[status(thm),theory(equality)],[48275]),
[iquote('0:Obv:48275.0')] ).
cnf(48286,plain,
~ ilf_type(skc6,binary_relation_type),
inference(mrr,[status(thm)],[25611,48285]),
[iquote('0:MRR:25611.1,48285.0')] ).
cnf(48310,plain,
~ relation_like(skc6),
inference(res,[status(thm),theory(equality)],[72,48286]),
[iquote('0:Res:72.1,48286.0')] ).
cnf(48311,plain,
$false,
inference(ssi,[status(thm)],[48310,140]),
[iquote('0:SSi:48310.0,140.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET657+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 09:02:01 EDT 2022
% 0.11/0.33 % CPUTime :
% 41.66/41.91
% 41.66/41.91 SPASS V 3.9
% 41.66/41.91 SPASS beiseite: Proof found.
% 41.66/41.91 % SZS status Theorem
% 41.66/41.91 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.66/41.91 SPASS derived 45046 clauses, backtracked 676 clauses, performed 7 splits and kept 23698 clauses.
% 41.66/41.91 SPASS allocated 135631 KBytes.
% 41.66/41.91 SPASS spent 0:0:40.05 on the problem.
% 41.66/41.91 0:00:00.03 for the input.
% 41.66/41.91 0:00:00.04 for the FLOTTER CNF translation.
% 41.66/41.91 0:00:00.40 for inferences.
% 41.66/41.91 0:00:02.93 for the backtracking.
% 41.66/41.91 0:0:36.30 for the reduction.
% 41.66/41.91
% 41.66/41.91
% 41.66/41.91 Here is a proof with depth 5, length 60 :
% 41.66/41.91 % SZS output start Refutation
% See solution above
% 41.66/41.91 Formulae used in the proof : p37 prove_relset_1_19 p14 p5 p29 p9 p21 p27 p16 p23 p7 p36 p35 p34 p33 p1
% 41.66/41.91
%------------------------------------------------------------------------------