TSTP Solution File: SET678+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET678+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:28:02 EDT 2022
% Result : Theorem 0.91s 1.13s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of clauses : 66 ( 12 unt; 11 nHn; 66 RR)
% Number of literals : 169 ( 0 equ; 104 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
ilf_type(u,set_type),
file('SET678+3.p',unknown),
[] ).
cnf(4,axiom,
ilf_type(skc4,identity_relation_of_type(skc3)),
file('SET678+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ relation_like(u)
| ~ ilf_type(u,set_type)
| ilf_type(u,binary_relation_type) ),
file('SET678+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ equal(compose(skc4,identity_relation_of(skc3)),skc4)
| ~ equal(compose(identity_relation_of(skc3),skc4),skc4) ),
file('SET678+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET678+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf18(v,u),u)
| subset(u,v) ),
file('SET678+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ member(skf18(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| subset(v,u) ),
file('SET678+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,subset_type(cross_product(u,v)))
| relation_like(w) ),
file('SET678+3.p',unknown),
[] ).
cnf(39,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf23(v,u),u)
| member(u,power_set(v)) ),
file('SET678+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ ilf_type(u,identity_relation_of_type(v))
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| ilf_type(u,relation_type(v,v)) ),
file('SET678+3.p',unknown),
[] ).
cnf(42,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('SET678+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ ilf_type(u,member_type(v))
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(u,v)
| empty(v) ),
file('SET678+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,binary_relation_type)
| ~ subset(domain_of(v),u)
| equal(compose(identity_relation_of(u),v),v) ),
file('SET678+3.p',unknown),
[] ).
cnf(48,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,binary_relation_type)
| ~ subset(range_of(v),u)
| equal(compose(v,identity_relation_of(u)),v) ),
file('SET678+3.p',unknown),
[] ).
cnf(49,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('SET678+3.p',unknown),
[] ).
cnf(51,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('SET678+3.p',unknown),
[] ).
cnf(52,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('SET678+3.p',unknown),
[] ).
cnf(53,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('SET678+3.p',unknown),
[] ).
cnf(54,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('SET678+3.p',unknown),
[] ).
cnf(60,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('SET678+3.p',unknown),
[] ).
cnf(79,plain,
( ~ relation_like(u)
| ilf_type(u,binary_relation_type) ),
inference(mrr,[status(thm)],[26,3]),
[iquote('0:MRR:26.1,3.0')] ).
cnf(82,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[35,3]),
[iquote('0:MRR:35.1,35.3,3.0,3.0')] ).
cnf(84,plain,
( subset(u,v)
| member(skf18(v,u),u) ),
inference(mrr,[status(thm)],[36,3]),
[iquote('0:MRR:36.0,36.1,3.0,3.0')] ).
cnf(85,plain,
( member(u,power_set(v))
| member(skf23(v,u),u) ),
inference(mrr,[status(thm)],[39,3]),
[iquote('0:MRR:39.0,39.1,3.0,3.0')] ).
cnf(86,plain,
( ~ ilf_type(u,subset_type(cross_product(v,w)))
| relation_like(u) ),
inference(mrr,[status(thm)],[38,3]),
[iquote('0:MRR:38.0,38.1,3.0,3.0')] ).
cnf(87,plain,
( ~ member(skf18(u,v),u)
| subset(v,u) ),
inference(mrr,[status(thm)],[37,3]),
[iquote('0:MRR:37.1,37.2,3.0,3.0')] ).
cnf(89,plain,
( ~ ilf_type(u,member_type(v))
| empty(v)
| member(u,v) ),
inference(mrr,[status(thm)],[45,3]),
[iquote('0:MRR:45.1,45.2,3.0,3.0')] ).
cnf(92,plain,
( ~ ilf_type(u,subset_type(v))
| ilf_type(u,member_type(power_set(v))) ),
inference(mrr,[status(thm)],[42,3]),
[iquote('0:MRR:42.1,42.2,3.0,3.0')] ).
cnf(94,plain,
( ~ ilf_type(u,identity_relation_of_type(v))
| ilf_type(u,relation_type(v,v)) ),
inference(mrr,[status(thm)],[40,3]),
[iquote('0:MRR:40.1,40.2,3.0,3.0')] ).
cnf(95,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ subset(range_of(u),v)
| equal(compose(u,identity_relation_of(v)),u) ),
inference(mrr,[status(thm)],[48,3]),
[iquote('0:MRR:48.0,3.0')] ).
cnf(96,plain,
( ~ ilf_type(u,binary_relation_type)
| ~ subset(domain_of(u),v)
| equal(compose(identity_relation_of(v),u),u) ),
inference(mrr,[status(thm)],[47,3]),
[iquote('0:MRR:47.0,3.0')] ).
cnf(97,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(u,subset_type(cross_product(v,w))) ),
inference(mrr,[status(thm)],[49,3]),
[iquote('0:MRR:49.1,49.2,3.0,3.0')] ).
cnf(99,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(range__dfg(v,w,u),subset_type(w)) ),
inference(mrr,[status(thm)],[51,3]),
[iquote('0:MRR:51.0,51.1,3.0,3.0')] ).
cnf(100,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(range__dfg(v,w,u),range_of(u)) ),
inference(mrr,[status(thm)],[52,3]),
[iquote('0:MRR:52.0,52.1,3.0,3.0')] ).
cnf(101,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(range_of(u),subset_type(w)) ),
inference(rew,[status(thm),theory(equality)],[100,99]),
[iquote('0:Rew:100.1,99.1')] ).
cnf(102,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(domain__dfg(v,w,u),subset_type(v)) ),
inference(mrr,[status(thm)],[53,3]),
[iquote('0:MRR:53.0,53.1,3.0,3.0')] ).
cnf(103,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(domain__dfg(v,w,u),domain_of(u)) ),
inference(mrr,[status(thm)],[54,3]),
[iquote('0:MRR:54.0,54.1,3.0,3.0')] ).
cnf(104,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(domain_of(u),subset_type(v)) ),
inference(rew,[status(thm),theory(equality)],[103,102]),
[iquote('0:Rew:103.1,102.1')] ).
cnf(110,plain,
( ~ member(u,v)
| ~ member(v,power_set(w))
| member(u,w) ),
inference(mrr,[status(thm)],[60,3]),
[iquote('0:MRR:60.1,60.3,60.4,3.0,3.0,3.0')] ).
cnf(119,plain,
ilf_type(skc4,relation_type(skc3,skc3)),
inference(res,[status(thm),theory(equality)],[4,94]),
[iquote('0:Res:4.0,94.0')] ).
cnf(127,plain,
( ~ empty(u)
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[85,82]),
[iquote('0:Res:85.1,82.1')] ).
cnf(128,plain,
( ~ empty(u)
| ~ empty(power_set(v)) ),
inference(res,[status(thm),theory(equality)],[127,82]),
[iquote('0:Res:127.1,82.1')] ).
cnf(129,plain,
~ empty(power_set(u)),
inference(con,[status(thm)],[128]),
[iquote('0:Con:128.0')] ).
cnf(158,plain,
( ~ ilf_type(u,subset_type(v))
| empty(power_set(v))
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[92,89]),
[iquote('0:Res:92.1,89.0')] ).
cnf(160,plain,
( ~ ilf_type(u,subset_type(v))
| member(u,power_set(v)) ),
inference(mrr,[status(thm)],[158,129]),
[iquote('0:MRR:158.1,129.0')] ).
cnf(167,plain,
ilf_type(range_of(skc4),subset_type(skc3)),
inference(res,[status(thm),theory(equality)],[119,101]),
[iquote('0:Res:119.0,101.0')] ).
cnf(170,plain,
ilf_type(domain_of(skc4),subset_type(skc3)),
inference(res,[status(thm),theory(equality)],[119,104]),
[iquote('0:Res:119.0,104.0')] ).
cnf(203,plain,
( ~ ilf_type(u,relation_type(v,w))
| relation_like(u) ),
inference(res,[status(thm),theory(equality)],[97,86]),
[iquote('0:Res:97.1,86.0')] ).
cnf(212,plain,
( ~ ilf_type(u,subset_type(v))
| ~ member(w,u)
| member(w,v) ),
inference(res,[status(thm),theory(equality)],[160,110]),
[iquote('0:Res:160.1,110.1')] ).
cnf(236,plain,
relation_like(skc4),
inference(res,[status(thm),theory(equality)],[119,203]),
[iquote('0:Res:119.0,203.0')] ).
cnf(294,plain,
( ~ ilf_type(skc4,binary_relation_type)
| ~ subset(domain_of(skc4),skc3)
| ~ equal(compose(skc4,identity_relation_of(skc3)),skc4)
| ~ equal(skc4,skc4) ),
inference(spl,[status(thm),theory(equality)],[96,33]),
[iquote('0:SpL:96.2,33.1')] ).
cnf(295,plain,
( ~ ilf_type(skc4,binary_relation_type)
| ~ subset(domain_of(skc4),skc3)
| ~ equal(compose(skc4,identity_relation_of(skc3)),skc4) ),
inference(obv,[status(thm),theory(equality)],[294]),
[iquote('0:Obv:294.3')] ).
cnf(740,plain,
( ~ ilf_type(skc4,binary_relation_type)
| ~ subset(range_of(skc4),skc3)
| ~ ilf_type(skc4,binary_relation_type)
| ~ subset(domain_of(skc4),skc3)
| ~ equal(skc4,skc4) ),
inference(spl,[status(thm),theory(equality)],[95,295]),
[iquote('0:SpL:95.2,295.2')] ).
cnf(741,plain,
( ~ subset(range_of(skc4),skc3)
| ~ ilf_type(skc4,binary_relation_type)
| ~ subset(domain_of(skc4),skc3) ),
inference(obv,[status(thm),theory(equality)],[740]),
[iquote('0:Obv:740.4')] ).
cnf(1498,plain,
( ~ member(u,range_of(skc4))
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[167,212]),
[iquote('0:Res:167.0,212.0')] ).
cnf(1568,plain,
( ~ member(u,domain_of(skc4))
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[170,212]),
[iquote('0:Res:170.0,212.0')] ).
cnf(1587,plain,
( subset(range_of(skc4),u)
| member(skf18(u,range_of(skc4)),skc3) ),
inference(res,[status(thm),theory(equality)],[84,1498]),
[iquote('0:Res:84.1,1498.0')] ).
cnf(1662,plain,
( subset(domain_of(skc4),u)
| member(skf18(u,domain_of(skc4)),skc3) ),
inference(res,[status(thm),theory(equality)],[84,1568]),
[iquote('0:Res:84.1,1568.0')] ).
cnf(2013,plain,
( subset(range_of(skc4),skc3)
| subset(range_of(skc4),skc3) ),
inference(res,[status(thm),theory(equality)],[1587,87]),
[iquote('0:Res:1587.1,87.0')] ).
cnf(2015,plain,
subset(range_of(skc4),skc3),
inference(obv,[status(thm),theory(equality)],[2013]),
[iquote('0:Obv:2013.0')] ).
cnf(2016,plain,
( ~ ilf_type(skc4,binary_relation_type)
| ~ subset(domain_of(skc4),skc3) ),
inference(mrr,[status(thm)],[741,2015]),
[iquote('0:MRR:741.0,2015.0')] ).
cnf(2078,plain,
( subset(domain_of(skc4),skc3)
| subset(domain_of(skc4),skc3) ),
inference(res,[status(thm),theory(equality)],[1662,87]),
[iquote('0:Res:1662.1,87.0')] ).
cnf(2080,plain,
subset(domain_of(skc4),skc3),
inference(obv,[status(thm),theory(equality)],[2078]),
[iquote('0:Obv:2078.0')] ).
cnf(2081,plain,
~ ilf_type(skc4,binary_relation_type),
inference(mrr,[status(thm)],[2016,2080]),
[iquote('0:MRR:2016.1,2080.0')] ).
cnf(2086,plain,
~ relation_like(skc4),
inference(res,[status(thm),theory(equality)],[79,2081]),
[iquote('0:Res:79.1,2081.0')] ).
cnf(2087,plain,
$false,
inference(ssi,[status(thm)],[2086,236]),
[iquote('0:SSi:2086.0,236.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET678+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 04:46:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.91/1.13
% 0.91/1.13 SPASS V 3.9
% 0.91/1.13 SPASS beiseite: Proof found.
% 0.91/1.13 % SZS status Theorem
% 0.91/1.13 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.91/1.13 SPASS derived 1847 clauses, backtracked 19 clauses, performed 6 splits and kept 1570 clauses.
% 0.91/1.13 SPASS allocated 100514 KBytes.
% 0.91/1.13 SPASS spent 0:00:00.77 on the problem.
% 0.91/1.13 0:00:00.03 for the input.
% 0.91/1.13 0:00:00.04 for the FLOTTER CNF translation.
% 0.91/1.13 0:00:00.05 for inferences.
% 0.91/1.13 0:00:00.00 for the backtracking.
% 0.91/1.13 0:00:00.59 for the reduction.
% 0.91/1.13
% 0.91/1.13
% 0.91/1.13 Here is a proof with depth 5, length 66 :
% 0.91/1.13 % SZS output start Refutation
% See solution above
% 0.91/1.13 Formulae used in the proof : p38 prove_relset_1_45 p13 p30 p19 p25 p26 p7 p22 p28 p1 p2 p15 p35 p34 p33 p32
% 0.91/1.13
%------------------------------------------------------------------------------