TSTP Solution File: SET668+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET668+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:27:57 EDT 2022
% Result : Theorem 3.77s 3.95s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 56 ( 13 unt; 9 nHn; 56 RR)
% Number of literals : 148 ( 0 equ; 92 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 : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
ilf_type(u,set_type),
file('SET668+3.p',unknown),
[] ).
cnf(5,axiom,
subset(identity_relation_of(skc5),skc6),
file('SET668+3.p',unknown),
[] ).
cnf(10,axiom,
ilf_type(skc6,relation_type(skc5,skc4)),
file('SET668+3.p',unknown),
[] ).
cnf(31,axiom,
( ~ equal(domain__dfg(skc5,skc4,skc6),skc5)
| ~ subset(skc5,range__dfg(skc5,skc4,skc6)) ),
file('SET668+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ empty(u)
| ~ ilf_type(v,set_type)
| ~ member(v,u)
| ~ ilf_type(u,set_type) ),
file('SET668+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf12(v,u),u)
| subset(u,v) ),
file('SET668+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ member(skf12(u,v),u)
| ~ ilf_type(v,set_type)
| ~ ilf_type(u,set_type)
| subset(v,u) ),
file('SET668+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| member(skf16(v,u),u)
| member(u,power_set(v)) ),
file('SET668+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('SET668+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('SET668+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| equal(u,v) ),
file('SET668+3.p',unknown),
[] ).
cnf(51,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('SET668+3.p',unknown),
[] ).
cnf(52,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('SET668+3.p',unknown),
[] ).
cnf(53,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('SET668+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('SET668+3.p',unknown),
[] ).
cnf(62,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,relation_type(u,v))
| ~ subset(identity_relation_of(w),x)
| subset(w,range__dfg(u,v,x)) ),
file('SET668+3.p',unknown),
[] ).
cnf(63,axiom,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,relation_type(u,v))
| ~ subset(identity_relation_of(w),x)
| subset(w,domain__dfg(u,v,x)) ),
file('SET668+3.p',unknown),
[] ).
cnf(75,plain,
( ~ empty(u)
| ~ member(v,u) ),
inference(mrr,[status(thm)],[35,4]),
[iquote('0:MRR:35.1,35.3,4.0,4.0')] ).
cnf(78,plain,
( subset(u,v)
| member(skf12(v,u),u) ),
inference(mrr,[status(thm)],[36,4]),
[iquote('0:MRR:36.0,36.1,4.0,4.0')] ).
cnf(80,plain,
( member(u,power_set(v))
| member(skf16(v,u),u) ),
inference(mrr,[status(thm)],[38,4]),
[iquote('0:MRR:38.0,38.1,4.0,4.0')] ).
cnf(81,plain,
( ~ member(skf12(u,v),u)
| subset(v,u) ),
inference(mrr,[status(thm)],[37,4]),
[iquote('0:MRR:37.1,37.2,4.0,4.0')] ).
cnf(83,plain,
( ~ ilf_type(u,member_type(v))
| empty(v)
| member(u,v) ),
inference(mrr,[status(thm)],[43,4]),
[iquote('0:MRR:43.1,43.2,4.0,4.0')] ).
cnf(86,plain,
( ~ ilf_type(u,subset_type(v))
| ilf_type(u,member_type(power_set(v))) ),
inference(mrr,[status(thm)],[40,4]),
[iquote('0:MRR:40.1,40.2,4.0,4.0')] ).
cnf(87,plain,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
inference(mrr,[status(thm)],[46,4]),
[iquote('0:MRR:46.2,46.3,4.0,4.0')] ).
cnf(91,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(range__dfg(v,w,u),range_of(u)) ),
inference(mrr,[status(thm)],[51,4]),
[iquote('0:MRR:51.0,51.1,4.0,4.0')] ).
cnf(93,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(domain__dfg(v,w,u),subset_type(v)) ),
inference(mrr,[status(thm)],[52,4]),
[iquote('0:MRR:52.0,52.1,4.0,4.0')] ).
cnf(94,plain,
( ~ ilf_type(u,relation_type(v,w))
| equal(domain__dfg(v,w,u),domain_of(u)) ),
inference(mrr,[status(thm)],[53,4]),
[iquote('0:MRR:53.0,53.1,4.0,4.0')] ).
cnf(95,plain,
( ~ ilf_type(u,relation_type(v,w))
| ilf_type(domain_of(u),subset_type(v)) ),
inference(rew,[status(thm),theory(equality)],[94,93]),
[iquote('0:Rew:94.1,93.1')] ).
cnf(101,plain,
( ~ member(u,v)
| ~ member(v,power_set(w))
| member(u,w) ),
inference(mrr,[status(thm)],[60,4]),
[iquote('0:MRR:60.1,60.3,60.4,4.0,4.0,4.0')] ).
cnf(103,plain,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,relation_type(u,v))
| ~ subset(identity_relation_of(w),x)
| subset(w,range_of(x)) ),
inference(rew,[status(thm),theory(equality)],[91,62]),
[iquote('0:Rew:91.1,62.5')] ).
cnf(104,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ subset(identity_relation_of(x),u)
| subset(x,range_of(u)) ),
inference(mrr,[status(thm)],[103,4]),
[iquote('0:MRR:103.0,103.1,103.2,4.0,4.0,4.0')] ).
cnf(105,plain,
( ~ ilf_type(u,set_type)
| ~ ilf_type(v,set_type)
| ~ ilf_type(w,set_type)
| ~ ilf_type(x,relation_type(u,v))
| ~ subset(identity_relation_of(w),x)
| subset(w,domain_of(x)) ),
inference(rew,[status(thm),theory(equality)],[94,63]),
[iquote('0:Rew:94.1,63.5')] ).
cnf(106,plain,
( ~ ilf_type(u,relation_type(v,w))
| ~ subset(identity_relation_of(x),u)
| subset(x,domain_of(u)) ),
inference(mrr,[status(thm)],[105,4]),
[iquote('0:MRR:105.0,105.1,105.2,4.0,4.0,4.0')] ).
cnf(112,plain,
( ~ subset(identity_relation_of(u),skc6)
| subset(u,domain_of(skc6)) ),
inference(res,[status(thm),theory(equality)],[10,106]),
[iquote('0:Res:10.0,106.0')] ).
cnf(113,plain,
( ~ subset(identity_relation_of(u),skc6)
| subset(u,range_of(skc6)) ),
inference(res,[status(thm),theory(equality)],[10,104]),
[iquote('0:Res:10.0,104.0')] ).
cnf(114,plain,
ilf_type(domain_of(skc6),subset_type(skc5)),
inference(res,[status(thm),theory(equality)],[10,95]),
[iquote('0:Res:10.0,95.0')] ).
cnf(115,plain,
equal(domain__dfg(skc5,skc4,skc6),domain_of(skc6)),
inference(res,[status(thm),theory(equality)],[10,94]),
[iquote('0:Res:10.0,94.0')] ).
cnf(117,plain,
equal(range__dfg(skc5,skc4,skc6),range_of(skc6)),
inference(res,[status(thm),theory(equality)],[10,91]),
[iquote('0:Res:10.0,91.0')] ).
cnf(119,plain,
( ~ equal(domain_of(skc6),skc5)
| ~ subset(skc5,range__dfg(skc5,skc4,skc6)) ),
inference(rew,[status(thm),theory(equality)],[115,31]),
[iquote('0:Rew:115.0,31.0')] ).
cnf(120,plain,
( ~ equal(domain_of(skc6),skc5)
| ~ subset(skc5,range_of(skc6)) ),
inference(rew,[status(thm),theory(equality)],[117,119]),
[iquote('0:Rew:117.0,119.1')] ).
cnf(121,plain,
subset(skc5,range_of(skc6)),
inference(res,[status(thm),theory(equality)],[5,113]),
[iquote('0:Res:5.0,113.0')] ).
cnf(122,plain,
subset(skc5,domain_of(skc6)),
inference(res,[status(thm),theory(equality)],[5,112]),
[iquote('0:Res:5.0,112.0')] ).
cnf(125,plain,
~ equal(domain_of(skc6),skc5),
inference(mrr,[status(thm)],[120,121]),
[iquote('0:MRR:120.1,121.0')] ).
cnf(149,plain,
( ~ empty(u)
| member(u,power_set(v)) ),
inference(res,[status(thm),theory(equality)],[80,75]),
[iquote('0:Res:80.1,75.1')] ).
cnf(151,plain,
( ~ empty(u)
| ~ empty(power_set(v)) ),
inference(res,[status(thm),theory(equality)],[149,75]),
[iquote('0:Res:149.1,75.1')] ).
cnf(152,plain,
~ empty(power_set(u)),
inference(con,[status(thm)],[151]),
[iquote('0:Con:151.0')] ).
cnf(179,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(181,plain,
( ~ ilf_type(u,subset_type(v))
| member(u,power_set(v)) ),
inference(mrr,[status(thm)],[179,152]),
[iquote('0:MRR:179.1,152.0')] ).
cnf(209,plain,
( ~ subset(domain_of(skc6),skc5)
| equal(domain_of(skc6),skc5) ),
inference(res,[status(thm),theory(equality)],[122,87]),
[iquote('0:Res:122.0,87.0')] ).
cnf(213,plain,
~ subset(domain_of(skc6),skc5),
inference(mrr,[status(thm)],[209,125]),
[iquote('0:MRR:209.1,125.0')] ).
cnf(273,plain,
( ~ ilf_type(u,subset_type(v))
| ~ member(w,u)
| member(w,v) ),
inference(res,[status(thm),theory(equality)],[181,101]),
[iquote('0:Res:181.1,101.1')] ).
cnf(1867,plain,
( ~ member(u,domain_of(skc6))
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[114,273]),
[iquote('0:Res:114.0,273.0')] ).
cnf(3589,plain,
( subset(domain_of(skc6),u)
| member(skf12(u,domain_of(skc6)),skc5) ),
inference(res,[status(thm),theory(equality)],[78,1867]),
[iquote('0:Res:78.1,1867.0')] ).
cnf(8488,plain,
( subset(domain_of(skc6),skc5)
| subset(domain_of(skc6),skc5) ),
inference(res,[status(thm),theory(equality)],[3589,81]),
[iquote('0:Res:3589.1,81.0')] ).
cnf(8490,plain,
subset(domain_of(skc6),skc5),
inference(obv,[status(thm),theory(equality)],[8488]),
[iquote('0:Obv:8488.0')] ).
cnf(8491,plain,
$false,
inference(mrr,[status(thm)],[8490,213]),
[iquote('0:MRR:8490.0,213.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET668+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % 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
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Sun Jul 10 10:42:07 EDT 2022
% 0.13/0.36 % CPUTime :
% 3.77/3.95
% 3.77/3.95 SPASS V 3.9
% 3.77/3.95 SPASS beiseite: Proof found.
% 3.77/3.95 % SZS status Theorem
% 3.77/3.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.77/3.95 SPASS derived 7512 clauses, backtracked 638 clauses, performed 5 splits and kept 6096 clauses.
% 3.77/3.95 SPASS allocated 105210 KBytes.
% 3.77/3.95 SPASS spent 0:00:03.53 on the problem.
% 3.77/3.95 0:00:00.04 for the input.
% 3.77/3.95 0:00:00.04 for the FLOTTER CNF translation.
% 3.77/3.95 0:00:00.08 for inferences.
% 3.77/3.95 0:00:00.20 for the backtracking.
% 3.77/3.95 0:00:03.10 for the reduction.
% 3.77/3.95
% 3.77/3.95
% 3.77/3.95 Here is a proof with depth 5, length 56 :
% 3.77/3.95 % SZS output start Refutation
% See solution above
% 3.77/3.95 Formulae used in the proof : p32 prove_relset_1_31 p26 p7 p20 p16 p22 p9 p30 p29 p28 p2
% 3.77/3.95
%------------------------------------------------------------------------------